Workshop 96 Brno, January 22-24,1996

&* & vjs ezi w? * «^? %&> !# *4^ y

TECHNICAL UNIVERSITY IN BRNO iNis-mf-i4829

CZECH TECHNICAL UNIVERSITY IN PRAGUE

WORKSHOP 96 BRNO, JANUARY 22-24,1996

PART I. Mathematics - Physics - Chemistry - Engineering Informatics and Cybernetics - Computers - Fluid Mechanics VOL 2 7JB19 TECHNICAL UNIVERSITY IN BRNO

CZECH TECHNICAL UNIVERSITY IN PRAGUE

WORKSHOP 96 BRNO, JANUARY 22-24,1996

PART I. Mathematics-Physics-Chemistry-Engineering Informatics and Cybernetics - Computers - Fluid Mechanics These arc the Proceeding of the Fifth Annual uiilvcrilty.wldc wmliinr WOItKHlIUI* 00 which will take place at tlio Technical University in Urflo from 22-24 January, 1990. Ths aim of the scr/iln/ir Is to ptctumt ami d'nr-tm tb«? M^t result* oliUlfiwl \y tmcMdwtn rnjirrinlly i\t llw Czech Teclinlul Uillvcnlly In PfAfjue, Tccliiilcfll University in Drno nriil At collaborAtlrrg Institutions' The organizing committee IIM iclccted A tot*l of 49t ««iitrifiiillotm divided Into 22 different arcM of Interest. IVit t IIM contributions In llifl «rcM of:

tnatlictiiAtlcs

clicmlstiy engineering Informatics and cybernetics computer! fluid mechanics

Organizing committee: Chairman! P, Climcla Co-ehftlrmAn; M. KAUI J, H«/-(Wt V. /Jr*i>«<;, M. JJ«diU, R )J«Z*JM, W, JJobza, J, Ja;i, M, KrAl, J, MalOTfc*, J, Mi«n, P, Ondraika, h, Viiby), 1. lluller, A. Strejc, M. 'AlifA-IWA, D. ZatrakrttU

Pragvt, December 1995

This book WM prepared with WTyC from the Input files supplied by the author*. All partial article* were prepared with WOO - a ipccial-purpoM t>Tj.;X-b*wd environment. Program- ming W96, general ityle, typographic corrections and the final composition of this book is by A. Streje (CTU Computing Centre).

Published by the Ciech Technical University In Prague. Printed by CTU Publishing House. WORKSHOP 90 CONTENTS CONTENTS

I. MATHEMATICS

MATHEMATICAL MODELLING OP ENGINEERING PROBLEMS 17 J, /'Varied, A. gtnlick, J. Daltk, J. Ntdomn, It. RHUktvA, D. SkabrahovA NUMERICAL SOLUTION OF 2D EULEIl AND NAVIER-STOKES EQUATIONS 10 L Uenel, J. Mnl, J. IhrAk, K. Kottl, I SUM MATHEMATICAL MODELLING OK I'OUOUS MEDIA FLOW AND TRANSI'OIIT OP CHEMICALS IN UNDERGROUND WATER 21 A/. Stjjblo, J. Maryika, J. btut&k,.'. Skokan, M. Tima, J. Ihkoiovd, M, llotlolntk, Z. Strakoi, J. Novik, P. Manltk, V. WtMtrhauir THE MATHEMATICAL MODEL OF PERIODICAL FLOW WITH MIXED BOUNDARY CONDITIONS 23 /'. A'tiifent WELL-POSKDNKSS ANALYSI.S OP NONIIYDJIOSTATJO TWO-UYEJl MODELS OF INCOMPRESSIULB FLOW 25 II. Liska, L. Margolin, II. Wtndnff TESTING STABILITY I)Y QUANTIFIER ELIMINATION 27 II. Hong, II. Liska, S. Steinberg STABILITY OF STEADY SOLUTIONS OF PARABOLIC EQUATIONS IN HILHERT SPACES , 29 J. Neuitupn GEOMETRIC MODELING OF MILLING 31 St. h'argirovd ENVELOPE OF SURFACES CREATED BY OSCILLATORY SCREW MOTION 33 E. KopincovA CURVES WITH MATHEMATICA 35 F. Uuhtnik, J. Cerny, I. SlAmovd EXPERIENCE IN MATHEMATICALLY ORIENTATED SOFTWARE IN TEACHING 37 V, Btnti, C. Zlatnlk APPLICATIONS OF ALGEBRA IN COMPUTER SCIENCE 39 SI. DemlovA, J. Aiimtk, B. PondilUtk QUANTUM FIELD THEORY AND EXTENSIONS OF STATES 41 J. llamhalter

3 WORKSHOP 90 ™_____B______CONTENTS

QUANTUM SYMMETRIES! MATIIEMA1CAL MODELS AND PHYSICAL APPLICATIONS.,,.,..,. 43 M, IlavlUtk, L tthvalj, B, Pttantovd, P. Stovtttk, J, Tatar

COMING FROM DISTRIBUTIVE TO ORTJIOMODULAR 45 P. t'ttk, M, Nnvam

SOME CARDINAL CHARACTERISTICS OF ORDERED SCTH 47 V. Novdk

DISTINGUISHING SUfJSETS ON MTT1CKS 49 J. Zapltlal

BXPONENTIALITY IN CATKCOIUES OK PARTIAL ALCJE1MAS ,51 J. Slapat

2. PHYSICS

MEASUREMENT OF NONLINEAR WAVES IN IIARD-WALLED DUCTS 55 M. IkdnaHk, 0, Jiflf.rk

PROPAGATION OK PLANE NONLINKAR WAVKS 67 M. DtdnaHk DEEP ENERGY LEVELS IN N-TYPE SI INTRODUCED UY SHOkT-TlME Pd DIFFUSION 69 V. Ihnda, J. PuttkovA, D. Stlpkovi PHYSICS OF INFORMATION AT THE FRONTIERS WITH INFORMATICS AND CYBERNETICS 61 J. Jtkn MOLECt/LAft DYNAMICS SIMULATIONS OF REFRIGERANTS AND MODEL FLUIDS 63 V. Vactk, A/. LUal, II. DuJInaky HYDRODYMAMICS MODEL OF INTERACTIONS OF SUDP1COSECOND LASLR PULSES WITH SOLID TARGETS 65 J, Limpauch, L. Drika, St. Tagirituhvili

LASER MOLECULAR SPECTROSCOPY 61 V. Fidler, P. Kapuila, M. llof, V. Kuhtitk, M, Vrhovi COMPARISON OF EFFICIENCES OF NEUTRON SHIELDS CONTAINING UORON AND LITHIUM 60 J. Kvbaila, S. PoipUil, I. Sickl COLLECTION OF RADON DAUGHTERS FROM THE AIR WITH AN ELECTROSTATIC PREC1PITATOR 71 C. Jtth, J. Kvhaila, S. PoipUit

4 WORKSHOP 00 CONTENTS

FLEXHJLE SYSTEM FOR MULTll'AKAMETHIC MEASUREMENTS IN NUCLBAll SI'ECf IIOSOOI'Y ,.,.,, 73 J. JakUck, J. Ocrmll, J. KubaStti, S, PonpUil, St. Vohccki MEASUREMENTS OF RADON IN AIR USINO ALPHA SPECTROMETRY WITH IONJZAT1ON CIIAMHBR U J. KonUtk, 8. Poipllll, Z. Jatwul, J. Kubniln, M. Vobecki}

UNESCO SElllES Of LBAttNING MATERIALS IN ENGINEERING 77 E. VtnlA, V, Sthinnvi, I'. Win, K. KvUoii

COMPUTATIONAL PHYSICS! NUMERICS FOR PEDESTRIANS 79 /,. Drikn PILOT PROGRAM PACKAGES FOR INTRODUCTORY PHYSICS TEACHING .... 81 L Drlka, St. SiAor GEODYNAMIC INFORMATION FROM THE RESULTS OF GEODETIC OHSERVATIONS 83 A, Ztman, I. Ptltk SOUND ENERGY TRANSFER IN A TRANSIENT SOUND FIELD,,,..,.....«...... 85 Z. Kynd

ULTRASONIC INVESTIGATION IN GEOPHYSICAL RESEARCH 87 K. Malituki J. Plocck

PRINCIPLES OF ACTIVE CONTROL IN DUCTS 80 0. JMttk QUANTUM MECHANICAL MODELLING OF CRYSTALS FRACTURE 01 P. Sandtra, V. Navr&ul, J. Poktuda

COMPUTER SIMULATION OF POLYEDRIC STRUCTURES 03 J, Pokluda, P. PonUll, P. Sanden

THE STABILITY CRITERION GIVEN IN TERMS OF INFORMATION GAIN 95 St. KhiilovA IN-SITU INTERFEROMETRIC THICKNESS MEASUREMENT OF DEPOSITED THIN FILMS 97 J. Spousta, W. Dejmtk, Z. llama, A. Ntbojsa, T. Sikola, M. Ml SURFACE ANALYSIS OF MATERIALS - DESIGN OF THE ATOMIC FORCE DDTECTOR FOR ATOMIC FORCE MICROSCOPY 00 T. Sikola, J. Spoiuta, L. Dillrichovi, L Tima, F. Matfjka, R. Kalouttk, F. Lcpour EXPERIMENTAL STUDY OF NO GENERATION IN ELECTRIC DISCHARGE.... 101 V. KHha, F. Itanilz, S. Ptkirtk, J. Ronnkrani WORKSHOP 00 CONTENTS

MATHEMATICAL MODELS OP FINITE-DIMENSIONAL QUANTUM MECHANICS , 10U 0, Chudiitattso$ INVESTIGATION OK Gc-Sl MONOCRYSTALS SUITABLE FORSI'AO CONSTRUCTION ,,.,, ,, 105 //. Frank, K, tkmal, I, Madia, I. Vrothfokit, 11. Sopko TUB FIRST MJCROSTltlP GAS CHAMHER MADE IN C/ECH REFUIJLIC 107 J, Mfon, I'. Ctmj, At. Kocldn, !. Mdeha, S. N/mr/tk, It, Sowik, D. NovAkovA, J, I'avtl, Ih Sopko, L Stupkn, SI, SllAroh, J, Sdmtny, L VytkotH, M. VnnifkovA PKAOUB ELECTRON CONDUCTIVE GLASS 109 J, Mhm, 1. Mieha, II. KriloeA, 8. Nlmtltk, It. Novik, J. I'avtt, I). Sopko, L Stupkn, M. SUAraA, J. S(

3. CHEMISTRY

CHARACTERIZATION OF CONSTITUENTS OF COMPOSITE MATERIALS 131 /. Simtk, II. Vupalte WORKSHOP 00 CONTENTS

TUB STUDY OP IMIOTOCATALYTIC DECOMPOSITION OK SURFACTANTS IN WATER SOLUTION , , 133 M, Vatlj, J. Toultn

NON-CONVENTIONAL APPLICATION OF LOW TEMPERATURE PHYSICAL PMSMA IN CHEMISTRY ANI> CHEMICAL TECHNOLOGY 135 I, Laplik, U. Mikuliikovi, /,', laptlk, Jr., J. Matouhk, I. Maitk

EXPERIMENTAL EQUIPMENT FOIt CHEMICAL APPLICATION OK THERMAL PLASMA 137 J. Ongor, I. JnkubavA, P. Kadlec, J, Stnk

MEASURING AND CONTROL SYSTEM OF PLASMA REACTOR 139 0. Satyk, P. Iknel, P. I'ivoAlit

QUANTUM CHEMICAL STUDY OF SMALL ORGANIC MOLECULES MI S. Sklenik, M, Vnely

AB INITIO CALCULATIONS WITH ELECTRON CORRELATION 143 S, SkknAk, K. LapM, Jr.

COMPUTATIONAL MODELING OF CHEMICAL REACTIONS IN A METAL-SI SYSTEM WITH PHASE CHANGE 140 II. Ctrnj, P. PHkryl, V. Chib

PROPERTIES AND RADIATION INFLUENCE OF NiO.»l,Oj MIXED CATALYSTS 147 V. Milka, M. PotpUit, II. Silber

DECARDONIZATION OF ELECTROLYTES FROM ALKALINE ACCUMULATORS 149 M. Ptkar, M. Ctntk

SENSITIVE LAYERS FOR DETECTION OF ORGANIC AMINES AND HALOTHANE IN GASEOUS PHASE 151 S. Urodiki, D. Soph, I. Mdeha, V. Paptl

STRUCTURE AND REACTIVITY OF COLOURED pi STANDARDS 153 Z. Fritdl, K. Stais

THERMAL DECOMPOSITION OF ORGANIC SUBSTANCES 155 1. Adamce, M. Barltovi, 0. Coufal, J. Ttptj

DIELECTRIC RELAXATION SPECTROSCOPY OF POLYSACCIIARIDES 157 K. Liedermann, L Upllk, Jr., S. llatsllltk, L GrmeU

X-RAY FLUORESCENT ANALYSIS FOR THE COAL INDUSTRY 159 T. Ctchik WOUKSHOI'Or. CONTENTS

4. ENGINEERING INFORMATICS & CYBERNETICS

GENETIC ALGORITHMS AND INVESTIGATION OK TIIKIIl PERFORMANCE .,,...,103 J, Ulamkv, J, /Malik, V, Mafik, 0, SlfpdnlioviS, SI, Dcmtovd, 'A, h'nvbn, T. Vlttk, J. Kophte GNOST/CAL NEURAL NETWORKS 105 /'. 1'nlntka

MULTI-AGENT SYSTEM FOR CIM PURPOSES .107 V. Mafik, 0. SUpAnkovd, J. Lnlnnnkj, M. Dtmlovd, L Llmttkd, L I'hulil, T. VUtk, X, Kouha, M. Ftnclovtf, J, Koulnik, '/', llatdra, J. Koul, 0. Htk, I. Marvitn A MULTI-AGENT SYSTEM IN TIIANSI'OHT MANAGEMENT (GO //, llronkovA-UioUkd, T. VUtk, X. Kuubn, L 1'ftulH, J. Ulantky, 0. Stipdnkovd, V, AlaFlk, J. KUma, T. llnutru IMAGE-HASED SCENE IlEI'UESENTATION FOUND AUTOMATICALLY 171 V. IllavAt, A, Lconardit, T. Werner LASER PLANE RANGE FINDER,,,,,,.,, , 173 T. I'ajdla, V. IlkvAe MEASUREMENT OF THE TOOL WITH CC» CAMERA 175 5. Kraut COUNTING OF HEALDS AND DENTS HY OPTICAL METHOD 177 V. Smulnj, M. Fritdl, P. Tai, I1. Vila

EFFICIENT ESTIMATION OF ESSENTIAL MATRIX IN MOTION ANALYSIS.... 179 T. Svoboda, T. f'ojdk VtCTORIZATION OF LARGE DINARY IMAGES 181 / Miller, P. Dvofnk

MORPHOLOGICAL IMAGE PROCESSING L1DRARY 183 /', AW/, V. lllavdi TRAFFIC SIGNS IDENTIFICATION AND AUTOMATIC TEMPLATE GENERATION 185 V. Ubal, T. Zikmund, P. Paclik, M. Krallk, II. Kovif, P. Zahradnik, M. Vlitk SIMULATION OF FLIGHT MANAGEMENT SUBSYSTEMS 187 Z. Pah, I. Stary

IIINFIN1TY DASED ACTIVE SUSPENSION OF VEHICLES 189 A", llyniovd, A. Stfibrsk^

THE IDENTIFICATION OF HEAT SYSTEM OF THE SCHOOL HUILDING 191 /,. Unrh

8 WORKSHOP 00 CONTENTS

EXPERIMENTAL IDENTIFICATION 01* A GLASS FURNACE 193 M. llofrelttr AN INTEGRATED METHOD FOH VEGETATION MONITORING,,,,,,,„<„,.,.,195 K. Pavrlka EDUCATION IN G1S AT THE CTU PRAGUE - COMPLEX DIDACTIC SUPPORT ,..„.„.,.,,.. ,,,. .197 M. Humt, I), Vcvcrkn, A. Cepck, P. Soukvp FORMAL AND I'ROCJIIAMMINCJ TOOLS FOR INFORMATION SYSTEM DESIGN AND PROTOTYPING 199 M, Cttkn, V. Janoultk IMPLEMENTATION OF COLOURED I'ETIti NETS USING HIGHER-ORDER FUNCTIONAL LANGUAGES 201 D. Kotif SIMULATION TEC!INIQUES IN INFORMATION SYSTEMS DESIGN 203 Z. lUhovi, P, Vtringcr, J, Janol GRAPH-BASED SPECIFICATIONS 205 M. Bind I'ETRl NET BASED ALGORITHM DESIGN 207 X. llanidlek HIERARCHICAL FUZZY CONTROLLERS - COMBINE FUZZY AND P1D CONTROLLERS 209 T. Kuien MOBILE ROBOT NAVIGATION 211 I. Krdl THE BASIC DANCE COURSE EDUCATED MOHOT 213 P. Nahodil, M. Gntnct, 2. Slanina, M. SafAt DESIGN OF ANISOCIIRONIC STATE OBSERVER BY DOMINANT POLE PLACEMENT 215 P. Ziltk, R. Pttrovi OTHER POLYNOMIAL WAY OF SOLVING LQ CONTROL 217 V. Soukup MODELLING OF INTERDISCIPLINARY DYNAMIC SYSTEMS 219 II. Mann PARALLEL IMPLEMENTATION OF ANN FOR EMBEDDED APPLICATIONS....221 V, Dvofik EXACT AND FAST COMPUTATIONS 223 J. Kunoviky, M. Paptiik, F. Zbofil

9 WORKSHOP 00 CONTKNTg

IMPLEMENTATION OF SIMULATING SYSTEM IN A TRANSPUTER NETWORK , 225 V. Ntmtt

6. COMPUTERS

COPERNICUS COPHODESs PROJECT INFORMATION 229 A/. Servtt, J. Schmidt ON EMBEDDING K-ARY COMPLETE TREES INTO OPTIMAL HYPERCUUES„ 231 J. TrdUika, P. Tvrdlk PARALLEL TRANSFORMATION OF RASTER DATA IN GEODETIC APPLICATIONS 233 M. M&btk INFORMATION SYSTEMS SECURITY CENTRE OF THE CZECH TECHNICAL UNIVERSITY IN PRAGUE 235 I Pftbyl MULTIMEDIA SUPPORT OF MARKETING 237 P. DarboHk PC-UASED DRIDC1E-ROUTER MANAGED BY SNMP 239 tit. Cervtnj/, P, Vandrovtc BLACK HOLE IN THE MIDDLE CASE TOOLS 211 A'. Ilichta EXPERIMENTAL MULTIMEDIA AND HYPERMEDIA SYSTEM EMUS 1.0 213 P. lhllay, S. Ihtlomki, I. Jtlintk, M. Snonk IMPLEMENTATION OF A GENERAL-PURPOSE PROCESSOR MACRO 2« J. DanUik, F. Dixtpat, A. Pkhditk, M. Strvlt EUROCODES1 SURFING TOOL 247 F. Walt, J, Demi, J. Filipovd, V. Ihra, J. Kos, J. Ptrtald, J. Prochatka, M. Pullar VIRTUAL REALITY IN THE DESIGN PROCESS 249 / Btta, I. Jtlintk DISTRIBUTED INFORMATION SYSTEM ON WORLD WIDE WEU 251 M. Urachtt TOWARDS KNOWLEDGE DASED SEGMENTATION OF BRAIN STRUCTURES 253 P. Ftlktl, J. 2ira, /». Mrittk PARALLEL DATABASE OPERATIONS WITH SATELLITE IMAGE DATA 255 P, farnitwk

10 CONTENTS

A SIMPLE DATAHASESYSTEM WITH WWW USER INTERFACE 257 /,. StiUUtk OLOHAL VISIBILITY.,,.,.,, ,,,„„.. „„,„,„„ „„„,„,,„ 289 J. liUtntr, A. Holthk 02 « OnJECT-ORIENTED DATABASESYSTEM..- Ifll T. llrulkn DESIGN OF INFORMATION SUBSYSTEM FORTHETUURNO.,.,. 2G3 E. SnlpkthiovA. J. Cihldt, St. Vtmttyth, M. Chattil MULTIMEDIA AND COMPUTER ASSISTED TEACHING .,,265 /', Zemdli, J. Stdiit, 1L SllpAntk FLEDGE; A FLEXIHLE DIGITAL COMPUTER ARCHITEOTUItE 207 0. f'udtk 'ME EXPERIENCE WITH THE WWW SYSTEM 269 /', Inmpn, IK I'tikryl HYPERTEXT INFORMATION SYSTEMS OF THE FACULTY OF CIVIL EtfCJ. Mil) tAOiLtYOV rMCttUCM KXG. AND COMPUTER mKNCIZ TUBRNO...... 271 St. Ihtka, I'. Umpt, I', h'riihf, P. ftikryl DE HttUIJN AND KAUT7, IIISECTIONS 273 /'. Ttrdlk, J. TntUlka, I, Vrto, J. Itolim APPROXIMATE STRING MATCHING WITH It MISMATCHES 275 0. Mtlithar FORM GENERATION THROUGH CASE DICTIONARY ORACLE 277 SI. Vtknlt THE LAHYRtNTH PROJECT 279 P. Ut)U, J. 2in PARALLEL PARSING OF STRONG LR(I) LANGUAGES 2*1 S SWtrCIIINO - AN ALTERNATIVE FOR HIGH SPEED COMPUTER NETWORKS 2*1

INFORMATION CAD CENTRE AND INSTRUCTION OF CAD 285 J. tiiAa, It. Nimtt, SI. IMI, R. Sttttnj SIMULATION OP ADAM ON A PAPALtEt COMplTTEtt „„..,.., »7 T. Shttk, G. Slatfun, J. AitU*

II CONTENTS

SIMULATION OF PLANT DEVELOPMENT USING EXTENDED STRAND MODEt,,,,, , 289 11. Dene/, M, Soeh AUTOMATIC IDENTIFICATION OF PLANTS GROWING IN HOWS HY MBANS OP NEURAL NETS 291 St. Snottk, St. Sktbtk, M, Jlfina ONE TECHNOLOGY IN CREATION OF VIRTUAL CITIK3 29.1 It. Uerka EXPERIMENTAL CARD FOR SHIFT-ADI) NEURAL ARCHITECTURE VERIFICATION .....205 M. Sktbik OBJECT RECOGNITION fIV A NEURAL NETWORK 297 /', Niipkva, SI. Snonk MULTIMEDIA EXPLOITATION FOR TEACHING EFFECTIVENESS INCREASING, ESPECIALLY IN THE DESIGNING SUHJECT8 239 P. t'rnktt, /', Svohda, It. Kotitik J. Umndtjt, J. DtoMtek, J. i'olihk PROGRAMMING WITH THREADS 30! /'. Lamps

6. FLUID MECHANICS ADVANCED-MODEL SIMILARITY SOLUTIONS OF DASIC TUHDULENT SHEAR FLOWS 305 V. Tunt SUMIARMONICS EVOLUTION IN TRANSITIONAL DOMAIN 307 M. F. Stiiilia, J. Lain, P. Stfafik UNSTEADY FLOW MEASUREMENT 309 J, Noliikn, J. Aiamie FREQUENCY DEPENDENCE OF EFFECTIVE TURBULENCE LENGTH SCALE IN A JET. 3tl J. Strboth, V. Ttut EXPERIMENTAL INVESTIGATION OP FRICTION AND MINOR LOSSES IN UNSTEADY FLOW IN PIPES 313 J. Jtkk, J. Adtmu, V. SoUik THE AERODYNAMIC OPTIMIZATION OF THE AXIALLY SYMMETRIC FLOW CHANNEL 3I5 P. Zima, P. SafaKk, J. Noii(ta EXPERIMENTAL FLOW RESEARCH INSIDE TliESPWAL CASE 31T 5. JttkS, J. IMtfk, V. 12 CONTENTS RESEARCH OF A SINGLE-STROKE COPMPRESSION .....310 M. Mick, V. Tunf, l>. lldtehbaeh, M TnUct, V. Sl/pAntk COMPUTATION OF PLOW VW,\M IN A CYLINDER OK ICE 321 / h'oul, L Souttk, J. Ktactlt, t(. Haul HOW PATTERNS INSIDE THE CYLINUKIl OF ICE 323 /'. ttaumruk, P. llatuhbach, J. Mnctlt UOUNDARY CONDITIONS OF COMI'llESSIULE FLUID FLOWS IN ENGINE MANIFOLDS USED FOIt FINITE VOLUME METHOD 325 / hhttk FUEL JET MOTION AND VAI'OItlZATION IN THE COMUUSTION CHAMllEllOFADIFmENOINB 327 /'. Dotiiln MIXING OF SUSPENSIONS IIYDIIODYNAMICAL ASPECTS 329 F. nttgtr, I, Pott NONSTANDAUD MIXING EQUIPMENT WITH HIGH-SPEED IMPELIEK8 331 / Mdtkt L Foft DYNAMIC EFFECT OF MACHO INSTAD1LJT1E3 IN AGITATED 8 VST EM S .333 O. liriha, 1. Foft, f, Srnolka LAMINAR FLOW 1NVEUTOHS 335 P. Slfaitk, II, 2ilnj, J, SeMk MATHEMATICAL MODELLING OF TRANSPOItT-DIFFUSION EQUATION 337 /'. lngtdutd, J. VofoU DRAG-REDUCING SURFACTANTS IMPLEMENTED IN RECIRCULATING LOOP WITH WATERGLYCOLSOLUTION 339 Af. barlik, St. Obtiht RIIEOLOG1CAL UEftAVfOUIt OF HIGH CONCENTRATION HOMOGENEOUS SLURRIES 341 V. Itavtik, J. Vyillal ELECTRORIIEOLOGICAL UEIIAVIOUR OF CERAMIC POWDER SUSPENSIONS M V. PttUntk, J. 7V/i<4, /'. Siha, 0. Quadtit SELECTING THERMOPLASTIC HINDER SYSTEMS FOR CERAMIC INJECTION MOULDING 3-15 M. ECOLOGICAL AERODYNAMICS 317 / Adanut, J, Nolilk* HYDRODYNAMIC LOADS ACTLNG OM A SLIDE GATE JW t. 5*le, M. Haluia, F. Poehffl

13 WORKSHOP OG

THK HYDllODYNAMIC LOAD ON THE FLAP GATE WITH 111011 UPSTREAM WATEIl LEVEL , 351 J, Mavditk NUMERICAL SIMULATION OF A NATl/tlAL CONVECTION .1«.1 II, Ctrnj, V. llavllk, /'. Sklendf INTEHFEKOMETItlC HESEAKCH OFTEMI'EKATUHK FIELDS IN HOOM3...,,35f) T. IhUhk NUMEUICAL MOOELLINO OF FLUID FLOW, HEAT TUANSFKIl AND SECOND PHASE TKANSI'ORT WITH MULTIOHID METHOD 357 M Jarol, St. Jkhn INTERACTION OF COLD AND HOT JETS ON VEtlTICAL COOLED SURFACES .., 3.W P. Mai* kk, It. Novy

14 Section 1

MATHEMATICS

NEXT PAOE(S) left BLANK WOUKailOl'PO MATHEMATICS MATHEMATICAL MODELLING OF ENGINEERING PROBLEMS

J. I-VfltieCi, A. 2en(6ek,J, D&Uk*, 1. N«tlomn, II. llASlfkovA, D. SkabrntiovA**

TIJ, Fnc.of MCCIIAIIICAI Ktig., Dcpl. of Mathematics Tfclmickn Z, filO C!) llrrio •TU, Inc.of Civil Kng., Depl.of Matlicindtlw 7,l2kov» 17,002 00 tlfito "TU, Fite, of Technology, Dcj.t, of Mathematics Mm, TOM 27.1, 702 72 '/Im

Key words! mathematical modelling, finite element method, convection-diffusion, numef' leal algorithm, Czochralski (low, abttract operator equation, Nemytsklj operators

Onc-dimcnsional nonstatlonary coiivcctioti-difTiinlon problem witli dominating convee- tloti I* studied In [1), A nmnrri™i mctliwl for thin ptot)lrniti| + pu,-CM,, a / Is ilrscrlbcd »ml wiivtywili Tlin mrtlwil In ^ rmnSliintlnn «f tin* iiifttiod of chnrBCtcrintlci urn] tlie finite dilTcfciicc mctliud. Aptioti local ctfot cstiiii&tc of tlic ordct 0(/>J 4 ''J) I'M l>c«n )>rovc(l, wlicii; /i, ainl A, hR- tiic illsta-llzatlnii »lc|i». Tlic mclliod U ulnlilc fur 3e/i, < AJ And It tliuwa only a uliglit Attiflclnl

17 WORKSHOP 00 MATHEMATICS

In [7| the problem of tlie two-dimensional nonlincAr <|iliwisUtion/iry magnetic field was discretion! In space by tfm finite elcftient method with linear polynomials wi triangles and In tltnfl by the Kilter backward method, A strong convergence of the approximate nolutlons tra prr/vrd without /my ;^>ilwlty /uisumplloii for tlic exact rotation. Tlie Initial condition WM qilitfl general; however, the Diriclilet boundary condition wn» only liomogciU'oUS. [a the ptacnlKtl paper |6] the considerations ate tfiitetnttml to the ense of a iiuiihoinogcncoin Dirichlct condition. For n greater simplicity jxiiygonnl domains nrc coimldi-ird. In (8| the finite element method for a ntfoiiflly elliptic mixed Lotindnry vnluc problem W unftlyzcd In the domain fl whose boundary Oil Is formed by two circle* l'i, Pj with the iRtnc center So und rndil //i, /rj » /f| 4 ^, where g < 7/|. O/i one circle the homogeneous LJIflcldet boundary condition in prescribed Atnl on the rcniAlnlnj; one the tionhoinogcncoua Neumann boundary condition, [loth possibilities for u « 0 Arc connldcrcd bccmisc the analyslit I) different. The nUndnrd finite elements ifttisfying the rniniirinrii AII^IC condition are In thin CMO inconvenient) thua trlanglci obeying only the maximum angle condition And narrow quadrilaterals are Used. The restrictions of (cat function* 011 triangles are linear functions and on quadrilaterals four-node isoparametric function*, Uotli the effect of numerical Integration and Approximation of the boundary arc analyzed, '[lie rate of convergence O(h) in tho norm of the Sobolcv space i/'(flj,) is proved under the following conditions; (I) the dat* are aufflclently smooth; (2) the lengths I>M and Ini of the smallest and largest sides, respectively) of every ele/neril M (M « T, K) sutlafy the relations C\h\t < &/if <. Ca'ijf whero T stands hr it trlanglfl and K for a rjuadrilatcral.

[1} DALlK, J, - FlO?,lCKOVA, H.: An explicit modified mtlhod of characteristics far the />ne-rllmen*!onnl nonatattonrry convtcllon-tiilJunion problem with dominating convec lion, To appear In Applications of Mathematics. (2| FRANCO, J,! Modelling of Ctochmhki flow, Preprint. Depl.of Math. TU »rno. |J) FIIANCO, J.! Solvability of operator equation*. Survey dirtettd to differential equation*. Proceedings of Workshop In Non-Linear Operator Theory, Ahuja, 1095. (4) FRANCO, J.: NemytM} eptraton. Lecture Notes for Diploma Cournwi in Mathemat- ics, International Centre for Theoretical Physics, Trieste, April 1995,10 pages. (1] Nr'DOMA, J.i An algorithm for bilinear degenerate finite $hcll element*. Report. Opt.of Matli. TU Dtiio. (6) SKABIlAIIOVA, D. - ZKNlSEK, A.: Tm-dimentionat nonlintar quatutationary mag- tittie fi/IJ with nonhomogtntout boundary condition*. Preprint. Dcpt.of Math. TU. (7| 7EN1SKK, A.: Finite element variational crime* in parabolic-elliptic problem*. Numcr, Math. «5 (1083), 313-376. (8) £KNlSEK, A.: Finite tlemenl variational crime* in (Ac «ut of temirrgular element*. Preprint. t)ept. of Math. TU Ilrno, 1995, 26 pages.

This research hat bten conducted 01 the Deportment of Mathematics a* part of the ttseanh project "Mathematical Modelling of Engineering Problem*" and has been supported it/ TU grant No. FV 350008 and FME grant No. FP 3591U.

18 WORKSHOP 06 MATHEMATICS NUMERICAL SOLUTION OF 2D EULER AND NAVIER-STOKES EQUATIONS

L. IJenpS, J, Vtint, 3, Ilorrik, K. Kt>tt\, I. SMdek

CTlii lac of Mechanical Krig,, Dcpt. of Tcclinknl Mathematics Karlovo t\km, 13,121 35 1'raha 2

Key words) fititer equations, NAvlor-Stokes equations, TV1) scheme, ENO scheme, coin- preitslble How*, incompressible flows, boundary layer

Till* work CI«AII with tiuirifrical solution of transonic flow* (described tiy nyntctn of Euler equations) through A 2D channel (\.r%\ ca«c) by four Inodcffl nchctncs (three TVD type schernm and ENO ichemc). One enn comp«re accuracy of method, rdlciency, convergence to atcady dale and entropy production of the icliernca. In the >ccond pirt we deal with problem of numerical solution of flows In atmospheric boundary layer described liy two iruMlcln; model of full lyatcin of Ineoiiipresalbte Nftvlcr- Stoke* cqitationi and model of equations of houndary layer. We present comparison of several 21) results of transonic Hows In Hon-llo-NI channel (A/a, «• 0,075) an

I. Numerical Solution. We considered the following numerical methods solving the 21) problem of transonic flows In a channel:

1. Cannon's simplified TVD Mac Cormack finite volume scheme (lj. 2. Full TVD Mac Cormack finite volume scheme [2].

3. Upwind finite volume scheme based on MUSCL Interpolation and Hiemann solvrr {i\. 4. ENO finite ilifcrrnce scheme (upwind) \\\.

To solve the problem of 2D atmospheric boundary layer one considered the following models; u, + v, - 0 (1)

UK, + till, B VUn

U, + Vt m 0 (2)

("' + P). + ("•>), « *(«li + »W)

with appropriate boundary conditions. The problem 1 was ntimcriraly solvnl by Crank- Nidiolson method (second equation) and u was found by intet^atiou from first f<|uatiou. Tiw »y»tem ot Nkvicr-StoliCT d)MkVions n soWtii \>y lulifital tompiosibilily anil finUc \o\nme method by multistage Runge-Kutta scheme.

19 WORKSHOP 00 MATHEMATICS

IL Some numerical rcaulti. Fig. 1, 2 tiiowa Mncli mitiibcr distribution achieved by methods 1, 2 eclicnw along upper and lower walk Fig. 3, 4 shows iioUtinn of entropy produced by methods 1, 2, Fig. fl, 0 uliows Much number distribution Achieved by method* 3,4. In fl.ltmentione d cases one considers numrriotl solution of Irnmonk flow* fa iton-Ut-Ui clinnncl where governing nyntcm of

Fig. l! Caiuon'a TVD Mac Corrnack Fig. 2: Full TVI) Mac Corrnatk

Fig. 3; C«uron'» TVD Mac Cbrninck Fig, 4; Full TVD Mac Cormack

Fig. 6: Upwind MUSCL »ch«mc Fig. fi: ENO ichptne

Reference*; (1) FUftST, J. - KOZEL, K.: TVD Schtmts for ID and Multidimensional Problems. Ap- plication* for tht Can oflhe Eukr Equation*. Proceedings of International Workshop on Numerical Modelling In Continuum Mechanic*, 1'rngur W)\ [2] YEB, II. C; A Clan of Ilijh-Rtiohlion Etplicit and Implicit Shock-Capturing Mtihod* NASA Technical Memorandum 101088,1089 [3] JACOBS, P. A.: Sinjlt-Ulock tfavier-Stoket Integrator. NASA Contractor Report 187013 [4] OSIIEIt, S. - SHU, C. W.: Efficient Implementation of Essentially Non-Oiciltatory Shock Capturing Scheme* ICASE Report No. 87-33 |5) FF.1STAUER, M. - KNOBLOCH, P.: Optrator Splitting Method for t'ompttmiblt Eu. ler and Navicr-Stoke* Equations Proceedings of International Workshop on Numerical Method* for the Navier-Stokei Equations, Prague 1994 TliU work was ipontored by grant* of Ctech republic No. 101/93/0^61 and grant of TU Prague No. 10028247.

20 WOHKailOPOO MATHEMATICS MATHEMATICAL MODELLING OF POROUS MEDIA FLOW AND TRANSPORT OF CHEMICALS IN UNDERGROUND WATER

M. Sty"blo, J. Mnryskn*, J. MuUk*, J. Skoknn, M. 'Iftmn**, J. Drkoiovrf**, M, Hossloinfk**, 55, Strnkos1**, J. Novnk***, P. Mnreifck***, V. Wiwgerbnuer***

CTU, I'M. of Nucl. Scl. k Phyi. Kng., Dcpt, of Mathematics TroJftiiaVA 13, 120 00 I'raha 2 *TU Llbcrcc, Fae. of l'!

u = - where p denote* the pic/oinelrlc head, u ia tho velocity, K ia the permeability tenior, q represents the density of liquid sources. We consider Dirichlct, Neumann and Newton boundary conditions. The balance of \L,\ dissolved substances can be expressed by equations

^ + u-Vc' + V.|' + c',+ =f/'9+ + r/(...,ci,...), l' = -D(u)Vc/, H-L.. where c* is the concentration of ^th substance, if' is it's injection concentration, r' Is it's production rate due to chemical reactions, D(u) denotes the diffusivity-dispcrsivity tensor and q* a max(9,0), q" <=> min(i;,0). The boundary conditions are c* a 0 on the inflow boundary and 1' = 0 on the remaining part of boundary. Dalance of \L,\ species in the rock can be written as the system of differential equation)

21 WOKKSHOI'iK) MATHEMATICS

Fur both flow Ami transport models, tlic primal, mixed ntid mixed-hybrid forttidlallonn we considered, Tlic time dlscetlzatlon of transport equation Is done by Hollm method, In order lo describe the character of strati/led scdlmcnlnl layers Mid complicated hori- zontal profile, trilateral prismatic elements with vert!™! turn ami grn, At present time, the prlitml How model with new clement nnd niixcd-liyltritl How model coupled with flnitc-volumc trnnsporl model M<; lined in practical npplirntions, The rnixrd- hylirid trAntport model rms been sucrrasfully vnlidntoil on test problems, For the simulation of long-time CIICUIICAI situntion development, the influence of gravity is considered, The further development of iii/itiifiimticM models will Include the solution of unsteady porous media (lu!d /low problem,

References! [1] ARNOLD, D. N, - IIRKZ/I, [•',! Miicil and nnnconforming finite clement mtlhodn implementation, poilproctBiimj and error utiinattt. Mathematical Modelling nnd Nu- merical Analysis, 10:7-32( 1085. [2] MARRCRK, I'. - NOVAK, J, - WASSRIUIAUKII, V.: Mathematical motkUimj of the influtnett of the Slrdl mill waste pound on (he graunttwaUr, IAEA Technical (Uitnmil- tee Meeting on Computer Application In Uranium Exploration and Production, Vienna, 16-18 Nov. 1991, [3| MAItYSKA, J. - MU?,A"K, J.! Hybrid mind model of the transport of chemical tub- stance/. In Proceedings of Numerical Modelling in Continuum Mechanics, vol. II, 1994. (1] MARYSKA, J. - MUZAK, .!.: Mathematical modelling of the transport of chemical species in the contaminated underground water. In proceedings of Congrcs Milieux Poreux, St. Eticnnc, 1995. (5] MAKYSKA, J, - ROZLOZNlK, M. - TOMA, M.: Mixed-hybrid finite element approximation at the potrntUI flow problem. To appear in J. Comput. Appl. Mnth., G3, 1995. [C) MAUYSKA, J. « HOZLOZNlK, M. - TOM A, M.: The potential fluid flow problem and the convergence rate of the minimal residual method. Submitted to Num. I/in. Alg. Appl., 1905. (7j RAVIART, P. J. - THOMAS, J. M.: A miied finite element method for S-nd order elliptic problems.. Lecture Notes in Mathematics, volume COG, Springer-Vcrlag, 1977. [8] SKOKAN, J.: MelSda konelnych prtkov v problemalike pridenia podtemmjeh tod v sc- vcrny'ch Cechich. Master thesis, CTU FNSPE, 1995.

This research has been performed in the Department of Mathematics as part of the research project "Mathematical Model* of Underground Water Flow and of Transport of Dissolved Substances for the Purpose of Remediation of Consequences of Uranium Mining in the Northern Bohemia" and has been supported by GA Cll grant No. SO 1/93/0067.

22 WORKSHOP flfl MATHEMATICS THE MATHEMATICAL MODEL OF PERIODICAL FLOW WITH MIXED BOUNDARY CONDITIONS

1\ Kuccrn

CTU, Fac. of Civil Kng,, Dcpt, of Mathematics TMkurovn 7, ICO 29 I'ralm 0

Key wordsi Navler-Stokcs equations, mixed boundary conditions, periodicity

In tills contribution, wo present the result of tfic existence theorem for tho system of tlic periodical Nnvlcr-Stokcii equations nnd the continuity equation with tlifl mixed boundary conditions and for sufficiently small data, 1. Definition! We tuppote tint fl C tl", where n m 'I or n m 3, (I la open, bounded and connected domain, (1 € O" And we suppose tfiat

on = i'i urJ(i'j mca* l'j > (l,( = 1,2,8,4, mcfu

2. Definition; Let us define the ipnce

£»{fi) = {u e [c°°(n)]"j dw u e o, mpimn r( B 0}, the Danoch ipacc lla an the closure otCn{U) In tho norm ot the ipace [//'(fl)]", the Dnnncli r space Vo'' as the closure o! fo(fl) in the norm ot the sp/ice [H"''((l)l" and the Uanach tpace D

1 {u e Vo'''i there exists / 6 /A> and for every v 6 Vj' ((u,w))i,, = ((/.t/flo.a) tvit/i (iie norm Mo-l/lii.. By the symbols ((.,0)i.J> ((.i-Bo.i we mean the ictlar product In (W"'a(n)]", [/.'(fl)]" rcspcc-

Let T > 0, Q «• H x (0,T) and n ii external normal vector. The motion of fluid is described by the system of equation!

°"i A • 0ut OP . _ . . •' + U^5U + ^ = * ittQ' tBl "• divu 3 0 in Q, u m o inr, x(o,r), -V • nt + v • •— a oi in Tj x (0,T), on u(r,0) = u(r,T) infl iio = 0 in r,.

23 WORKSHOP DC MATHEMATICS

3. Definition! Let ua tklina Urn [hunch ipaca

Xu m (u;u e //•(<>,7',tf)i«' e l,\0,T,lla)M0) •<

with the norm

lol un define the Dnimcli tpnee

4, Notntlom For u,v,w^ V^*1 via menu )iy the nymbol b(u,v,w) tli« cxprcmlon

5, Dcflnltloni Let u« define the operator Un i X/( -• Yu,

where F ** [f,u0] Mil

and u(0) B Ua Tor u, F «nti every v € V^1'1 fc h the consttnt viscosity), 0. Remark: It is obviousthc function u ii A weak Holution of the Navicr-Stokcs cquationa with the right side / if and only if Afn[u) = /. 7. Theorem: There exist neighbourhood U of zero in Xu nntl neighbourhood V otvero in Yn and Afir is one-to-one from U to V.

This ntearch has been conducted at the Dtpartment of Mathematics as part of the rt- search project "Solution of Partial Difftrtnlial Equation) with Special Boundary conditions" and has been supported by CTU grant No. 10110.

21 WOltKSHOI' 00 MA't'HKMATKM WELL-POSEDNESS ANALYSIS OF NONHYDROSTATIC TWO-LAYER MODELS OF INCOMPRESSIBLE FLOW

II. Mskn, L, Mnrgolin*. U. Wendrolf*

CTU, Vac. of Nuet, Scl, k I'Jiyn, Bug., t)ept, of J'hynieal Electronics V llolciiovlckaeli 2, 180 00 I'ratm 8 •Los Alarno* National Laboratory UM Alamos, NM 87544, U.S.A.

Key words! Incompressible, iionliydrostntlc, two-layer, Orcen-Naghdl, imposed

Several reduced dimension two layer models of incompressible (low, which arc of the interest* for e.g. global ocean rnodelling, arc developed and their wcll-po!iedticss analysis Is performed, Tlic models arc derived liy verticnl * integration of Navler Stokes equations fur invlscld fluid with constant density p, velocity (u,w) In the (/, t) direction respectively and pressure ;> uf + wf«*0, (I) f>(u, + uu, + urn,) a -/), + /"•', (2)

f(Mt + UUI, + Wit,) « -fl, - Dfl. (I) Tim two layer models assume constant density in each layer. The variable bottom of the height *o(i)'' Allowed. The variable thickne««rs Are li){z,t) for the bottom layer and hi(x, t) for the top layer, The bottom layer Is between surface* zg and t| a>0| U\ and the top layer is between surfaces x\ and rj a *i + hj. The boundary condi'.ions (DCs) are either free surface with zero pressure at i} or rigid lid with constant tj and continuous pressure at the laycn Interface i| h assumed, The equations (1), (2), (3) are formulated for each layer independently with different densities pt, velocities (u(, wt) and pressures p,, • = 1,2 for bottom and top layer respectively. Models (lifter in assumptions how the velocities depend on vertical coordinate t. Using these assumptions and [ICs the mass conservation equations are derived from (I) (for rigid lid HCs one mass equation is icptaccd by ft jump condition). Further (3) is vertically integrated and solved for pressures p,(i) which arc substituted into (2) together with the assumed form of velocities. Then these equations are vertically integrated over corresponding layer resulting in momentum equations. For free surface DCs the vertical integration of (3) expressing p,(i) goes down from it to i < n and finally we obtain a system of four nonlinear partial differential equations (PDEs) for A|,A),U|,U] depending on t,i) only. For rigid lid DCs the vertical integration of (3) expressing p,{t) goes from J| to i in both layers and finally we obtain a system of four nonlinear I'DKs for /i|,U|,Uj and the interfacial pressure pi(ti) a ;>](*|). The same procedure can be used to reduce 3D problem to 2D. After linearization the wcll-posedncss analyiis it done by standard dispersion analysis by replacing partial derivatives of all unknown functions v by

25 W6ftKSH6P 66 MATHEMATICS

Till* tfntiUi In l))« line/if aytlem t{utk) vsO. the roots uj{k) of (let t.(u,k) = 0 In (l>« \\tn\h ff -t i» /»)W t>» *» »M«m\nn If. the otl|(ln*] system In well- of Ill-posed, 'f lie «yitcm Is well-JM>se'3(A) ^ 0, In inch * cue tlir* otiglnnl system In well-j>lital*tl model o( pf«t«?wl!K) lltimf w wild ftec miffntd HC'rf tin? l/oltofn frKjffH-ritiifii t(|ii/iliofi Is N turn of 69 lertna) nm\ (fir (li«ppf«iofi Afmlysf* Involve Irdioin /tl^cbfa the wrll-fHwvlnMi anxlysls li« l«vn tlofie l»y the cbinpiiiet «l^ebrji nystrm l(Kt)UCB |l), TfK fiMt «n»lyi"v| iitwlrl li »lisll(jw wAlcf inotlcl with hydrostatic Aptifuxltnallon (act' tlrij! If/I liitnd Me o( (3) to teto) and Is Includnl for completeness. '1 he ahxllow wntcf frre Kirface model \» well-|Hraed only In mime regions of parameter*. The iliallow wntcr rigid lid model li well'pf«etl iff (ui - iij)1 ^ g(p\ -/>j)(A|//i| + AJ//>J). The next moilel Msiirnei the vertical component of velocity w being t'lectrwlse linrnf in t and is p-Mta\\/.a\\050il iot both frr« mirf/irc and flgM l/d MC# liwwf «*» (/# frguUfi/eil hy fmttlh vtdct tll«*l|>atloit In the rigid lid cow;, Flifllicf generalization allows w in be plrrmvi** t|iii«ilritlie lit J utul IN, foe ftoo lutfucti t)Ca, weil-pimii tor wnall AJ/AJ *tii| fli/flj. Th« fgi'in d{ llin wp|l.|><»vilfteM (or tli« liwt ttuxlcl can be enlarged by Intnxliiring a <)uAdi.ilk potitive wci^fit into ifif vertirai «yrragfng <>{ motnenturn c]tiations or rrpluing the lnU^f»U by point Values. We have verified ?he results of well-poitedneis analysis origina'ly performed bj- hand (1,4/)| for six tux* by using tomptilet algebra and analysed two otlnf new »»«, Most of th«? model* are nwnlUlly M-pmed, More detailed prenenlallon can be found In (Gj. ttcfc renewal H) HfiAUN, A. O.i IIKDVCV. lhtr'» Monuat. Vtnion 3.3. IIANO Publication CP "8 (Itry. 10/93), ItAND.S^U Monica, 1991. |2j C5HK.F.N, A.E. - LAWS, N. - NAGIJDf, P.Hf.: On Iht Thrary of Wattr Watts. Vtuc. It. Serf. lemd. A, 33«, 4153, 1974. (3j WKNDFOFF, O.f Compete Hota,. Phy*\e» D, 60,20^212,1992. [i] WKNOFOFF, H.: IVrHra/ Attraginj in Oetan Dynamic*. LAUI19^723 (revised), In AUmo* National LaWalofy |{ppnrl, 1991. |3J WENDFOFF, «.i Mr/ira/ /Ipfnijtnfl «n OrruN (*V«m<«, It. LA-UR-9J-2200, Lo. Alamo* Natk.ial Laboratory Iteport, 1991. |6j LISKA, R. - MAtlGOUN, 1. - WENDtlOFF, II.: SonhyHwIalie Tvo-Uytr MoiiU of lntompn»*AU Ho*. Computers and Math, with Applic, 29, 9,2V37,1995. TfiU ttuittxh hat httn tonimttti In part at iht fitpartmtnl of thpieat Liitttonie OJ part of Iht ttnanh projul 'SfrnMit Jirintien, an*ty>it itn4 pngrammfaf of Jifftrtntt trh'mut *nJ nlgihraic algorithm*" and Kan ittn uppttitd in part iy iSt Cttch Grant Aftnty ft*Ht iVo. S0I/9I/H09. TAu rttrarxh hn4*<(r

II, Hong, K. Makn*. S. Steinberg"

Johannes Kepler University, ItISC Una A- HMO l,lnz, Austria •CTU, Foe, of Nntl, St\, U I'hyn, Kng., Dept, of Physical Electronic* V HoMovllUcli 2, 180 00 f'rah/t 8 "University of New Mexico, Department of Mathematics and Statistics Albuquerque NM87l:lMMl, USA

Key words! stability analysis, Inltlnl value, problem, boundary value problem, quantifier elimination

Stability |g one of the incut important properties of ordinary differential equations (OI)Ks), partial differential equal |i,ns (l'l)Ks) and their discrete dilferenrn analog*. The standard trielliod for tlie itdbility nnnlynU of (y«l«ti of co»it!niious DE<< Is U«e(! on perform- IJIJ! L*plac<' twjisfurjjiatluu In t))»? cuortMunlvt rwmin% over wuMnftnlU! Idtcrya) {*.%* {\nv> or counlinntr with boundnry condition) »nil Koiirie.r trxnnformation in coorilinstes running over infinite Interval. After the trnn«if<»rr!intioiii one obUin clinrnflrrlstir polynoinUI of tlie ayaterti And for lmiind>ry value pruliletm ANO «ytnbol of UMitidnry condition! (IIG'n), Uilfcrent stability propectles rnn then lie nUled HJI «|iiAnlifler pliiiiSnation (QK) prohlern* Involving characteristic polynomial or aUi lytnbol of lid. Similar approach tnn be used for discrete problem* wliere continuous Fourier/I.Aplare tranpfcial trial nolutions, In ft] we have shown how the stability properties of following problems can he slated M QH problems: initial value problem for continuous ODtln (for Applic*t!ons of this to control l!>«>iy M* (2|); di«t(ele nutnetical meth- oiU tor ODRs Initial value problem, Including llMiifteKulU methods; Initial value pioblem for continuous I'DF>; finite difference •chemn fof numerical solving of initial value problem for PDK*; initial boundary value problem for continuous I'DF,*; finite ilifferenee schemes for numerical solving of initial lioundary value problem for I'ftpjt; srrnidiicfeti/ation met hex I for initial boundary value problem for I'DKs. QK problctn Is defined by formuU including quantifier;) (Vor 3), quantified variables, non-quantified, so called free, variables, logical operators and polynomial equations ami Inequalities. The QK procedure eliminates from the formula quantifiers and quantified variables »nd constructs a quantifier free formula which Includes only free variables and which Is equivalent to the original formula, for solving the QK problems we are using the QKI'CAI) [3] package based on (he partial cylindrical algebraic decomposition method (l|. In QK problems arrising from the stability properties Analysis the quantifier) variables Ate Laplife/Fuuiirr transform variables and free variables ate parameters of the Analyzed equations. So if we succeed to solve the QK problem which is equivalent to stability then the fttilt give u* IIK cucvlltloo* M fux*i»*(«t* tttvlrt wliWd tb~ atuJyini pcilrUtn U «lal>t- is precisely what it needed as A mull of (lability analyiis.

27 WtfflKSIIOI' m MATIIKMATlca

To dliow how these method* work we present here one particular example, In |0| bound' My conditions for compact higher order finite difference schemes that flpprixlirmte the scalar onc-t|iiati6a using ttiesemfiliiercCrzatlcfi approach are studied. The fourth=order sefnlillacrcllzfttlon (only space |g dUctrtlml) for tlm Inflow problem h defined by £*i + *Ji, + l'm.t + 3(/«t, - /.-.)/A/ • 0 in the Interior point" (here /' Is (lie time derivative of / a/id /m(t) « f(l,tnbi)). The combined first* ami aecondorder bonndary condition l» (4(1 + 3/>) - 1) /,' + (1 + 2/IJ/J + |-2(1 + W/i + 3(1 + %fi)Jt\ /A* « 0. The trial solution In the acmldintrcte c«e IIM the form f*(t) => fJ'wM. S'ulntitiitlrig thin trial solution Into the above difference achctna we obtain the tlmriicterlsllc polytiomlnl of the Interior icheme C(S,w) a (I + 4U> + HJ*)A+.1(U)* -1), where A «= AA/, and Hid »ymbol oi* the boundary conrlition W(A,w) » |4(l+ 2^)- 1 +(1 +2/J)(«)A-2(I+^)+3(i + 2/>)u), The existence of the unstable solution* (l.e, IOIUIIOIII Vrhich »rc botmded in »|>nee but are cxponrnllally glowing in time) l« te«trd by the QK ptoblern 3A € 0 A \w\ < I A C{\,w) » 0 A Z/(A,t«) « 0}, where (7 are comptfrX nutnberi and H denote* real jm method la extremely high (double exponential for QEPCAD which Is the beit general QF. package). So the method can be applied only to relatively simple problem* on the other hand it haa already produced several new result*.

Referenced |l] MONO, II. - LUSKA, It. - STEINHKKG, S.: Utinj <}«anlif,er tlimlnatfon to lot tta- bllity. i. Symbolic Computation, 1996, mbtnitlftl. 12] AI1DALLAII, C, - DOKATO, P. - YANQ, W. - MSKA, It. - STKINHEUO, S.: Appli- taliont of qvenltjitr elimination theory to controllytttm dtiign. 1FAC World Canpni, 19%. iubmittr.1, [3| IIONO, II.: Imptvttmtnti in CAUbnird Quantifier ttimiwttion. Ph.D. Dissertation, The Ohio State University, 1090, (4] COLLINS, O.E. - IIONCJ, II.: Pirtht Ci/tindrhcl Atgibraie Decomposition for Qvnn- lifiir F.imlnatlon. J, Symb. Cbtnp. 1J(3), 299-328, 1991. [S] CAHI'KNTKIt, M. - nOTTI.IEII, 0. - ADAKEIANEL, S.: Stable end accurntt boundary trtatmtntt for compart, Mghtr-orJer finit<-differtnce nhemtt. Applied Numerical M»l!icmatk», 12, 6-V-87, 1993.

Thit rtiearrfi has bttn conducted in part at Iht Utpurtmtnt of I'hyiical Eltctronlt at part of the mrtnh pnrj'el "Symbolic dtritatian, analyiU and programming of Jifftrtnet ithime* and ejjttnie al)

US STABILITY OF STEADY SOLUTIONS OF PARABOLIC EQUATIONS IN HILBERT SPACES

J. Netiitupn

C'I'U, Fae, of Mechanical Ktt&., Dept, of Technical Mathematics Karlovo IIAIII. 13,121 .15l'r»liA2

Key words! 1'nrnMic partial differcntl»l equations, Stability, Navlcr-Stokrs equations

We JCAI with Asymptotic stability of the mo solution of tin differential equation J « lu + N(t,u) (I)

where // in A linear operator And N(t,,) is a nonlinear operator in A rent Ililbert ipAcc //. We assume that the spectrum of A symmetric port of L IIAJI A nonempty intersection with th/> Inlrrv/il (0,+eo), whlrb mr«ns thxt thffoprr/it/ir A In not fllMlpitllvn, Tlio sscro tolntlon of equation (1) CAN bo ttAblc If A ikcw-nyrriinetflc part of (lie oprmtor A IIM AM «ji]iroptlfttc »tatjl]J/Iu^ Itiflii'.'iiw. ')'M» Ju/lufiicB)« usually ejrprfatwJ by t)j« jusiijiiptlo/j tlutt JteX < "-6 for Kinc j > 0 »ri'l All A € )i where o(L) drnotra the xpectrnrn of I, However, this Assumption Is not satijlinl tf o(L) IIJU An riucntl/il part which touchrs the Imaginary AXIJ, Such A cAse l.t typical for problems In exterior domains. We formulate sufficient conditions for itAbility which tan bo fulfilled even In this CASC And which nre A substitution for the condition "1UX $ -S for all A € o{L)". Let (., ,)o be A scAlar prwluct And ||.||i> \m An AssocUlcd norm In //. Suppose that L ** A + U, + !)„ where A Is a aclfadjolnl operator in // which docs not have 0 at iti eigenvalue and o(A) C (-,0). I), and I), arc linear operators in // such that their domain* D(U,) *ml P(l>.) contAin D(A), U, Is tytntiftrk and II, is skew-tyrmtietrlc. N(t,.) is for each ( € (0,+oo) a nonlinear operator in // with the domain D(N) which docs not depend on / and D(A) C D(N). We put

for 4 We use the following assumptions about the operators [I, and II,'. (I) 3d, > 0 : \\ll,ih < ^ \\t\\\ tot € It,,

(II) 3ae|i,i) 3cuet20 : ||AW||o S c,||(-/l)^||0 + c,||^|, for i «= D({-A)"). It follows from condition (i) that the operator A + O, I) •elfadjoinl. Let us denote by £(A)

Its resolution of Identity. Put I* * f0*" o s ((/l + rg^s-e«D*Di fo'i»6wnD(A). If <•< € (0,1) then the operator A + 1/(1 - r<)//, it alw sclfadjoint. Ut f,'i(A) be Its * =/,••• J£,(A) miiJ WJ = /» WORKSHOP (16 MATtlKMA'lTO

Lcrnmn 1. If Ihcta exhln e< e (0,1) so llmi the Incr/im/ity (/U+#,^/(i-fci),'#Jo £0 /ioW# /or a// ^ <= /'";/| 0 «(/») then condition (III) h nullified. 'flic »(ince II', cm \>c /liillc-illincimlorml In ninny practical rmrn mid mi there exists it l cl)n»ce to Verify tho assumptions of Lcrnrrm I, It follow from (I) and (II) that o|icrntor (-/,) Is »ectorlal, Tlitm, A giMieriiM BII analytic Ll acmigrmip t In 7/( Wo denote \>y llg K M culled cinii|il«xific«t!on of 7/i Tlic lirxt eo/i'liilwi we use i»:

(Iv) 36 > 0 «o f/i«( /^^ € //'«/;«»I'1 HK(IJ) enn bo cxlviiiktl (In ilepeiulena) an \) (mm (A to art lla-vnlurd minlyllc funrtlun In g{l) U {* 6 Cj lie t > -6),

{lk{l.) » (L - Xl)m> »ml f(/0 l» the fCTolvrnl »*t of A.) We can present conciete cxntn|ilcs of |)dfnljollc equntlotM in II) mid Ul) mid we t«n show that conditions (l)'(iv) Arc natWIrd, Lentrnn 2. If eamlllloni (i), (ii) unit (iv) nrc tntufial ihwi thrte nxhli c» > 0 no lltsil

Nonlinear operator N In mippmoj to satiufy

,l) 37 2:2-/^ 3r«>0 ;

wluliuiM the pijutttlon (1) hi n tlnic liitrrvM |0,V) (wlierrr '/' «i (0,+oo]), wo functions u met) tlial &) if J Is a tompact Interval In (0,'/') then u e /^(Jj W(/l)) Tl /,'(./; //) «nd 0, there cxitti K > 0 in tint If u M a •o/iif/on of etfiintlon (I) in the Interval (0,7'), |lu(0)|jo + ||u(0)I|i < K thrn ||»(OI|o + ll«'(')lli 5 « tor*.*, t € |0,T). Moreover, if T a -f oo thru lim^tno ||u(<)||| a 0. If we study •taljilily of a iteady nolution U of the Navirr-Stoknt rr|iiation« In an exterior domain it then we can t ransform this problem to the (|UMllon of liability of the zero solution of an equation of the type (I). We fan ffiow that if U \n "mnooth rtidiifh" Ihrn tohAiliun* (I), (II) and (v) arc intiified. Thin, we (an formulate a th«ircm where the only cotiditioni for liability are (iii) and (Iv). Moreover, the solution* which are "»nuilJ enough* at the limp t B 0 rxi«t rm thr whole lirrwr Inlrrval (0,+oo) ami they have some ilrtny propcttirs ttir

n«fcrencc«! (1) NKU.STUf'A, J.: Stnbiliiintf influmcc of o iktv-tymmitric optntor in trmilinear parabolic tqvation*, preprint 1995

This rtttarth hn$ iten supported by the Grant Agtncy o/ the Cttch hepublie, grant So. S0I/93/8I11.

30 WORKSHOP 06 MATHEMATICS GEOMETRIC MODELING OF MILLING

M. KnrgerovA

CTIJ, I'W, of Mechanical Kiig,, Ucpt. of Technical Matlinmfltic* Knrlovo n/iiti, 13, 121 35 l'ralm 2

Key wo-dii geometric modeling, milling, circular cutter, elementary motion*

A geometric model of four-axial milling machine will lie presented .The considered milling process la A composition of five elementary motion), two translation* and three rotations, tec Fig. 1, The surface of (lie culled body I* given by Iti section* in planes i m count. These flections CAII he expressed !iy parametric equation*

y •* -x(l where the cutted body revolutw around z-axia. A circular cutter with center at the point S{X,0,t) lies in the plane t = const. It has parametric equations

t = A' + »', cosu, y a i;ttti u, i = z.

Tfiii toot can rotate around vrrtioil nm wild equation* x « /', t •» t, (he angle of rotation bo 0, The rotated point [I'Iy',11] of the tool is given by parametric expressions

i' a l>~ [[• - (X + r.cos o)| coo/?, i/' a r.slna,*'«»» + [/'- (^ + r,cos a)] sin/?.

The rotated center of the tool Is given by

,lM/>_(/'_X)co»/}, i/, »0, j,=i + (/'-Jtf)sin/?.

Milling conditions arc:

1) The tool and cuttcd body have a common point. 2) The tool and cutted body have common normal and the point of contact.

Theac two milling conditions mean that the cutter and the cutlet! body have common tangrnt plane at the point of conUct.Tbis improve* the aeur&cy and smoothness of the milling process as the result of effective use of the lut degree of freedom. Using this two milling conditions we obtain equation* for all necessary parameters of the milling. They arc

I'-(P-X -r,coso)eo»/),

r.sino,

31 WORKSHOP MATHEMATICS

cm a[I< cm p + SIM ji[ i «!n ip-y cm y>)) = 0, cos « cos/)(i cos i/5 + j/sliiy) - tin f>(A sin v5 ~2/

Tlicso equation* rnn lio explicitly HUIVTII nn

V .-.i o| — — a u

References: (1) KAItfJKHOVA, M.i C'romtlry of tnittiny. Sfmrtifk Sedmiliorky 1995

7Vit.i rttrttrth hna brtn conducted nt Ihe Dcpartmtnt of Technical Mnlhematicn a« part o/f/it rtunrth projrct Mathematical Mtthuiii in Kinematic* of Machines and Koboln and has bnn lupporttdby GA fit ID 1-930^1. WORKSHOP 06 MATHEMATICS ENVELOPE OF SURFACES CREATED BY OSCILLATORY SCREW MOTION

E, KoplncovA

CTU, IV, of Mechanical Kng., t)cpt, of Technical Mathematics Karfuvo nAm. 13,121 .'15 Praha 1

Key words) oscillatory screw motion, envelope, contact line, cylindrical earn

Oscillatory screw motion Is created by the composition of tlic screw motion and the harmonic oscillation in the direction of the axis of the screw motion. Length of (he displacement Is given by tc function

v. Is the parameter of the icrcw motion, A is the amplitude and rt is the frequence of the harmonic oscillation. Tl»* surface / by the oscillatory screw motion creates l-parameler family of surfaces which can bo given In the parametric form iur« r(u,i/,y>) where y Is the parameter of the family, 'I'lie point of tho itirfoee T laying on tlic contact linu satisfies the equation

(r. x r*) ry => 0. (2) For each value of the parameter v» a Vo the oscillatory icrcw motion Is substituted r lc by the Instantaneous screw motion (the axis d, the parameter C0(vo) i° '' translation, I for the revolution). If the generating surface T Is a rotational surface (the axis o, the meridian m) described in a suitably chooscd orthogonal coordinate system "£ then the analytical solution of the equation (2) exists. The choice of the system *E is shown on the Vig. 1 (the h%\» *i| = o, the *x3 \t the axis of the skew lines o, d). In the coordinate system *£ the axis o) i» t(u,w) = (n>i(u), rn)(u)cosu>, mj(ti)sinu)). The Ungcntial vectors are r, •= (m'i(u), mj(u)cosu;, m'2(u)t\nw), ru a (0, -rnj(u)»inu), mjcosui). The velocity vector of the contact point by the Instantaneous screw motion for the parameter ( = 0 (rcsp. =« (WJ(II) sin ID sin a + 0,(v»o) cos a — rfiin o, - rnj(u) tin w co« u + C.(v>o) «in a + rfcoso, mj(u)co»u)co8o - mi(u)aina). The analytical solution is suitable for the computer aided construction of the envelope by the sequence of contact lines. In mechanical engineering applications the oscillatory screw motion modclls the movement of mcdianisms transforming the revolution to the translation in the direction of the axis of the revolution under the change of tl e motion velocity, e.g. during the change of the direction of the movement (Fig. 2). The programme was used for the design of lbs envelope of the follower of the cylindrical cam (F'g. 3). The follower is modelled by the rotational truncated cone (the midpoint 5 = [30,15,0], rpip. S* = jW, l&,0), the railius r = 5, rcsp, r* = 12), The displacement ol the follower is given by the following function (// = 33, A = 120*, v. = ///A, A = ///(2r), n = 2ir/A)

33 wonKsnop oo MATHEMATICS

«(v) " "oV + Aril) no, If 0 v> < 2*, Aii Important technological parameter fur lliu design of tlio cnrn in ttin prvnaiirc nngln, It Is an angle tlint tlio norinnl vector of tlic cnvclopu nukes witli tlic pntli of the follower, Tlio pressure angle in points of the nine contact lino In MKIWII on tlio I-'fg. \, 'I'lio first and ttic ninth conttict linen are morked (,y the nornmis of tlic envelope on the Fig. 3.

*t\ " a

I'Ig. Is Ciordirurto system Fig, 2; Cylin'lric*) e»m.

Pig. 3: Contact tines of the envelope, Fig. 4: Treasure angle. References: [1| KARGEH, A. - NOVAK, J.: Protlonvi kintmalika a Lieovy gnipy. Praha, SNTL, 1978 [2| TSAY, D, M. - WEI, H. M.: Duing and machining of cylindrical cam* with translating conical followers. CAD, Vol.25, Num. 10, p. C55-C61,1993. This research has been eonducttd at the Department of Technical Mathematics as part of the nsearth project "Mathematical Mttheds in Kinematics of Machines and Robots'' and has been supported by GA Cfl grant No. t0t/93/0Ul (intern. 130 210 20). WORKSHOP 9(1 MATHEMATICS CURVES WITH MATHEMATICA

V. l)iib"iilk, J. Corny1, t. SMmovA

CTU, Knc. of Civil Uiitf., Dc'pl. of Mutlii'iimllM Tlinknrovri 7, ICO 29 I'rafia 0

Key word*! animation, curves, MatheiiiAllea

Tim results of the work may lie selected into two parts, First prcient* ttio mo of tho software Mathcmallca fur educating mathematical subjects, The second is «u individual work with talented students or llic ones wlio Arc Interested in advanced methods of solving riiAtlicrnntlcAl problems in nn cxlrnordlnnry stntidnrd. The mnlii nttcntioii wan focused to geometry both in to the lining of graphical Abilities of the MathcrnAtlcn and the nxploltritlon of the possibilities of symbolical calculatloni, One of the output* was to provide A collection of particular problems in the concrete which in A demo way would show to students the powcrfiilnras of the soflwnrc particularly in kinemntlcAl creating of curves. A collection of useful routines was worked out to demonstrate various types of plnne curves. It concerned, for example, the cottclioidal curves (in pnrticulur conchoid of Nlcornrdrs), prrlnl curve* (lernfilnr»t

Animatr[Pht\f[i,t\,{x,tt,Xi)],{t,li,ti,&t)],

and others. To show tlic true proportions of the Image and to ensure that all images have the same icalc there arc given options AaptclRatio and I'lotliange. The programmes Are supplied in a general form when A student can by choosing of parameters watch changes of the shape of the curves In dependence on the values of these parameters. Let us present now some results of tingle problem* that was established within the work with talented students. It concerns the creating not so frequently presented examples of the plane curves (skew pedals, counter-pedals) and spAce analogies of the plane curves (space involutes and space pedals etc.). On the following figures there arc four examples of plane and space curves. On Fig. 1 there Is a countcr-pcdal of an asteroid?, Fig. 2 presents the orthogonal projection of a skew pedal of a space astcroidc. On Fig. 3 there is shown a Viviani's curve And its pedal and on the last figure there are ^resented in addition their orthogonal projections onto coordinate planes.

35 WoitkSiibt* MATHEMATICS

Fig. Is

Fig. 3: Fig. 4:

References: [11 DOYLAND, J. ct al.: Guide to Standard Mathcmatica Packages Wolfram Ilcncarch, Inc., 1091 [2] OKAY, A.: Modern Differential Geometry of Cunt* and Surfaces CKC Pros, Inc., 1903 [3] CERNY, J..' Darsteltung der Kurven an/ FlSchtn mit der Software Mathematica in Proceedings [ngcnicurp&lagogik 95, p. 223-231, 1995

This rtieareh has been conducted at the Department of Mathematics as part of the research project "Education of Talents in Mathematics on Technical Universities" and ft«J been supported by FR No. 32011010 and "Application of Software Mathematica'', grant FCE CTU No. 1048.

36 WORKSHOP 00 MATHEMATICS EXPERIENCE IN MATHEMATICALLY ORIENTATED SOFTWARE IN TEACHING

V, UcncS, 0, Zlntnfk

CTU, 1'ae. of Mechanical Kng,, Uepl, of Tcclinicnt Mathematics Ksrlovo n/iin. 1,'J, 121 3f> Vtnhn 2

Key words! teaching of mathematics, mathematically orientated software, didactic use of computers

It Id ft remarkable feature of last years that computers equipped by mathematically orientated software produced l>y leading world software firms become a new tool In teaching matlicmatica. This kind of software include*: Mathcinaticn, Maple, Derive, Czech made Fatnulun and a lot of others. They nrn appreciated for their high professional level, user- orientation when solving the problem* of numerical mathematics, computer graphic* and symbolic mathcrnftticJ. Hence there la no doubt about tlie important role of computers in mathematical activities. Due to these new attractive possibilities, Interest of teacher for other didactic function* o( com[>tit<-rn way df-crea*? - sec [1, 2], Questions that conrrnrn concrete applications of computers in teaching mathematics arc often discussed. As a partial contribution to this problem, we present a short survey of our experience (and experience of our colleagues) with system Famulus (since 1093) and system Maple (since 199.1) in our department - sec [3) 4] and nomc oilier departments - see ||

1. These systems were used also in usually recommended mathematical subject*, whose structure originally docs not suppose the use of computers (Mathematical Seminar in the 2nd term, Applications of Mathematics in Hie 4th term).

2. 3-5 lectures, eg. 25-40% of the whole time in the term were devoted to individual students' work in specially equipped laboratories.

3. It is useful to divide a lecture in the computer laboratory into two parts. At the beginning of the lecture, a teacher works with students and In the second part students work independently.

4. It is necessary to reduce a systematic instruction of functions of the computer system. The most important information* are to be given at the first lecture and then students can look for informations individually and use "helps", So the student's skill of using the system is increasing and extending.

5. When working with the computer we have opportunity for pedagogical activity. It can be expected that students will apptcciatc mathematical soRwaic because it tibctatcn them from non-creative activities.

37 WORKSHOPS) MATHKMATICfl

0, However, It l» nltio nwrnMcy to lend »IHII«

• YoAfly tlicrc nrc at tlia faculty acvcrnl tentlin of (itiidcntn \mnf, acqiininlvd with m/tlli- cmatlcnl software dtio to inclilioiiwl liiicintive, which in oidy n few percent from tlie total, Required extension (while atiidvnta linppcncd to uliow ^rvnl inturenl) h limited dun to economical nnd organization ren«oii», Cvrtaln positive orgnnlxatloii nnprct l« tlie aystcm of recommended inntlicinalical niibjectn witli more free curriculum, Wo lire confident that condition* will gradually improve,

• Authors of the contribution alito arrangm! tavnrtti tt'in'mnnt for dep/irtiiientfi lecturers wliicli shown Intcrpst about (inch wrnnn,

• 'Die maUiemnticnl software we start to use to solve certain technical proldom* (fa.it Fourier trnnnfornmtioii, npplicntioii of function of complex vnriabic),

• As per our experiences commercially programmed procedures nro not millMent nnd it appears necessity to make own proredurrs. In tlio nydtem Faitmlu* we linve created several tenths of procedure anil more te»ctier« of our department were involved. Till* our remark has indicated Hint bfuricn of programming »)IOMI

Reference*' (1| KOLEK, I. - VAVRA, S. - ZI,ATNlK, C: Communication in Ihman-Computcr- Sytittm. Today's Trends In Education, Kava-I'cch, DobFicliovicc (I'ralia), 1995, pg. 100-111, (2) UENBS, V. - VAVIIA, S. - ZLATNlK, C: Two Conception) of the Didactic Uting of Computer* in Technical Mathcmniicii. Workshop 05, J'art. I. CTU iti Prague, 1095, pg. 53-51 13] HENES, V. - CERNA, R. - VAVftlNCOVA, M. - ZLATNlK, C: Vyuka mnttmatiky pomoci Famutn. Workshop Famulus, CTU in 1'rogne, 1!W3. |4] ZLATNlK, C: Druhi ttrdnka poiitaiu v inlcmjrtkc matemalict. Rfzcnf osvojovacfho procesu XII. VVS I'V Vyikov, 1991, s. 23-27. [5] DOCKAL, J.: SysHmy "PoMa/ovi poJpory matcmaliky" a student, ftfzenf osvojo- vaclho proccsu XIII. VVS I'V VySkov, 1995, s.72-75. [C] SlKULOVA, I).: Zmlny obiahu maitmatkkiho uliva vlivtm poiitati. TamteJ, 8,36-44,

This rtntorch hat been comliiclrd at the Department of Technical Mathetnntic» as part of tin research project "Theoretical analysis and Numerical Solution of Dynamic Inter- action of Elastic Uoiy with Ihr Flowing Fluid" and has been tupportcd by CTU grant No. I0t/9t/0280. WORKSHOP 00 MATHEMATICS APPLICATIONS OP ALGEBRA IN COMPUTER SCIENCE

M. Dcmlovn, J, Adlimok, D. Pomlclfcck

CTU, Faculty of Electrical Engineering, Department of Mathematics TccImlckA 2, IGG27 P»*ha (J

Key words: subdlrect product, variety of algebras, category, functor, fixed point, semiring, grftph

1. The aubdircct product of algchrfts is onn of the moat Important construction*! of more complex algebras from a given collection of "simpler" algebras: one forma first a direct product of the given collection and tlien one considers any subalgcbiu of the direct product rii6/'/l( for wlilclt the i-th projection is the entire algebra At (for nil i (• I), Algebras U which cannot be decomposed in tills manner (i.e. those for which whenever H is isomorphic to a aubdircct product, one of the projection* is necessarily An isomorphism) arc called subdircctly irreducible. Hy virtue of Hirklioff's Subdircct Representation Theorem every variety is generated by Ilia class S'i'r(V) of its milidircctly irreducible members vis. the mibdirect product. Hut it can also happen that every algebra A G V can be embedded Into an algebra D € Sir(V). Such a variety V, which we call tubdinclly dominatnl, la then generated by Sir[V) in a alwiplified way, just by closing Sir(V) by mihalgebraii, The prico to pay is the structural complexity of the subdircctly irreducible algebras in V which is no less than that of all algebras In V. The variety of all semigroups, or of all groups, or of all lattices may serve an examples of aubdlrectly dominated varieties, In [1] a general categorical construction it given that enables us:

• to show that a variety of semigroups is aubdircctly dominated whenever it satisfies conditions (ideal-C), (rcd-C) and (cong-C) for C cither the variety of all left zero semigroups, or right zero semigroups, or groups; • to describe all varieties of nilscmigroups, commutative semigroups and varieties consisting of completely simple semigroups that arc aubdircctly dominated.

2. In the formal semantics of computer languages, it is often important to define data types recursively, and the semantics of recursive data types Is then provided by fixe] points of functors on the category of data types. In the papers [2] and [3] the interpretation of recursive definitions via the largest fixed points (i. c, the terminal algebras of the correspond' ing endofunctora) ia investigated. It is proved that in topological categories the existence of two fixed points of neighborhood cardinalities implies the existence of a largest fixed point. Surprisingly, the existence of one fixed point docs not guarantee that the largest fixed point exists even for such simple categories as sets and functions, In the latter category it ia shown that whenever the largest fixed point exists, it can be constructed by the dual of the initial-algebra construction. A different problem in the above area js addressed in [4]: categories with the property that every endofunctor has a least fixed point, a concept introduced by P. Frcyd without

39 Arty tout Me examples, We »fiow that cotintalifc srli «(nl filiitll'iiis, eoilfilalily-ilSriu'rultjiial yrf (/;» upturn mid Hrwir dlfictiiifin a»e r«atfi|>lr>i of talrgorirs wild llip additional properly Ihal Die Wit fixrd point of every rnrfnfimctnr is nmstructidfe. .1 Cnlt-pitif* n\tfilt)i»h]i by finhaty skcUlics WOIB liitfutlucttl In |0j, A full dmrnftpr- iMllon of Mich entrnoilrs \iy inrnrn of fir«'.-or(ift/il < A U tiK'iniifnlilo mill (2) tfiffpfufr, fifiitnry tketthatifatalfffitirii Me (>lFthr)y l)\mr wlikh tun t/e tnmpUlt rnlfgnrirn. Information ami Compulation*, IW*, H«. 1-10

It) ADAVIKK, J, - KOUIIKK, V.! On Ihr krg,,l JinA point of it tit funttor, TlirorHknl Coinp. Sdrntr,!!».'», 15, 1-19 |5J ADAMKK,J.-JOIISTONK.I'.-MAKOWSKV,J.- HOSICKV,J.: frniinty»ktUht», acrrptr'l fcif pntiliralion In Journal lit .SyinMic I/»i|(ic [f.J ADAMKK, J. - HOSICK^, J-: Finilary nkilrhn and fnitary pmtHlaHt. tnUiotitt. mrrjilnl fnf |iiil>lkAllot) In MatliriiMtical Stliicltirn of Computer .S(ivn«> |7) I'ONOfit.lCF.K, II.! Inrmr utminngi and Ihrir titllirr ttf (ongfHtntt*. Cictli. Math, Journal, to apprar (^) I'ONDf.LfCKK, II.! Inrrmt atmiringi «A« Hrtiiitirt tniamarphhmr an mutliplieit' lift. S This n*tnnh Am bttn tonr/ifffi/ nt thr IhpMtmtnt pf Stathimttitt o/M« I'd rutty ef Hrrtrirnl f'npttftrih^ ««a purl oftht rutarrh pm/rrl 'Application* rfAlftkttt in Compiler Seintrr* amlhn* brm mpporhd by CTV grnnl So. 1003*1 tl. MATHEMATICS QUANTUM FIELD THEORY AND EXTENSIONS OF STATES

J. Himilmltcr

CTUi Faculty of Mectrlcnl Engineering, Department of Mathematics TctlniJtU2, ICO 27 I'MIIS 0

Key word.il ulatrfi on operator Algr.bfM, algebraic quantum field theory

The paper iummarlw* Kim* recent result* of the author concerning mate* on operator algebra* and their «(t[ilkatiotm In (lie algebraic quantum field theory, The theory of jUtea (I.e. normalize, positive, functlon/ils) on operator*, sometime* wiled the non-commutative mrasutc Uieoty, owe* It* fttlfllnt o tlm i!i*UiriiiM.icM (oumUllon of f|tt&n\unt phy»k» MtAlt-tl by J, von Neumann, F.J. Murray, I1, Jordan, I, E. Segal, K, I', Wlgner, «nd M. Id Stone (19'W-IOIO). tldng ft natural '|H?iitum counlctparl of the traditional tneaaure, intrgrntlon, AM'I prohahilily tlirory l»ulll on rl/Milral ll'mlean ftinrliirrn, tlir non-commutatlvR inrMtirK theory hw becotne essential far the structure theory of operator algebra* and related (iel«l» of functional uialyals and ouaiitunt pli>'ilc»- It haa a^gulrnd iiiomciitudi)» GO'* a;id 70'* when U.NV. Mackey (0) retonnizrd it» importance for axiomatic quantum physics anil when discovery of "noti-fock" reprevntatlons lead to an interplay of modern phyniai »nd Tomita- Tnkesaki theory of von Neumann algebras. Contemporary, the theory develops rapidly and ha.t application* In many fields of analysis, Motivated by sonic fecenl problems of independence in the axiomatic quantum field theory and by our previous reiwarth on extensions of ulates, we have focused on application* of general extension principles to the relativistlc quantum field theory. In the *equel we iiiltimarize A hw biutlr. reaidl of am research effort. In Accordance with the usual convention [3] the relativistic quantum Held is described [>y Ml intlutlWe Km'rt A of » i»t of openloi aigrtitu A\O), wheie O run* llitmijli the wt of «ll bounded Open fegiotu ill the Mlnkuwskl ipjuc-llmc (principle of loCAlily), The •ubalgebru A(0t),A{0>) "r IA'(' to '* >t*li'tically independent if for every itatc i^t and V»i of» iiihalgebrft A(O\) and A{0i), respetttvrly, there is A itate J. We have proved in |7| that (general) C'-algebra* A and // are statistically Independent if and only if for any pair of positive norm-one element* n g A, b(- H (taken In ihr tin!vers»l representation) there is a common eigenvector corresponding to eigenvalue I. This natural condition can be viewed a* a weakened version of the well known principle of strict locality [1,IO,II|. This result also provide* an equivalence of autistic independence and ttricl locality in the case of C'-algebra*. Moreover, we have itiown that logical Independence of Commuting von Neumann algebra* an introduced In [11] is equivalent to logical independence of their center*. In addition, we iticceeded in extending classical result on equivalence of ilati.ttic independence and logical independence from commuting C*- algebra* to both the non-commutative case and the C«LV of Jordan algebra*. (The proof of Jordan ea*e require* new method avoiding ipalial lenmr product construction used in (10).) lime tnuita toottibut* to lt>« itwiy o( op»r»loe »J»»tr»* ami UIIIM wove linpotlaat open question of relativistic quantum, theory (formulated e.g in [II]).

41 WORKSHOP fffl MATHEMATICS

'the method* of proof* of the above reaulls Imvo been developed in fm|if« Jf) a^br/i I* unl(|ii«ly determined by Its puro restriction to mitiM singly gftirralf)! MIUCUUVC lubslgcbra. l^itllier extension rrtdlt* lot UAHA*li-i|)flcC'V«!ue(l rnrsmirw tm ojwr/itw (ilgpbriw MI<1 gniiemi itftlctiKM IIM IHTII oliUirinl In (1), Till* |>«rt of t)ie fpwnttli iirognitiitric conlribtitea to general theory of iibsUMt operator «lgebrM,

Hefcrenceii (I) AVALLONE, A. - JIAMIIALTKIt, it i'tltniinii thtonmt (vtctor mtaavrtu on quantum logic*). Czechoslovak MMIJ. J>, to Ajiponr. (2| tJtiNCK, L.J. - IIAMIIALTEH, J.i Etttntlon* oj Jnuch-l'iron »Mt» on Jordan atgc brni. Mnili. I'coc. CMHIHURC I'liil. Hoc, to appear. |3) IIAAO, H. - KASTLEIl, D,l An algebraic approach la quantum JitM lhtor\). Cominun. Mftlli. I'liyalcs, 10, 1970,2M-21G, \\\ IIAMIIALTEH, J,i Oltaton property and etltntion* of ilnltt on projection lagio. Mull, London M«tli. Soc, 199J, 20, 307-372. (5| HAMIIALTEtl, J,: HiUmlon propertlt* of itntti on optrator algebras, Int, J. Tliror, f'liyolor, 103ft, 04, MI-MI. (C) I1AM1IALTEII, J.i t'urt ttatti on Jordan algebra*, to appear. (7| HAMHAWEK, J.: Iwirprndrnte t>f optmlor alyebrat. to appear [8] HAMIfALTEK, J. - NAVAUA, M. - 1'TAK, P,! ,9/^" on nrthonlffrbra,, Int. J. Theot. f'hyalca, IMS, »t, H39-HM. [9] MACKKY, 0. W.: The Malhtmatlcat Foundation* of Quantum Mtchankt. IlcnJ/iniin, N«w York, 1903. (10) IIOOS, II,! Indeptndtnee of local atgtbrat (n quantum fit Id thtory. Cortitrmn. Math, PhyilM, 16,1070, 238-210. (II] UKDKI, M.: Logically indtptndtnt ron Neumann hltiet*. Int. J. Thw. f'liyiiei, 31, I«I9.>, 1711-1718.

Thit rtitatth hat Ittn conducted at the Dtpartmtnt of SttlhtmaUti of the faculty of Ettctricnl t.'nginttring

M. HnvlUck, L, Hlnvfttf •, E. rdnntovfl, V. Sfovfcek, J. Tolnr*

CTU, Vac. of Niicl. Scl. k. Pliyn. Knjr., Urpt. of Mathematics Trojsnovn 13, 120 00 I'ralm 2 •CTU, KM. of Nucl. He!, fe I'fiya. Kng., Dept. of I'hysles UfchovA 7, 11810

Key words! quantum theory, I illegible inutM*, quAiitum groups, contraction of Lie Alge- bras, gradings of Me algebras, qtuicryitali

MAtlicirmtleally tifptom Invrstigatlon of r|iiniiliim symmetric* WM performed In (lie following three mnln MCM:

I. Qii/intnm mpcimnkn on 'limrretn nfturrn; I'/rvlomly olitalnnl foriiin) npfmtntim WAD reviewed |1). In till* setting, the deformed «t«r product wiw Investigated |2)< The undrrlylng dlncrcte •truclure WM ttudlrd in Its own rlgtit In the franiGWork of the graph theory [•)). II, G«n«rAlized lymtnctrics in physlcit: Do*on reali^Atloti of MM qtianlum groups wan used for diAgofializatloii and computation of correlation functions for XX'/ model. Floson realization of Yuigiant WM Applied In SU(2)-lnvarl»nt Thirrlng model |4, 5), Coherent stairs for quantized compact simple groups helped In [C| to study non- commutative differential geometry. Graded contractions with recent* result were sur- veyed in [7]. They were applied to the conformal group in [8, 9]. Grading* of simple algebra* were obtained in [10J. A *et with the five- fold symmetry M a new model for quaaicrystal wu described In (11). HI. Physical models, quantum llamiltonlans: A great deal of interest was paid to the application of new symmetries in quantum Intcgrable models: non-ultralocal f lamiltonian field theories were studied by means of braided blalgebra.1 [12, 13). Time dependent quantum ll/imillonlsin with the potential periodic in time were studied In connection with (he stability of the corresponding quantum system (HJ. A geometrically simple model of A parametrized syntrm with A first-das* constraint WM quantized [15],

References: [I] TOLA II, J.: Quantum itnttturti in tht Ititbtrt ipaet of finite dimnnion Nonlinear, Di»*ipatiw, Irreversible Quantum Syttenw (eds. II. D. Docbncr et al.) World Scientific, Singapore 1905 (2] CHADZITASKOS, G. - TOLA It, J.: Finilfdmumiontl •• prndutt and matrix nlgt. inn Quantliation, Coherent State* and Complex Structures (ed.«. J. I'. Antoine et al.) Plenum Press, New York, 1995

-13 WORKSHOP 00 MATHEMATICS

|3) JAaOER, J. » STOVfCEK, I'. - TIIOMAHON, A.! MulUplkltltt of »ubgrnPh» (in print) (4J MUltttfK, 0. - NAVltATIL, 0.] Uoton rcntiiatlan of Yangkns Y{»1(2)) and Y{sl[3)) Czech, J, of f'byn. (fn print) |ft) KRMJCAR, II,! KuntovAnl a Yangtdny Y(BI(2)), V(*/(3)) »tu

This rttearth hat been conducted at the Department* of Mathematics and I'hysict of FNSPE •»« part of the rtMearch project "Quantum lymmtlriei; mathematical models and physical applications" and hat been supported by CTU grant No. 815(

i\ WOltKSHOl' W_ MATHEMATICS COMING FROM DISTRIBUTIVE TO ORTHOMODULAR

I'. Vt&U, M, Navnra

Gl'U, I'M, of lileclricnl Kng,, Dept, of Mathematics TcchnlckA 2, IGfi 27 Praha ti

Key word*: orthomodtilnr ponct (OMP), (|iiAiitiuti logic, nrl-rcprc^rutahlf OMI', coupling of OMIN, states on OMI's

Tlio theory of orthomodular posets wns initiated liy Hirkliolf unit von Neumann (10.10). Tlirir intention was to provide a Mathematical model of quantum experiments, Though this theory began to live relatively independently of it* source — A phenomenon which I* typical for moat brnnclica of Applied mathematics — the problems inspired by phyiiicn arc atill Intensively pursued by mathematicians AM! theoretical physicists, Tlic present note contribute* to tills line of research, It la observed tlmt certain llooleaii (sdistribntivc) conatrui:ta help resolve problem* In urlbnnioiliiUr (=iir»ii-rlliitrll)iillvn) ntnicturm, Tim first exampli in III* renearcli carrlwl on In |3-7). The departure point U tlm notion of a, kernel OMI' which comes into existence &a a null set of a gtuup-valued measure on & MiKjIeiiii algelirii. It l» sliowii ttiAt kernel OMI'K enjoy [nletoniiiig propcttles both In llic algebraic and meaKilre-theorrtic setine, In particular, OMI'fl enn be cotislrtictcil the state spaces of which consist of subaddilivc iiieMiirea. This has previously been unknown. The second example la an application of A Mootcnn power in the realm of orthornodiilar structures Jl], It is proved that a tensor product of A classical Ami a tpinntitm structure can be reasonably defined. This contributes to quantum axiomatics. The third example is an analysis of two-valued states on OMI'i [2j. This research brings some novelty to the hidden variable hypothesis. A technique is developed which allows us to construct orthotnodular pewcts with a given set of two-valued states.

Reference*;: (1| KOULIS, D. - ('TAW, I'.: On the Unsor product of a llooltan algebra and an orthoal- gtbm. Czechoslovak Math. J., 1095, 45, 117-126 [2[ FOULIS, D. - PTAK, P.: On absolute compatibility and Iwldin variable* in quantum logics. To appear in Hiccrchcdi Mathematics, IMC [3j MAYCT, II. - NAVARA, M.s Ctamei of logics rtpntentablc as kernel* of mta»urt$. Contributions to General Algebra, G.I'il* (ed.), Tcubner, Stuttgart/Wien, 1905, 9, 211-218 [4] NAVAHA, M.: Quantum logic* reprtientabk a> kernels of mcaiurri. To appear In C«cchoslov»k Math. J.. 1995 [5J I'TAK, P.: A note on inbadditive ttalts. Preprint, Dcpt. of Mathematics CTU, Prague [6j PTAK, P.- NAVARA, N.: On ring-valued measures on crthomoJular posets. Preprint, Dept. of Mathematics, CTU, Prague

45 WORKSHOP 00 MATHEMATICS

(7j t'TAK, I'.I States on orthamoduhr patch (rtcciit retails on tmntommulntivt mennurc H theory), Proceeding* of the conference "HMII Aimlyscn nml Meiuinr« 'rii«.firy t Clrwlo (Italy), 1093, 27-45

ThU rtienrch hat been eomlucltil til the Department of Mathematics of the Faculty of Electrical fingtnecrlng at a part of Hie n»torch project "C'oitiblniitortnl Method* in the Theory of Orthostructurtt'' ami hat betn tupportal by CTU grant No. 10038SB7.

16 wortKgiiopoo MATHEMATICS SOME CARDINAL CHARACTERISTICS OF ORDERED SETS

V. Nov/ik

TU, Vac. of Mechanical Eng., Dcpt. of Mathematics TcchnlckA2,010C9Urm>

Key words) Ordered act, Ideal, 2'psciidodimcnsion, order blue, complete ring of sets, weight of A complete ring of sell, denso subset, separability of an ordered set.

The classical concept of the dimension of an ordered sot ((3|) CAn be modified B* follows, Let 2 be n two-clcmcnt chain {0,1; 0 < 1} and G be on ordered set. A system (/<;'€ T) of mapping* of 0 Into 2 is called a 2-realher of 0 ill

x,V eO,x<,v*> f,(x) <, f,(y) for all ( 6 T,

Further, put 2-pdim0amin{card7<; (/,;( 6 T) Is a 2-rcallzcr of (7); this cardinal is called tlio 2-pscudodlmcntfon of Q, The cardinal power G" of ordered nets (7,// (|1|) is the set of all ordcr-prcacrvlng ing* I; II -* O otAettrA hy tli« rule

/ S a «• /(*) < s(a) for all x € It.

The following can be eaaily proved: 1*1 C be an ordered set, let T be a set. Then the following statements arc equivalent:

(1) Tor any ( g T there exists a mapping f,:O-*2 such that (/j;c € 71) is a 2-rcAlizcrof <7, (2) There exists an isomorphic embedding of G into 2T.

A subset /t of an ordered act G Is an icfeaf i(T y € /I,I C (V,i < J/ =* I G /I. A system (A,;t € T) of ideals in G is called an order base of G ([5]) iff x,y € G,x £ y <$ there exists t0 6 T such that y £ <4(,,x £ A,,. If (/,;i € T) is a 2-rcalizcr of G, then, trivially, (/i*'(0); J S T) is an order base in G. Conversely, if (/I,; I € T) is an order base in G and /, i G ~> 2 is defined by f(A,) a 0,/(G - /!,) = 1, then (/,;< € T) is a 2-rcalizcr of G. Thus, the following cardinals arc equal:

(i) 2-pdim(7 (ii) the Icaxt cardinal m such that there is an embedding of G into 2m (iii) the least cardinal n euch that 0 contains an order base of cardinality n.

A system A of subsets of a set G is called a complete ring of seta on G iff 0 € -4, O € -4 and LM< € -4, D^ € 4 for any sysltm (At;i € /) of elements of A. Clearly, for any *y.-irm B of subsets of C there exists the least complete ring A of sets on G such that B S A; we say that 0 generate* A. Further, put for a complete ring of sets A

47 WORKSHOP 00 MATHEMATICS

wA « in\ii[cnii\B;t} C Att) generates A\\ this ca«lin«! fa r/tll«! liteweight at A: If /V In MI onlrtwl art, tli»'« th« m>t of nil U« Miwl* In « «iinpl/.'tc rln# of M

(I) 'i-iuWmO (II) the Inmt cnnlitwl m ntirli Hint tdcrn Is nn cmherUtiiig bl 0 Into 'lM (ill) the !CAH cnrdintil n nnch llntl 6'coiilnini AII order \mnn of ctirdirrnlity n (Iv) toA wlipre /t 1* tli« «;ii)|)ktc ting of lilcnla In fl.

A »l)l»sct // of an ordered «cl (1 is f/err.ie in 6' iff it IIM ffop

2,1/ G O,x < v s* there cxiitt «,tr € // mtrli tlinl x

t,y€ G,x || y nml r > y for any J € 6\* > x -> * G II. Wo put »f!j)i« jiwwii,1 If f/ In MI infinite chain, then 2-pdiinG=s<:pC Ifcriri1, for any InfinHi? chnlti G tlm following t/ifiiinnU ntt; M\\itA'.

(I) 2-|>r«in<7 (il) the leant cnrdiriftl m mich tlmt G tun Jic embrtlitrd into 2m (iii) tint l«?(«t cardinal n mith tlmi O «mtain» an order luwc of enrdinsility n (iv) tw^ wtirrc A i* td" conipMc ring of all Meat* in 6' (v) »rp6'.

Kcfcrcnceii: (I) HlltKHOFF, 0.: Gentralitut arilhmttiu, Duk

{5J NOVOTN^, M.: lltmerkunn Cber die Drmttllunq Ititwtist geortlntttr Mtngcn, Spi»y pfif. fak. MM. Univ. IlrnoSCS (1955), 1-8.

TAi* rcttanh has been eondtttltd at the Department of Mutlttmalies a# part of the ixxcrth project "Mathematical Slruthrtu for Computer Science* and has i«n supported by TUgmni No. FU35MHL

•18 WORKSHOP DO MATHEMATICS DISTINGUISHING SUBSETS ON LATTICES

J. ZnploUil

TU of Urtio, Fac. of Elcctr. Eng. and Computer Science, Dcpt. of Mathematics Tcc!itiickAS,G10 00 llrno

Key words: kitten, Join nticl mect-lrreduciblc elements, irreducible circle, distinguishing subnet, beta-lattice

III trie present work, we prove betides other results the necessary And sufficient condition for tlic existence of n distinguishing subnet on a finite lattice. Some results CAII be immediately generalized for semi-discrete lattices, i.e. for the case, where between nil comparable elements there Is A finite maximal chain, and for lattices satisfying the maximum chain condition. Tlio questions of an existence of distinguishing subsets of semigroups, monoids, groups and icmilattkcs were studied in [0-8]. The construction of the distinguishing aubaels of join-Bcmlliittice* wns given by J. Niemlnlon, ice [2], the starting point for which was [7). Let S a (S',A,V,0,l) be a lattice with rncct and join operations A, V nnd the least and greatest elements 0,1. It is said to be it finite lattice, If S la a finite set. An element (x,y) 6 5s in mild to bo nn edge of S if i < y and {u 6 S;x < « < y) » 0. Wo also write x -< y. Furtlicrmorc, let // denote the set of of all edges of S. An clement z of a lattice S is said to be mcct-roducihli!, if there ura dements i,y 6 S satisfying * =* x A y (x,y > x). If some * € S him no decomposition of the upper form, it is said to be mcct- irrcduciblc. Dually, some clement z of S is said to be join-rcduciblo or join-irreducible, depending on whether or not it can be represented in the form ; = iVf,(i,|/< z). II) € J U M tat j = 0,l,..n — 1. Then C = {(II,,I/H.I);0 < i < m - 1) U {(«/, vy+i)',0

49 WORKSHOP 00_ MATHEMATICS

The definition of /7-scmilaUicc vrnn givrn i/i [!)J. VV« remind this dellnlllon, A lattice B I* said to bo A lower /3-lnttlco If for any two elements i,|/GS, !•/JI,IAJ/^O tlicro is V 6 5, which natlnflca cither v < * nii'l ti||]/ of w < (/ find t)||x. Dually, S in *nl y, /V y -/• 1 there Is u e A'( which imtisfics cither x < u And y\\u or y oth A lower /(-latlice mid upper /MnUlcc la Bald to IM) A /7-lAltla1. For a /3-lntticc, vvcobtnin thu following rwnlU, (1) livery joln-itrediiclhlo (mecl-irrcducllilc) cleiricnl of S Is Atomic (diml-fltomle), (2) Tim set (0) ({1}) 1» n (lifltlngiilnliirig act of S According to tnflmum (nupn-tniirn). (3) The net {0,1} l» ft (lintinguliililng suhsct of S. In the liut part of thin paper we aupposc 0 •/• 0 to bo n finite net. We put G C2a And tliAt O satisfies Ilia fullowi/ig conditions. (I) {ij GO for every * € 0 (I!) /I n W € O whenever /I,// g O (III) 0 € G We define /lfc/V = D{A/M U«C M, M C G}, Wo prove, that »(G\G) = (G,n,6/V0,O) Is the lower /Mtittlcc mid tlint for nrliitrnry lower /Mntticc S there exist O And G C 2 such that S And O((7,G) Arc isomarphic structure*.

Reference*! [1] JURCJENSEN, II. t llaltigruppcn und Spracltcn. Dericlit dnt hint, fur Thcor. Inform. Tecliu. Iloctinchule DAruntadt, Tl 2/7!), [2{ NIBM/NINKN, J. I Remark* on Distinguishing Sublets oj Joinsemilatlicc, Dcnionslra- tio Matticmatlca Vol. IX, No. 2, 1970, 239-242. [3] NOVOTNt, M.: Algtbraical Structures of Mathematical Lhguiitics. Hullctin Math. dc 1A SOC. des Sciences Math, dc In Ilep. soc. dc Koiiinnnlc, N. S. 12, 19G8, 80-101. (4) NOVOTNt, M.: On Some Relation* defined by Languages. 1'rague Studies in Mathe- nwticJil Linguistics 4 (1972) 157-170. [5] SCHEIN,B. M.! llomomorphumt and Subdinct Decompositions of Semigroups. Pacific Jour. Math. 17 (19CG), 529-547. (6j ZAPLETAL, J.: Distinguishing subsets of Semigroup) and Groups. Arehlvum Math. Brno, 4,(1908), 211-252. |7) ZAPLETAL, J.: Distinguishing Subsets in Semilattices. Arcivum Math. Drno, 2, IX: (1973) 73-82. (8| ZAPLETAL, J.: On the Characterization of Semilattices ... Archlvnm Math. Brno, 2, X:(1974) 123-128. [9] ZAPLETAL, J.: O relaci tolerance na spccidMm typa svazi. Kniznice odb. a vid. spUfl VUT v Urnc, 1970, A-12, ij5-19G. [10] ZAPLETAL, J.: Konstrukce rozlihjlckh podmnolin na beta-polosvazech. KniJnicc odb. a vM. »pi»fi VUT, 1991, B-131, 5-19.

This research has been conducted at the Department o} Malhetnatitt as part of tht research project "Afatematicke' struklury pro computer science" and has been supported by TU of lino grant No.

50 WORKSHOP 00 MATHEMATICS EXPONENTIALITY IN CATEGORIES OF PARTIAL ALGEBRAS

J. Slnpnl

TU, Fac. of Mechanical ling,, Dept, of Mathematics TcclinlelcA 2, 010 09 IJrno

Key word*: Exponential subcategory of a category, cartesian cloned category, initially structured category, category of partial algebras, Interchange Inw for partial algebra*, diagonal partial algebras,

It is well known that concrete categories having well-behaved function spaces, l.c, being initially structured mid cartesian closed, play an important role in application) to many branches of mathematics, It in therefore worthwile to look for such categories also among categories of general algebraic system). In this note we focus our interest onto categories of partial algebras. Definition 1. Let K be a category with finite products and S,T be full isomorphism closed subcatcgorics of K, Lot T be finitely productive in K. We nay that, T is exponential for S inK provided that for any two objects A e S and I) € T there exists an object A" € K wllh |/»w| = M(»7f(W,/t) wieh thai (jM (ii) the pair {A",e),wlicrc e : D x An -* A is the evaluation map (given by e(y,f) = /(y)), is a co-universal map for A with reaped to the functor U x - ! T -» K. If A category T is exponential for K in K, then T will be called an exponential suhcal- egory of K. If K is an exponential subcak-gory of itself, then K is cartesian cloned, i.e. the functor D x - : K -• K has a right adjoint for each object B € K. We shall use sonic fundamental concepts concerning partial algebras. Throughout the paper, fi will designate an arbitrary, but fixed set, and r will designate an arbitrary, but fixed family of sets r = (K\; A 6 fi). The family r will be called a type. Dy a partial algebra of type r we understand a pair (A", (px; A e (1)) where X is a set and />> is a partial Kx-uy operation on X (i.e. a partial map p\ : XKi -* X) for each A 6 fl. For any K A € fl we denote by Dfk the domain of the operation p\, i.e. the subset of X * having the property that px(xk,k € Kx) Is defined iff (i*;fe 6 K\) € Dn. If G = (X,(px;\ 6 fl)> and II a (V, (7»; A € 0)) arc partial algebras of type r, then by a homomorphitm of G into // we mean any map / iX -*Y such that px(xk\ k 6 K\) = x =*• q(f(xi,); k € K\) — f(x) for each A 6 fl. The set of all homomorphlsms from G into H will be denoted by IIorn(G', //). We denote by Pal, the category of all partial algebra* of type r with homomorphisms an morphisms. Dcllnitlon 2. For any pair of objects G = {X,(p\\ A € fl)),// = (V,(<;A; A € fi)) € Pal, we put G" = {Hom(;/,O),(rAjA e fl)) where, for each A € fl, m is the tfvary partial operation on IIom(//,Gf) given by rx(fk\ k € Kx) = / iff / € IIom(//,C7) is a unique homomorphism with the property that qx(Vk',k € Kx) = y *> px(Sk(Vk)\k € Kx) = /(»). The objects G" will be called the powers of G and //. A partial algebra (X, (p»; A € 0)) of type r is called idcmpotcnl if for any z 6 X and any A € ft the family (it; it € Kx) given by Xk = z for each k € A\ fulfils (it; it- e A'A) € £>„ 51 WORKSHOP 00 MATHEMATICS and pi(xnk G K\) m x. Wo denote by Il'al, the full subcalegory of Pal, wltoso objects aro precisely the Idcinpotcnt partial algebra* of typu t. Theorem 1. lPal, is un exponential tubcategory of Pal,, Corollary 1. Wai, in a carleiian cloicit category. Definition 3. Let G =» (X,(j»Ai A € fi}) b« & partial algebra of type r. a) O la mid to fulfil tlio interchange law if for any pnir of elements A,/i <= fl from {tu\{ G #,) G />,„ for each k G Kx,{l>A*uii G W 6 ft) G 4., and (unit G A'A) € Dfi for each / G K,, it follow* that (PA(*MI* € A*);/ G /^) G D,, and ;»AM**<'.' € #„);* € A**) a pM(*ui* G AA);/ G /^). b) 0 \t called diagonal If for any clement A 6 fl from (xt/i / G A'A) G Z)pt for ench k G A'A ami (p\(xu;l€ Kx)',k € A'A) € Dn It follow* tliat (/«;* G A'A) g £»„ and px[n{*H'A G )) We denote by Ct'ai, or DPulr the full suljcatcgory of /'a/r wliosc objects arc precisely tlio pnrtUI nlgcbrM of type r fulfilling llie Intcrchang'j law or the diagonal partial algebras of typo r, respectively, Next, wo put CDl'at, => CPal, D DPat, and CD!PatT = CDPal, 0 IPal,. HcmArk If For total algebras the notion of interchange law coincides with the notion of commutativity studied in [2j. On the other hand, the notion of dingonality in the case of total algebras Is more general than the notion of diagonality defined and studied In [3] (the dlagonality in [3] means both diagonality and idernpotency), The following assertion is a generalization of a result which Is well known for total algebras («ec e.g. (2j)i Lemma. Ul G = (X,(PA)A G fl)) G CPal, and II = (Y,(tal algebras. The Corollary 2 then coincides with a statement from [4], b) If K Is a set with card A' = 2, then the mono-A'-ary total algebras fulfilling the Interchange law arc nothing else than ttic known medial groupoids (sec e.g. [1]).

References: [1] JE2EK, J. - KEPKA.T.: Medial groupoids, Rozpravy CSAV 93/1 (1993), Prague. [2J KLUKOVITS, L.: On commutative algebras, Acta Sci. Math. 34 (1973), 171-174, [3] PLONKA, J.: Diagonal algebras, Fund. Math. 58 (1906), 309-321. [4] SLAPAL, J.: A cartesian dosed category of universal algebras, Acta Sci. Math. 58 (1993), 93-97.

Tins research has been conducted at the Department of Mathematics as part of the research project "Mathematical Structures for Computer Science" and has bren tvpported by TU grant No. FU3500fl.

52 Section 2

PHYSICS

NEXT PAGE(S) left BLANK WOHKflTICtl^Pft _ I'DVBlCfl MEASUREMENT OF NONLINEAR WAVES IN HARD-WALLED DUCTS

M, UednaKk, O, SifUek

CTU, Fac. of Electrical Kng,, Depl, of I'hyslw TechnlcM 2, ICO 27 I'raha 0

Key wordsi Durgers equation, notillnesrlly, boundary foyer effect, measurement

Thl» work I* tcitifffinl with An jfivetllgalion tit the nonlinear behavior of ulnusoldal plane progressive acoustic waves of finite amplitude In tin alrflllcd lube at a frequency of about 70 kit*. The aim of this Work MM to compile applicability of the. ge.httaliaed Ilurgefi equation ((lilt,) (2j with reaped to experimental data. Kxperlment* were done In * tube 10 in long anil 8 mm internal diameter with an absorbing termination, A* an aeomlle source waa u*t 0 where v is parlkle velocity, t Is distance, rat- */r0 Is retatdnl lime, < Is actual lime, fo Is small- lignal sound ipeed and 0 Is the copffitient cf nonlinearily. The term A(v) Is the linear time operator which represents absorption and dispersion mechanisms due lo the vlicotity and heat coducllon, the rtlaxatkn, the boundary layer or their combination. If we put the operator A{v) equal to Mo then the ODE describm* plane waves in non-dlsslpalive fluids. A* distance Incrraaes, the effect* of dispersion, which Is caused by the lube>w&tl bound* ary layrer ami the molecular vibrali

(i| MEKKULOV,LO,-KitAKITONOV, A. V.; Utor,o/5«l.OnalConunlnlor,. So*. P AtlHUlia, S, p. IS3=15O» WOItK.4110)' 00 IMIYHICfl

|2] UEDiNAftlK, hit Propagation oj t'hnt Nimllnmr WW WOIlKSHOI1 00,

This research has h(tn eonttnclftl ttt the fbparttmnt nf t'htj'lr* n* putt of IU*. projtct "OrncHpUnit and (hnrtathn aflHgh'Intcntllu Sou ml FiehW awl hn* btcn tvpportrii hfi CTU grant So. I00J8S0S.

Comparison of «/pflrim«n(»( and Wffipufed data of harmonic component), 0*101 S, 0*0.315 1601——-i—~r -I-*——i——•' !••"• r r-—n i rr

18 20 PHYSICS PROPAGATION OF PLANE NONLINEAR WAVES

CTU, FAC. of Klwlilwil En*,., Uopl, of I'hyilea TrtlinlckA 'i, JCfl 27 I'falm 0

Key wordai Ilurgrrs equation, boundary layer effect, noiilinfarlty

In many physlcnl proMc-fris Involving sound transmission in duels, the iminil-prrsstuc levels Involved are »rr on the WIWR propagAtlon wliltli enme» tlie MlpnuMloii And dlnneralon of waven, The firopA^Atlon of fifiitc-Ainiilittidp WAveit can bn dened by mcAtts of MIA g^nnrAllz^l Durgr-rs r.|untion ((il)F,) whlrli Is A very good npproximatlon of tlin rtpi«t|i»» uf itKjtloti fur tlifniioviicoiiii flul'l** In »I««U In tlie necond Approxlnintlon: h b fl'u ... wlietc v U the particle velocity, f => t - xjt - l/f.) Is ilisslp»tlvc coefficient, fj, ( are the ihear and diUllonal viscosity coeflicients, * is the lirAt-condnclivity cortficlrnt, tf *nd cv Mtt I lie flpecific heats at constant pressure and volume, 0 *> 0.5(ir 4 I) in the coefficient of noniinearity for gaiKu, i a c,/ry, II m fiif!f>nrl

In/H'fllri^ the v»lue» V =» v/vn, * » flMtycft,, y w fttf/t,, Go p Do " tti%Jz',lvm0 we obtain the convenient nonditnmtiorial form of ¥A\, (1): OV UiV* , >-„ fllV I 0*V .„. at—it?+ *"••&'a;??- W where i>m is the peak particle velocity, Mt * i'^/r0 It the peak Mach number and t, is a charactcrlitlc distance. For harmonic waves, it Is conevenlrnt to take t, a eafu> a A where A it the wave length. Unfortunately, the i'/\. (2) cannot be solved analyticaly. For this reaoon, It Is necessary to solve this equation numerically by means of Fourier expansion. I*1 V{*

(3)

57 WORKSHOP on PHYSICS where

lly inmenlinn Kt). (3) after a finite number of terms S, V^i,]/) can bo cx|»fcs«ed M follows:

»m.)N \m.-N ) where VH(») w 0 fof |f»| > N. ftp. (3) AIKI (1) In 1>|. (2) given

-V; + —V^C +>il«num(fiJJ V, » 0. (5)

It Is clear from Inspection of t>|, (4) thkl by cxprcwing ^(a.tf) M tlic Fourier »crlc» In the ]/ domain, Kq, (Z) JIM been rcpfuccd by w-t of ordinary Hautiiiem tYiftttwnlfa) n|ual)on« which can be stcpwls« nntiicrlcAlly |n(rgrat«d by the tlmi^c-Ktitta mctliod to obtain the Amplitude* of the harmonics nt progressively Increasing IIMAIKW. Kcnulti of cxt>«rimcnt which confirm the validy of the GH12 are presented in the pnper |Hj In this proceeding.

References! (1) DLACKSTOCK, I>, T.i 6'enchi/W Umytn tyuilton. JA9A 77(0), p. 2050-2053, 1985. (2| OCifMAN'y, M. - MAKAKOV, S.: iUpn.untitintt of the Abtorption of Nonlhtitr Wavti by [YaeUQnal DtrivaUvu. JA3A 91(0), p, 3392-3399,1993, |3j tlEDNAftlK, M. - JlftlCKK, O.: Mtaiunmtnt of A'onlinrar Want In Hard Waited Vueli. WO»KSHOP'!W. Th(» nttnrth ha* bun conducted at the Dtpnrtmtnl of I'liysict an part of the nitarth projtct 'Dc$criptlon and Gtntratlon of Iligh-lnlennily Sound t'itldi" and hat bctn lupporlnt by CTU grant No. 10038268. WORKSHOP W !'[IY3tC3 DEEP ENERGY LEVELS IN N-TYPE Si INTRODUCED BY SHORT-TIME Pd DIFFUSION

V, Detain, J, Fuffkov/S, D. StepkovA"

CTU, I'nc, of ICIeclrleal Kfifj,, Dept, of Electrolechnology TeclinlckA2, ICO 27 1'rnliK 0

Key word*! silicon wnfer, palladium diffusion, deep energy level*

Palladium Ilka many other transition metals (Au.l't) occupies both iubslttutlonnl and Interstitial »lt«t In ulllcoii crystal* and it can also create complexes with other Impurities, It in usually accepted [I-'I] that the ctcctricnlly Active palladium exhibit* two deep energy levetj tu be located; the first Acceptor level within 0,18-0.22cV below the conduction band And the second donor level within 0.30-O.McV nbovc the valence band and both may be associated with siibstltutional I'd. IlcnWlcM these two level* several other deep level* where reportcfl to he iwwicinlcd with the both Interstitial palladium and complexes of I'd with other impurite* ami defect* »nd their origin depend* on the sample fabrlratlon technology use. I;j thn IIIIMI aiifit vwn>studied aaaiplfl* wiicre was iltlcun doped with pallfuJlutj] at twu- pcratnrm above lOOO'C and the long dilTiiiiion time WM UJCI), The Pd clilfiuion coefficient in SI, D a 2.05 • 10'1 cxp(-0.22/kT), found in |0) t* very high, to that At the temperature 8G0'C only about 30 ficcond* is ticcemry for nearly hotnogenou* distribution. In our experiment* we focused on the origin of the levels connected with short time I'd diffusion. Our work wa* undertaken to access the electronic properties of active I'd centers In SI with a view toward evaluating Its effect in controlling minority carrier lifetime, We atarted our experiment on n-typc phosphorus doped and (1,1,1) oriented Si wafer* with a thickness of 'UJO/im and resistivity about 600cm. The wafers were cleaned with standard technology and after this process a thin layer (below lOnm) of I'd waa evaporated on one side of the wafer*. Pd diffusion WAS performed at temperature 800'C for 4 And 20 minutes. After diffusion the lurplu* film wu laped off from the front aide of the wafer. After that the samples were etched in CI'G to remove the damage surface layer, rinsed nd cleaned and than were samples divided Into two group*. Schottky diodes with an arcs of 3.67mm1 were prepared by evaporating Au at the first group on the front itirf

59 WORKSHOP 00 PHYSICS can bo connected with hitcrstltinl I'd or Intcratltlal I'd related cowplexeii, aimilnr level WAS pilbllahrd [i, 4] M V,t - 0,37oV. We cnn note Ihal concentration of eiibslitutlotittl IM la much higher nt aurfacc from which IM wm dlffuwd, while tlio difference In concentration of lnl<7st!tl«l JM \» not to n]^niDrnnL TM» »gr»» with th« Miwmptfon that * M/{h dllfinloii coefficient Ijcfon^ to tfi« Intcratlttal Pd (tlffuiion and that interstitial Pel tranntormB in (iihutltutloiml pwiltlom by the kirk-out itificlmninintti (&j. Our px|icrlinc[itnl result* allow Hint this process 1« very fut. For the short dilTiulori time iiitcr»titlnl IM rdntcd deep Icvcia enn be more atablc than In the CM« nii|)Cf»AturAlloti reached In very (|iilckly <|uenclicd lamplca [4| becanao tbia level enn be Idcntlfled ftlno in Si diodes after Alloying to molybdenum dlnca wltli AISI at 700'C |7|. l)L't'S apectrti of the tinrnpicn dilfini'd at 800*0, back fiurffiro, reverse blua 1U Vi

M Juo isii no IVJ us Fig. l! The dilTusion llrno Is 20 minutes. Fig. 2i Tlio dilFusion time la \ mliiiilrit tlcfcrenccs; It] WOOnUVllY, 11. H. - LUDW10, G, IV.; Phpleal Rtvkm, vol. 12/5, pp. 4GO-470, J0C2. (2] I'ALS, J. A.: Solid State Electronics, vol. 17, pp, 1139-1140,1077. [3| CZAf'UTA, R.; Applied Physic* A, Vol. 49, pp. 431-430, 1088. [4| OILIi, A. A. ct al.; Stmkond. Sci. Technology, vol. 8, pp. 075-681, 1993. (5) V1NCKNTB, J. ct al.: Journal of EUclrochtm. Soc, vol. HO, pp. 808-870, 1993. [0] FRANK, W.i Deftcl and Uiffufon Forum, vol. 75, pp, 121-148, 1988. |7j HENDA, V. et al: Proceedings ej Iht ISSE'95, pp, 172-177,1095.

This rttearch hat bun conducted al Iht Department of Elcetrolcthnotogy at part of the niearch project "Recombination in power $emiconductor dtvictt" and hits tctn $upported by GACil srant No. 108/0^1363.

CO WOKKSHOPJM PHYSICS OF INFORMATION AT THE FRONTIERS WITH INFORMATICS AND CYBERNETICS

J. Jclcn

CTU, VAC. of Electrical Eng., Dent, of Physics a'A ICG 27 Pr»h» 0

Key words! Information, entropy, chaos, synergetics, computation, quantum mensurcment

Physics lntrodiic«M fundamental concepts fur all (lie selcncM, It traditionally ntudlcn characteristics and interactions of fundamental dementi of matter (subnuclenr particles, Atoms, molecules,..) nnd various properties nf structures composed of them. It provides hardware components inch M microchips, memories etc. for modern brandies of technology tuch M informatics, cybernetics ele. However, this is not the only contact with these sciences it has. Physics can offer mute, Oven at technical uiilvcrsltkn when teaching engineers, physics should not bo given the role of a service only. Contemporary phynles bring* Its own contribution to the study of complex systems, furiiiJiitrin of structures, evolutionary processes, etc. Tho key role hero Is plnycd by tho notion vf information. This concept docs not belong only to informatics, computer ncicncc, cybernetics etc. It also belongs to the new physics, The concept of entropy, inherently connected with the concept of information, has been applied to Information theory from statistical physics and thermodynamics. The amount of one lilt of information appeared, implicitly, for the first time in Szilnrd's analysis of Maxwell's demon activity In the one-particle heat engine in 1929, Today it Is possible to interpret statistical thermodynamics in the framework of the information theory. Computation Is nut an intellectual performance only. It is also a physical process. "Informational" and "physical" arc only two complementary sides of a total natural event. Flows of information arc linked together with flows of energy. Action of a computer is accompanied by a dissipation of previously "ordered" energy (at least when cleaning memories). Dissipation of energy (entropy increase) is closely connected with time asymmetry observed at macroscopic level. An energy dissipation is also an essential feature of open dynamical systems in which syncrgctic processes of cooperation, ttructurc formation and evolution may develop, Let us briefly mention some other connected problems such as deterministic chaos, limited predictability of timccvotution in somedynamical systems and interrelated questions of provability In formal loglral systems, algorithmic processes in computation, theory of algorithmic randomness, etc. The concept of information is very important also in interpretations of quantum mechanic*, particularly in quantum measurement and in understanding of "reality" of quantum objects. At the very frontier of physics a number of scientific speculations about the toU of information appeared. Some of them deal with the phenomenon of consciousness (Penrosc... J, some others try to establish the "physical reality" and "existence" of objects just on the concept of information (WeizsXcker, Wheeler: It from tot).

61 WORKSHOP 00 PHYSICS

It In poaalblo to conclude tlint In tlm nrcn of cominun frontier* between phyalca, Infor- matics And eybernetlca there arc tunny attractive and promising problems containing Ilia notion of Information. Solutions will probably help considerably to n development of IJIJMIIYII knowledge, tcbnccantl technology biH on It, It I* certainly iMcful ftiid, maybe, even desirable In pltysics departments of Die faculties of electrical ami Infer million engineering thai some attention be devoted In them; problems, Research in these field) should be connected with teaching A suitably deaigned elective course, which enn even help to Increase the popularity of physics among students of certain specialisations. At the faculty of electrical engineering of CTU aiich n course ollcrcd to senior and PhD atudenta covcra the following toplca: • Problems At the contact between physics, conipiitnlloiii nnd cybernetics. « Dynamical systems. Conacrvativc and dissfpatlvc systems. Kxnniples from physics, arlencc and technology, • Deterministic CIIIUM and Ita description, Kxamplca of chnolie belihvloiir, Malheinatl- cu) tools, • Chaotic attractora of dlssipatlvc ayatema, • Nun-Integer dlmenalon*, • I'mctnls In mathcinatlca and In nature, Computer picture* of fractals. • Dctermlniain. Algorithmic randomncaa, Provable and unprovahlc. • Fundamentala of (|iiHiitnm meclinnlcSi Quantum phyaica aa the very physics of the 20"' century, * Quantum structure of matter and atom*, Some Application! of the Schrttdiriger equation. * Quantum theory of measurement and ita information aspects, Problem* of interpretation. • Macroscopic irrcversihility of tiftturnl procesaea, Knl.ropy in thermodynamics and in sl.nti.nllrnl physics, • Mntropy in the theory of information. Various kinds of entropy conccpti. • "Maxwell's demon11 and hla timtatlona in the uiie-liuiidrtul-yeiu* old liistory, Computing la not an iiitclJectual performance, but A phyaical proccaa, • Flows of information and Hows of energy. Information a» a physical notion. • Open systems. Self-organization, Dissipativc structures, • Iliologicnl connections, Expansion of the universe and the possibility of life on Earth. • "Complexity" and physics. Synergetics, Chaos and information processing. Simulation* of "life". Evolution. • Open questions. Unsolved probferna, Peripectives of phyaica.

References; [1] JELEN,J.: Some connections of ittttrministic chaon. CTU Seminar 94, Part A, p. 119, CTU Prague 1931 [2] JELEN, J.; Informational aspects of physical entropy. CTU Seminar 91, Part U, p, 89, C'f U Prague 1M4. [3] JELEN, J.: Compulation and Physic*. Proceedings of FEI 25 Conference on electrical computers and informatics, p. 2C2, September 1991, TU KoJicc 1991, (in Czech). (1) JELEN, J,: Order and chann in nature, llealismus vc v5il5 a filosofii, p. 152, Filosofia, FU AV CR, 1005, (in Czech),

This research ha» been conducted at the Department of Pkytiet, CTU Prague, and has been partly supported by TU ttmo.

02 WORKSHOP Oft PHV91C3 MOLECULAR DYNAMICS SIMULATIONS OF REFRIGERANTS AND MODEL FLUIDS

V. Vacok, M, Lhal*. R, Diidlnnky

CTU, Kac. f Mechanical Eng,, Dcpl, of Physics .cluikk/l 4,1GG 07 I'rnha C •ICPF, Czech Academy of Sclenelcn, K, Hala Lab, of Thermodynamics Praha 6

Key words; Gibbs-Duhem integration, HFC refrigerants, molecular dynamics, tlicrrno- lll JWOJ>MVU», Cwo-ccnlic Lcnnnrd-Joncs fl«W, vupoui-litluU! equilibria,

Introduction: ThcrmopliyaicAl properties of fluids can be studied by experiments, macroscopic corrclAllons, computer simulations, nnd molecular theories. Experiments played and will play a central role. The availibility of fast computers enable* us to calculate the llinrtnophyslcal properties by computer simulations. It Is generally dilliciilt to achieve accuracy comparable with experiments by the computer nlmiilntlons, but the computer simulations enable us to tackle problems wlicrc experiments are not possible or arc very difficult to perform (thin layers, ports, high-pressure regions, non-homogenous fluids, etc.), The computer simulations also serve as an experimental bane for molecular theories. Computer simulations of HFC refrigerants: Since the Montreal protocol of 1087 banned the Industrial use of chlorofluorocarbons, It has become Increasingly necessary to search for an environmentally safe refrigerant with a low contribution to ozone depletion and global warming. It is well recognized that hydrofluorocarbons (HFCs) arc promising alternative refrigerant). Although a large number of experimental reports on thcrmophysical properties have appealed, Ihcic MC rtill few sUiilicj bancil on microscopic connnlciations. HFCs exhibit unusual physical properties due to the high clcctroncgativity of fluorine; many HFC properties remain puzzling and still defy theoretical understanding [1, 2j. Vapour-liquid equilibria (VLE) of model fluids: Model fluids, e.g., hard-sphere, Lcnnard-Joncs or two-centre Lennard-Jones fluids are used to establish relations between macroscopic and microscopic properties of real fluids, One important Information is the kno-vledgc of VI/E. Direct evaluation of the VLE by molecular dynamics with help of the Oibbs-Duhcm integration (3] will be described during the workshop presentation. The two- centre Lcnnard-Joncs fluid is taken as an example (Fig. 1). Experimental support of simulation: We also Intend to design and build ft complex experimental equipment for thermodynamics measurements based upon velocity of sound investigation in liquid state.

References: [I] LlSAL, M. - VACEK, V.: Molecular dynamics studies for the new refrigerant IIFC-32 u>i!h titt-tite effecliet pairpetenliat, Proceedings lVaoUhe I'M International Congress of Refrigeration, The Hague, The Netherlands, August 1995, pp. 383-390

63 WOIlKSIIOI* 00 PHYSICS

|2] LlSAL, M. - VACEK, V,: Effective potential* of liquid itmuIMm nflhr. alUrnuttue. re- [rigenmh UFC'l3Jai CF3C1I%F and lIFC-IBUi CF3CIIF,, Proweiliiign of tlin Fourth Anlflii Tlicfinopliynicdl I'ropnrtlM Conference, Tokyo, Japan, September 1095, pp. GOB- G08 (3) I;fSAI/, M< - VACBK» V,; Dirrr.l rvnhntlnn of vnpnvr-HiiuU tijulliliria by molecular dynamic* lining Oibh-Duliem integration, Motcculnr Simulation, 1UU5 (in prcsn)

1,10

3.60

1.40

1,30

2.00

1.10 0.00 0,10 0.10 ".JO 0.40 0,50

Pig, 1: Vftpouf-li<|uid (!<|iiilit)riJi of two-centrn I^nnnrd-Joni.'s Iliii'l with clongntion 0.505

This rtstarch has bttn conducted at the Department of Pliytict and 11. llala Lab. of Thermodynamics. The research in a part of the research project 'Engineering Thermody- namics-Experiment and Simulation" and han been supported via co-opcratio with Cornell, Keio and Kyoto Universites, and via financial support of the Ministry of Education and Culture of Japan (Monhutho),

Cl WOKKSHOP 0G PHYSICS . • -M •• .iiii.ii iiii.i..lliliiiMl.l.l-..-i..,^..n.ii.,w.» „, .iiiM_i4i.ii»M.4iii|^j,^jjii-Jl.j^i^.q HYDRODYMAMICS MODEL OF INTERACTIONS OF SUBPICOSECOND LASER PULSES WITH SOLID TARGETS

J. Llmpoucli, L. DrSkn, M. Vtigvlnihviil

CTU, Knc. of Nucl. Sci, k i'bys. Kng., Dept. of Physical Electronics V IIoleSovlcMcli 2, 180 00 I'rnU 8

Key words: ultrashort laser pulse*, resonance absorption, ponrlc-roiiiotivo force, loiilzallon AIKI recombination kinetics, radiation processes Plasmas produced mid heated by interne sul

C5 WORKSHOP W , HIVMICS excitation mechanisms; stationary rate equations usimily uncd for ttamUrd \mtr-pttu\uan\ plasma arc not applicable, (2) lonlzntlon And excitation processes both by electrons and photons; systems to bo studied arc not usually optically tiiin nnd radiation trapping effects could bo important, (3) Optical-field ionizntlon should be accounted in systems driven by extremely fritensc beam*, it could be « tlomintml prom* in thn /ir»t phase of tlie interaction, (-1) Effects of non-Maxwclllan electron spectra has to bo studied and respected; in situ calculations baaed on cross section data rnnst be performed for strongly distorted distribution*. (G) The effects of plasma non-Ideality, resulting in pressure lonizntion and energy levels shift) haa to be analyzed and eventually Included In high-density target*. A careful evaluation of tlic Items of this list has to be done and nn optimum version of their Implementation in the aimulation code must bo found to manage this complicated and Intensive-computing challenge. The study of tho tasks (1), (2) and (4) IIM been carried out in the period of the work, referred In this contribution, A detailed analysis and selection of available^ atomic data is an important part of this, study. Also some related codes for estimation of these data were implemented (5] and tested, Detailed calculations of radiative characteristics of dense systems, realized as a part of the international project, described '" (G]i Ify may provide a starling point, which could allow to attack tho problem (S). A simplified description of atomic processes bused exclusively on collislonal ionization from the ground state and three-body recombination has been accepted in the first complete model of short-pulse irradiated target.

"Reference*: [I] MROZ W. - DIT5SAN, I1. - DItSKA, L. - LIMPOUCII, J, ct al.s Energy Tramport through Aluminium Foils in loiter Target Experiment*. Laser an I Particle Beams f (1089), 3-14. [2) RENNER, O. - KOPECK? M.i Theoretical Analysis of Double Crystal Spectngraph for Iligh-Rctolutlon Speclroscopy of Later-Generated X-rays. Laser and Particle Beams 10 (1992), 841-8-18. [3] ANDREEV, A.A, - LIMPOUCH, J. - SEMAKII1N, A.N.: Absorption of Energy of Short Laser Pulse at Oblique Incidence on Strongly Non-Uniform Plasma (in Russian). Izvestija Akademii Nauk, seria fizkheskaya, 58 (1995), 167-174 [4] ANDREEV, A.A. - LIMPOUCII, J.: Theoretical Model of X-ray Emission in Ultrashort Pulse Laser Target Interactions. Proceedings SPIE, SPIE, DcIIingham 1095 (in print) [5] COWAN, R.D.: The Theory of Atomic Structure and Spectra. University of California Press, Bcrkclcy.CA, 1981. (6j DRSKA, L. - SINOR, M,: RACHEL Opacity Code. In : WorkOp-JII;94. Third In- ternational Workshop k Code Comparison Study, Garching, March 7-11, 1994. Final Report. MPQ 204. Max-Planck-Institutc fur Quantcnoptik, Garching 1095. [7) DRSKA, L. - SINOR, M.: Opacity Calculations for Eilremt Phytical Systems: Code RACHEL. Computer Physics Communications (submitted).

This research has been conducted at the Deparlmtnl of Physical Electronics as part of the research project "Detailed Investigation of X-ray Spectral Line Profiles Emitted by Highly Ionized Atoms' and has been supported by grant No. 202/9^/0110 of Grant Agency of Czech Republic. Scientific visit of dr. Tagviashvili to CW has ken sponsored in part by the Office of Foreign Relations ofCTU.

66 WOUKSHOP 00 PHYSICS LASER MOLECULAR SPECTROSCOPY

V, Fldlcr, P. Kapusta, M. Ilof,

V, K.jb*c>kr M, Vrbov/i

CTIJ, I'M. of Nucl. Scl, ie I'liyi. frig., Dept. of Physical Klcctronlc* V IlolriovlfkAdi 2, 180 00 Praha 8

Key wordm thne-rcsolvcd fluorescence (n«/ps), Intramolecular energy transfer, tryptophan fluorescence, decay-associated spectra, fluorcsccneo llfctlnio measurements

Czech Technical University in Prague 8",|iporU a project to establish a new Laser Spcc- troscopy Laboratory at the Department of Physical Electronics in order to combine an existing potential of the Department in advanced laser technologist with new research ar- cas of molecular pholophyslci being Introduced to the Department. Initial stage (1995) of this project was supported by CTU grant No, 35041004 (without Instrumental money yet), support from NlSMT C'R and GA Oil is expected during next two years. Presentation at WOIIKSIIOP 9G will summarize so-far activities, e.g. concept of the laboratory; utilization and cxtcntion of existing experimental facilities for apectroscopyj In- troduction of laser molecular speclroscopies to both, undergraduate and postgraduate study; International collaborations and new research programme devrlopcment for the laboratory. Following paragraphs illustrate two research topics already elaborated!

I. Intramolecular excitation energy transfer, Two scries of reactive fluorescent dyes were studied. The dyes were Intentionally designed to achieve donor-like and acceptor-like properties, as well as to allow a donor-spAccr-ncccptor bifluorophorc to be formed. The bifluorophorc (D-Sp-A) is consisting of a pyrcne (donor) chromophoro and a benzanthrone (acceptor) ehromophorc, both connected to the common spacer (substituted tri- azine) via amino bridges. The two scries of model compounds, D-Sp and Sp-A, have analo- gous design, without acceptor or donor cliromophorc, respectively. The bifluorophoro excitation spectrum is essentially asum of the D-Sp and Sp-A spectra. While the donor contribution to the excitation spectrum of D-Sp-A is the dominant one, its contribution to the emission spectrum of D-Sp-A is very small. This indicates, that efficient electronic excitation energy transfer to the acceptor part occure* after the selective excitation of the donor part. Fluorescence decay kinetics on m and ps thnc-acalc were measured and analyzed for both, D-Sp and Sp-A model compounds in different solvents. Based on those results, photophysics of the two groups of compounds was elucidated: In the cw of D-Sp compounds, charge transfer from amino-nitrogen to spacer triazinc occurcs (leading to fluorescence quenching), while in the CASC of Sp-A compounds, the governing process is a charge redistribution across the benzanthrone scclcton after excitation. In collaboration wi'.li foreign laboratories, ft time-resolved measurements of D-Sp-A acceptor part fluorescence is under preparation. This will provide direct data on energy transfer rate, as well as information on other relaxation processes in the biduorophore.

67 WORKSHOP 00 PHYSICS

Hi Molecular mechanism of blood coagulation. Dlood coagulation process is, at ft molecular level, controlled by prothromblna - c/ilclim? ions - procongulnnt membrane interaction. Much Innlght into such process can be gained using selective liicr time-resolved fluorescence ipectoscopy of some natural putts of tlio syntcm, namely of tryplopliari (Trp). Prothrombin In the mibstrak- of (do ptotiitomlAaase complex. Prothrombin fragment 1 (DF1) In the 1-150 aminoacld N-tcrminu* of prothrombin nnd it Is believed to be tin binding part of the protein. It consists of 2 parts, the Ola- and kringle-dotnain, l!y />» time-resolved tryptoplmn (Trp) fluorescence structural changes In those domains can be Investigated separately, Tlio calcium-Induced quenching of (lie DFl-'frp-fluorcscenec, which is indicative for the rnc/nbrano binding, was Investigated, It was diown, that cnlcitim addition does not change the microcnvironment of the 2 kringlc Trp, but catublithcn an equilibrium between a non- fluorcxccnt adduct (formed by the Gin-Trp and a diaullidc bridge), and the "free" species. A direct involvement of nuch equilibrium In the binding process of DI'l to phosptiolipid membranes was concluded. Trp-fluoresccncc ntudica of membrane bound fragment 1 indicate that binding to phos- phatidylacrlnc-containing membranes does not change the protein conformation, whereas binding to membranes, containing a lipld with similar binding affinity but much lower procoagulant activity, changes the Gla-Trp-fluorcsccnce,

References: |1) 1'KAItOK, K. H. - HOP, M. - LENTZ, U. R. - THOMPSON, N. L.: Comparison of the membrane binding kinetics of bovinr, prolhrambin nnit Us fragment 1. J. liiol. C'hcm. 28G, 22984,(1993) |2J HOF, M. - FLEMING, 0. R. - FIDLEIt, V.: Timonsohcd fluorescence ttntly of a calcium-induced conformation^ change In prolhromtin fragment 1, Proteins: Struc- ture, Functions and Cenctics, In press (190G) [3] SCHOLES, G. D. - GHIGGINO, II. P. - OLIVER, A. M. - PADDON-ROW, M. N.s In- tramolecular ttcctronic energy transfer between rigidly linked naphtakne and anthracene chrornophom. J. Phys. Chcm. 97, 11871-11876, (1003) 14] KAPUSTA, P. - F1DLER, V. - MACHAL1CK"?, 0. - NEPRAS, M.: SoMe-sohent interactions and photophysics of N-subslitutcd aminobemanthrones. XVIltli Interna- tional Conference On Photochemistry, London, England, July 30th - August •1th 1995, Hook of Abstracts, p. O50

This research has been conducted at the Department of Physical Electronics as a part of the research project "FH CVUT1S95: Laborahf laserovych spektroskopll" and has been supported by CTU Prague grant No, 350-flOO^ and partially supported by Czech Grant Agency, grant No, 203/95/0155.

68 WWHWW *W COMPARISON OP EFFIC1BNCES OF NEUTRON SHIELDS CONTAINING BORON AND LITHIUM

J, KUIJRUA, 9, t'twpflil, I, Stekl

CTU, !•«- of N.itl. Scl, fe I'hyj. Kn«., Drpl. of I' IMAT, 11$ 19 l'r*h« I

Key w

Tin* propowtl j|ilrldin)( dgalrnt hit nefitfr>n« Imlflf IIH* AT I. A.4 sji)>if frr«lf>m« nh'l )tr»rlkm, A,, -'M\ kt.V), thin aiipprrMittj siftdlfinuiUy tlio tiAcbgrourifl cnvifonriii'iil. Tli« (lUiuIv«,tti((o of kifurt lnucil slilcld comoii from the p{(imfrm-t«y ptodmtl'in In Ihc truction wll(n,n)fl.l*, K, =» 478 ArV, whlth In

To avoid this diiatlvtifitiiKC it Is guggntcd to use M « Dcrutton slilrld lUhiurn doped foijrrlhjrlcnc (l,il'KT), In which llip f cur I km *U(n, rt)"*Il Is trupohniMe fot hrtitron (nptuip with no KAftimi'My ptwluttlon. To rh«k ibU sutxInntUI M*1*, npvrltrirnls h»vs t*ffln| o«it In which shi'l'lin^ rfficiriicir* l il«l«tlnf)«nrl j'i*. 2 (m>mr In the miil'll* ofll boUl*1 TilM with *»l'f of wjliilkifn). Two fxenrtwUf 1 h»»f Iwrn ttwuiir^J: «[>«l»» r>{K»mm*r«jtV lyiUugrn lin«. Th« multt *f inrnmnriitnl tn T»!«. t *ml T«h, 2.

RfUl, ikiw Miilrnn (I'U H?H»t*i.» p.*k [ml.) tl«rnn |M-ak ffnltj ~p|«jr- 1 0 nrtt 0.1.1 TCI 79'Ot Tain. 1: M'jutifptnrnU with l)*kln' ihieMi R»l»l, nfoir neutron ftnt ttjitntm fiik (ml*} llofofl |^*li [rnlsj " 'i til* 0 1*1 IWli IM? 0 7Softl 0.3T 973 0 3 ft of 1.1 DM 0 oilli II,O «olnli

From these figures It \* evident UiAt both shWtls, with liuron and with lithium, nrc ghly ••'itilvfcliFMi with tMfjctt to ncutton atis'jrpt\mp*fif)g- in ih* nh'fUi f«jflUtiiln< "°'y lfl"J«"e*ir ''''''.T. wftifr), only a tliange of ^Aiiiifiv My energy from 222-1 keV to 478V^V Wkr* p|iv one can etearfy we, tdat frxfritn«-r«y (inxliiclIn/1 in litlilutii diifwd ililfld ;t iM'Aiit»] i'l<-'l I'KT) inU> In ATI.AS tlttcctof design. m

«•'!«. li Setup with I'ET (Jll'KT) bricks Fig, Z; 8etii{» with ilii(tr»n

,H, I • #«!

tW ) ID* .f^ M )rt J)#

I « ll=! w m

(I) ATLAS Tithnieal I'rnponal for H GintrnUVnrpou pp tUptrimtnt at the l,atyt Matron ColtiJtr at CHUN. CEH.V/MICtV9M.1, tHCC/M, fVc 15 l»l, u. 18-1.

Thi* rtttttrth han lew tondnthi at the Dtpnrtmrnt of 1'hyie*, FNSl% CTU t* part eftht rtstnrth prvjrtt 'tkttttion Str*etnn$ far ATtAS Inner Dtltelor at Cl'HN* and has it en mpparttj Iji CTU grant Ho. 100(8238 anif hat iten nt'O svpporirit by Iht Ministry of tndvlry anJ Ttajr of the Cueh Itrputtie.

70 WORKSHOP 06 PHYSICS COLLECTION OF RADON DAUGHTERS FROM THE AIR WITH AN ELECTROSTATIC PRECIPITATOR

C. Jecli*, J. KubMlta, S. 1'onj.fJll

CTU, Fa«. of Nucl, Scl, k 1'liyi, Kng., Dent, of 1'hysles HfrhovU, IIS 191'rMm I •'Kin J, lleyrovsky' Irnl, of I'hyslcal Chein., Ats.l. of 8e. of tlic Czech Hep, UolejSkova 3,182 2.1 1'MIIA 8

Key wordsi radon, tliofon, daughter products, electrostatic prccipitator Whew measuring concentrations of radon daughter* In the air with methods based on collection (,(daughters ami evaluation of their Activity with a solid slate detector, (tie precision of the result) Is dependent on a) the counting efficiency and h) on the volume of air from which the daughters were collected, The highest counting efficiency is obtained when the daughters are collected directly on the surface of the detector window or on a thin foil pbteml dlrretly In front of llm detector window, In both raws alph/i upeetrofnetfy fan be uied fur Identlficntloii of individual products (e.g. radun and thoron daughteri), lu the f>r«i*yjl v>t\t>»oti>xpn\imul» pot«utUl imelufom* otUjwaftoilynimletmlilMiep.ot an electrostatic prrcipitator lyntrm, when wwil for eollrction of radon daughter* from large volume*, IIM been Investigated. The ayitcm used coniinted of five corona needle points mounted in front of the silicon detector window covered with a 10/nn thick alumlnized mylar foil. Axial air flow of typically 200l.mln"' over the system was maintained with A blower a* shown in Fig. 1. After a collection time of IStnln, the activity collected was meaxurcd with a I'SDA set |t| and eventually analyzed ipectromctrtcaly. When lainptinK air from the laboratory which contained 201)'| in*' equivalent radon activity, the activity of the collected daughters (immediately after the end of collection) was SO counts per minute. In the alpha spectrum peaks corresponding to llnC and ThC were clearly resolved (see Fig. 2) and from their respective areas the ratio of activity of these products of 40 ! 1 wtu determined. The ptulti are energy shifted due to absorption In the foil. The activity collected with the preripilator wa* more than one order of magnitude higher «s compared with simple electrostatic collection (2] in * simi'ar time period In A 10 liter open m *h basket type chamber.

References; [1) POSI'lSlL, S. et al.: IMioaklitita a iivcM pntlrtdit. 9, 6 (1986), 313. (2) JKCII, C, - KONICEK, J. - POSPlSlL, S. - SlSOIl, M.: Dtttlopmtnl of tttctnitatic Collation MtthoAt for Union Decay PwJath. CTU Seminar 93, p. 71.

This ntianh ha* inn eonJaeitJ at the Department of t'hyaict, FS'SfK, CTU inrf Han iVrtt lopporlUit GA CR ynmi So. 202/93/0393 "Ntm S(ttfiod»/or Mtatunintnt of Hadon oi

71 WORKSllOi' 9(i 1'HYSICS

corona points blower

Q7 •{H || dofocfor filf tlOW

mylar foil 0

Fig. I: Illnck tthtmt. of ttutmtatic pncipitatar

Fit/. 2: Alpha Dprclrum of pntipilnlar coUrcltd radon daughttr* WORKSHOP Ofl FLEXIBLE SYSTEM FOR MULTIPARAMETRIC MEASUREMENTS IN NUCLEAR SPECTROSCOPY

J, Jnkflbok, J. GerncU, J. Kuunltn, B. 1'oapllll, M.

CTU, F«c, of Nuel. Sel, A; I'liya. Kng,, HfeliovU, 116 19 1'nirm I Mint, of Anal. Chemistry, AcAilcrny of ilcicnu<« of the Czech Hcpubllc Vfdcii.kA 1083,142 20 l'rali» 4

Key wordm colncldnicc trtlinl(|iic, energy ipvctroxcopy, tinio upectroficopy, Q»A» dclcc torn, clinr^c collection, nuclcnr reaction Annlyais, Co detector', NIM modules, l A itiultlpArAMictric Hyatein for coiticidcnre apectrotiietrlc mcfutirctncnta IIM been built, 'Die Annlog purt h biued on NIM ttttndiird inodiilea, For dnta acquiaitiuri and processing llic VMK Utu »y«tcni l» utilized, 'i'lic whole tyitetn l« flexllilo enough to cover« quite wide g p VVllli the nim of Investigating clmrgc collection efficiency of GnAa or Si detector*, we built up M i*»t-*W aAnd<\riK» *ynUm with A pLwlJe wlnililidJH n» * lityjpr (»**• Y)fr I), which rnnhlf* two dinv-nniotiM mp(wnrpm''nt of rtoth tharg" rollrrtion time «n

l1 Ccrtnodentesyittmfotimrsligiiting Fig. 1: A gMninik-gamma tmncidente »y»- of G.iAs or Si ifmieonductor detectors tem utilizing Ge

Furthermore, the VMB part of tlie system l» planned to bo used lot readout signal from pixel detectors [2|. Development of software hi llil« piirpow It In progress. At present the NIM bused analog part of tlifl system ha* been completed nnd its time tcnottitiou lias tieeri optimized. Bohr/arc far cnnltoftfag WiJw»r« configuration ami data ncr|ulalllon of up to ) parameter* (04 )>iU per event) Including user interface (ace the. block scheme In Pig. 3) has l/ccn developed nnti twlcd, IVrfor»n*rie«of tlio wliolo lyotcjn l« demormtruled In Fig. 4, where the following spectra arc depleted: tlic ipcctrum of a set of gRiniim noiirtes (hitliidlng "Ns, mCu, I3'C* and IMKu) meMuteA \>y A »!;igle III'Oo detector, the coincidence •pcctrimi of the «Bine net of (oiirccit uwmutcd \>y llin untric detector In coincldenco with the nccond llt'Clw detector in tlic COO n» time window, and the Appropriate time *pertrmu, One rnti find tlic coincidence ipcetriJM »lgi)lfic«iitly nlmpler containing only fill kcV, 1275 keV, 1173 keV nnd 13,'JU kcV coincidinff gamma lines,

€flPfpilWfJftow ffff^fn V ii: VMB M BVMK Controller B 210 (tKllU) i:iILL i .1. D UVMU MUM4 0AIJ U Mtewt 210 (AilLlUW S Ml

./>«.*m*uft>iifAUG' 1:1: | Vtfi'i )m*rf»?# « m«n» (y**«n wttli * MWfMI

| EVMM daflntfkJfi. dMa cHlttflcw. )- fi«a ******** | fttefc W laMtmitMn out AllCa 1 | WXhwm fur BVMCixta. 1 | mw«. wm cm m VM in. 1

Fig. .1: Block schemes of VMB based »AQ Fig. \: Onrnma-ray spectra (»inglc mode, system and DAQ software coincidence mode, time spectrum) Heferenccs: (1) Statiu llepoH ofllD-8 CoKnbonUon. The GaA» Collaboration, CEHN/LHCC 95-87, LDUII Status fleport/KD8 Nov 7,1D95. |2J IIEIJNE, E. II. - JAK0DEK, J. - KUUASTA, J. - t'OSI'ISiL, S. ct nlt 3 Year Jltporl on HD19 Dcvclopmtnt of Hybrid and Monolithic Silicon Micrepattern Detectors, CEHN OtlDC/91-yy, Oct 20,1994.

This mearch ha> bttn conducted at the Department o] Physio, Faculty oj Nuclear Science* and Physical Enginterinj as part of the research project "Ftetible System Jar Fast Data Acquisition" pismena vclka and hat been supported by CTU grants No. 10048287 and No. t00j8S88, and hat been also supported by the grants of GA CH No. S0S/9i/0901 and No. 203/95/0260 and by the Ministry "f Industry and Tradt of the Czech Republic,

74 WORKSHOP 00 MEASUREMENTS OF RADON IN AIR USING ALPHA SPECTROMETRY WITH IONIZATION CHAMBER

J. KoniCck, S. Ponpdii,'/,. Jnnotit, J, Kubnitn, M, VobccUf*

CTU, Pac, or Nucl, Sel. k I'hys. Kng., Dcpt. of I'liyslc/i UMmv&1, MlOl'rnhn I •Inst. of Anal. Chetn., Academy of Se. of the Czech Rep. VldeJiskA 1083, M2 20 1'rAlia 4

Key words) rndon, alpha decny, daughter product*, ionl/.Atlon ehftrnbors

Testing of loiiliintluti chamber for incMurcuienlii of radon in air ftnd it* results arc presented, The ionization chamber, which I mi been used for alpha spectromctry of radon and Its daughter products I* of cylindrical shape with Inner diameter of 118 nun And height of 180 mm. Thn centra! electrode with diameter of fl trim lit connected to n positive potential of MOO V, The cliamhrr m fllk'd by mlxtnroof radon anil nir panning through a deoxitlnting apparatus which had to remove elcctroAlltnc molecules of oxygen, for tlic imwiurcinvntii pure i]Uroi',cii was added to reach pressure of 1 a1 in. The ch/iinber was connected to a «po- cinlly developed portable regislrAtion »y»ti!in with Ugh voltage power supply, preamplifier, amplifier, discriminator, pulse counter and timer. The tignal from spcctronielric out put of the amplifier was used for Amplitude analysis by a multichannel analyzer SILKNA, In order to determine the UAH'IC properties (resolution niul charge collection efficiency), the alpha, spectra of'^I'li and w Am sources placed on the aurfacooftlic chamber WAII were measured. The influence of the concentration of oxygen in the chamber on the height of the pulses and on the shape of alpha spectra was studied. Scries of spectra measured with different amount of air added to the nitrogen atmosphere is presented id Pig, 1, One can cc, that even a smull addition of clcctroam'nc molecules of oxygen result* in a remarkable lower amplitude of output pulses. Furthermore, & direct measurement on an air-radon tainplc was performed. Radon wan taken from a dry radon source based on A piece of uranium ore. Amplitude spectra of Kn and its daughter products IlaA and IUC arc shown in Fig. 2. Three peaks from alpha decay of the above mentioned nuclei arc seen in the left figure. The central and the right figures show spectra of daughter nuclei which were deposited on the chamber wall and had remained in the chamber after this lind been refilled by pure nitrogen. The spectrum on the central figure exhibits two lines from IUA and RaC. The spectrum on the right figure was taken 13 minute* after radon removal. There are no alphas from HaA which completely decayed, Further testing of the ionization chamber as well as Investigation of radon volume activity determination techniques are In progress.

Tliis rtstanh has been conducted at the Department of Physict, Faculty of Nuclear Science/ and Physical Engineering, CTU and has been lupportctl by a grnnt of the Grant Agency of the Cicch Republic No. 202/93/0392 "New Methods for McofunmentM ofRadon and it» Progeny in the Air".

75 WORKSHOP 00 PHYSICS

W.ofnlr

O.SWfllr A MO MO

U'/.ofnlr

0 I0O JVl lorj w> HJO

IcnM) r « -

(—«-_^.- Kig. 1: The influence of added air on alpha apectruin of T'u and J

Fig. 2: Alpha spectra of radon and it* progeny obtained by formation chamber

76 WORKSHOP !lf. UNESCO SERIES OF LEARNING MATERIALS IN ENGINEERING

B, VescKS, B, Schlirerovrt, P, %««*, K, KvStoft

CTU, 1'V. of Mechanical Enjj., Oept, of Physic* VethokU 4, tGS 07 1'rahft 6 *CTU, I'V, of Ek-ctricnt Hug,, Dept. of Electric Drives k Traction TechnkkA 2, IC0 27 i'ralm 6

Key words! learning And leaching materials, iltnulittion And animation software, software Famulus, UNESCO, SW TherniodytiiiiHic package, SW Mechanical package, physics

Introduction, 'flili article presents short nummary of a part of UNKSCO project concerning creation of learning ami teaching materials in physics for Engineering education, meant especially for Africa and oilier developing countries. The learning noftware covering two parts; Tlictmodyiiflfiiits and Engineering Mechanic*,

Main tflskn. UNKSCO initiated In 1990 tho timjor project Scries of Unrnifig in Hrigi'fiwrlng Science*, The main otjatSye fn the fkvchymenl of the leafnlng package* is the prrwliictjon of xuStithin comhlniitlon of learning 'noduloi that iitiliw recent advancpii id information technology to facilitate self-tutoring Ly pc»lgfn

• Structured written texts • Video and audio cassettes • Interactive Computer Assisted Learning proyams.

Two cootracW (in years 1991 and 1995) between UNESCO and Csiech Technical Univer- sity (contractor 1GSC) were signed for the production of computer software on two learning modules: Thermodynamics and Engineering Mechanics. Two otlicr modules, Principles of Electrical Engineering and Strength of Materials will he probably add in 19%. At present time, the two first parts (Thermodynamics and Engineering Mechanics) were finished and UNESCO itartcd to disseminate them into African, Caribbean find other developing countries. EMII pstt

77 WORKSHOP 00 ^ PHYSICS

UNESCO SERIES OV LEAttNtNa MA'MIUAW IN ENClINEElllSa SCI- ENCES THEIlMODYNAMfCS pnckflgo tor Fmnulut- T)io Cnrnot Gns Cycle. Description; Ciunot Oas Cycle In «Imalc reference cycle for heal engine* and oilier gn* cycles. It consists of) ft) Isothermal expansion (1-2), 1;) adinbatic expansion ('2-3), c) isothermal compression (3-4), it) ndinhmk comptnmfan (4-1). Tlic Curnot reverse cycle lit hti Ideal cycln working between two temperatures, Ju efficiency linn tlic ninxtmuin v»I«e compnritig' with (lie efficiency ol all other tevnnu Uln»] cyekt. You win read tin! dlicli'iicy of llilii cycln from the screen after your clioice of tlio Iwo tcmiicrntiires. Whnt you can sec on tlie ocri'cn! A) p-V diflgram with marked boundary poinU (In tlin upper left graph}, b) T-S diagram (In the upper rlglit graph) where the arwi currenpotnllng to tlic work the g(i» gnina In yellow nnd the area proportional to the heat removal by the ga» U gray. The total heat the gn* receive* In one cycle is given by the auin of both nrciui. c) The simple animation of the process Is presented In the lower left window. It stops after each utroko of the cycle, d) lbrmtilaj* and laws for the nctiial process are displayed in the lower right window. How to control the program: When the menu ia displayed in lower right window choose the desired action by pressing the key corresponding to the enhanced character. During the animation the keys: <+> (plus) and <-> (minus) switches give faster and slower animation, <«paccbar> pauses tlic animation (to continue press again) and quits the animation and returns to the menu. You can nlwnys pause the run of the program by pressing key - e.g. to use Famulus tools (for example cross-hair to read Vfllucs from graphs) or to quit the program. Change of parameters of the cycle Choose Hem l'arnini'tcrit from the iiicnu in the lower right window. To change default parameters of llm cyel

Thi» work hat been conducted at the Ptpnrtmint o} Vhysict and ICSC- VC

78 W0KK3H0P 00 P11Y31O8 COMPUTATIONAL PHYSICS: NUMERICS FOR PEDESTRIANS

L. DrSkn

CTU, I'M. of Nucl. Sci. & Phys. Eng., Dcpt. of Physical Electronics V IIolcSovlcMch 2, 160 00 Praha 8

Key words! numerical methods, introductoiy physic* courses, computer aided education

Numerical methods play a key rolo In Application of computers in teaching of introductory physics courses [1], They allow both to solve phyaica problems not tractable owing mmijiricicrit actual knowledge of mathematics of freshmen and atudy realistic, for students Intorrtntlng phyaical systems. To capitalize this attractive cnrlchcmcnt of physics education ft ttioiV and effective introduction to numeric* ia ncccas&ty. To support auch effort a small package of programs explaining and illustrating clc- mentary rmrncrlcnl methods for algebra and calculus has been developed. The package is based on the generally used and to students well known simulation and graphics syatcm FAMULUS (Version 3,5) [2]. A typical module Includes: (1) A short introduction, (2) explanation and illustration of the presented method on a simple example, and (3) concrete application to a physical problem. Tho physical problems, selected from mechanics, molecular physics and electricity, need only minimum knowledge of physics, mostly its mastering at the high-school level Is adequate. Graphic capabilities of Mm program FAMULUS atid its standard numerical libraries arc hcavllly used. The package consists of approximately twenty modules, typical sizes of the modules arc 20-30 kB. Detailed list of the programs, showing their themes both in numerics and physics, Is presented in TAD. 1 (next page). The programs have been tested in real teaching environment as a part of the course "Introductory Physica Using the Computer" [3) tauglit in. the second semester of standard engineering curriculum at the Faculty of Nuclear Sciences and Physical Engineering, CTU Prague. The package was successfully applied and by the students well accepted also in the bachelor study program at the same faculty. Comment: Qualified users interested in testing of this software/in cooperation on this software, please contact drskaOlilit.fjfi.cvut.c:.

References: [1] DE JONG, M. L.: Introduction to Computational Physics. Addison-Wcsley, Heading 1091. [2] FAMULUS ETC.: Famulus 3.5. Utcr's Guide. Rtftnncc Guide. Basic Application LibraritB. Famulus Etc., Prague 1993. |3] DRSKA, L, - SINOR, M.: Pilot Program Package) for Introductory Physio Teaching. In: WORKSHOP 00. Abstracts. CTU Prague / TU Drno 1990 (these proceedings).

This research has been conducted at the Department of Physical Electronics and has not been supported by any grant. 79 WORKSHOP I'HVSICH

TA1J, 1. NUMKIlJ(J,<> (•'Oil PliDlvSTJUANK: LIST OF I'llOCJllAMS i'rogrnm Nuinvricnl topics l'liyolcnl Applicntloim ALUKIMA NAKliA Non-litiear i\ln<;lnt\\c Atomic potciitinls NAK1$» c

AIN2S Approxiinatioti fi inlcrpolntion 2 Properties of nir / atmosphere J'JIO* Miniprojcct J; Clinrnctcriitic value problem: Hounded aacillnlara CALCULUS INTU Numcricnl Integration 1 Axial potential of charged ring / disk INT2IA Numerical integration 2 Of-nxis potential of charged INT2SD ring / dink l;lvii$A Ordinary

DE12SA Onliimry diirerr'utiiil ei|i)nLloi)s Serial UL circuit DK12$I) of the first order 2 Uli21"i Ordinary dilferential equatioim Galvanometer motion of the second order 1 DE22J Ordinary differential equations Charged particle trajectory of the flccond order 2 I»I2O$ Miuiproject 2: Non-linear ordinary differential equation: Driven and damped oscillator*, chaos ADIJKNDUM I'UlilSA Partial differential equation* Vibrating-Btring problem PDE1SB

80 WORKSHOP oo PHYSICS PILOT PROGRAM PACKAGES FOR INTRODUCTORY PHYSICS TEACHING

I. Drikn, M, Siftor

CTU, Fac. of Nucl. Sci, k l'hys. Brig., Dcpt. of Physical Electronics V IIolciovickAeh 2,180 00 Praha 8

Key words: introductory physic* courses, computer aided education

The complementary pliyslcn course "Introductory I'hyaics Using the Computer" (1|, [2] taught in the second and fourth semester should l>c characterized by the followig features:

Presented topics: Computer reconstruction of historical experiments. Study of realistic systems. Topics related to every-day experience. Pedagogical nppronch: Individual selection of study materials, Maximum of student's individual work, Realization of student's miniprojects. Tcclitilcnl solution: Completely computerized course delivered in coiupu« Utlonal laboratory, The use of general software tools fur simulation, graphics, and symbolic computing,

The structure of the course in both semesters consists of four teaching modules and one evaluation seminar;

Computer as a physics tool 1 Computer as a physics tool 2 Numerics for Pedestrians Selected topics in physics 2 (1) Algebra. (2) Calculus (1) Electrodynamics. (2) Optics. Milestones of classical physics I'rcludium to modern physics Selected topics in physics 1 (1) Relativity. (2) Quantum physics. (1) Mechanics. (2) Heat. Evcry-day applied physics Students presentation seminar 1 Students presentation seminar 2

As a part of the software support of ttie course until now three pilot program packages based on the simulation and graphics system FAMULUS 3.5 were developed: (1) Numerics for Pedestrians. (2) Motions and Heal. (3) I'rcludium to Quantum Physics. Each package consists approximately of twenty codes. More detailed information about two of these packages is presented in TAB. 1 and TAD. 2 (next page). Some programs developed for the course use symbolic computing; integrated computing systems DERIVE / MAPLE arc applied. Examples of these codes: TA13.3 (next page). An illustrative selection of the programs mentioned above is available; please contact sinor

81 WORKSHOP 06 PHYSICS

TAlTT PILOT PACKAGE "MOTIONS AND HEAT"" Linear motion: A dish on a table. Accelerating vehicle, constant nml limited power, Accelerating car, horsepower curves, Accelerating enr, limited power and gesrs, •Mlniprojecl 1: Analysis of tlic rocket (light, Ilnlllstlc motion: The throwing a ball, Spinning tennis/baseball bnli, The trajectory ot a pilot ejected from an airplane, Control motion: Orbit control, Non-inverse square forces. Orbits in the solar wind, •Mliilpfujcct 2: Restricted three-body problem, Kinetic theory: The approach to equilibrium, particles in box, Moxwcll-Doltztrmn distribution function. Salm and rate cqitAtioris. TiicrmotlynnmicB; Equation of date, plienoinenological formulnjt, Bencdict-Wcbb-ttiibin EOS, Jlcat transfer, slab problem*. •Miniprojcct 3: Refrigerator and licnl pump. Addendum: Nonlinear motion: Elementary model of heart,

TAH, 2. PILOT PACKAGE TMaUlJlUMTO QUANTUM PHYSICS" I'Jiotono and mnttcr waves: lllackbody radiation, Planck g radiation law. The Bohr model of hydrogen atom. Photons ft do Uroglic'a waves, Wave packets, the uncertainty relations. •Miniprojcct 1: Double-slit experiment, Elementary quntitum models: ("article inside an infinite/finite potential well, harmonic oscillator, elementary and detailed description. Potential barrier, the simple step and the rectangular Wrier. •Mlfliproject 2: Morse oiciilator. The hydrogen atom and periodic table: Hydrogen atom, elementary quantum description. Quantum theory of hydrogen atom, radial and angular wave functions. The periodic table, cctral field approximation, • Miniprojcct 3: Energy levels of low/medium % atoms. Addendum: Barrier problem: Tunneling, numerical solution.

TAB. 3. EXAMPLES 01' COMPUTER ALGEBRA BASED PROGRAMS Formula recalculation between Bygtcms of units Dynamics of the falling raindrop Anharmonic oscillations, slightly nonlinear cases Tliermodynamic functions of nonideal gascg Derivation of the Wicn d'splaccmcnt law Verification of the radial wave functions for the hydrogen atom

References: |1) DIISKA, L. - LISKA, R. - SINOR, M. - VONDRASEK, J.: Development Project* in Computer-Supported Education of Physical Engineering. In: WORKSHOP 95. Ab- stract!. CTU Prague/TU Brno 11195, p. 891. (2) DRSKA, L. - SINOR, M.: Introductory Physics Course Based on the Coordinated System of Programs (in Citch). In: HYPERSEM: Proceedings. Military Technical Institute of Ground Forces, Vyskov 1995, p. 95.

This research has been conducted ot the Department of Physical Electronics and has not teen supported by any grant.

82 GEODYNAMIC INFORMATION PROM THE RESULTS OF GEODETIC OBSERVATIONS

A. Z«m«n, 1.

C'tU, I'M. uf Civil V.ng., Dciil, of Advanced (Wtrsy t 7, ICfl 29 i'ralm G

Key word*! gndymmh!, height »y»lfth.», hclwotk adjurirnrnt, gw<\ynamle InforrnAtlon, optical i

TV ff>lfonwifJi5 f>iol>!rtfn wrtr1 f Thwifrtital (Iwlfliy of Trchtiicul Univrrsily Vienna, Was prepared and will oc putllthnl in joijfn*! O»t«fritlil»fli

(oufiltl(-4 «liiti'(MI (t-ft uty lo pFfM-ii(r tw II wan rMoiiittti'iulfil Ly (J(vLN ((/utiftl K g ) t (p lf M ) TV ((toftsttucliOfi cf tfie aJjuslmchl tf (ictwotfe tovrfifi*( ihe lemtofy of foKnct Auslttv ftun^AfUn Empire «t« (Aftinl out afnl (lie IMHIH w^re aif(i(>Arw IpTvllinp (itinioly frotn 1W\ri of thU frtilury) on Ib*1 Irttiloty of lhw« slnl'i, which *(•(«• otiKitixly Ihe pnHii of Aiistto-lltmgMiati Kmpite bill si ihnl tittw? tlicy wrte Ihr pMt of f/wlctlfnjK'iin ti'lmifli with liri^tilt f Dullic Sr». Tli" tompArimn hrini^hl Inlcrmtin)! rmilti, which crmfifm sorne ptctiotM fimfinp »nni. MrtitionH twofk t'HI.N,»liirh U itrfirn-d dy !!«>|»>«cntUI n»imf>»f» •rvl IM to lh«? Nwih S»» M AnutrtoiUm. Th*> pjit^r, f«iw ({rw'd (wilh loolutkm »e*ft»l cm) on lh« tuae of »imfUk daU ol Im4h ttrinlffcr*. 3. fjipff "ffirpsfilifm to Infinite lfn» Utrtlin^ Nrlwofk oti the Trifitofjr of Cttrh b Ifnifitd Ea{r>v«*ft Lr»«l!ing Netwotk* w« ptibtisfmj in journal Co«lrtitli^ tfo* (It. tn'i. No6. |>j>. 119-131). the aalhot* iumnvu!/*- iVre th#- f«$«tl* <4 intfiilijAlKXM on ctfM* of kifnt of (finfil* WHI iwighl syitfm i(x!'i'lin< drUilnl •wnpi»#i«nn >4 ih^ thff*rrit*r* f)Hm>rn (^Fni-I *ft»| fjfi*tfgJiwt'l on llw* I'ffitnty of jwfclk. SimnllAftfwwIy Ihe (x'llmiruifj klj^ltfynltif bi»if(M 6»f"wtk, wlikli tw p IOWI ID UfXN, •*• (Mtirtl wit. final ftndiftg* iifff intojtt) »!••» lalh* «ori M WORKSHOP00 FUVSICS

"WA.H Activities In tlie Czech Republic" on KIIIIF1' »ytipo«|iim In I'IIIUIHI (May 1995), which WM presented there by Ai Zeman, Further aim of research wa/i achieved l»y the renulta of adjtialirir'nl (if heights on the toritofy of Czech Republic nt very nVnw nrt*m%, b«r»J (llilk tfffitofy in vettlc/il ditrcllofi, Aftff f!hlithlnf( the lrwn(i«-tl[»t of tlic (i«pvr (he rrmilt* will t llll In joiirnxl (Jffxlftlcky «Imrtogfaflck^ ohzor At the first fmlf el 1 '*:>'>. 1, One of oilier ftlmiof the prujret WM the cimtrilruilon toi-nUMi'liing the f network for gTOtlyn*fnle» on lh« trrtltoty of the C/.wh ttr-jMiLIic; whitU will h alrttetwl hy Gl'3. OwJynnmle nctwofk In tnninly l)*vii on levelling [nAhlt which tills network slmnlUtieomly to putopran gtHxIynnnilc ti'twurk *nc'. At present we can drily «t»t*« ttiAt after cliKU-isinn on luUitc tonerplUm on I'lena/y Mrctih^ of 1A(I (Intcrna' tlonal AnvicUtldO of (Wlcs,) In July of thii* year at llotjlder (U.9.A.), the proMcm vt*» poatponecl la further meeting of l\w V,xrnil\yn )tnntt\ in n^l yaf (IMfi), 5, I'roljfein of eoritiPttln|{ the optical and radio feferencf frameji, particularly- iSnkltif! Ik? tfdrtn id U^" HippurvH rAlA/Jt> to «« Inwtla) tium, ivptemtln] by lim ejslr«g»l(i*;l|f tA'Vm ttrtlirf, hm\ raiivd • nemaitjr nt intmiive ulnrrvation* of r*ilio utars, ifx- onl b oliwfvaltlc dy tneana of the optical and radio aatrometry, l'o«itlon» *nlrophyil(a Siippl'ltifnl Serie* [i|.

Reftrencess (I) ZKMAN, A. - Srli'KK, f. - ASCHF.KMANN, I: I'fipmtn pfipojtrl tytkorf till nit uttnit Cuk( ttpMky da trropik/ tilt. {Uvl * ValU^t. uhlut 41 (19M), N'o- 6, pp, 119-129 (2| ZKMAN, A. - BRNKS, V.S VELS atlirilitt in th Cttrh IttpMie. I'irsenietl on KUHI.K Sytrpfwinni. lintand, May 3-6, I Ml. p\ VVtoK, 1. - lltfTY, 1. - SKOUI't, V.! Op!irnt pi,«lim» nf MtrnUm tnJio War. from cirttm :««•(««/ «tHrrnttan» hy tht mrl/toJ of ffW nllilnrl't. (lo b« »dbfriHed to and Aslrophyt S

Si SOUND ENERGY TRANSFER IN A TRANSIENT SOUND FIELD

V,. Kyucl

CtU, We. of KlMlrlal Kng., t)e|>t. of Pnysk* Teelinlck* 2, lfiO 27 I'MIIA 0

Key wordu transient sound field, energy transfer, diffraction, JOIIIKI intensity, gradient Analysis, Fourier Iran.iform

Otif effoft to investigate the. noiind energy Irantfrr in A transient sound field IIM liecn stimulated l/y tlif dillicullle* which have fared us In • nieanureinenl of the iound adsorption coefficient liy (lie impulse method lis.«rd on n acaUr nnalyiii of (tie Imnilrnt response of A incMutnl siiifpicc |l). This intllunJ wirtlis i|iiili? well If a liomogrnroii* )»lnn«r Mirfatc Is inrii- Kiirrd; lint, It gives faltc rrault* wlirti applied Ui hhomogfltrvun und/of tlirec-ditncnsioniil «f>v)rl>rM, 'llir diffimllin urc (Allied l/y dilfractlon of llic reflrcloi Impulse wave lircmne tlin acalar AnalyaU of the ilKfrnetpd mm ml field dura nut ylrlil « »iilllflrnl Infuriimtlon AIKIIII rellcrtrd noiin'l furry. This pflp'-r i* (onccrnnl willi Introdurio/t tin; pUy»kn\ (|iMtitil|r,i A^lillhliU* tu iiwAKttttitvftil «>f Miuml rtttAtC then the full in- i nliout tiitiiid ('Wtgy ifniufcf li A£i|iiir(y AD impiiUc inrtlrod (I), llirn the inirnl Mittnd field Utnmrti motec«tnpllrAtc«l lieratiwiof ililfmtlloti l>y llicolnlncli", Then not only the uMiind pressure li^t) hut *\v> the ((jjlklc velorlty f^(r, () iliottld lie kiiowrl fur Arr|iiirlng A VAliiililr In for in A linn AIKKII mninel enrrny Irnmfrr in A tr/iniimt field. If wr mtnAgtr tr» drtrt mine a gradient of tlir MJIIII'I prnwure, »p can evaluate the particle vrkxily l/y intrgiukin Mcording tu tli<< i'jtUt «<|iiAtion fvitt)Ar (I)

C««iwf|rii«illyr the Sound Yjnvtfj Transfrf Density V',(f) Ihruiigltout iff Mther. point r"ln • noftn*t 'litrftion during "" rntltr tfAnsirnl rvrnl ran IH* olitnlneil t>y linir integration of thr Instantanrou* Intensity [l|

If the rWwt ttstisfwin /'(/,/) «nd Vm[t,l) <>f pji'.l) uti.t f.(r,l), rrsprttWely, Is determined then the »pectr*l rxprcasion of wiund energy transfer In » transient field can by lining lh« lUyleigKI'afsev*! thei>»eifl. Th<* »ptlt*l density of lh# »p»eifi« rti'tfjr IfAnsfer tan li« rxprnsnl u

83 WOKKSHOP (t(i PHYSICS

Tlio fre^uency-baml vnlue of the specific notiml energy trAfisfrr K«(f) ««

where /i And /j me the lower nnd upper frequency limit* respectively. Tlifi portion of found energy trnnsfcrrd through « »fKrlfle»J mitbu* *WJI ,V/; iliiriii/; tlie entire Ir/iMilrnt event wltliln A i)iecined freijiteiicy liinit* i«. / .»Md*. (5) lit) Lei llic itnpulsc loiiml wave l>n einltled l«y A dotirfc In « fr"* *\>nrv. 'Died ilic «|>rdfal f ir ipeclflc nviuiil energy ttftntfer in tlic ritdlnl dlrcclloti li

gc Fr<*'|i)ency>lMnd value of (lie njtrrific lumnil rnrrgy lr«infer in A rmlinl direction is

|'d/, (7)

ill'.' Is given by a simple formttlA J /i«, = 4»r F,fl. (8) The tnetliodoflnrMtireitientofiWiiilid etirtfj itiniitit i* btwtiati l\irtnirf'irtil p ut the two channel record of the noiind prcmtire |1), (1),

(I) KINTSL, Z. (Kyncl); tntnlttjitlfon of the Sound Ab*<>n>linn of the Wall Stctian fry n /W»f Ttchnipir. iwiv. I'hys. Acoiut.,2l(l), |>. 30-32, I!)7.'F. [2| KYNCL, Z.: ffrw Conctpl of impiiUt. Stathtic* An*ly*i» of Hnntn Arontlltn. Acoml. Lellm, 3(11), 200-207,1980. (.1) FAIIY, V. U Sound InttwHy. Klwvier Ap|»l. He, ID89. ()) JlftlCKK, 0. - KYNCL, Z. - KASt'Alt, l-,s Crni/ifnl /tnd/y«(/» nf Tnniitnt Soumt t'irUn. I'rrK. of the 3t»t Confrrmee on Acwmllci, p. 1II-1U, Prague, 1991.

Thit nitanh hnt htm eondutttd at Iht Dtjnrtmtnt of I'hytir* of Iht faculty nf Eire- trie al Enginnrlnf CTU Prague. WORKSIIOPDO PHVSICS ULTRASONIC INVESTIGATION IN GEOPHYSICAL RESEARCH

K, MrtlJtiik^, J- Ploeek

CTU, toe. of Electri'al Erig,, Ucpt, of l'liy»lc» TllU 2, JBO 27 I'raha 0

Key wordm Ultrnflouml, rocktnnsa, geology, wining.

Tlifl use of active ultriuouiid (< mnnrcu mine, Kladno, since March 31,1991. At the same place, hjrdrogrological and convcrgotnctrical meamrement* ate made.

87 WOilKSIIOl' 00 I'JIYHICS

Tlio dmiigcD In receiving level were +IH,% to -60% during tlic iiie/isiirlnn (corrttijg l>y Ad » -H% to 10-4 %•)• Tim velocity of elnntic wnvei W/M cnlnldlfilipd on »Iton-holi! ron;! c « 2530 m/a. Tim entire |>liMfi shift A^ lit M,(>", corrrHporidlng tlmn with tlm velocity f)iflng

Htfrrrrtrr

t - Transmitter >• • McflMiring receiver H - M|iii(il & DC lupplying 2 • Kllttltlll!! 7 • Output Icmli nil Hir J • Hiirtliotci with wnkr mtrriKriifllienilne 9-TfjlCKt.le 4 - Trnmniitliiig transducer (2 Iclephonr pnirii) 10- A/I) cnnvcrlcn 5 • Kctf ivinjj tmntductr 11 - Computer ( PC) with preamplifier

Fig. I: Tin" nrrntigrmrnt of thp inciunring urt

Hcfcri'ttccs: [1] MALfNSK^, K. - I'f.OCKK, J.S Active ullrunnund in grofogiral rtirarch in liltldnti Act/i Mimtans, Scrlra A, No. 7(06), |». 7.V8I [2\ MAMNSKf, K.: Ultrnaonir inwiligalion in a rnnl mint The lClli UltfMonic lntrrn.\- IIOIIAI coriferrucr, lv>lirit>urp;li, .1 -7 July I!)'J" (.1) 1M.OCKK, J,! Equipment /"<" ullnununH intetligulion in mints The I6tli Ultra-tonic intrrnatiotial confrrriuf, lvliiiimrgli, 5 7 July 1995

Thin rtteatrh lm» bttn tontluetrd at the thpartmtnl of t'hysit* u.i a part of Ihr re- tturch projtct "Inductd Ctodijnamicnl EJJect in Mining' and /in* kern nupportrd by grant So. 530330.11. WOltKSIIOl'OO PHYSICS PRINCIPLES OF ACTIVE CONTROL IN DUCTS

O. JlfUek

C'l'U, l'nc. of Klcctrical Eng., IJcpt. of Physics TcchnlckA 2, IfiO 27 I'ralm 8

Key words! acoustics, active noise control, multiple sources

Altliogh the first sound cmicclatlon pntcnt was awarded to 1'n.ul Lucg In tho ltCO'n, the Active noise control (ANC) li'ui been an area of intensive research during the last two decades. Tin1 cftncol/ition of noiittd wnvi'n in ducts Is OIK* of the inont important practical application of ANC, since the physics of KOUIKI propagation Is very straightforward under the Assumption tliat thctc »te only plane waves pfopa^ntiii^. Tliis Msitmptlon l§ valid if the maximum frequency is below the first cut-oft frequency of the duct, t'or A circular duct It can lie expressed In the form A > 1,7/), where D la the diameter of the duct. In tills paper we ill li-iffly review the theoretical basla and practlc*! possibilities for active control in duct, iislii//, one «nd morn dwomlnry Iwidnpr/ikrr/i, The simple geometry of one dimension allows to control the sound by using only one m.'toiif.nry tourcv. Following N'.'IMII and lilliolt |]J vm am*\i\t.(*)-'gW-W'-JI). (2) The condition for zero downstream radiation is ft(*) + M*)-0, x>L (3)

This requirement, together with equation* (I) and (2) gives the relationship between the complex strengths of the primary and secondary sources

i.e. the secondary source itrenglit must be identical to the primary nourcc strength but of opposite sign and delayed by a time which Is taken by the sound to travel from the primary source to the secondary source. With one single secondary source, a Urge change of impedance Is realized at Us location to that the incident wave is reflected back into the upulrcam direction. However, a real duct ba» some reflecting termination at llm upsttMm end. Ttwrrfor* th* trflrrtii waves will

8D WOItKSHOl' 06 1'liYSICS interfere to act up ft standing wave, iind the sound pramurc in tliio region e«n severely increase. This sound can break out of tlic duct wall M turn;, Tlin nolutlon of this problem wa* proposed by Swlnbanks, Ho developed a unl-dlrcctlonal source, consisting of an array of two sources (loudspeakers), spaced apart by tfw distance (/ («cc Fig, 2), TIic soUiid pressures produced by Cher secondary sower* arc; fJ ^jt|* - L - ./|). (5) The condition for veto up«trc«n> rndlfttion />,( 4 /;,, H 0 for x <, L results In cxprcnloii L + tl, U

From the equation (7) follows tiial the downstream pressure of lite Stvliibanks source Is frequency dependent, I.e., there arc jorne frequencies whom the downstream radiation Is zero, This results in bandwidth limitation. Several authors recognized that this limitation could be extended by adding further monopolc sources.

jr-0

Upiuiim

If Pnmi/y icurci

Fig. li

i-O ft.

1,1 If} Stcendtry wircn

Fig. 1:

Referencei: (Ij NELSON, P. A. - ELLIOTT, S. J.: Active Control of Sound, Academic I'rcsi, London 1993. |2) WINKLEIl,J.-ELLIOTT, S.J.: Adaptive Control of llivntthandSound in D<.ctt Using a Pair of Loudspeakers. Acuslica 81(6), p. 475-488, S. Hirzcl Vcrlag - Stuttgart, 1995. |3J GUICKINO, D. - FIIE1ENSTKIN, II.: Broadband Active Sound Absorption in Ducts with Thinned Loudnpraktr Arnyi. Proc. of ACTIVE'95, p. 371-382, Newport Ucaeh (USA), 1095.

This research has been conducted at the Department of Physics.

90 WOKKSHUI1 90 QUANTUM MECHANICAL MODELLING OF CRYSTALS FRACTURE

P. Siindcrn, V. Navr/Stll*, J, Pokludn

TU, Ivc. of Mcchnnlcnl Eng., lust, of Engineering I'liyslci TcclmicU 2, G10 G'J Urno *MU, I'M, of Education Dcpt. of Physic* I'oFtff 7, GOD 00 firno

Key words! theoretical strength, Interatomic potential, crack-slip corifigiirntlon, electron strucLurc calculation

The first part of the project is devoted to the completing of the fracture theory bnscd on classical inieromcdmriics M Well M to the preparation of a necessary software

91 WORKSHOP 00 PHYSICS

Pnxlon ct nl [5] for fee And bcc cm™ on the I>MI» of density functional theory, The arc close to tlw CIMAICAI Krcnkcl value*, Thin la In agreement with our result* ban«d on improved Mackenzie Analytical npiiwnth siiupurtcd by computer modelling lining nnniiMii- piricnl interatomic potential* [1], Nowadays, tticr most effrctive rne- tliod for the electron strucliiri! calculations seems to be the LMTO method |fi). Tliis method I* charncterisa'd by Using fixed basis functioriH constructed from pnrlinl wnve;i find their first energy dcrivativex obtained within the iniif[lii- tin npi>roxiiiintioii to the potentinl, It ICMIH to ncculnr c(|imtioiis wliicli tiro lin- CM in energy, thnt \n to well known eigenvalue conations. Itmidu tliu irmffiii- tln nplitre, the potential is assumed to be upliericnlly ayinuietric nnd the wnve Fig. 2: Charge density in Si (diam. structure) fuiictioiiB Eire cxpntxled in the pnrtial- wave Holutiona IIHCII by Wigncr nnd Soil?,. Outnide of tli« »t>licr<:H llic potential is mwumcil to l>e flat or slowly varying, and In thin no-called Interstitial region ft plniiR wnvc ox|mn«i«n I* lined. In Fig, 2, the chnrgo drim'ity at tin; (l!0) pUuu In Wi Utxk'forinud diiuiioitd structure of Si cryntnl in tiliiiwn enlcn- latod using llic LMTO rnrthod. In order to determine the theoretical strength of crystals, the dependence of charge density function on tlic drain pararnpO^rs Hit; U> )/

References; |1| KKLLY, A, - TYSON, W.Il. - COTTHKM., A.II,: Ductile and Urittk Crystals. Philo- sophical Magazine 15, 1367, 5G7. [2] RICH, J.R, - THOMSON, It,: Ductile vcniu flrittlc Itcuponsc oj Cryxlalii. Philosoph- ical Magazine 29, 1974,73. [3] POKLUDA, J. - SANDERA, P.: On iht Mrintic Ductility ami Ilritlkntia of Crystals Physica Status Solidi (b) 107, 1091, 'M. [4] SANDERA, P. - 1'OKLUDA, J.: Improvement of the Mackenzie Theory tm hhalShtar Strength. Scripta Metallurgies ct Mntcrialia29, 1903, 1-H5. [5) PAXTON, A.T, - GUMHSCH, P. - METIIFESSEL, M.: A Quantum Mechanical Cal- culation oftht Theoretical Strength of Metals. Philosophical Magazine Letters C3,1991, 267. (C) SKUIVEIt, II. L: The LMTO Method. Springer Verlag, Ilcrlin Kcidclbcrg New York Tokyo 1984.

Thi» research hat ttnu conducted at the liutitvte of Engineering Pliynies aa part of the ntiarch project "Quantum Mechanical Modelling of Crystals fracture* and hat been supported by TV grant No. FU 350039.

92 WORKSHOP 00 PHYSICS COMPUTER SIMULATION OF POLYEDRIC STRUCTURES

J. PokliKln, I\ PonfJiii*, I'. Snmlcrn

TU, Fnc. of Mcclianienl I^ng., lust, of Engineering I'liyaica Tcclmicka 2, 010 CO Brno *T(J, Fnc. of Technology., Dcpt, of I'hys. Mnter, Kngincerlrig Mnsuryk «<|uare 275, 7G2 72 Zlln

Key words: stochastic geometry, simulation, polycdric structures, structural parnmctcrs, damage mechanisms, process zone

The mnin content of tho research rnprcsents nn applicntlon of computer generated 2D and 3D materials-like structures to the modelling of damage processes occurring within the process zone in engineering materials. In this paper, results of the first part of this research arc shown, i.e., the simulation of inlcrgrnniilar brittle fracture process in ndvnnccd high strength material niiing 21) Voronoia tessellations approximating tlio grain houndary network, \for«ovor, •••oiiir-gcornctri'inl properties of .11) Voronoift tessellations are nWrinnstratrd, A regular hexagonal network approximating the real 21) structure of grain boundaries was originally lined [1,2] in order to elucidate the incrcain of the fracturo toughness with the increasing aha of primnry aiistcnitc grains in case of the ultra high Hlrcngth steels. Votonoin mosaics generated b/ meant of l'ois.ioii point process [.'I) represent a much more better approach to tin; real boundary network. Therefore, the intcrgranular crack growth nlong the boundaries of Voronoia cells wan simulated using the same physical rules as in the previous model. An example of such crack aplittcd „.,„,. , . . into two branches is shown in Fig. 1. The driving Fig. l: forked crack in mouue force of lh,g crack ,g co,,,i(icrauly lower than that of an equal sized straight crack which causes an improvement in fracture toughness. More than 1300 various mosaics with cracks were statistically evaluated. The result of statistical evaluation is shown in Fig. 2 where dashed lines represent a 99 pet. confidence intervals of the A'/e vs. d (mean grain size) dependence. It is in a good agreement with the previous more simple models and confirms the assumption that the main contribution to the improved fracture toughness of coarse grained UliSLA steels originates from the intcrgranular crack branching phenomenon. 'i lie really plausible crack growth model must be based on a 3D Voronoia tessellation. Nowadays, we arc successful in constructing 3D tessellations containing up to 1 millior. cells. In the Fig. 3, one polygonal ell of itich mosaic rotating round the vertical axes is shown in five deferent space positions. In the final part of our research, a 3D crack growth model will be developed.

93 WORKSHOP 90 MIYSfOS

10 too 1000 Ql/'ldnf villkoil irna ri [wml Fig. 2: Dependence of Ktt "" ''

Fig. 3: View of the rotating cell

References: [1] POKLUDA, J. -SANDERA, P. -ZEMAN, J.: Effect of Inkrnramilar Crack Branching on Fracture Toughness Evaluation. ASTM STP 1131, 1992, C53. [2] POKLUDA, J. - SrtNDEIlA, P.: Pofitadovy model metikrystatovc'ho vttveni (tU trhtiny pfi ikouice lomovd houievnntosti. C«. las. tyz. 40A, 1990, 470. [3] PONfZIL, P. - PELIKAN, K.: Crack Growth Modelling in Simulated Structures. In: "International Conference on Fractography '91", c

This research has been conducted at the Institute oj Engineering Physics as part of the research project "Computer Simulation of Polytdric Structures" and has been supported by TV grant No. FU 3500^.

9t W0nK9I10P 90 PHYSICS THE STABILITY CRITERION GIVEN IN TERMS OF INFORMATION GAIN

M, KhollovA

TU, I'nc. of Electrical Kng. k Comp. Sci., Dept, of Physic*

Key words! Noncqiiilibrlum statistical operator, Cibbs entropy, Excess entropy production, (llaiisdorff-Prigogino stability criterion, Infonnntlon gain I'rigoglno's stability criterion In expressed by mean* of the information gain depending on two noncquilibriurn coarse-grniiicd statistical operators. The form of the noncquilibriuin statistical operator can be derived using tho Jayncs vMinlionut principle (1,2|, Uio nuuutnmn tnltopy formalism (MEF), including memoty effects, nonlocality arid Prigogine'a dynamic condition for disslpativity [3-C], According to tlie MEF we obtain the best choice for the NSO g{t) by rnaking extremal (rnnxiirjuin) Gibbs entropy ( with u(l) duduud In the Interval (/„,() and normalized at ail tiniua, mibjcclud to the con- straintit imposed by equations Qift 0 " rp^tOfftOI = TriPtf, (' - 0J(01 . (2) for ta < t' < I; The macroscopic variables Qj(t) are the average values of the dynamical quantities Pj(t) over the noncqtiilibrium ensemble. This procedure leads to the result that

/;<0)|nj((',i'-o) , (3)

where

The NSO ?„,(/) and i(t,0) express the same macroscopic state but differ in detail due to the microscopic processes developing in the media. The auxiliary NSO

95 WOKKMHOjMK)I'HVHICH

«\tvt« SQt(l>,t) a Qj{f>,I) - Q>j(?), hl',(?il) * IW,I) - f?(Oi Index S>.rro re fern to tlie Vnliles of the <|1l«ntitlr» in ihc dtrnily sUlc.

Wrtoinlilrf tliflllifoft/mtluliKnlii(KI) furtwdciiatsngrnltird NSO J(((,(J),5j(/,O), Tlic gcncrnlfantton of Ki li> <|\ii\ntmii mi-rhfiiiica U [?j

K{tuHi) - '/V(p,(hi d - tne,)], (7)

Jly time-diirflfPiitintlufi uf 10 A'(5(<,0), f), wlirrr j" i» tlip roiirj

(Joifi|inriMg K<|, (8) with K<|, (0) we derive for the time tlerivnllvc of 10 the relation

~ « -AW'C) • (0)

From t>|, (0) it follow* tlmt the f|imntity -dlifilt run lie Intrrprrlcl M exce« entropy firorltictiun. We now rxprraa Uie (ItnrmlorfM'rigngiiie uliiliility critrrlnn Using KI |Hj: I'or the givrli conittrnlnit, if

tlic rrfercner steady state i.i stadle (Ksyrnptotic stalilc), Mid if

the ri'fereiirc atearly ttAte in finsUlile. In the cjotnnifi of linear irrevcmilile llirttiKxIynniiiirii the zero time derivative of Id rurrrspoiwl* to A minimum of entropy production and the K thrtirern run he forniiilnlrd (8j.

References: (I) JAVNKS, E. X: /'/.(/». lit*. lOfi {mi) 620 [i] JAYNK.S, VJ. T.: My*. Ikv. 106 (1951) IV. |1) IM'M, tt. - VASCONCKLI.OS, A. It.: t'nrtichrillt

|C] VASCONCELLOS, A. It. - I.U/,/1, It.: l'hv»ica A ISO (193!) 182. |7| SCIII.OECiL, ¥.: H. I'hyiik Stf (1911) 301 |«1 KIIKH.OVA, M.: Cirrh. J. I'hyi. U (I39i) 8.

This ttntatth hat bttn comlurtnt at the Drpartment of Physics an part of the rtttarth prtijrti "Application uf irrtvtrnAU thrnnoiltjtinmic* anil Information ttalutirnl phytici mtthoitu nl tht ntudy of tcnhitinn of ntlfargnnitation lytrmt" and ha* btrn mppnrtti iy W Ml W0HK8II0J' 00 __ I'HVfltCH IN-SITU INTERFEROMETRIC THICKNESS MEASUREMENT OF DEPOSITED THIN FILMS

1, tipoutith, W. Uejrnek, '£• Ifnrna, A. Neliojgn*, T, Slkoln, M. J/ikl

TU, t'ae, of Mpcfmnkal KIIJI-I l»«l' «f 1'hyslcal K«g- Trchnlcka 2,010 G'J tlrrio 'Mil, Fiic. of Scl., iJrpt. of Solid S't«to Physic* KtUhkA 2, (137 11 Itfiio

Key worclil tliin films, In-aitti thickness

To improve lh« quality of deposited films and reliability of technological operations, It li necessary to control the. parameters of thin film* already throughout the deposition process (l), Optical methods fire one of the most frequently used fof In litu Investigation of layer growth [2jr In the Institute of Physic*! t'tigltirrritig of TU llrno An i'? tot tlfpHhlon tui4 etthUw *4 lh)n Mm* I* t/jWiUrt}, Aumi.i of thn ittfrl »rn npiittwrl Into tliw v/icimm rhdmber (Inr to IntrrMtion with Im- pinging Ion* And form thin film* on »ult*l>ly ponitloned mhstratn. Quality of the growing UyrM, proprttlc!) for fxainple utirh M cornpmilion, stmctiifp nnd Index of refraction, c«n be modified during the deposition hy IjotribAfilmrnl of Ion* from a urcomlary Ion ioiitcc |3). However, thla titnultanrau* txitntiArdtucnt trtK^mU a instructive ptoefss which rnn trautt In the negative growth rale And io In etching instead of drpositlon of thin film*. To keep this ptocng under control we arc developing A new equipment for in-aitii monitoring of film thicknesses bawd on the interference of the reflected light, In this method the Intensity of the monotlmminllc light reflected from A tliin film-milnUate lystvrn \n ine.v • Ired. Depending on the phase shift between the light reflected on the Air-thin film And thin film-iulntrate Interface of this system the light Intensity Is changing periodically ai a function of the thin film thicknes* bttwrrn It* minitnutn and maximum values. Knowing Index of refraction of the growing film we run determine from IhU rtieMiirernent the film thickness [l]. To test the ability of this technique to monitor A layer thickness development, we have carried out a *erle* of relevant cx-aitti experiment*. The Ilc-Ne !«.•"• r lieam was aimed Uhdcr the Angle of Incidence of 5" «t « ml^trale with s thin film (e.g. polymcthyl- melacrylate) ami after its reflection detected by it lilicon pholodiodc detector. The growth of thin films w«s simulated by moving samples with nonhomogeneous thin film thickness via • step motor driven manipulator across the laser beam. Contrary to homogeneous thin films, the Intensity dependence related to the nonhotnogeneous thin films showed up the significant periodic behaviour. The thickness profiles obtained from profilonietric and el- lipsomctric measurcmenti performed on the corresponding samples were in the agreement with tho«e gained by the interference meuurtnwnU. The ability of the method to monitor thickness development of thin films in time wu thus confirmed. Supposing the index of rrfrtctkm «ftd irArmiiy «?f thr light rrSexIni from {fir clean ratatrate (th^ brsinninf of the

97 WOUKflllOlVDO PHYSICS deposition) Are known, th« method makes It possible (o provide absolute values of Ilia flltn thlcknea* during deposition, At th" p?mjr>o«. H)m* *!»*• eotnpact, modular equipment for inbtiHotUtg tlie lliln fllin lllltkness development in being dcvclopcdi ilio wiwln nystcin will l>« allncticii to tliL' fldflgfi of Hie de|ioslfion apparatus equipped witli a tvl/iJotv, To Mliiliolw the sl/o of the equipment, lli« semiconductor laser with wavelength G70 nm «» a light noiifce will be used. A |j||

Reference!) |l) SlKOLA, T» el al.i An in-niiM Sluij/ oj I'rocemtt tnkinD I'ktt on u gltiem Surface Durttt'j Ihmbardmtnt by Cl'j/Ar• Etching vt, I'olumrrifatinn, SAfit'ttl, HlntermooK, 20-2.ri March 1001. (2) KMTTL, Z.i Optin oj thin Film*, J. Wiley and Sons, Undon 107C. (3) SIKOLA, T, et a).: Dun/ ton than Dtpmilion of Thin Fitmi, 9th Int. GW, on Sur- fare Modification of Metal* by Ion Uesnu IM5, accepted for publication in Surface k Coating* Technology. [I] Y.CKVAXtOVk, L: I'hytiet of Thin Film*, Plenum Pre»«, New York, 1986.

This rcteitth hai bttn tonducltd at Iht Intlitute of Physical t-'nginttring as part oflht wealth projtel "In-tilu Inttrjtromtiric Thieknim Sttniurtintnl of Depotiltd Thin Filmi* dh bttn tupporltd hy the grant of Fac. of Mtehanieal Eng., TU, No.Ft'3505SS. WOjtKHIIOI'M 1MIYB1CH SURFACE ANALYSIS OF MATERIALS - DESIGN OF THE ATOMIC FORCE DETECTOR FOR ATOMIC FORCE MICROSCOPY

T, Slkotn, J, Spoustn, L. DlttrlcliovA, I. TAtnn*, V. Mfltejka**, 11. Knlousek, V. Lopoiir

Tilt I1'"''' "f Mechanical Eng., lint, of 1'hynlcnl I-'ng, T«li«kka 2, mC'JUtno •TUSCAN, l.ld,, LlbtiSlna tfldn U, (523 00 Hrno *"l'U, lac of Metrical L'ng., Dcpt. of Microelectronics CMolnl G3, Hrno

Key words! surface nrmlysls, A KM, HI'M

In this ittldy tlircirrllrnl annlysis of the problems related to Urn detection of Atomic hiacd. forces in scanning force microscopy (St'M\ tit* been frthrtmrrl, In principle, similarly to STM the scanning force rnlcroncope CM be opcratml both In mnbictit ulr mid In ultriililgli VAcuiirn. However) until now n nmjorlty of cotnmrrciftl •canning force tntcroicopcn were drjiignCTl for the nlmonpherlc operation only. The renron for tliflt In that the optical detection aystctn (OI)S), apptirtl preferentially In the slalc-of- thc-att mlcroticopeii, inimt be act up very precisely almott Ix-fofi" each measuring cycle to aim properly the optical beam at a tiny cantilever and position icnxitlvc detector a* well. Hence, a special technique must be chourn to perform this procedure without breaking iiltrahlgh vacuum In the analytical chamber. One of (he reasons for the frequent realignment of the ODS in the conventional contact SFM in a utiort lifetime of the cantilever due to mechanical contact of the tip with an investigated iiufftcc. Changing the cantilever is, as a rule, followed by new adjustment of the ODS. Recently a noncontact dynamic force detection mode in SPM ha* been improved (1], In thl» method, the tip Interact* with surface atoms by means of long-range attractive forces and li not In a direct contact with the surface. Thus the lifetime of the cantilever Is substan- tially increased and the alignment of the ODS need not fro performed no often. The term dynamic means the probing tip oscillates at a certain frequency, driven by an external oscillator. The dynamic force microscopy (DFM) technique belongs to nondestructive methods and Is suitable especially for surface analysis of soft, for example biological samples. Our work was focused on studying a time development of cantilever oscillations in DFM mode as a function of the lip distance from ar investigated surface. In our model the oscillations of the cantilever are described by (he equation of motion of an effective mast point oscillating with the resonant frequency corresponding to typical values of commercial cantilevers («a 10"' kHz) [2j. The amplitude of the external driving force was of the order of 10*" N. The frequency of this force wa» chosen close to the resonant frequency of the l Tlifc damping totditififit, depending strongly on the ambient pressure varied

99 oo from 4.I70 ' 10"* to 2,088 • 10"11 N«m"' «nd were determined I rum ty(>kn) values of quality factors of Ilia cantilevers In these environment [3], The Atomic forro between cantilever And (hff BiirlM* Mam* CM >klir>r>i i>*'mg tliflrmnt )»l» jiotrntMi, van det Waal* J4) Ati«l tammrd-Jofie* potentials: [5) having been preferred, Potential parsmctcri were determined (win the experimental values of the forte between the cantilever and surface |fl), The etjua- tion of motion win solved numerically by Eiilrr-Klcliiudjon method. The results obtained showed the appearance of beata In Hie oscillations during AII initial transient period, The beata were formed by superposition of the force and free oscillations of the cantilever, The frcrjiicncy of the Utter o-iclllntions It modified hy the force gradient between the cantilever fcnd surface (to-called effective resonant fre(|iiency). It menu*, tlio ctmractcr of beat) is changing when tha cantilever cornea into the Area of the higher force gradient, l.c, closer to tho mrface, 'f fie dtwer to tlio surface the cantilever 1», th« W^er i» the difference between the effective resonant frequency and that of the force oscillations, tlecau»e of damping the free ofldllntloti* of the cantilever i* decaying In time and after A certain period it remain* cntcillatlng with the frequency of the external driving force. The amplitude of this steady *tate forced oscillation* h Ihc ifnaller, the dwicr to the «urfacc the cantilever in, The change* of the uteady atatc amplitude serve in Ihc conventional I)I'M detection method* for mapping the turface corrugatloim. On the other hand, we have paid our at' tenlion to Investigation of the tr.inolent period of the onWllallonn, VVc have found that the amplitude and frequency of heat* chAnge monotonously with the cantilcwr-aurface distance, WhcrcAD the amplitude of the beats la growing almost linearly with an Increasing ilUUnce of lh« cantilever from the aamplc surface, tho frequency of the tiratu In failing exponentially with thin distance. Doth effect* are caused (>y the fuel tlut with I lie growing distance from the surface the clfeclivc resonant frequency of the caiilllcvi-t U «p|>tou hing ilt orlglfml vfilue (i.e. milnfliirnced by the aurfacc) which liea close to the chosen frequency of the force vscilla- tiona, Summarizing, the Application of the dependencies found could be potentially used as an complementary method for mapping tlie surface topography. To prove the luitability of this technique based on detection of transient atatc oscillations, simulations of the cantilever oscillations AS A response to the motion of the cantilever above a surface with the defined topography are being carried out.

References: [I] LUTIII, It et A).! Projttu in Noncontact Dynamic Font Micronopy, 3. Vac. Scl. Tcchnol. 1)12 (1091) 1673. (2] Silicon and tilieon nitride eantiltvtri, Park Scientific Instruments, Catalogue 1904 [3] ALIJIIECIIT, T. K. ct at.: Frequency Modulation Detection Viing high-Q Cantileveri, J, Appl. rhys. C9 (1991) 60S. (4) LUTIi, II.! Surfaet$ and InterfaciM of Solidi. Springer-Verlag, Berlin, 1W3, p. 429. |5) XV, I. el al.: Inlirprttation of Alomicllttolution Image* in AFM, Phyi. llev. D. 51 (1095) 10013. [Gj MARTJN, V.: AFM — Forte Mapping and Profiling, J. Appl. Phy». 61 (1087) 4723.

This rtteanh hat been conducted in the Institute of Phpieal Enginttrinj at part of the rtteanh project "Surface Analysis of Materials - Deiign of the Atomic Forte Dtteclor for Atomic Force Microscopy'' and h

100 WORKSHOP 00 rHYSlCS EXPERIMENTAL STUDY OF NO GENERATION IN ELECTRIC DISCHARGE

V. Kfflm, F, Hanltz, S. I'ckArek, J. Ilcioetikrnriz

CTU, Fiic. of Ktcctflcal Kng,, Dept, of Physics Tt-ehnlekA 2, 100 27 Vttihti 0

Key words! pollution control, non-thermal techniques, electric discharge In grui flow

Introduction- Non-thermal plasma technologies based on tlic unc of electric discharges arc characterised by the fnct that the mean electron energies arc considerably higher tlinn those of the Ambient gas, Consequentially the very reactive radical) Arc produced which CAD In turn to decompose the toxic molecules, Presented paper deal* with (tic atudy of the production of nitrogen oxides In the atmospheric pressure electric discharge in A fast moving Air How,

Experimental nppnnttus and results. The electrode system for trio study of nitrogen oxide production Is tliown In Tig, 1, It consist* from four parallel electrode* (I', 2, 2',3, 3' and <) which arc situated along the length of a rectangular channel. The primed electrodes represent the edges of razor blades, the unprimed electrodes are in the form of metallic blocks. The distance between primed and unprlmcd electrodes was 1.05mm. The velocity of the air How in the channel can be changed up to 200 m/s. The NO concentration) were measured with gas analyier OA-C0 , Madur, The typical volt-ampere characteristic* for the velocities of flowing air 163 and 193 m/s are shown in Fig. 2, Three different sets of curves correspond to the different possibilities of the electrode connection to the high voltage source and grounded electrode. The electrode 1* was in all three situations connected to the high voltage source (IIV), the electrode 2, 3 and \ were grounded. It is seen that within the range of measured velocities the VA characteristics do not show remarkable dependence on the air velocity, Figures 3 and 4 show dependence of the ratio of NO production per unit of volume of the discharge channel versus current for velocities 153 and 193in/a. It Is teen that the production of NO increase* with increasing current. From the comparison of these two figures it is also seen a weak dependence of NO production on velocity. The NO ploduction also Increase* with the number of electrode systems which Are connected in terles. From the presented results It may be concluded that for this electrode arrangement the NO production Increases lineally with current, tt Is supposed that presented electrode arrangement will be also u«ed for study of volatile hydrocarbons decomposition.

Reference!: > (1) ROSENKRANZ, J. et al.: Ettttric discharge in air flow at atmoipherie prtuurt. pp. 332-334. Proceeding) 17-th symposium on plasma physics and technology, CTU, Prague, 1995.

101 WORKSHOP 90 IMIYSICS

(2) AKI3I1BV, Y, $, cl nl,: Spatial structure of DC glow duchnrge in atmotphcrir. nir. pp. 325-320, I'roecwllngJ I. ICI'ld XXI, AIM' llulir UnlvnrsllM, Doclmm, Clcrmniiy,

(3) AKISUKV, Y. S, ct «l,i Study on DO glow dhcharge In humid air. \,\u 117-118, l'fo< ccwHngn f. ICIMG XXt, APP ftulu lf»(v««tnl, fJocfiUm, Gurti.auy, 1001 |4] NAPAHTOVJCH, A, 1'.: DO glow dlnchnrgc tuilh Jtul swg, 1093*

Fig. 2: Voll-nrnprrr

Fig. 3: CM0 -/(/)

102 WORKSHOP OS PHYSICS MATHEMATICAL MODELS OF FINITE-DIMENSIONAL QUANTUM MECHANICS

O, Clindzltnikoi

CTU, Kflc, of Mcdi, Mug,, Dcpt, of I'hyslca, TcdinlckA 4, ICO 07 f'rnlin C

Key words! quantum symmetries, quantization theory, quantum groups, representation theory Our Investigation of tnn.tlicmr)r* over thi* pliMi npnr.r - A/ x A/ real tnatrlecs, The (|iie»tlon which arisen la whether It la possible to (lnd a discrete nnnlogy of quantization via deformation of the algebra of classical obncrvablci on a continuous phone space (a* Moyal-Vey deformation) |2). Thut the comrnutntivlty is deformed ond the pnrnnictcr of this drfortimtion In clmslcnl limit goes to zero. It meant tlmt the noncom- inutntivily is of order of the parameter of deformation. In discrete CAtc there is not such deformation in apace of M x M dimensional matrices, These matrices In this case we find a (continuous) one-parameter family At of algebras of real square matrices where the corn- niutAtlvc multiplication law given by the multiplication of corresponding matrix elements, is deformed into the non-commutative ^-product multiplication Using the framework for the discrete ^-product we canlrnclcd the onc-par«irietcr tmooth deformation with specific algebraic properties. Our results were presented AS A contributions at Mill Winter school Ceomctry and I'hysics (Srnl, January 1091) and at XI1V'K Workshop on Geometry and Physics (Uialo- wicza, July 1095). It will be published in Czech. J. t'liya. [.1j. II. It WAS find out « basic calculus for construction of coherent states over both aides open onc-dimcnaional chain. We started from the q-deformation of quantum mechanics of one degree of freedom [4]. We modified difference and integrate calculus for the case, when q \* a root of unity. We defined difference operator acting on polynomial functions of general Crassmann variables x (i.e. i*1 = 0)

It modifies the differece operator for real parameter q € (-1.1) acting on functions of complex variables which is introduced [5]

103 WORKSHOP 00 __»_^_____« PHYSICS

Our definition of dllfcreiico operator lend* directly to comniutnllim relation of ry-deforitied IMscnt/crg-Weyl *lge!>r» and to q-ljyooii reAliwition of it, W« Introduced

ThiM we w« CAII rcallzd the (/-deformed Hciscnbcrg*Wcyl nlgcura «o ft operator /dgi;l»ra on polynomial function* of GriuMtfiatiti vnrlnltk'a. Referenced! |1) CIIAUZITASKOS, (I. - T01.AR, J.: ftynman path Integral and ordering rule/ on dhcrtte finite tpact, Int. J, Theorel. Pliys., 32 (1903), 517-527, (2) KLATO, M. - MCIINBIIOWITZ, A, - STKUNIIKIMER, I).! Deformation of I'ohxm Iraektli, Dtrae bracket* and application), J. Math, I'liy*. 17 (I07G), 1764'1702. |3] CHAD'/ITASKOS, 0, - TOLAIl, J.i finite-dimensional ^-product and matrit nlgtbrut Czech. J. Pliyn,, will he [lublialicd [4) MAXIMOV, V, - OD'/IJKWICZ, A.: The q-deformatinn of quantum mechanics of one degree ojfreedom J. Matli. Pliyn. 30(1995), p. 1C8I. [6] KMMYK, A, U. - V11,ENKIN, N. J.! lleprtnenlation Lie Group* and Special I'mcltons KAP, London, iWl rctearch hat been condnelcd at the thpnrlmcnl of I'lipkt of the Faculty of Aft- chonkal Engineering a» a part of the nttnrr.h prtijttl "Quantum tymmttriw Mathematical models and phy»ical applications", ani ha* kttn supported by CT If grant No. IOO'J8l5f.

tot WORKSHOP DO PHYSICS INVESTIGATION OF Ge-Si MONOCRYSTALS SUITABLE FOR SPAD CONSTRUCTION

II. VrnnU, K. Ilnrnnl, I. Mnchn, I, I'roclidzkn, I). Sopko*

CTtJ, Fnc, of Niicl, Scl. ti I'hys, Kug., Dcpt. of Holld State Engineering V HoWovlcJcncli 2, 180 00 I'rnliA 8 *CTU, Vnc, of Mechanical Kng., Dcpt, of IMiysles TwhtilckA 4,100 07 I'ralia 0

Key words: Ge-SI alloy monocrystah, optical absorption, band-gap, mole percent of Gc, photoelectric devices, resistivity

Tim Application of Si pliotodctcctors in ttir* interesting opto-clcctrorilc wavelength range from 1,3 to 1.5/im is excluded due the width o( silicon band g/ip 1.1 cV is added to the silicon. An the dependence of tin; optical abnorptlon cocfllcient on ttic Gc-Hi alloy composition ia well known |lj, wo tried to Improve til'.1 spectfal tnpom* of »ingl« plioton avnlanciiR i\'\ot\n (SPAD) by adding ntnnll amount) of Gc to Si In the hope of not lowering of tlia other electrical parameters. Boron doped single crystals of silicon of 2 inch diameter with additional 2 and 4 weight percent of germanium, rejpectivrly, were grown by the Czoctiralaki method1 at the CKD Semiconductors Ltd. McAfliircmcnt of electrical and optical pnramctra were carried out on 1 mm thick slices ground and polished on both aides to an optical aurfacc of julisfnctor flatness. For comparison samples of pure silicon with the same thicknes and surface preparation were used. llnll elfcct and resistivity measurements using Van dcr l'nuw's method gave the following results (permanent magnet 0,32 T). sample resistivity mobility (tma/Vs) type T (°C) SI+2%G 0,31 (hca,l) 0,29 (end) 210 ±3 2.11 db 3 21 ESI+4 % Ge 0,28 0,20 237 ±3 228 ± 3 20 The composition of the samples was determined by weighing in air and water, with following probable errors : Maas m±0.01 V±D.l density g±0.2g is given by (with x weight percent of germanium) g = 100/(i/fa<+(100-*)/^si, from which the composition x% (Ge) «• 532,3(p-2.328)/2,995f can be computed, where ca, = 5.32.1 g/cmJ, QSI = 2.328g/cm1, (il,o => 0.9975g/cm* at 23*C. sample meastirpd density (g/cnr1) lie weight percent CJe mole percent S1+2%G« 2.351 ± 0.001 1.7 ± 0.4 0.7 ± 0,2 Si+4 % G« 2.3S7 ± O.OCH 2,2 db 0,4 1,0 ± 0.2 The optical Iransmittancc of the samples was measured by means of type Pcrkin- Elmer spectrophototneter1, the absorption coefficient a of the samples, calculated from the

'W« are indebted to Mr. D. Mriiek, piorn. them., for pnpailnK the Ge-Si 'We are very gieattul to Dr. ), Adumec of lVi

105 WORKSHOP1)0 PHYSICS amoothcd-out reglstratcd trartsmltanco spectrum, as sticn In tliu ncroiii]i(iyliig Fig, 1, is In llin following table RMnpfft purs 81 XM%U* Sl+4%(J» ifiiiipla tiiim HI SS+4%Cto thletmtM BSM.Tfim fifi«.4|im WiJlpm W,7/7m" m,4/im «Uil.7/»n_ A runt) n (cm"'5 fi (tin"1) n (em"') X (mui) n (tnr1) n (cm"1) n (cm"') .05 13.1 13,4 l.'l,4 1.2(1 1.33 1.41 1.07 T.34 7,35 T.34 1.14 0.785 0.809 0.0(14 1.09 4.28 4.28 4.28 1,10 O.62.'J 0.601 0.004 1.10 3.34 3.44 3.K0 1,10 O.34A 0,373 0.307 1,11 2.51 3.03 2.7 1,17 o.Mt 0.20 0.178 1.12 1.89 1.01 1.04 1,18 0,11 0,18 _

,,,61 so -••- ..8l*2%0«

40 /

30 /

i 0 1 . 1 t 1 . 1 1000 1020 1W0 1080 10«O 1100 1120 1140 KM HW 1300 Wavelength (nm) Fig. 1; From the ipcctral transmitUncc tncasurcmctit follows that the absorption coefficient of Gc-Si samples is practically unchanged, the increase above 1.1 /'in is scarcely perceptible and doci not warrant an improvement of SPAD performance. According to (1 - Pig. 3], a significant spectral range extension of SPAD sensitivity could only be expected fur Gc-Si alloys with Ge contents exceeding 5 mole percent. More over the investigated samples had a far lesser Ce contents than expected, instead of nominally 2% and 4 % respectively, only 1.7% and 2.2% Gc, respectively, in reality, and thessc only weight percent. In (1] It is stated that monocrtalllne Gc-Si alloys can be gra;vn with M mm !I nn 10 mole percent of Ge, which would be highly acceptable, but it is to be feared that diodes prep red from such Uc rich crystals would have a Urge dark current and high noise figure with invcrs effect on SPAD performance. Nevertheless further investigations with higher Gc percentage should be tried.

References: (1] DRAUNSTEIN, R. - MOORE, A. R. - HERMAN, F.: Intrimie optical absorption in Gt-Si alloyi, Phy*. Rev. 109 (1958) pp. 605-710

106 PHYSICS THE FIRST MICROSTRIP GAS CHAMBER MADE IN CZECH REPUBLIC

J, UOlim*, V. Ceriiy", M. KodnV, I. Mrfclm**, S. N«inc«ck*F H. NovAk, D. Novrfkovrf, J. !»«vel, 0, Sopko, L. Stupkn*, M. Stfdrofi*, J. Stfnstny"*, L, Vyskocll*, M. VnnttkovA*

CTU, I'ac of Mechanical Eng,, Tcelnileka4, ICO 07, i'mltft C •Instituteof Physics ASCII, Na HlovnncR 2, 180 00,I'raha 8 "CTU, Pnc, of Nucl, Scl. b I'hys. Kng., IJWiovA7, 115 10,1l

Key words: microstrip gas clmmlicr, rlcriicntnry (mtticlc detection

Mlcrontrip KM rlminlirr (MSCiC) nrn pntrtillnl ilrtpctoi* for the forthcoming IIIRII lumi- nosity collider LUC id CKHN, but there also exist possibilities of the MSG'C Ap[ilicxtion in medicine, technology and other fields [1], The detector has iliown very promising fenturcit proportion^ gninn up to 10 (100, position accurncy for x-rnys and miriltiiuin Ionizing particles of the order of 30/I, rntc cnpnljility 10*iiim*'.i"1 nml low cost |2j. The biulc MSCiC consists of thin anode and c,itlio

References: |1] A, Otd. Instnm. Methods AS63 (1988) SSI [2] RD-SS Collaboration. Preprint CEtlN/DRDCffl-95, January 9, 1995.

This research has been supported by GA CR grant No. 102/93/S033 an

107 WOttKSIKH'flfi

if/r.,1*_

;.» *W

K'lt

• - -A. —

'JO '»» li'i'ji

m it*/

• **«

* 'i

* f

* i, *

Fi£ 3: WOltKHIUJP Ofl PRAGUE ELECTRON CONDUCTIVE GLASS

J. IIMim", I. Mttcfin*, U. KrKlovri, S. Neniecck**, It, Nov/lk, J. I'nvel, U. Sopko, L, Sttipkn**, M, fltMrofi", J. Sfoglny"**, M. VmiKkwvA**, S, Vyikoeil**

CTU, fte. of Mwlwnlttl I'M*., Dept. of Physics TrclmkU i, ICO 07 I'mlia 0

•CTU, Fflc. of Nuct, Scl. h Pliys, Hug,, l>pt. of Solid State Engineering fjfoliova 7,Pr*h» 2 "ASCII, ln*l. of I'liynlw, Nil Slovance 2, 180 00 I'f aim 8

Key wordit semlconductlvc: glass, electronconductlvlty, MSOC

In last ye*r» wi* tirn icfi'iwi-cl Intrtcul fur >ff of inlcrnitrl)) )$M rlmmlirtu (MS(KJ) for lunlxullng m<)Utloii, Tin? finygtmn In lnt»gr»tw| Hwlfonlfii fn»M« lo ronalmcl dctcclori bascj en MSGC willi cxcclcnl tp.\cial tesolulioti &t comp*rally low cosl. Thai is tin' tcftjMiii wfiiy MSCJG'tf, laltly pfoiliici.'d In InhorAlory «c«[(< for tfit* fcscAfcli on ctcri^ntary pAftiflcn, (jctictfslc In Induntry *nns[st of onidet of iron, uttonciutn, baryum and vanadium. In the Fiaguc QI«M 2 oxides of baryntn are rrpl«r«l by oxides of line. We have measurer) the elctrie conductivity and its temperature dependence on samples of the Prague glass. The measurement of other electric properties such as the value of mobility of charge carriers are being carried out now. For comparison, we chose a widely spread Schott Glass with commercial denotation S8900, which has been reported as suitable for application In MSGC. The volume electric resitivity of Prague glass 1 is less than one ordf higher then resistivity of S8900. The electric rrsMivity In the temperature range from - IO*C to +WC falls tpproxirnit ly by two orders but the relative change of the resistivity li within measurement error* the same for the Prague glass 1, Prague glass 1 and comparative i). in I'UYStCS

The change of composition In the l*wgn« RIM» 2 tegm ding lo Ik fragile glass 1 re»ii Ited in (IcCff/wIng the volume rcalsllvily, IVfufwiver, reduction of portion of limvy nloiiis irmkcn W f k ( l ( llU According lo th«"W fMtilU we found llie PM^IW g)«» lo be very )m>mfv(ng e «i*l«l*l fof MSOC, We tidve isUfJdJ work (J» \tt*piit\tt& lh\n Mini hy M px g itivfe of (li« Prague gl/ut». Costing liifliilntlng

•IJ1

fig. I:

7A/* Mttttth hint hrm nuppnrtid iy ff/1 C'ft jranf A'o. S02/93/S033 and AV Cll grant No. 110122

110 % 1'IIYSICB STUDY OF ELECTRICAL DISCHARGES AT PARTITION OF DIELECTRIC LAYERED AND POWDERY MATERIALS

Z. Stn/iek, I, Aubreclit, J, Koller

CTU, I'M, of Electrical Eng., Opt, of Physic* Technltka 2,1C5 27 I'raha 6

Key words; destruction of materials, partition of tutaticcn, electrical double layer, M*x- we''-Wagner pollination, election and vibration excitation, work environ-

Intended and purposeful! destruction and partition of materials belong* Indisputably among the moat Important productive and Manufacturing activities. We can Include there various methods of indilnK of mulerMs, numerous demolition works, motion of powdered Mi't Hrantilaled materials, jetting of fluid*, combustion, generation of cxhauit gases, etc, Destruction or partition of materials is mostly followed (beside* f«m!nl»ewio* effect* [2,3, 6]) by emission of elementary and microscopical electrically charged particles and by generation of electromagnetic field* and electrical discharge* [5, 8, 0). Uccatuc of quantity of destruction mechanism! and electromagnetic effects, the Individual typea of destruction and partition must be studied separately. This article deals with electrical microdischargn following in many eaten separation of contiguous dielectric materials, especially foils and fibrci. For example, this can occutc at the motion of powdery dielcetf ic materials. The chara«tf r of diwhurgni, m«ch»nl»m of their Inlclali/atioit, time cotirio and duration of the discharge current arc studied experimentally. It can be teen, that all these parameters depend on the type, shape, dimensions and physical parameters of materials and surround and atso the velocity of their separation, Haste hypothesis come from the assumption of the existence of spontaneously formal- led electrical double layers Inside materials, for example at the points with Varying physical parameter:) (density, relative permitivity, orientation of fibres, etc.). Approach of electrical double layer* after Maxwell-Wagner polarization (4| Is used in our theory In contrary to the theory in (2|, Separation of the generally layered dielectrlral materials during manipu- lation leads often to the Increase of distance «>f the local layers with positive and negative charge. This fact causes decrease of the capacity of double layer for dielectric* with high relative resistance and subsequently Increase of voltage sufficient for generation of small ipark discharge. Experimental Investigation of microd'iKharge* has been performed with help of the model processes on the strips and fibre* from different materials. The special experimental apparatus h*» been developed for the purpose of the study of the microdischarges. Voltage induced by the dijeharge current in one of the differential coil* 1* recorded and the local surface charge released during the separation Is measured directly by the elettrometric amplifier. The charged partida released from tbedfech»rg

1) Knowledgf of tlic clmrnetrr mid incclintilitrri of foritintloti of Miinll Ami ilivtcclc l 2) The p<««Il(lc Iiiflucntd of llio liivmtlijntrd dnclinrKCH on di.'soliidon mid inlettvtenamf cotnttitliiktillot) dcv)fc* And sirnil/ir itLitrutrifntn, 3) 'I'hcsit (llacliAfgcD CAM hr colnldrrrd A/l ft fnrldr of work inviroiiliiMit fur |)CU|i|x r%\H>in\ to InstAnt contact with them, We* iniisl Iticri MU myi'lf if tlil.t tnclot U (indcsirnble or even Imrrnftil. Tin's In (df rrinlrr ol/Jrct of tlilx ('.tft

|1) K1TTBL, C: (?uoJ rfo/i/»% pfi/njfr/i Mir*, Aca-l<-ml«, i'rnlm l!)Hf», t'2) SODOMKA, L: A/tr/innoliirninf.iccni'e tt jrjl jutuiitt, AKMIUIIIIK, I'tulm 1985 (3| TJ1JFMSBN, J'. A, - MKYKIU K- • JIKJNICKB, (J,i Gnmtllngm hr 'Mlmhrmtr,

Akfldrmln Vrrl«gf Ilrrlin I9fi7 |4) AUTIJAUEH, X - SEDOVIC, J, - ADAMKC, V,! Manly a itoUeit, Alfa, Hrntislnva 10CJ |6) Sl'EftKOV, 0.1'.: Pttikochimia Innifa, HCJ(/, Ml^k I9T8 (C) VOJUCKU, S. S,: h'ur, Uoidnl chtiuh, SNTL, I'MH* 19SI [7] SJMOKDA, J. - STAUOIJA, J,: SMitki iltktfinn v primytU, SNTI,, I'mlm 1959 |8j K«ACJK, J. - SESTAK, l». - AUHttKCHT. L: '/AkUuty klwkU a ktanlovt fyiiky plmmttlu, AendrtnU, I'rnlis 1974

(9| LLEWELLYN-JONES. K,: The Stow dmhargt, Methucn, London tOCO (IO| LO'/ANSKIJ, E. D. - F1KSOV, O. H.: Tfrn/d i»H Alorn««t,

ThU rtitdfth ha* btr.n conduct/J at the Department of I'hytiet of CTU Vmha.

112 WORKSHOP PO _ I'HYDICS FORMING OF THE PLASMOIDS IN THE HIGH CURRENT DISCHARGES AT ATMOSPHERIC PRESSURE

P. Kubel, J. Krnv/irlk, L. Knrplnskl*, M. I'nducli*, K. Tomnszewikl*

CTU, Fac. of Electrical Kng., Dcpt. of I'liynicn TechnlckA 2, ICO 27 l'raha fl 'Institute of I'IAAMA t'tiyslca And Inset Mlcrofusloti, t)cpt, of Diagnostics i'.O.Hox #.00-908 Warsaw, Poland

Key word*! /?-plneli, plasm* optic diagnostics, spherical plasmolda

In the discharge between (wo electrodes with cylindrical symmetry, tlie magnetic energy of the current l» transformed Into kindle energy due to Ampere force, wlicn a high current (mure than lUOkA) flow* through plasma with n diameter lower than I cm. Electron* And Ions fttii decelerated to lli(< tixls, wliuiv a. hl^li energy elifciinel form* (#-plncli fffect). During the peak of comptnwion, higti rnrrgy riecUotin, lorn nml X-rny pul»r» ate produced, whewe pltysic«l origin Una not been determined, fn liic conical electrode configuration, » second phase of acceleration is observed when tlie pinched plajmn near the lop of the electrode* ii thrown (due to the Imrrcl form of the electric und magnetic field) into the central Men, where » spherical structure with high energy density Is created. A» WM t>tit>IWIicd III (1). the kinetic enrrgy, olilalnrtl In both pha-nes of acceleration, is not dissipated. It l> conacrved in the rnagnctohydrodynaiidc vortexes in the central spherical structure. In argon plasma, when the diichargc l» operated under A high pressure of (2-80) kl'a, the compact pln.imoid with strong magnetic confinement, diameter of 3 mm and life-time of 1 /u is generated. In paper [2] the results of the same geometry configuration arc described for higher energy 30kJ, voltage 180kV, current maximum of 100 k A and A quarter period of discharge of 9/i», under atmospheric pressure. Under these conditions the dense structures with diameter of 5mm And life-time of G/i« were observed. The results presented In this paper have similar energy conditions as discharge in the lightning channel. The discharge was studied In the regime of capacitor bank energy of (100 -250) Id, when the current reached maximum value of (2(XM00)kA during 50 /is after the breakdown. The current channel WM formed between the conical electrodes with 120* top, 4 cm apart, connected by copper fiber with diameter of 70 (im In free atmoipherc. the diagnostic system consists from the Quadra four frame high speed electrooptlcal camera and the automatic Image capturing And processing system. The objective of the Quadra camera Imaged the whole electrode gap through the 596nm interference filter. The time delay between two *Mp* varied from 10/ii to 40fit and the time exposition of lOna enabled to imagine thr development of Dremstrahlung emission from plasma with density higher than 10" m~3. The pi&smoid* were observed in 67 A of discharges but in 30% wrre formed on the top of the detlloJe Hid only [u 37% lite pluhioid w« located in the centre without touch of

113 WORKSHOP 90 PHYSICS

the electrode. In 33% the pinch elfcct V»M not observed Ami the dininclcr of llio current channel wiw (2-3)cm during whole discharge evolution. The observed plnniiiolinriiA enn (>•: cxptiuiitit d(i(i to the liigtt magnetic rtiefxy bumjded lit Die *|ilicfi'. Thin niAgiictic cnvrgy wni prohnhly Irnnnfrrrd front kinetic energy by the current induced during collltloli of both opposite slfcnms of plwrrifl. Tfic conditions fur sclforgAnl«At!mi promt in pU«nu with r.-«i«llviiy mnnt Ue fulfil ddfin^ (he cotli*ion, when (nlemivc riullntlon flows tlic cliflcitlc energy out from the pl/uirm (,l).

Fig. I; Shot Na <)2/!2 QMAiIro c/xwrn picture 40/is after breakdown

We mpposc tlint tn future the experiments of the regime with ihnrp increiuc of current In the discharge may be Investigated. deference*: (1) KUHES, P. el alt Stable ftruelurr in the Interrupted %-pinch il'AiK Tffttm»ctions on I'lusma Science, Vol. 22 (19f)l), Nu. 5, p, 980-988 (2J KtilKS, P. et al,: Dittgnottict ojConical l-'kttrodcZ'pinch Diitharge at High I'nsturt. Vtoc. Planma'95, W»r»»w 1095, Vol. 1. p. 03-00. |3] SATO, T. H •).: Scenario oj StlJ*Orgnniiaeion. All1 Conf, Proc. 345, ICPP1994, p. 335-350.

Thin natarch hn* bun tomtudnl at the Department oj Physics as part of the nttarch prajtet "Study oj Stable Struclurts in Magnetic l'inehr.$" anil hat bun supported by GACR grant No. $02/95-0118*.

!U WORKSHOP 06 PHYSICS TWO STEPS IN THE GAS-PUFF Z-PINCH

I1, KiilieS, J. Krnviirlk, A, K. Kal&tek*, M. P/ulucli**, K.

CTU, Fnc, of ICIectriail Rug., Dept. of Physics TcrlmlrkA 2, ICO 27 I'rnlia 0 •Institute of I'IIMIJI/I IMiysIcft, Academy of Sciences, Short Uvlng I'liwinn Depl. Za Slovnnkou 3,182 00 t'rnlm 8 "Institute of I'IIUIIIA Physics mid L/urr Mlerufuslon, Depl, of Diagnostics I'.O.lJox 40,00-008 Warsaw, I'olnml

Key word*', Z>)>itith, jiUsmsvtt'mfciKMlkii, ItwtsilMlHiRs, nolf-oigMii/nlloii

The explanation of mechanism of fast electrons nml ions beams, X-ray pulses nnd hot- spot* generation nnd the |jiv™tijr,atlcm nnd niiiiiiiinliziitloii of the injlnbllitlni development is tlio principal tiuk of tlip ^•pincli dHrlmrgn ntucly. The nim of till* study li the elective nsag« of tlifcac1 plit'lioliWlitt fot faut ulocliuiix, ions uud X-my Ki-iii'ii>tloli itlul fusion iniil/.nlloii. Tho (if the gM-pulf //-|iiiuli nnd Drnnn t'lnntnn I'ucim rcfirnrrh liy Srlilirrcn find X-ray j were piifilislicd in |l-3j. In this paper the evolution of neon Implosion of low energy discharge (4kJ, dOkV, 150kA, quarter period t,l/n) WM studied due to X-ray, Scliticrcn nnd Qimilro cnmcia dlagnosticD. The geometry and liclicnt structure of plnchrd eolninn, two atepa of pinching and X-ray emission have been olisctved. The hypothesis of axinl component of magnetic field generation, licllcnl shape of magnetic lines and reltwc of rnngncllc energy during second step of pinched column are di.icuitned. On the baxe of the complex diagnostics it is possihle to formulate next conclusions, 'Hie pinched plimnit colrtimi lornis conncqtiantly, firsl near tVic niiodc anil next due to zipper effect in the parts nearer to cathode, lleginning of this pinching correlates with beginning of the soft X-ray emission and maximum of rmission relates to the maxlinnt tength of column between both electrodes. Hoth emission and length Increase during (100-150) ns. On the surface of the column the 2-.I nodes are presented in the distance of (.p>-10)mm. Their contour i* somewhere symmetrical ring like and somewhere helical like tube twisting the imaginary column. The Implosion of this locality progresses more (lowly than the implosion of the neck. The plasmit column obtains probably more complex form. The contour, which we observe, is influenced by visualization method. The most narrow column with radius of (0.3-0.7)mm has very high plasma density (greater than S x 10" rn'3 and 2-3 nodes in distance of (5-10) rnm. Countour of the nodes is helical like turn with the pitch of 2 mm. These shapes of the column were observed in the pictures with low sensitivity of the Quadro earn- ers. In the pictures with higher sensitivity the radius of the plasma column was (0.7-1.5) mm with typie&l necks and node* with radial symmetry. The Sf lilieren method* Imagine the column with electron density 10" m"1. lleie the local contour, ViVc a tube with diameter 2 mm turns the inner Imaginary column with diameter of (3-t)mm.

115 WORKSHOP 00 PHYSICS

During Ilia Mubscqucrit evolution of the pinched column tlio (tcftlnlegrMlfMis In some locality of neck* starts (10-150)(in ftfifr soft X-ray iimxlniiitn, when Uic necking and In- terruption of till* locality I* observed. Till* conversion is followed by radial explosion of nelgfibmring noflm* and iwiwwlng •>( p)»»w* ikmHy in tlm rentr* of this node, This trAtmfoririAllon confirm* I IK; Idea of AX)A) acceleration of plmmm from the neck to ttio node, During (2-5) rift Wore Interruption of the column, llin short (4-fi)nj pulse of harder X-ray WAS registered, Further, the; spatial correlation between centre of nodes And liot spots WAD corilirnied. In Schlleren pictures the Itilcrtstltig tciidcticy (if helicnl tiiljc-s conversion into toroldtil and iplicricAl structured Arc observed. Tliero in a ^notion «l;oiit origin of liellcnl forms, secondary pinching ftnd rmlinl ejection of plwinn. One punniblo cxplorntlon in given due to liypothcni* of genef Atlon of axial lung- nctlc field during plwina Itiiplonion, wlini tlio plAatriA colufnn Is formed (unnlogy ot alpliA effect mid tnAgnetic dynamo [I]), The reuniting magnetic, linen in pinguid column IIAVC not Azimuthal but IICIICAI form. The liclkity in the m-ck* in lower tliAii the licllcity In the nodca, TJic higher axial magnetic field In the node* c*n frmilt the »|ower comptcstlon Arid later forming of cqullibtltiin in tills pnrt of th« column. During the jikirrm Imploaion the part of kinetic energy transform* into energy of frozen and comprised nxinl inagnetli: field. The second pi/ielilng can be connected with tratinfomintlon of axial rnaguctic line* into nzliniitlial (alio alpha, effect), The Intermediate e<|iiililjrliim in column i.t broken and the instability begins to develop. The column Is pinched, the plasma Is ejected In axial direction to the ends of the neck and tlm interruption ofpbuirnacollumn l« observed, Simult. neoiuty in nodes the Azliiiiilhftl component of magnetic field transforms Into axlnl, tlir pitch of hclicily dectcaiicii wA i\\n ttuWiA eruption ot ptiunm it obtcivei). In tilt* centre of nodes tlie plasma density increased. The next other layers ot imploding plasma could turn due to helical magnetic field into helical form of current tubes during plasma column forming, So the development of instabilities of the plasma column may be limited due to weak external axial magnetic field,

References: [I] TAKASUOI, K. rl al.i Macroscopic Behavior and X-rny lladintion Characteristic* of SHOTGUN Z-pinch I'lmmn, All'Conf. I'roc. 299, London 19M, pp. 251-257. [2) CHOI, I*, et al.: Dynamics of Hot Spot) Formation in a Dtme Plasma Focua Optical and X-ray Observation AIP Conf. Proe. 209, London 1993, pp 288-298. (3| CHOI, I', et al.s Dynamics of a Medium Energy I'ltumn Facut. AIP Conf, I'roc. 209, London 1993, pp299-307. [i] KIlAUSE, P. - HADLER, K. II.: hltan •Fitld Magndoht/drodynamics Dynamo Theory, Alcadcmic-Verlag, Merlin 1980.

This rtstarch hat been conducted at the Department of Phyaict at part of tht retearch projtdt "Study of Stable Structure) in Magnetic /'inr/i'i imri Complex Investigation of Z-pinch Discharge" and hat been supported by GACIl pants No. 8Q2-95-0178 and SOS- 83-1023.

116 WORKSHOP 00 PHYSICS Z-PINCH EQUILIBRIUM WITH NON ZERO HELICITY

J», Kulluinck, M. Urbnn

CTU, FAC. of Electrical Erig., Dcpt. of Physics Tcclinlcka 2, ICO 27 I'faha 0

Key wortln: i-plncli, plasma c(|ullibrluin p i« a ptiuniA column with current dc fully along t-tixh. The corresponding Mslmutlial magnetic field CAUSCS the Lorcntas force opposite to the pressure gradient. In the equilibrium (Ucnncllc equilibrium) the 2-pinth is unstable, especially due to Uie tn « 0 and m a I instability rnodc«. From the experiments it is obvious that the i-plncli lifetime Is much longer than predicted from the Mill) theory. An azirmitliAl component of the current density (axial component of the magnetic field) Is generally supponcd to be tlio stabilizing factor, Equilibrium of the j-pinch in the presence of both Axial And azlirmthal current densities will be discussed in this paper. Equilibrium pressure-radius dependence will be derived for power dependence of current dcimitles, Let us consider A planma column In cylindrical coordinates {r,if>, i) •• sec Fig. 1.

Fig. li Z-pindi cylindrical geometry

Let us denote

rq z-pinch radius, / «-pincli length, /, total axial current, /^ total azimuthal current, 7,(r) total axial current in the interval (0, r), J+(r) total Azimuthal current In the Interval (ro-r, r0), j,[r) axial current density, j+(r) azimuthal current density Assuming power dependence 0)

117 WORKSHOP 00 PHYSICS

m The magnetic M'l rnn );<• d«rlvm| from tjw Am)>nrn Uw, The ri/iiHJbrlpmi iKjii/ilion

J x JJ =. - fjrod /> (3) can bd rewritten with the licl[> of Maxwell cr|!lflll«i rot Ii a J//'o In eylimlrlenl coordinates

yio r dr This equation represents AH ordinal differential cqtiatln for the hydrostatic pressure. In Addition with the boundary condition ;>(r0) a 0 the nolutloii lit 1 * I - 0 lhn (I - r wlicrc Ho « (0)

Results for «»2 (ilcnncttc equilibrium) ftl"l w:vi-nil Values of l> Mo piuavnlvd Iti the following figure:

p/rv.1

Fig. 2: Current densities Fig. 3: Equilibrium hydrostatic pressures

References; Jl) KULHANEK, P. - UltDAN, M,: Z-l'inch Equilibrium with Aiimnthnl Current, Czech Journal of Physics 19%. In press.

This research has bten conducted at the Department of t'hytics as part of the research project "Study of Stable Structures in Magnetic Pinches and Complex Investigation of Z-pinch Duchargt" and has keen supported by GAClt grants No. 202-95-0178 and 202- 93-1023.

118 WORKSHOP OO PHYSICS NEUTRON DIFFRACTION STUDY OF THE Y-Ca-Ba-Cu-0 SYSTEM

M. Dlouhrf, 8. Vrntlslnv, Z. Jlrrik*, J. IlcjlmCiiek*, K. KnfJek*

CTU, Fnc, of NticL Scl. U Pliyi. Etig., Dcpt, of Solid SUto Engineering V HoldlovlckAeli 2, 180 00 I'raha 8 •Institute of 1'hyslcs, Czech Acad. Scl, N/i Slovancc 2,180 00 I'MIIA 8

Key words! neutron diffraction, superconductivity, Kiclvcld Analysis, oxygen content

Among pof»iblc cntlonic substitution)) in tlic Yll&jCujOy superconductor, tl'c partial replacement ol Ysv by Cn1*' liadWcn found lobccspcclallylnlcrcstlngsincollicliclcrovalcnt substitution changes the hole concentration and ncccasarilly Influences the charge transfer between conducting layers. Early studies have shown that such replacement was limited to about 25 % of yttrium and critical temperature for the superconductivity In the orthorliom- bic samplns (y

References: [1] MANTH1RAM, A. - LEE, S, J. - GOODENOUGH, J. 13.: J.Sotid State Chtm. 73 (1388) 278 [2| JIIlAK,'/. - IIEJTMANEK, J. - POLLERT, E. - VASEK, P.: Physika C 150 (1988) 750

119 WORKSHOP 90 I'HVSICS

•trticlura ortliorlioniliic 1 otlhothamlik 11 tijtr/igtmnl 1 tcclrngonnl II 1/ 0.88-0.70 0,70-O.CU 0X0-0,40 0.10-0,00 (i [inn] 0,3830 0,3849 0,3859 0.IJ859 l> [iun| 0.3873 0.386-1 0.3859 0,3flW c [rim] 1,100-1,108 1,109-1.171 1,171-1,17-1 I.174-1.18O HIKJ 80 0G 25 - a |/

Tub. 3: Four gtriicturnl region* In tlio Yo.«C(i«.jl)(ijC'ii3O» tystcni

Thii rctearclt han bun conducted at tlte Department of Solid State Engineering as part oflhc research project "Neulronogrtiphk Structure and Tciture Aniitytia" and him not bun supported by CTU grant,

120 WOUKSIIOIMIO PHYSICS

ENERGY TRANSFER IN Hg2Cl2 CRYSTALS

7- Uryknnr, V. lVkn, Z. 1'otiVek, P. Jirouiok

CTU, I'ac, of Nucl, Sci. k 1'hys, ftiig,, Oept, of Solid State Knginecring V IloleSovifkach 2,180 00 l'raha 8

Key words! rncrcurniii chloride, luminescence, emission spectrum

In HgjCI] crystals broad luminescence bands excited with UV light havn been studied in the spectral range 0.8-2,25 oV. Tlie tncftsureiiienlfi have been performed on as-grown crystal* and on crystals previously exposed to UV light at I IT, The emission spectra consist of nix band* peaking at 0.S2, 1.06, 1.2.J, 1,39, 1.51, and l,72eV with l'WHM of 0,21-0,33oV. Their intensities depend conspicuously on tlic concentration of ttic photochemical producti induced by irradiation of the crystals At I IT. It in concluded tliAt the infrvrcd luminescence of HgjClj originates from crystal defects, especially that complexes (UgChjDrj.,)" and (UgCljllr^.,)'" arc responsible for these emissions. A mudul for tho luiupuriituru quenching of luminescence iuid unorgy transfer bi'lwceii two

121 WOKKSilOr

IB 3.44 W

««... .«..«.,, r^ - i...... 1 ..... «... • NXi )....T... I .-l.100i i 200 250 300 Temporals o (K) Fig. I: Temperature dependence of the LSI cV HgjC'lj etnls.wf* hmii of the m-grown crystals, I'aratnetetn are Uie bjtellthif photon energies. A solid curve rrprrswil* Urn relation of C'j. (l)ltlll)»l*Xt,

At higher lempMaluK* we »uppow, the emission U* -» H (l.72cV) i# exriterl only by energy transfer from the Jevr, M, The energy transfer from level M to II centres (M-« 0') occurs with the activation energy Ei, where fVj Is an energy difference betwi.-n the bolto«n of the M Hate In the potential dingram and the cromover point between the M »late and li* excited itate. The activation energy of luminescence fiticnthing: for the It* excited itate U denoted as /-'j. Then (he pfobability of the ra'Dative tratisUion considering iuperposition of LSI and 1.72«V emissiorn will br. p, « p,A + ltpfg +1) exp(-£i/)iftT) and the probability of ihe nonradialive transitions: p, a p,u+A e«p(-/;,/*flT)+C exp(-i?j/*sT), where p,p Is the radiative transition probability of the 1,72eV emission (U* ~* U), k C I rharactcrises lh« contribution of l.7UeV emissiott band to the luminescence observed at l.6i eV, II and C »te constant! independent of temperature. The temperature dependence of the luminescence intensity observed at LSI eV, I.e. In fact * superposition of emissions peaking at 1.5I and I.73«V. ean be then expressed M

M tJ where d u {p,A + p,a)f{p,A + h>t>) > ° HP W) * t(P'*t(P + /^^ 4 *^B) , and A'/ii n$t*tth AM it in to*i*tU4 at Iht Dtfttlmtnl efSelU Suit Enp-nttrinf

Z, Tomlflk, 1, Michn, S, I'oipflll*, I). Sopko**

CTU, Vne. of Nuil, Scl, k I'liyii, Eng,t Depl, of Solid State Engineering V HoleSovlfkAeli 2,180 0(J Pratm S •CTU, I'M- of Nutl. Scl. fe I'liyi. Eng., Depl. of J'hyslcs II/chuvA 7, 11A 111 t'rnliA I "CTU, Fae. of Mechanical Eng., Dept, of I'hyslcs Technkka 4,166 071'Mhafi

Key words) sefiilinsulatlg semiconductor, deep level), I'ICTS method, SEM voltage eon- tfd.it method

Gallium Arsenide Sthotlky delexlw* made of gcmliflsiilatlng material Ate supposed to work with nearly 100% dntmtirm rflirkney «nd to withstand tnilhlhm l^vrlx i/f> to 7 • ID14 neulrotu per em', In spite of tlie*e very sutlifoctury propcrtlw, the ch«fgc-coilcctlon ell)- clcncy wns fuund to be lower and till* lu fovrl* Are mponaible for t)i« depletion layer (e.i, the region of high electric field Intermlty) bring stnnllrr than rxpretrd, and for the trapping of the fraction of charge carrier* created within thl.i region. Therefore, we have tried lo find the Appropriate method* which allow lo oWrve directly (he actual potential profile and lo measure the deep level concentration. The electric properties of aotidntate OaAt detectori arc generally controlled by the in- trimic compensation rnerhanittn and mainly by the denni ty of trap* NT< present In the bulk. Namely, the collection efficiency of Ib-i «.ii»rge crratnl by ionizing particles and consequently the detector signal to noise ratio depend very tlrongly on the electrical field distribution UHK* the detector structure. The electric field depends oil the apace charge density arising from Ionized ilullow duiiort and acceptors, free carrier! concentration, and from the Ionized deep level* jVf acting M traps. H I* nec««a»y lo know the concentration of deep levels ttr to " lo calculate the potential distribution by means of the f'oiason equation. In cane of undopetl GaAs the EL2 (the nature deep donors) play the main rote. These level* are situated Just below the Fermi level In intrlsic CaAi and are ionized when their energies itay above the Fermi level due to the effect of the potential, and of the temperature. The sensitive f'hotolndiiced Current Transient Spectroscopy (PICTS) technique enables to determine both the type and concentration of deep levels, and it appears very tuitable for determining the deep levels in OaAs where they acl as traps. The PICTS method is based on observing the temperature dependence of the semiconductor current relaxation after the tight excitation hw been interrupted. The basic values which are measured are the sample temperature, the electric current, and the time. At we were Interested mainly in disclosing the deep IcveU coocefitrttiofl, the simpler so-called double-gate method wa* Ifitroduccd. To fill the traps by electrons, the GaAs laser with wavrlenth A m 8.>lnm was used. After the ioU-ifUplloo of ttie UlumJiulloa * ilow tWji>A*e of tuttufi. due to A tfxvaully •lim>jl»l«l release of carriers from traps ran be oWrved. In PICTS the time dependence of delrapping

123 W0ltK3H0l'gtf is of (lie main Interest. Tlie b/u!c question Is under what conditions the plow drereaM part of the decay curve cart be approximated by a simple exponential law, and how tliti putt Is re(»lc( lo ttvc pataiTi«ttf(( 6f (6e tfSfW. Ifl Otff C&K? W hltYlf M*'l I))* *)*M)«»1 approximation applied In I'lCTS (1|, e.l. ictf lipping ami linear recombination were neglected, the flCTS data obtained In the temperature range dotn 90 to iOQK *rre »n*lytril in * ntmuUtd way by finding I lie tm|"r*tuic Tm totttmionSng (a « peak of the I'ICT.S cunrn tot various vuliien fif the time gate at a constant temperature change vcloeity(Zj. To Investigate the potential profiles In the detector milirnlttrd to blat voltage V&, the method of SEM potential contraat WM nwd. the ttictliod I* t;aned on the fact that the yield of sreoftdary cictttoiu depends on the value of the surface local potential. The beam of IdkeV primary electron* h K*MWI) over t cleaved nitfatc of » detector ntfiitlute which Is connected to an external blw V«, The emitted wcojxlaty election* MO then uttelttaled by a hlgft voltage agalriit • iclntillator. The (ignal from It is converted Into a tlgnal suitable for imaging etectfoftltl. The aamplcs used for the Invcutigatlon were prepared In the lame way M the detector structure [.1]. The«! structures were then cleaved lircmw « sittlnee frtcpnteil in this way cxSbit* a low iutfiK« cunrenlratloi) of abaorhed Impurities and negligible nuilacv conduc- tance. The results were compared with the corresponding I-V curves and with the values of detection efficiency obtained ou the name structure* before thcif cleaving, It follow* from the comparison that only a Material sullklcntly pure (wU)inul (It linpiirities) Is tiseful M a tmtrce material for preparing detectors, the main advantage of the potential cotitftutt method i» i\uA H «IW# Ut oti~T*e lh* mind yjirnlki dktrlbulloii In the delator »lru1, 15 Sept, 1087 (3) TOMIAK, Z. ct al.: Ihlh G*Ai rndklion dtttrhrt. CTU Seminar Workshop 05, frague, p. (A. This rtitirth AIM kttn tondtclcd at iht Dtpattmtnl of Solid State Engtnitrirtj, CTV Prague a* part of Iht meanh pmjtcl 'Semiconductor Vttetlert* and hat Itcn mpporteJ iy CTU grant No.

121 AN EQUIPMENT FOR CHECKING OF CARRIER LIFETIME DISTRIBUTION IN PNP STRUCTURES

J. KoZfJok, V. UendA*

CTU, VAC. of Klecttlcal Eiig., Dcpt, of ttteclrotechiiology TeciiiilckA 2, WO 27 I'ffllm 6

Key words! homogeneity of large-area wafers, CArrier lifetftue distrlljiitloti

All characteristics of bipolar power devices, I.e. diodrs, transistors, thyristors depend on the tnle of recombination of excess carriers which Is usually evaluated by excess carrier lifetime. Bipolar devices of the name geometry but with different ex ecus carrier lifetimes have dilferent on-itAtc and dynamic chAractcrinlIc*. Therefore, A large-Area device with nonunlfurm carrier lifetime dlitribution over the area of the device can be considered an A set of parallel connected device* with different excess carrier lifetime. In such A «A«« tin; tm-nUU: cum-ul deutlly will differ In different partial devlu* And eoim't|ii«nt[y, power dissipation and Junction temperature will AIMJ IIO Inliotnogrnomly distributed over tho area of tfic device. For determination of carrier lifetime distribution in VHP ttructutea a simple cptlc&l rnctliod wu used (1,1\, The b/nlc principle of the operation la demonstrated In Pig. I. A constant voltage is Applied to the wafer of sample using point contact system And one side of the wafer li locally IrradiAted by GAA» \,VA). Assuming that light is fully Absorbed in the P-lypc layer and that injection efficiency of 1'N Junction is very low, we can cxprc** current Increment! for both polaritlen of voltage as:

Alt " where U the light intensity coming on the surface of the wafer, II is rcflcxivity of the dirfftce, D is A constant depending on the efficiency of electron-bole pairs generation snd the surface recombination rate, ftp is An effective transport factor trough the P base, 0s Is on effective transport factor trough N base. Ily deviding them! two ^nations we receive the expression far /?/v. And knowing the diffusion coefficient of holes Dp and the distance u>« between the Junction Ji and the boundary of the apace legion of the reverse bia*ed junction J\ it is possible to calculate the carrier lifetime in the N-ba*e. fa » Mil&h

A piece of equipment for large device homogeneity measurement by described method has born developed and realised. The b*»ic concept of the device suppose the device of a circular form as is usually used in the case of power silicon devices and the equipment h»J teen adopted fat meuorement cf carrier lifetime distribution in polar coordinates. That

125 WORKSHOP 86 PHYSICS tncnn* the device In turning mid Ilia LED in moving in »tep» from t)io edge to the mitral <>f the device, Tha device to he mcMiircd lit fastened to the revolving holder And tlie d.c. nilJiuUlile voltngo \» Applied And

Ng. 1.' I'rinclple of operation Rg, 2: The map of 0n distrilnitlon

|l) HKNDA, V. ct A!.: A limph optical tnrthod of in-prnetu chicking of GTO uniformity. I'riK. EI'K'OJ Conf., Vol. 2, p. 69,1093. |2] IJKNDA, V.i tn-procf$* chtcking of tarritr lifetime distribution in hijh-powrr drvictt. I'roc. MIEL'05 Conf., Vol. 1, p. 401, 1999. Thit rtttanh hat been conducted al Ihe Department of Eltclratechnology at pnrt of the rtttatth project "llteombination in potter lemtconduetor devicea' and hat bten tupported by CTVsnnt No. 103/91/136.1,

I2C WORKSHOP 00 PHYSICS 2-D PARTICLE SIMULATION OF THE GLOW DISCHARGE

Mi Z66eU, H, I'cknYek, J> Hosenkrnnz

C'I'U, Vnc, of Klcctrlcal Mng., Dcpt, of I»liy»lc» Teclinlcka 2, ICG 27 Praha 0

Key wordu plasma display, glow discharge, numerical simulation, PIC

Presented model Allows two-dimensional numerical ilmulallon of the glow discharge by the Partlclc-ln-Ccll (PIC) method for the system of electrodes with defined potential, PIC algorithms were used since fiftieth first of all for the solutions of tdo onc-dirncnsional models, later on with the development of the fast direct methods for the solutions of the Polisun's equation they were used for multi-dimcnaional models. The detailed description of I'lC methods is given id III. PIC method including collisions of particles is described In |2|. The PIC method consists from repeated calculation in two steps, In the first step we Integrate equations of motion for charged particles (approximately 1000 particles) for a short Inntant of time. Form ncling on thn particles deponili on the distribution of the. electric field w'.iidi is & function of the charged pit tides distribution. In the second step the Poissoti's equation is solved for the now positions of particles. KlctlrosUtic field is approximated by the values of potential in the points of the grid, the charge densities in the points of grid can be obtained frotn the positions of particles in each cell of the grid by so called weighting at the grid points. Integration of equations ol motion, moving particles

Weighting Weighting

Integration ol Hold equation on grid

Fig. 1: Flowchart

For the efficient solution of the Poisson's equation we use the Fast Fourier Transforma- tion (FFT). Before eAth iticccctlinginttgtation of the equations £>/motion simitar weighting of the electric field is done in the grid points into the point which represents positions of the

127 WORKSHOP 86 PHYSICS pntlklcn, Thti* we Mil find thu force ra|iilrml for future integration of equations of motion. Tim (low rlmtt of tlio PIC method U iliuwn In Fig. 1. My repeating the calculations wo enn obtain tin? tlinc development of pliiMim, or even pitamn fli/ir/ir.lrrUtlcd At stationary iitate. 1'IC method* Involves position!) of charged particles an n source of clixtric field iw well M velocities of charged particle* iw A nuurcd of ni»giu)tk field, In llic unwmlerf model ll WM supposed tlint for collcctlvL' intrrnction of particle;! the most important role Is plnycd by llic electric field, Mngnotlc field WAS neglected, Using Mania Carlo method the Ionising collisions of electron wltli nciitrnl ntoms were nlnmlntcd.

Fig. 2: Kxaniplc of the solution of clcctricl field by FFT method

On till! contrary to the ntnndnrd IMC Algorithm cither only the region with defined potential of the electrode*, using FFT Algorithm for the calculation of the clrctroitntlc field, or A region with n VAriaMe. po' inl when taking into Account outside electric circuit Is considered. The FFT nlgoritl. ..i.-ful cnty for the calculation of the electric field on the hue of defined clmrjr.c density And for periodic boarder conditions. The example of the calculated electric field between two electrodes IJ uliown in Fig, '2. For this calculation the square grid 32 x 32 KIU used. This paper dealt with the study of the p!a*ma displays which i.t carried out at the Department of Physics of FEE CTU. 1'rotenled model is an improvement of model which WJU presented in [3], In that model collective interactions of charged particles were neglected, Numerical timulation using PIC method allows us not only to determine working or breakdown voltage of the planrna display but also optimisation of its electric parameters.

Reference*: (1) IIIIIDSALL, C. K,: Parlick-in-Ctll Chargcd-f'arlkte Simulation*, Ph* Monte Carlo Collithm With Ncutrla Atom», PIC-MCCTrans, on Pla«m» Science, Vol, 19, No. 2, April 1991 (2) IHIIDSAI.L, C. K,: I'humn physicB via computer $imulation New York: McGraw-Hill, 1089 (3) HOSENKKANZ, J. - PEKAllEK, S. - ZACEK, M.: Numtrical noddling of the turfact glow discharge. ESCAMI'ING 9J, Noordwijkcrhoul, NelhcrUnds, August 2.1-26, 1991

This mcarth ha* been conducltd at the Department of Physics of FEE CTU

123 Section 3

CHEMISTRY

NEXT PAQE(S) left BLANK WORKSHOP 00 CHEMI3THY CHARACTERIZATION OF CONSTITUENTS OF COMPOSITE MATERIALS

55. Slmek, n, Vespnlcc*

Faculty of Chemistry, TU Hrno, U«pt. of Environmental Chemistry and Technology

VeslnfskA 2:iO(C:)7 00 Ilrno 'Institute of Annlyticnl Chemistry, Vcvcfi07,61M2Urno

Key word*: electrokinctlc phenomena, inverted chroma'ography, surface analysis, active centres, silicate*

Effective development and utilization of new technical mntcrinls require an information on surface <| inlity of raw-materials, eg, data on reactivity, sorption ability, quantity And character of Ai-tlvc centres, There arc number of spcctroscopic methods supplying information on qualitative and quantitative composition of several alornar layer of surface. The data however, do no*. Inform on the type and activity of surfacu active centres in different conditions, This technique* arc not able to «. information about physico-chemical phenomena in the '.olid-liquid interface. Investigation of this phenomena is necessary to understand of re&cl ivily of Industrialy important solid matctiala e.g. silicates ceramics, organic and inorganic pi lyincr materials. The basis foi development the method fulfilling the above given requirements is offered by knowledge from the basic research of analytical chromntography, Experimental arrangement and mcthodohgy of liquid chromatography in its invcrscd mode, make possible to investigate properti's of surface of solid phase on the basis of different chromatographlc behaviour of sp'cucd test solutes. It is possible to determine extremely small differences in inter'.vlion of solutes with surface centres, which is accounted for the efficiency of chro- mato^raphy. The interaction depend on the amount of activity of reaction centres. One of the method for measurement of this one is chrornatographic titration, A powerful 1 tool for the characterization of solid surfaces is investigation of interface charge equilibria. An important factor and a source for one seems to be zcta-potcntial measurement frequently used for the characterization of the polar solid materials. The only simple way how to obtain zeta-potential is e.g. clcctrophoresis method. Such A method may be applied only for diluted suspension. At for the application those conditions arc far from the real situation in industrial mixtures. Measurements of streaming current generated in the chromatographic method, if the selected liquid is flowing through the dense bed of a grained solid, give a real data for study of charge equilibrium. Zeta potential is received from the data obtained in such manner. The aim of first stage of the grant project was construe" tion of the experimental set-up for clcctrokinetic routine measurements in chromatographic arrangement. The result is a modified comcrcial chromatographic equipment with modified inlet and outlet of usual chromatographic colomn. This equipment allow to carry out both the chromatograpohic experiments in the invcrsed modes and the simple simultaneous measurement of streaming current as well. Special attantion was payed to selection of outlet

131 WORKSHOP oo mmmiw filtcfa. Five of different materials were tented to obtain appropriate result*. Tlio special clirortifttograplilc software wu tested for data processing,

References: |1) OHALYKH, A. E, - KOLOMIETS, h, N. - I.AKIONOV, 0. 0. - VINOGKADOVA, N. I.t [nvttUgalion of Solid Surfaces hy High-Performance Liquid Chromalography, Journal of Chromatography, £02,121-120, 1002, (2| VESPALEC, R, - NECA, J, - SlMEK, 'L\ Measurement of Steaming Current and Cal- culation ofZtta Potential for titdi of Wide-Diiptnhn MUroparlUulate Solid) Interact' ing with Water, Colloids and Surf/vcen, A: I'liynkochcinlcnl and Engineering Aspects, 92,147-157,1934, (3) TALMNO, D. - DIMNDSTETll, J.! Ciinktr-Fnt Conerttti tlaied on Alkali-Activated Slag. I'rogrcsa In Cement and Concrete, ADI Uooks, New Delhi, 1002.

Thin retiarch has betn conducted at the Department of Environmental Chemistry and Technology of TU Brno as part of the Ttteatxh project "Characlertenlion of ConiHtutntt of Composite Materials" and lias teen supported by TU grant No. 650070/95$

132 WORKSHOP DO CllttMlSTKV THE STUDY OF PHOTOCATALYTIC DECOMPOSITION OF SURFACTANTS IN WATER SOLUTION

M. Vosely", J. Tou*fn*

Technical University Ilrno, Faculty of Chemistry, Dcpt, of Conaumcr Chemistry Vcslafska 230,037 00 llrno *Maasryk Unlvenity, Fac, of Sciences, Dcpt. of fnorganic Chemistry Kotlafska2,01137Hrno

Key words: photochemistry, pliotocatalysis, titanium dioxide, surfactant

In 1072, Kujlshlnia and Honda discovered the photocatalytic splitting of water on titanium dioxide electrodes. This event marked the beginning of a new area in heterogeneous photocatalysls. Since then, research efforts in understanding the fundamental processes and in enhancing the pliotocatalytic efficiency of titanium dioxide have como from extensive research performed by chemists, physicists and clicrnicfil engineers. Such studies arc often related to energy renewal and energy storage. In recent years, applications to environmental cleanup have )MXII one of tlie taunt active arc** in heterogeneous photocatalysi*. Heterogeneous pliotocatalysis is an excitant method for decomposition of mnny organic micro pollutants in aqueous medium on the surfaces of semiconductor powders. Many kinds of semiconductor powders such as TiOj, 'ZnO, WOj, CdS, FCJOJ, SnO2 and othcra have been used ta photocatalysts for the photodegtadatton of org/wiea by many investigator*. The surfactants, which arc used in large amounts in industrial and domestic applications are one of the sources of water pollution. The removal of surfactants from the water can be done by two ways: biological and chemical, especially by pliotocatalytic way. The characteristic of biodegradation arc the following:

1, it occurs by the action of bacteria, 2, it is slow (weeks or months), 3. its selective with poor results for some surfactants, 4. the degradation may only be partial, 6. the aromatic moiety Is difficult to degrade.

Photocatalytic degradation has the following characteristics:

1. it occurs with TiOj catalysts under UV light illumination (for example by solar exposure), 2. it is fast (hours or days), 3. it is non-selective, 4. degradation is complete to COj and HiO, 5. the aromatic moiety is degraded more easily than an alkyl chain.

133 WORKSHOP 00 CHEMlSTltY

Only tiUtiiuin dioxide were used in our laboratory, because of Its Mgli Activity, electrochemical stability In aqueous lncdluAlid possibility to form Immobilised particles by «o]-^»'J process. Tlio photocnUlytlc experimental set was built. Tlic Immcrnion Y/c\) photwh™i«»l reactor wan completed by pump tot continuous stirring nf tlic reliction nimpciiiilon Arid by measuring vessel with pll-mctcf Add cofiductomctcr. Tlio photocatalytlc dogradftllomi of Botue tion-iotiic mirfactflnts were curried out. Tlio reaction products were fttmlyicd by IR (ipectroacopy and mass spectroncopy. tlefcrcnecR: |1] FUJ18II1MA, A, - HONDA, K.! Nature, 1972, 37, p. 2.18. |2) SW1SI1ER, II, V,t Surfactant Htoilcgrudalion Marcel Dckfccr, New York, IV10. |3) ]'EM7//BTTI, E, - MINKIIO, C. - MAUItlNO, V.i Adv. Colloid [nltrfact Set., 1992, CO, p. 307. |4) SHERRARD, K. B. - MARRIOTT, 1'. J. - McCORMtCK, M. I: Anal. Chern., 1934, CO, p. 3304.

This research has been conducted at the Department oj Connumtr Chtmintry as part oj the research project "The Study oj I'holnattulylic Dtciiiniionition oj Surfactants in Water Solution" and has been supported by TIJ grunt No. H/95.

131 \

WORKSHOP 00 CHEMISTRY NON-CONVENTIONAL APPLICATION OF LOW TEMPERATURE PHYSICAL PLASMA IN CHEMISTRY AND CHEMICAL TECHNOLOGY

L. Lapifk, D. MlkulMkovA, t. Lnpcfk, Jr., J, Mntoiiick*, I. MftSck*

Faculty of Chemistry, TU IJruo, Dcpt. of Physical Chemistry VcslarskA 230, 037 00 llrno 'Faculty of Chemistry, TU Drno, Dcpt. of Environmental Chemistry and Technology Vcslafskft 230, 037 00 Drno

Key words! low temperature physical plasma, rnacroinolcculcs, biopolymcr contlngs, surface modification, adhesion

There were studied the tranafromntloiu of planar nincroniok'ciilar materials by low temperature physical plasma. As a starting material* subjected to the action of different types of plfisman wero used: poly(v!nyl chloride) (PVC), carboxymctliylcellulose (CMC) (Hercules), hydroxyctliylcclluloso (IIKC) (Ar|iinton), polypropylene (PP) and thin layer of poplar wood. As the pl&ama source, the discharge techniques were used: corona, silent and high frc<|tieiicy Inductively coupled discharges, The basic parniuctcrit of tlie latter plasmas aro mentioned. It has been found that dominating reactions seems to Lei

• physical evaporation of thin adsorbed gas layers from surface of studied materials, • under the presence of air or oxygen, surface oxidative degradation via free radicals generated from peroxides and liydropcroxidcs produced in n system as a first step of the transformation, • vigorous degradation in the inncrt atmosphere (Nj, He) connected with branching and network forming.

Material surfaces were studied by ATR and Specular Reflection FT-M, UV-V1S and contact angle measurement methods. On the basis of kinetics of swelling the values of diffusion coefficient were determined nil well as the mean value of internal pressure in the swollen surface layer. The corona treatment on air of all examined polymers leads to the Increase of tensile strength and to decrease of internal pressure as & result of decreasing scgmcntal mobility of polymeric chains. On the surface of studied materials also the non-regular etching was observed leading, especially in the case of biopolymcrs, to the creation of bcardcd-likc surface structures resulted from the partial hydrolysis of saccharidie (polysaccharidcs) or hemisaccharidic (wood) parts of the matter. There was also recognized very interesting effect of plasma treatment on the contact angle and glass temperature of PVC. This effect it also connected with increase of the m WORKSHOP oo_ CHHMISTHV polarity of tho turtnccs mining from deliydroclilorntlon nnd /iiimwilvooxldntlon (vU pnraxUk puthw/iy) of vlnylclilorldc inommierlc units.

References) [1] LAPClK, L. - PELIKAN, V. - CEPIVW, M,J I'twtorhrmtral Vrnw, Alfn, JJfAtJ- •UVA, 1980. {2] MI'GlK, L-MIKULA!3KOVA,U.- LAPClK, Jr., L -MASliK.l.! LowTcmperature I'lntma Polymer 't'rannformnlion. Part I. An Introduction, Junriml of Polymer Mate- Halt, to lio tuibmlttcd. (3) I,AI'ClK, L.: PUuma ChtmMry an it Tool for Polymer Trantformaiion, CIHA-CIEICIY Ilcsctttdi Center, UJW«I, SwitstcrUnd, Sc|itcml»cr 15, 1990, Invited lecture, Thin rtitanh Ann bun conducted at the Department of Pliynicnl Chemistry mid Dt- parlmenl of Knvlronmtnlal ChtmMry ami Technology of TV lima n» purl of the retearch project "Non-Conventional Application of Low Temperature Physical Plwwiu in ChtmUlry and Chemical Technology" \) TU grant No, 65UI)b9/95,

13G WMMMH' 9« EXPERIMENTAL EQUIPMENT FOR CHEMICAL APPLICATION OF THERMAL PLASMA

J, Gregor, f. Jakubov/(( V. Kfldlec, J< Senk

Institute of Sp«e. El, Engineering »»d Quality, PKKCS, Tetliflleal U«ivcr*Ily of flrtio, Ho!ctetliw»2,6l2fi

Key wortlti thermal plamria, are, plasnialrou, reactor

Application* of thermal plasma in chemical technologies Involve the high-temperature processing of material* with the aim to thange their ittucture and propertle* and also the dentructloti of ecologically harmful and lo*le tuinUnte* of organic origin. The core of the technologies using plasma processing i» heating the carrier ga/i In arc heater (plMmatron) and mining it with the utibstanre to he proemwd. The energy transfered by the carrier gM to the lutMtance \* tonsutned for \U reprocessing or for It* dissociation In tlie CAM of Uixic nubiilftiKcii di'!iltij(:l(oii. To ifivcalin.ili' tuclt ()foct'HR('» ilia experimental c(|ulpiiit:iil con

I - UK ibBMUiiaa fnxluttt ipxlmM Ukjji| ofl

IJ-KMMK> I1 • filumlf

I37 WORKSHOP sc cmmmw

The main part of tlic experimental device Is tlie ptiunutrufi with utepwlse extended an> ode which Is Very suitable for heating of varioim gases to the temperature of a few thousands of Kelvins. The main geometric pAfamcConi of f>Iasfiia.tfGfi h&ve teen estimated, from the system of energy and continuity equation and tho seinlcmplrlenl relation for tbo arc voltage, using the giv

Reference*! [1) COUFAL, 0. - OUEGOK, J. - IIIIAOOVSKV, M. - SKNK, J. - TEt'LV, M.s 'Etptr- tmtntal Eij»ipmtnl for Tntir S«t»l Dtttructinn Uninj Vlanma I'nctulng". Vtoe. of 12th Int. Symp. on Plasma Chemistry. Vol. II., p. 819 8.'M, Univ. of Minnesota, Minneapolis, USA August 1995. (2) GREGOn, J. - JAKUHOVA, I. - KADLEC, V.- KOLAftSKt, J. • SENK, J.: "Work- ing thnntltriititi of the Etptrimenlal Plmmttlron" Int. School-Seminar on Electric Are Plasma in Technology Prctaturs, Rook uf Alnlratls p. COG], Minsk, 1995. |3J COUFAL, O. - DHESSLEII, M. - GHEGOIt, J. - SENK, J. • TEPI.V, J.: • Toluint Dt- cornpotilion in Atjon l*>v-Timptrahrt Vta*mt* Journal of High Temperature Chem- ical ProccH, 4 (1995), p. 7-21. l/ni*. Pierre et Ma/'e Curie, Paris, Vtanct, 1995. \\) ADAMEC, L. - DARTLOVA, M, - COUFAL, O. - TEPLf, J.: TAtrmn» Dttompoii- lion of Orgtnle Stbtlantu" Procrrdings of this Workshop. TtiU rutarch ku Ittn conindtd «t Me Diptrtmint e} Spteial titttrieid Knjinttrinj tni Quality, FEECS Tlflirno u m part of the rttfttk prvjtrl "Untonttnlional Appliealicn of LiK0*T*mftrml*n PUtm* in ike Chimlttry and Chtmkal Ttthnotopt** and hat iten npporttd hy TU Brno f«nr JV». FVS50069. WOKKSHOI'JW OJIEMISTltY MEASURING AND CONTROL SYSTEM OF PLASMA REACTOR

O- Snlyk, P. Ilcnei*, P. Pivoftlcn*

TU Ilrno, F«e, of Chemistry, VmUMcA 2:10,6.17 00 Drno 'TU limn, Kite, of t'.lrdf, l-*ti^. nnd Cotriji. Science, Dent, of Automatic Control And lintrmiirriUtlon 2, 012 CO llrno

Key word*! plasm* tr.iu.iot, plasm* treatment, lignite, control of realtor

i'l/intim treatment of solids \» A modern method of the Improvement of surface properties (I] and volume properties in (iw of small particles [2|, Powder material (like grounded lignite) U tre/iled In «lr |>l«»rn* for oxygen mdirAU bonding, wnter evaporation, obtaining of poroin atructure «tid surface extending [3j. I'lasifia reactor for treatment of powder materials was built. It Is 1)M«I on tf, dis' tbturr ('l.bMUt) In nltnoiiplierlc |irc»fiure. The principle of th« renctor with lu control mid t unit) iion Fig. i,

ftrng

l r'tctMfl

Fig. I: I'liMma rr«tor

139 WORKSHOPS CHEMISTRY

The central putt of the reactor li tlio discharge pipe with coaxial graphite electrode, where tlii discharge burn). Tim powder la doted through « feeding screw Into the itilxcr, where It In dispersed Into s bearing and reactive gas, this mixture la transported Into the rjjj*Wg»f t))*ri It )»«KI)«I and transported Into thrro tuned cyclone separators and divided to three fraction*. The treated powder }» distributed according to particle tizc and the rent U exhausted, The control of the reactor consists of following devices: The doaer and giu (low Is act up of Intended composition of reactive dispersion. The air (tow (up to 600 l/rnln) Is Adjusted by Ik bypass And measured with a calibrated I'itot'i pipe And A differential pressure gAugc. The tl. power wu computed Itom the temperature difference between Input And output cooling wilier measured by t'tlOO rcalslor sensors In piping And Its flow rate (up to2O0/mln). The flowtnctcr Is turbine typ« with optical scanning and gives the pulsing output ilgnal, Afterwardi the temperature of output g

[)) LAl'ClK, L. - LAPClK, L, Jr. - SALYK, O.i Ditpotymtr ShUriaU for Spuitl Ap- ptitathn. Workshop D5, CTU-TU l'raha, 1695,1't. I, p. 123. |2) SAI.YK, 0. - LAPClK, L. - VESELY, M. - LAI'ClK, L., it,; SouhrnnA tpriva o vyvoji ntkonttnlnleh aptikaci jihomoravikfch ligniti; V. ZprttoviniJihomonvik^ch ligniti tie v]/iokojnk\'tn(nim tyboji. Oponovana vyzkumnA zprava, VUT tlrno, 1995, str. 1-23. |3] LAPCIK, L. - LAPClK, L, Jr. - SALYK, O.i Studium pHpravy, ttrvktury a vlattnottt malcriili pro tptti&M aplikaet. Oponovnn* tptiv* gruitu Atfl/03 VUT tlrno, 1003. [i] PIVORKA, P. - SLADECEK, L.! Simulate dynamitkych tyiUmi. Automatizacc, 3, lWl.itr. G6-G0. [5] P1VORKA, P.: Ritiy PI, I'D a P1D ngulitory. Automatlzace, 12,1994, itr, 355-359. (6j riVOSKA, P.i ffttimnov/rcfutdtory, Atitomtthiue, 2, 1995, itr. 39-43. [7] DOHAL, V. - KUDALCIK, M. - P1VONKA, P.: Software Tool for Dttign of Adaptive Controller*. Workshop 95, CTU-TU Praha 1095, Pt. I., pp. 16I-1G2. |8] PIVONKA, P.i Modelling, Adaptive, ffturo and Fitity Control of Coat Powtr Plants. IFAC Symponium on Control of Power Plant! and Power System, Cancun, Mexico December 1995 (6 pagea).

This nitanh ha» httfi eoniuelti al iht Department of Automatic Control and In- itnimtntation and Faculty of Chtmittry at part of tht rtieareh projtct "Control System of Plasma Rtador" and hat tten lupported hy TV Brno grant No. FU 4500(9.

140 WORKSHOP 06 GHEMISTRV QUANTUM CHEMICAL STUDY OF SMALL ORGANIC MOLECULES

8. Bklendk, M. Vcsetf

Fatuity of Chemistry, TU Unto, Drpt of f'Jiysicnt Chemistry VcslafakAZnO.CIITOOIIrrio

Key wordsi Ab Itiltio, SCF, Ml'2, IK, KAIIIAII, Quantum Chemistry Tlic go/il of our work la in ab inltto study of conformation* Arid Interpretation of Ill/Hainan spectra of nrnn.ll organic molecule*, Tlic molecules under atmly were following: ll,NCIt=C(CN),, ClfjNIICfUC(CN)i, (ClIjJjNCttaCICN),, (3-0,0) ClljOCn=C(CN)i, (3-'lY 8, 11*12] where K=ll,Cllj. We carried out an ab initio SCF calculations to find optimal geometries of all possible conformed, HuzinagA OZI' basis net WM employed. Tlic SCI' optimized geometries were checked on nonnegative vibrationa! modes by vlbrallonAl AnAlyals, And zero point viliratlonal energies were calculntccl. To Improve Mm Accuracy of ab inllio energies, MI'2 CAleulationa were performed for All eotiformcrs At the SCF optimized geometric*. Tlic molecule* under itudy arc Intensively used in the organic synthesis and the Intensive theoretical study of t!ia pliy«!r«l and chemical properties of tlieac compounds h

References: [I] SKLENAK, S. - BISKUPIC, S. - GATIAL, A.: Ab Initio Study of 4-AziJobutine. J. Mol. Struct. (T1IEOCHEM),336,1993, 75. Ml WORKSHOP 00 CHEMISTRY

(2| OATfAL, A, - SKLENAK, 9, - KLAKHOB, I', ct *l,i the Infrared and Unman Spttira, Gonfnrmallan* and Ab Inltlo C'/ileuliilloiig of J-Aililotiut-l-yiie, J, Mol, Struct., !M(J, 1095, Ha, (31 SKLENAK, ft, - HISKUWC, & - dMUh, A.; Stmkmplrlcnl Stu.li/ of Mclhtuy -and (mt)SubnUluUd Amlna-Mtthyhnc-EthyUdcne I'ropanedinilritc), Act* Ciiimtca Kung.ir- icn - MODELS IN CHKMWTKY, Ifi |.«-«. |4) SKLKNAK, 3. - MSKUI'IC, S. - CJATIAL, A.! Ab Inlth Study of Mtthnty and (un)Suhilllultd AminO'Sltthylcnc-t-Jtliylidtne I'ropantdinitrilt*. 'theotellen G'Mfiiiea Actn, tiibmittcd. [fij OATIAI;, A,- SKLKNAK, 8, - MII-ATA, V, ct nl.: The VibmthnntSptttru, Conforma- tion* and Ab Inllio Calculation of Aminointlhyhnt-l'ropantdMtrik ami tin N-mttht/l Dtrlvallvts, Striictiirnl Chemistry, ncctpled, [0] GATIAL, A, - SKLKNAK, S, - MILATA, V, ct nl.i The VlhratUmal Sptctra, Con- formation and Ab Initlo Culcvttitloti.i of Aminometliyknc-propancdinilritc and lit N' methyl Derivative*. XXIInd Euruprnn CVmgrcis on Molecular Spcctfoscojiy (EVC- MOS), September 11-10, 191)1, ton, KHO, [7| OATIAL, A- -SKLKNAK, S, - KLAKFIOK, I'.tl«!.: the VihratiannlSpectra Including Mnlrii lialaiion. Conformation* and Ab Inilia Calculation* of ^Alidobul'l-int. XXII- ml Europe/in Congrcm on Molrculnr Hpeclroscoiiy (KUCMOS), Spptrnilicf 11-1G, 11)01, EMCJI, PRO. [Hj (!AT!AI, A. - SKLKNAK, S, - M1LATA, V. ct «l.i Tint Vibrntional and NMlt Sprctrn, Conformation* and Ab Inilin CnlfuhMnnn nf l-AinlnotlhylitlcHr-propuncditiilrllt and itiN'tnclhyl Derivative*, 10 III Sjirflwopic Confrrrnro, June M-16, 11)05,

[9| OATIAL, A. - SKLENAK, S. - MILATA, V, cl «l.i Vrowdiny* of the XXIt-nd A'u- ropcan Congrem on Molecular Spttlrotrcpy: "tlit Vibratinnal Sptctra, Conformation! andAb tnilio Calculation* of ** ,>• •ntlliylr.nc-propnntdinitrile and it* N-melhyl derivative**, p. £88. GwlUchnh IJt. - iicr Cti'mikcr, 1901. [10] GATIAL, A. - SKLENAK, S. - KLAEDOB, f». ct a).: I'ncerding* ofthf SXII-nd Eu- roptnn Congrts* on Molecular Sprtlrvntopy: "The Vibrational Spectra Including Ma- trix Isolation, Conformations and Ab lnilio Calculation* of j-Aitdobul'hint'1, p. 338. GweUgcIiaft DctiticJicr Chernihrr, 1991. ill) GAT1AL, A. - SKLENAK, S, - MILATA, V. ct *l.: Proceeding* of the 10 th Spec trofcopic Conftrtnct: "The Vibrational and NMlt Spectra, Conformation* and Ab Ini- tio Calculation* of t-AminoethyUdtnc-prapancdinHrilt and il» N-methyl Dtrivativet". Sprctrttscoplc Sotinly of Jiin M. Mftfcl, 19M. (12) GATIAL, A. - SKLENAK, S. - HISKUI'lC, S. ct »l.: The V&mtionnl Spcclra, Con- formation* and Ab Initio Calculation* of l-Aininoethylidtne-propanedinilrile and it* S'mtlhyt Dtrhative*. Sprctfocliimicn Ada A, to he inilitnitlcd.

This rttearth ha* been conducted at the Vacuity of ChtmMry of TV llrno as part of the ntearth project "Quantum Cliemieal Conformalional Study of Small Molecule* and a Thtorcticat Interpretation of III Spectra of Theie Molecvlrjt" and ha* been supported by TV grant No. II 19/91

M2 WORKSHOP % CHEMISTRY AB INITIO CALCULATIONS WITH ELECTRON CORRELATION

9. Qklen/lk, t, Lnpclk( Jr.

Faculty of Chemistry, 'tU Hrno, Department of 1'hynical Chemistry VcnlnFnkA 230, 637 00 Ilrno

Key wordii electron correlation, Mollcr-I'lessct, quantum chemistry, moleculnr propertied, ab Initlo

'I'lw! goal of our work Arc ab inilio chemical calculations with »ti Inclusion of correlation energy. An Inclusion of electron correlation in wave function 1« necessary for a good description of molecular properties. Our work WAX alined to thu conformatlona! study and theoretical Interpretation of IK/IUmnn spectra of Delected molecules. We used ab initlo calculations mainly at the MI'2 level of theory, because of the size of our molecular systems. Huzlnaga TZ2I' basis set wan employed. The molecules under study were HI follow*: hydrazotc acid, methyl azide, ethyl azide, 3*Azldopropincm azldoacctonltrilc, azido^-butlnortt nllyazlds, 2-azidO'l,3-butfidicne (1-flJ and 4-azIdobut'I-laa [i\. Alt initio calculation* of organic alkyl azides showed tliat some of them can exist as *rveral rotational l«wr», IH/Raman upcdroscopy revealed that the ctliyl azidc nample consisted tm two conformers - gauche and antl, tlieorctlcnl ab inUlo MP2 results were In excellent accord with experimental observations, The calculated (MI'2/MI'2+K0,vib) and the measured energy differences arc 1.15/0.59 and 0.5G0.1 kJ/rnolc respectively, the gnu die conformcr being the more stAblc one, Ifl/Raman spectroscopy and electron diffraction data suggested that tho sAtnpleH of following Azides contain only one conformcr: 3-azidopropinc (gauche), azidoacctonitrilc (gauche), a7.ido-2-butlnc (gauche), 2-azido-l,3-l)iitAdicne (trans •yn). Ab inilio MI'2 Tl'lV calculations of mentioned «!

143 WORKSHOP 90 CHEMISTRY give two strong bunda In III spectra In mentioned wnvcmmibnr fiinga And right Assignment Is not»" straightforward. Two Azldo group dcfotniAllon vltirntiona cm he due to alight bend of tliia group divided on bending In'plaw? (bip) /wl h*n>Y>»?t «nt-of-pUn

|l] SKIENAK, S, - GAT1AL, A, - HI.SKUI'lC, H.t Ab Inlth Study of Small Oruank Aiitles. J. I'liya. Chcjii., aubmittcd, [2) SKLENAK, 9. - HISKUt'IC, S, - OAT1AL, A.! Ab Inilio Study and Conformation*! Analysis of Small Organic Atides, MotccuUr Quantum Mcchnnkn: Methods and Appli- cation*, An Intcrnntioiifll Conference in Memory (>f Sntrnirl Kmnciii Hoys And In Honour of Isaiah Slnvitt, St C/»tliiiriiic'» Collcdge mid I)rpArttncnt of Clicinistry, University of CAinbridgc, September 3-7, 1995. {.'»] SKLKNAK, S. - IHSKUI'IC, S. - OATIAL, A.! Pivettdfng» of the Molecular Quan- tum Mtchtintm: Method* and Applications, An Inlrrnnlionnl Conference in Memory of Samutl Francis Boys and in Honour of liaiah Shatill, "Alt Inilio Study and Con- formnttonal Amtluth of Small Organic Atldes", p. DI03. University of Cambridge, 1905. (4) OATIAL, A. - SKLENAK, S. - DiSKUI'lC, S.: The Vibrathnal Spectra, Conforma- tions and Ab Inilio Calculations of 4'Azldokut-l-j/ne. 'To be submitted. (5| PELIKAN, P. - LAI'ClK, Jr., C. - MAHIAN1OVA, D.! Charge Distribution in Model Organic Polymers, Clicm. P*pem, 43, 1089, 229.

This rtscarch has been coniudtii at the Faculty of Chemistry of TU Brno as part of the research projett "Ab Inilio Chemical Calculations of Molecular Properties with an Inclusion of Electron Comlation" and has been supported by TU grant No. 330/0081/95

111 WORKSHOP 06 CHEMISTRY COMPUTATIONAL MODELING OF CHEMICAL REACTIONS IN A METAL-Si SYSTEM WITH PHASE CHANGE

H, Ocritf, P. Pflkryl*, V. ClinV*

CTU, Faculty of Civil Engineering, Department of Physic* TliAkurova 7, ICO 20 I'raha fl 'Mathematical Institute, Czech Academy of Science* ?/ilnA 25, 115 67 I'rnU 1 '•Institute of Physics, Czech Academy of Sciences CuWnrntdtfc 10, 102 00 t'raha 0

Key wordai phanc change, chemical reactions, silicldcs, cxcinicr laser Following the classical theory of solid-itatc reactions (I) and the previous experimental work on metal sllidftat (*«!, e.g., the nxtennivn review [2j), wn mippodo that tlm chemical reactions in both the solid state and liquid mctnt-Si system Arc driven by diffusion effects. Thus, a cheuilcal reaction can «Urt when mrlai atoms dl/TuM! into the Si bulk ami/or Si atoms dilTine into the metal layer. Since it i» not yet known exactly how the reaction between metals and Si runs when the system Is irradiated by a Inner, we choose an empirical treatment and assume that only a part of diffusing atoms can be trapped in the lattice of the majority compound to form a silicidc, whereas the remaining atoms diffuse further. Therefore, the diffusion equations for metal and Si arc written in the form

where C is the concentration in mol/m3, DM, An arc the diffusion coefficients of metal in Si and Si In metal, resp., the subscripts M, Si denote metal and silicon, rcsp,, <7M• <7si arc determined by the amount of the minority Atoms available at the particular point x. The time development of the concentration of a silicidc can be then schematically described by

2%^ = 2fCB, (2) where w denotes the minority clement at a given place, to = M or Si, C'u is the concentration of the minority atoms, qv is also related to the minority atoms, and z is cither t or y, I.e., the number of metal or Si atoms in the silicidc, whichever of these is the minority clement. The type of reaction which actually runs in a M-Si system depends on temperature primarily. Therefore, tlie diffusion equations (1) have to be solved together with the heat conduction equation. For a simplified case of a laser irradiated system with chemical reactions the heat conduction equation reads

145 WORKSHOP 00 CHEMISTRY wlicro p lit llio density, c ttio specific heat, K tho thermal conductivity, 8 the heat-source term originating from the absorption of the Inner energy (SMJ [3], fur example), A// is the reaction liuftt (In J/mol and negative for tho formation of ullieldcti). llimlcully, we have |>cet> working in tlic eoliiUUtc conditions, until now, In genera!, A chemically reacting system enn undergo phiuo clmnges, too, Alno here, wo nolvo n coupled licAt and mass transfer problem, naturally with different i/mtorial parameters, and with A moving boundary between tlic solid and the liquid plumes wliicli enn change their composition duo to the diffusion effects; thus, it kinetic plume diagram is necessary to solve this problem, Since the segregation coefficients generally Increase fnst with the velocity of the phase change process, wo enn simplify the phase change problem mid nmmw Hint thero U no concentration Jump At the phase interfaces. CoiiBeqiiently, it I) sulflciciit only to forrnulnte the bnlnncc of internal energy on the interface, In the corriputationnl experiments, wo simulated the chemical reactions in a Ni-Si system induced by XcCI excimer laser (308 ntn, 28 m FW11M pulse length), with Hie Initial thickness of tlie Ni layer A € [200nm, 5/IJD), the Si bulk tliickiiea.i i)a8 /nn, and the energy density of the laser pulse E e [0,8 Jem"1, 1.5 Jem"']. First, wo tested the numerical accuracy and stability of our algorithm, We varied the length of finite elements In the particular plumes atid iiiAteriftls and th« maximum allowable time step, wo also tested tho influence of the numerical pnrnmctorn of the Iteration procedure, namely the relaxation factor and the user tolerance. In Ihu nocoud purl of our calculations we aimulatcd the influence of energy density I! of the lancr pulse for A' e [0.8 Jem"3, 1.6 Jcrn"3], which are the values above the melting threshold of tlic system. We Iwvc chasm A => !0) run and H = 8/ini M the values of the Initial thicknesses of the Nl and Si layers, I'innlly, we studied the influence of thn initial thickness A of the Ni layer for A e (200nm, 5/»n| with E => 1.0 Jem"1. Laser synthesis of silicidc* has not been experimentally mventigatcd frequently in the past, first papers appeared just recently [4,5]. Therefore, we did not have innny opportunities to compare our results with the real experiments. However, we note that our computational results qualitatively Agree quite well with the preliminary experimental results of [4]; for In- stance, the whole 600 nm layer of Ni has fully reacted after otic laser pulse in our calculations as well as in tho experiments.

References: [1] SCIIMALZIUED, II: Solid State Reactions, 2nd fvdition, Vcrlxg G'hcmic, VVcinlieirn 1981. [2] von KANEL, II.: Growth and Charaeitriialion of Epitaxial Ni and Co Silicidee, Mat. Sci. Hep. 8,193(1990). [3] CERNY, it. - PfUKRYL, P.: A Computational Model of Laser-Induced Milling and Solidification with Density Change, Comput. I'liys. Commun, 73, 179 (1092). [\] CERNY, II. - PRIKRYL, P. ct al.: Kinetics of M Silicidet Synthetis with Excimtr Laser I'ultet Studied by TIM, Mat. Res. Soc. Symp. l'roc. 320, 415 (1994). (5J COMRIE, C. M. - HOFFMAN, V.: Lestr-lndntd Epitaiial CoSij Formation, UtX. Res. SOC. Symp. Pro*. 320, 421 (1994). Thin research ha* been conducted at Iht Department of Physics of the Faculty of Civil Engineering and at The Academy of Sciences of the Czech Republic, and has been supported b]/ the grant of the Grant Agency of the Czech Republic No. S0S/93/S383.

146 WORKSHOP 1)0 G'HKMIHTItV PROPERTIES AND RADIATION INFLUENCE OF NiO-Bi,O, MIXED CATALYSTS

V. Mdfkn, M. I'ospfgll, II. Sllbcr

CTU, Fac. of Nucl, Sci, k Phys. ling,, Dcpt, of Nuclear Clicmmtry Hr<;liovn7, 110 19 Praha 1

Key words) catalytic activity, Ionizing radiation, hydrogen peroxide decomposition

'I'M* contribution describes some rewilts of systematic research of the selected two- component mixed oxides from the point of view of physico-chemical nnd catalytic properties and their influencing by ionizing radiation. Attention iian been devoted in last three years to the systems containing DijO.i oxide in interaction with CuO or NiO oxides. Tlic chemical reactivity tested by hydrogen reduction of both above mentioned scries of catalysts i.e. CuO-HijO) and NiO-USjOj mixed systems wan investigated and the results obtained in 1993-1094 have been presented and published earlier [I, 2|. A morn detail study concerning the catalytic behaviour of CuO-HijOa mixed system was performed in last year (3) no that In 1095 our (!(fbrt waa concent rated on the investigation of NiO-UljOa catalysts and radiation Influencing of their catalytic activity. Fifteen samples of various composition containing 0-10(1 wt.% of onr, component were prepared by calcination (3 h at C00°C) of simultaneously precipitated (10°C), washed and dried (1GO°C) carbonates of both metals, The basic carbonates were obtained from starting nitrate notations (1 M) using the solution of sodium carbonate (2M). Prior to use, part of each sample was irradiated in air or in water, with ""Co gnmma rays using a dose of 1 MGy. Some irradiated and original samples were, prior their use, heat treated in air for 5-120 minutes at different temperatures in the range of G0-200°C, The catalytic activity of all samples WBJI tested by the decomposition of the aqueous solution of hydrogen peroxide (1.2 M) at different temperatures from 25 to 10"C. The samples irradiated in water suspension were prior to testing filtered and dried at <10°C for 36 hours. The prepared catalysts were found to be composed of cubic nickel oxide and three major phases of bismuth trioxidc. The specific surface areas of the samples containing 0-20 wt.% of BijOj oxide altered from 7.6 to 16.7ma.g~' and were found to be generally much lower (from 1.1 to 2.6 m'.g"') at higher concentration of BijOa oxide. The surface oxidativc abilities, expressed as the surface concentration of thn O~3 ions, reached a pronounced maximum when the content was about 1:1 of both oxides, The maximum ntayed unchanged after 5 months of sample storage in air, however after 25 mon'^s the storage led to a dramatic decrease in these values. This showes that a new equilibrium was attained between the catalyst and atmospheric oxygen during this period. As compared with earlier studied CuO-HijOa catalysts the NiO-UijO3 system seems to be less stable. This difference may be connected with the higher affinity of the NiO oxide to oxygen. The different affinities of the NiO and CuO oxides to oxygen lead also to different irradiation sensitivities in both systems, The enhancement of the surface oxidativc abilities after irradiation was observed just in the case of the NiO-liijOj system. Probably a new oxygen equilibrium with dominanting ionic forms

147 WORKSHOP 00 CHEMISTRY of oxygen (O~,O1~,Oj") wu attained during Ifradltlcn. Uccama the snrnc radiation elects were observed After Irradiation of tlio samples in air M well as In water A direct Interaction of the Irradiation with the surface of the catalysts can be presume! here, The mutual influence of both oxides In t.ho system studied resulted In a non-monotonous dependence of the catalytic activity ofl the composition of tfifl samples, Tlii* inflii"^ remained fjtmlita- lively unchanged after Irradiation of tlic samples unlike tin; Cu-DhOj catalyats although its Intensity decreased after irradiation, Because the decrease in activity wan higher with the aamplca irradiated In water, an Indirect influence of irradiation (caused by radiolytic products of water) can bo Msumcd in this caw, The decrease In catalytic activities, accompanied by the rise in surface oxidativc abilities after irradiation of the sampica allowed, tiiat the activity of the system studied did not accrn to bo connected unainblgously with its surface oxldatlvo ability. Tlic stability of the negative radiation catalytic effect wag found to be lower with tho samples containing an excess of NIO oxide compared to that of samples with an equal ratio of both components, Tlic higher stability of the radiation effect in this second caac may be caused by tlic stabilization of radiation defects on the Intcrphaac areas which reache the highest valuca In the samples from the central compositional range of the scries. The feature of the catalytic sites acting in both cases seemed to be the aame because they gave the same value for the apparent activation energy of the t"at reaction, The fact that the annealing of radiation effects proceeded at low temperatures supported tho idea that the irradiation of the catalysts leads to a creation of charge defects in the oxides (free clcctrona and holes). The catalytic sites of the test reaction may be therefore connected with charge defects stabilized on the surface of the catalysts, The S-shapc of the kinetic curves suggested that the annealing processes may proceed as the autocatalytte ones. Perhaps any annealed defect destabilizes the charge equilibrium established after irradiation and, in this way, any further step of the annealing process may proceed more easily. This may be one reason why the slow first phase of annealing was followed by a dramatic rise In the rate of annealing and then finally by a slow third phase, This last phase was due to a low concentration of the defects in the treated material.

References: [lj MOCKA, V, - POSPlSlL, M. - SILDER, R.: Radiation Influencing of Catalytic Activ- ity and Reactivity of Two-component Mixed Oxides CTU Seminar 94, Part A, Sec. 2, pp. C9-70, CTU Prague, 1994. [2] POSPlSlL, M.: Physico-chemical Properties of CuO-BijOj Mixed Oxides and Modifi- cation of their Hydrogen Reduction Reactivity by Ionizing Radiation J. Therm. Anal. 44 (1995), 133-146. [3] MOCKA, V, - POSPlSlL, M. - SILDER, R.: Radiation Influence of Catalytic Prop- trtits of CvO-DiiCh Mixed Oxides Workshop 95, Part I, Sect. 3, pp. 127-128, CTU Prague, 1995.

This rtstarch has betn conducted at the Department of Nucltar Chtmislry at part of the mtanh project "Study of the Catalytic Properties of Selected Two-component Oxide Catalysis and their Influencing by loniting Radiation" and has been supported by CTU grant No. 100J8S1L

143 WORKSHOP 00 CHEMISTRY DECARBONIZATION OF ELECTROLYTES FROM ALKALINE ACCUMULATORS

M. PcknF, M. Cenek*

TV Brno, Faculty of Chemistry, Ucpl. of I'liys.Clicmistry Vcslafska 230, 0U7 00 Hrno *TU Hrno, Faculty of Elcclr. Hug., Dcpt. of Elcctrotcchnology AntoiiftiskA 1, GG2 09 llrno

Key words: alkaline accurnulatora, dccarbonlzation, electrolytes, regeneration

In alkaline accumulators, concentrated solution of alkaline hydroxide is used as an electrolyte. During operation of the accumulator, the electrolyte is continuously contaminated by carbonates formed due to the electrochemical processes and from the aerial enrbon dioxide. Carbonization deteriorates the properties of accumulator. Used, carbonized electrolyte* arc neutralized and store or poured Into the watcr-cotirsc. Environmental impacts of such procedure arc evident. Regeneration, or decarbonization, of used electrolytes would enable to lower these impacts and, moreover, would decrease costs, as the decarbonized fluid can be re-used Again ta An electrolyte. The main task is to find safe, environmental friendly, and simple method of decarboniza- lion. In the past, a lot of work was done in regeneration by the use of baryum hydroxide. This process was very successful in lowering the content of carbonates. Strong regulations, however, had to be obeyed because of the toxicity of baryum compounds. The problem of exploitation of the formed baryum carbonate was not completely resolved. Therefore, customers were not very satisfied by this process. We started our work with two possible ways ofdecarbonization. The first one was based on ion extliangcis. The second was &Smt< &l leplaccmcnl, o( baryum hydtoxide by much more convenient calcium hydroxide or oxiue. In the first case, both cation and anion exchangers were tested. Cation exchangers in tho H-form were used as a source of hydrogen ions. These ions were expected to decompose carbonates forming gaseous carbon dioxide and hydroxide ions. The problem was to find whether this process works at the very high concentration of hydroxide ions which form the electrolyte. Anion exchangers in tho OH-form were used as real exchangers to exchange carbonate ions for hydroxide ions. Again, the proMem wan whether this exchange goes In the concentrated hydroxide solutions. Kinetics of interaction of carbonate and hydroxide ions with the exchangers was measured. In the case of anion exchangers, selectivity of the exchanger to the both ions was examined. In the second case, calcium hydroxide or oxide could be used instead of baryum hydroxide to precipitate carbonate from the electrolyte. This is, in fact, the well-known caustidca.tion process for hydroxide production. In out case, however, thctc is high wnount of hydroxide already in the beginning of the caustiflcation. It follows from the experiments

149 WORKSHOP SO C11EM1STUY tlmt under such conditions standard catislifkfttio/l dots nut probably work, {fallibility of calcium hydroxide in ilia concentrated hydroxide solutions Is too low to obtnin Hulllcicnt concentration of calcium IOIIK in the solution, which is ncccmnry for precipitation of calcium carbonate from ilia solution. Wo tested llic poanSbilily of llic "heterogeneous" Cfltistifitfilrrcrii i,c, rniHlitkM'mii on- cutting on Die surface of solid calcium liydrtwidr, Tlio key prolili'iti scrinnl to be very fine, maybe colloid, dispcr^Atiou of calcium hydroxide in the electrolyte, Various methods of dfapcrgfltion were unctl and kinetics and equilibrium of heterogeneous cauntificJitioii were measured, Finally, feasibility of precipitation of c/irbonntcs from concentrated hydroxide, solutions was checked,

Thi» rtuarch hat been conducted at the Faculty of ChcmMry and Vacuity of tike- trolechnfeal Engineering, TV ttrno at part of the rttenrch project "Regeneration of cltttnical compotitton of electrolytes from alkaline accumulator*" and hat been nupporliil by TV grant No. l'VGH00TJ/95.

150 SENSITIVE LAYERS FOR DETECTION OF ORGANIC AMINES AND HALOTHANE IN GASEOUS PHASE

S, DrodikA, II. Sopkrt, I, MMifl, V, Pnpel*

CTU, rW. of Nucl. M. U t'hys. *'<*« l>epl. e>f 8oli«l State Knglfieerlng Trojshovi II, 120 00 I'rafiA 2 'Academy of Sciences of the Ciccli l(rf»(it>lic, J.lleyrovsfcy Institute of Physical t'hcmlsiiy Dolejskova 3, 182 21 I'rahs 8

K«y worclif conducting polymer, adrorption, polypyrrofe, propylarnine, polypyridme, gas sensors, liuer induced chemical vapour deposition

The vapor substance adsorption on conducting (Kil/mrf laym Is Intcrpstlng ttotli from giw n*-fi«Kif frr^fil ftf v|p* »m! fot nlmlyiiig of »«n itudiril in detail, the unaffiWg'Joii* effctl of conducting polymer oxldatlve »•• ,\e on this pro« changed In a Urge range [l\. We focnwil on polymer Jayef adwrplion projwrty (rwarch. t'wpjrUmin* »»f>o< a^wtptinn IM ofjwtvefl «n thin rnnducting polymer film* in ile- their oxidttive »t*te. TKe wtsotption vrM tnrMuml on th« Kttvin viol* (wiwiltrtA wotk [vinclion cl\Mge) and using the qttaitt tryslnl mlcrobalance. The example of potypyrrol detrmnslrated that adsorption proprtties of conducting polymrr film* are dependent on their redo* itate. The propylarnine afinlly l» highest tm polypyrrofe onidiied form. Adsorption depends on its pr» tolylieal reaction, con»ef|tiently In dry medium the adw)fplion is negligible. On rcver* •ton physical adsorption propylamine behaves M an arcrptof of electrons. Reduction of pyrml polymer layer enable* tft achieve erm Invtirirtn of the change work function during etposutp, which Indicates the change of it* d«nor-acteptor pt»perties toward propylamine. It was proved that adsorption p^perlies of (onducling polymer films ean be Affected by electrochemkal polatiiaticii. The advantage of Kelt in probe mraaiiremrnl cunsiil* of limultaneotis Information about tensing layef behaviour in the g*» sensors wtifking on lranti.ttnr bale |3). further was tested a possibility of tensitite polymer layer deposition on transistor gate by the method of t*.*ef Induced chemical vapour depoiilioa |1). Frotn voltage-current tran- sutor charac^stici measurrmrat before and after depmition (polypyridine was use In this experiment) it Is evidenl that IhU method! U,l>e»!d«s a«ual eletlrocKemical drpwitlon, an e'??raiShr «r d sresiJhe lajrr tfe^jsiika oa tix ttsmhtor ga'&

151 WORKSHOP Wi (JI1BMI3TUY lletetenceal (1) MOIlltlSON, S. ll,i Tin ChtmUat I'hyMct of Surftttu, I'foiimi I'twrn, New Yotk (1090) |2) TOl'AHT, P. - JOSOWlC'/, M,i C/innicfrrWinii i>/(/ie fattrttlio* (Mwetn Cot^f- fttle and Altthanol Vapor, J, l'liya< Clu'iu, 00, 7821 (1!)!)2) [3] JO8OWICZ, M, -JANATA, J.i Clitmicnl Senior Trcltnolagy, Vol. I, \'A, Klncvlcf, AffiAtcnUui, 15.1 (1988)

(

T/ifa ttmtrth hai ittn contltirlnl nl Iht Dtpurlmtnt of (itillil Stale lititjiiirtrtttt) tin part of tht rettanh projtd 'SeniiUoe \,a\)tn for thttttion of Vapourt of Organic Amlnn and llalolhnne (with Attt/tance GHHSIFtiT Sttuan)* mul Imn bttn tuppotttH by C'TU grant No,

152 M(WKMIiffltV STRUCTURE AND REACTIVITY OF COLOURED pi STANDARDS

Z. Fried), K, Slnlx*

VDT, I'AC. of CVttilstry, fnit, of EtivlfoMncnUl Chem, Tcctinol, VnLhkn 2.10, C"/-6:l?0t) llrno, Czech Krpuhlic

'Inst. Anal, Client., Acmt, Set, Czech l(r|>,( Opt, of Mipild Cliroitwtogrnpliy Veveff 07, CZ-6IM2 llrno, Oeh Itepublle

Key words) pi jUntlnrds, (ilrucliitc vs, rcscllvlly, Isoeiedfle focusing, cliernoinclrks, 2- X'4-fnetliyt-C-iiiofpholliiometliylpheiiols

hodeetric focusing (IEK) represents An efficient l«link|ue fof the»ep»ratlon of amlio- tcrlc nnnlylcs M protein*. A principle of this method Involves focusing of AM Ainphotcrlc iriolrcnle nt llie point In migration »ynteiii, where |>ll value of oolutiott eorrtnpomN to Its inoclrctrlc point (pi). Tu clmrficteri/t* the niialyle, nn ex Aft pll value At the pUcc of III foaming nhoiilct lie known. An sllrrfmllve tn pil ineMiirettient !>y ineAn« of« »erlrs of pi! inlrroelettrodr* or tu the off-line pll inenniirciiieiil In collected frACtlon* After iqmrntlon I) «n utilization of cntlbrntccl mixture of pi stdiidftrds. Til! the present time, cxept for a some COACH comprising Methyl Heil ur phrimtitlirollne coitiplexeit, the imturnl protein* Arc lined. tlrvrtlUrlriH, tticli rwrifiowl* An n'A wH nil flrrfidfi'N wi » good pf standard. To mcti the nnnU of IEF, fdpeclslly In Cnpillnry and preparative modes, the low-molecular pi slumlords Arc * promising solution of this problem. In previous pnpern (l-3| we liAve proponed the use of the AminometliyUteil tiitruphenol.t M pi BtmuLifdi, With the si in tu optiini/,e the tP.F ywopntics of nUtnpticnul bwrnl slnrnlnnls, vie \inve ptcpwnl a MtWs ot 2.X'«til»thiltwl •l-Cftj-C-iriorphollnoinethylphrnoN (Fig. I) X

CH3

Fig. li General utriicture of 2-X-4-CH]-(>-morplioliiiomcthylphenots where X o Cllj, OCII), Cl, Hr, NO], and COOII group. The a^td-biuc proper lie* of the prepared compounds were evaluated by potrntiometrie titMtion. The determined |>K| Add pK] values Wcic plotted Against pK« values of related 2-X-snlistituleJ phenols. Tlie result is a poor correlation of both pK values, on the other hand the very good correlation «u

153 WORKSHOP 00 CiiEMM'itY obtained for pt value* of all pi standard!! with tlic empirical equation pt a (pK/i-X-jilienol •V 0.3 + 0.9)/2 , The term 0,31* * wftettloti of pK, value* for 4-CHj gioup t>[2l9 And the second term 0,9 In A pK, vnluc of parent 2-inorpholinomethylphcttol,

0,0

0.2 O.4 0,6

F}g, 2; Plot of pi value* againiit am constants

Finally wo have correlated pi values against Hammett an constant* (t|. A very good fit wu obtained ( r « 0.993, » « 0,101, n •=• 5 ) and the resulting equation pi a 8.937 • 2.510

Hefercncci! (1] SLAIS, K, ' FHIEDL, 'L% Low-Motecular Standards for ttotltclrie Focuiing. Czech Patent Application 141-93 (1993). 12) SI-AIS, K. - FRIEDL, Z.: Low-Motuular-Man pi Markers for hotlictrie Foetuing. J. Chromatogr. A C01, 219 (1901). [1] SLA IS, K. - FHIEDL,'/,: Ampholitic Dyes for Sptctroacopie Determination of pit in RectrofocvJing. J. Chromatogr. A 695, 113 (1093). [i] EXNER, O.i Correlation Analyst* of Chemical Data. Plenum Press, New York 19S8.

77ti* rtitorch has been conducted at the Faculty of Chemistry, Technical University Brno, Institute of Environmental Chemistry and Technology a* pttrt of the rettarch project Structure Optimhation of Coloured Standards for Isoctttlric Focusing and has bun supported by VUT grant No.0011. WOtlKSllOPOO CHEMISTRY THERMAL DECOMPOSITION OF ORGANIC SUBSTANCES

f,, A«lnrncc, M. Hnrtlov/i, O. Coiifol, J. Teplf*

Technical Unlvcraity of Urno, BoJetechova 2, 012 (iG Drno, Czech Itepublic •Institute of Analytical Chemistry, Acndc/ny of Science* of tlic Czech Republic Vcveff 97, 01142 Hrno, Czech Republic

Key word*! Thermal plasma, plasmalron, thermal, decomposition, organic substances

The application of thermal plasma in chemical technologies involves the high temperature decomposition of ecologically harmful nnd toxic organic substances. The core of the technologies using pliuina processing is heating the carrier gas In Arc heater (plasmatron) and to mix it with the substance to bo decomposed. The energy transferred by the carrier gas to the aubstancc Is consumed for its decomposition. To Investigate such process the experimental equipment conslotl/i^ of the plasmalro/i, tlie chemical reactor and the scrubber wan built up And described In [I), Toluene an a model toxic sulutanrc wa* addird In the form of vapour (at the boiling temperature of loluen) at the beginning of the reactor. Samples of the gas pliano for the diTotnatographic analyali were taken «t the end of tlic reactor. Thirteen cxpcriinctila with argon and toluene are evaluated in Tab. 1. Toluene amount « In a medium flowing through tlic reactor is given by 100(7,./

where O U the flow-rate of the carrier gas and C,,i Is toluene (low-rate. The used method of sample analysis led to Identification of benzene, toluene, and other alkylbcnzcnes. The mass of toluene In the sample to be analysed Is m. The mass of toluene added to the reactor that corresponds to the volume of analysed tamplc Is denoted by m". The efficiency of the toluene decomposition is characterized by

lOOtm* - m) m* Other followed quantltie* arc: the mass of benzene in the (ample volume, the benzeiie/to- luenc rnaas ratio r, the mui of other alkylbcnzenes and the electric energy W consumed for decomposition of 1 kg toluene

where UI is the power supply of plasmatron, The energy necciuary for healing of toluene to the boiling point and Its evaporation Is not Included in the value of W because it Is negligible.

155 WORKSHOP 1)0 CHEMISTRY

The results of llic experiments are given In Tub. 1. Efficiency d of the toluene clccom- position Increases wllli the: incrcMlng reactor entry temperature T, from 70.10% to 99,09 % In tlii neighbourhood of 2400 K. For T, >2<100 K d decreases with Incnvwinf, '/„ This effect can be due to rccornMrifltim? rmrthn* )n p)**-** M>M Urn reactor, 'l'lio main new aromatic 2300 K this mui i> below the detection limit with an exception for the highest temperature vntuu 2035 K. Tim toluene amount s In the medium wa* approximately 1,1 % at the above-mentioned experiments 1 - IX, The small (lifferendcs In » have no effect on the expetUncnlni rcniilti, B.g, «t * « 2,80 - 2.88 % (lie efficiency of toluene dccompusltlon d Is the mine (coinjmre cxpcriinenti X - XI! in Tnb. 1, lint at » value 9,05 % d is lower (see experiment XIII In TAII, 1), Kricrgy consumed for total decomposition of 1 kg toluene (IV) Is dependent on temperature T, and on > (Tab, 1), Our value* of W are coui|>arnblc with those published by HAD [2],

Tab, ii No, VI a » T, d r W [W] for1] \%] IKI \%] [kWhkg-'l ( M7U 10.72 LOG 1082 79,10 o.;io 60,1 II 18193 10.00 .07 1791 89.10 0.48 02.6 ((( 17^1 10.S7 M im 0114 2.29 48.0 IV IBWi 10,87 M 1977 f)7,fiO 4Ai 47.4 V 201G3 10,84 .15 2120 98.84 4.84 48.0 VI 20C07 10.93 1.14 23^2 99,99 90,00 4G.2 VII 22 619 10.92 1.14 2529 99.90 C.C7 50.1 VIII 24160 10.91 1.14 2727 99.82 1.20 53.0 IX 2S210 10.90 .01 2935 99.C8 0.35 68.6 X 25345 10.71 I2.80 2514 99.91 5.25 23,0 XI 25532 10.71 :2.88 2518 99.93 3.50 23.2 XII 2G723 10.71 '2.88 25C0 99.93 2.92 23.4 XIII 27701 10,73 ).O5 2CCI 00.51 1.34 7/J

References: (1) OIlKGOri, J. - JAKUHOVA, I. - KADLEC, P. - SENK, J.: Eiperimenlat tquipmtnt for chemical application of thtrmnl plnama. Proceeding* of this workshop, [2) IIAN, Q. Y. - ZHUANO, Q, - TOHMANEN, W. - HEDEKLEtN, J. - PFENDEK, E.J The deilruetion of Morinattd hydrocarbon wa$let in a counter-flow pla/ma rtatlor. 11th International Symposium on Plum* Chrmiitry, Loughborough, U.K., August 1993, Proceedings, Ed. Harry, J., p. 7.58-763. This rtftanh hat been conducted at the Department cf Special Electrical Engineering and Quality, FEECSTU Brno as a part of the rtitarth project "Unconventional Application of Low-Tcmpcmlun Plasma in the Chemistry and Chemical Technotogiti* and has been supported by TV Dno grant No. FU650069.

156 WottKSIlOl' 00 CHEMISTRY DIELECTRIC RELAXATION SPECTROSCOPY OF POLYSACCtf ARIDES

K. Mcdcrrriflrin, L. Lnpc'lk, Jr.*, 3. llavlfcck**, L, CJnneln

TU of Dniu, Inc. of Electrical Eng,, Dept, of 1'hyslcs TcclinkkAH.GIOOOHrno •TU of lltno, KM, of ClicmUtry, l)cpt. of I'hyulcnt Chemistry VeslarskA 2.10, C37 00 llrno **TU of Hrno, Fac. of Electrical Eng., t)ppt. of Eleclrotechtiology AnlonfnskA 1, C02 09 llrno

Key word*) dielectric relaxation, low frequency spectra, polysaccharides, liyaliironic Acid I'olysaccharide based materials arc widely used In medicine nnd biology as pill coatings. Their main potential advantage in their ability to release active components of the drug from the pill Into the ambient organism gradually, In a controllable manner, thus allowing more efficient drug action in orgiuiSsm. Physico-chemical and physiological properties of polysaceharldes are strongly dctermine

157 WORKSHOP DC CIIKMISTIIY

(Sigma), cliomlroltin sulphate C exctractcd from iliiftk cartilage, approx. !)0% (Sigma), hydroxyethylcellulosd Natrosol 11 (Hercules), hydroxypropylcellnlose Klurcl \, (Hercules) and poiyftthylcnc oxide) I'olyox WSlt - 303 (Union Carbide), Typical distliafge-time dependencies a( Kltirel h mmr/lr* nri" thnwn hi )%, I, '>')« changes In llio sliapo of (lin dependencies are attributed to Did Amie/illug of the polymer film during lU storage at 43% humidity atmosphere And It* thcnrml atrnin irnlii«:y the trnnsport of rclntlvrly lilgli currcnla through the aninplcs during the experiments, fjlrnilnr cfTuctt* wefu ol^crved nlio during our previous attidics [I]. Fig. 2 shows a typical frequency dependence of the Imnginary part of complex permittivity t"(w) of |jydroxyctliy]cdlulo.ic, All wmiplwi exhibit a steady dccrcMc of c"(ui) toWArda IncrcMing Ite^unncy. The dnt/i enn be natiafactorily fitted with a turn of one AC conductivity component (c"(u) = /1w"n) nnd one llnvnlUk-Negaini rnlaxntlon proccm (t"(w) =» At(l + (/«()'')"'')> '" l'i« c«"e of hyclroxycthylcrlluloAn the opti- mixed parameters calculated for thin simple model [I] HK At => 0,3015, » n 0.k'n nm liit'd n* a reference data for our novel composite matrices prepared in our laboratory from the above-mentioned polymer* by the low temperature planrim induced radical polymerization.

f • firiC MtttwtHM

•7,2J

•7,5

gt.OM •7.75

•10

Fig, 1; Time dependencies of discharge cur- Fig. 2; Frequency dependence of the imag- rents of Klucel L samples repeated after dif- inary permittivity of hydroxyctliylcellulose ferent time periods Nairobi H. References: [1| MARIANIOVA, D. - UPfilK, Jr., L: Electrical Conductivity Mtniunmtnti of Hynluronic Add and Colkijm Colloid Polymer ScL, 271, pp. 113 - H7 (1993) [2] LIEDKHMANN, K. - LAPClK, Jr., I.: Die/criric RtkiaHon Spectroscope of ['olytae- charidet Chcm. Papers, (19%), in press

This rutanh has been conducted at the Department of I'hysies of Faculty of Electrical Engineering and Informatics and Faculty of Chemulry of TU llrno as part of the research project "Dielectric Relaxation Spectroscope of Polysaccharidet" and hat been supported by TU in Brno with tht grant No. FU J50063/95.

158 WORKSHOP 00 CHEMISTRY X-RAY FLUORESCENT ANALYSIS FOR THE COAL INDUSTRY

T. CccMk

CTU, Fae. of Nucl. Scl. k I'hys. Eiig., Dept. of Dosimelry & Appl. of Ionizing Had. UWiovA7,116 10 1'ralial

Key wordu XHF Analysis, stilpfiur In coal, ash in coal, matrix effect

Tlio X-ray fluorescence Analysis /XIU''A/ is one of the most frequent spectral radiochc- mical methods, Its advantages are a relatively low cost of the equipment, simple preparation of the snrnplcs, and vnr'icly of clement* the concentrations of which arc measurable. Coal is considered to be a two component mixture of coal substances And aali. Ash consists almost entirely of the decomposed residues of silicates, carbonates, sulphides and other minerals. At least 09 % of the chemical composition can usually be expressed in terms of the same oxides found in other crustal rocks. The composition of minerals Is a useful guide to the toh content of the coal. Sulphur IIAA been identified AS A potential source of atmospheric pollution. Measurement of the sulphur content of coal has become of increasing concern. The possibility of measuring the 2,308 keV S Ko - X Ray lias been discused by several authors [1] ami till now It is the problem to use so low energy In industrial conditions. It was demonstrated tliat, for British coals, some of these problem* can be overcome by cxploating the correlation between sulphur and iron In the coat and measuring the Fc Ka X Ray, C,<103kcV. The philosophy was, that the concentration of organic sulphur which is chemically combined within the coal substances is reasonably invariant for a known coal type from particular geographical area. Since, in IJritith coals, sulphate sulphur is normally presented only in vciy low concentrations, variations in sulphur content .vhich do occur arc principally due to variations in the pyritic sulphur (2). This method cannot be used In the conditions of the Czech Republic. The concentration of the nonpyritic sulphur is higher and pyrit is not the main source of iron in the coal in many areas, The technique of radiosotope X ray backscattcr for the measurement of total ash content includes compensation to reduce influence of matrix effect. The matrix effect is caused by variations in the ash composition and decreases the precision of the analytical results. The backscattcrcd X ray intensity decreases inversely with increasing ash content in the coal. From variety of methods for matrix effect correction, the method of empirical coefficients was chosen. This method is based on obtaining equation the coefficients of which arc determined {rom measurement of standard samples where the concentration of investigated elements arc known.Using these equations the concentrations of investigated elements may be calculated even for the unknown samples. The total ash content /Ij was computed using the following regression equation:

Ad = 00+ Z-Oej-Tflii+IT* ft 'B IB 159 WORKSHOP 00 CHEMISTRY

The total sulphur content C(H) vtnn tnmptiled iidln^ the following; regresfili/ii

rrvai urn t)jc coefficients, In is the Intensity of bnckscatlcred rndinlion, /( I* Urn intensity of characteristic radiation from tlic itli clement One purpose XIII' analysers with proportional or Hi (LI) detector controlled by micro- computer were developed \\\ and arc modernized now. Fig. 1 illintrntes the conl spectrmn by the Ye cxcltdtlon natircn. Tlic obtained results nrc prcnentcd in Tnb. I. detector d'^iMion % nali cont. At proporti 1.0 C - 10 % C(S) proport. 0.3 OA • 5 % qs) Si(Li) U.I 0.4 • 3 % Tab, 1: Comparison of chemical laboratory results with Xltl'A results

Fig. 1: The spectrum of coal by "I'e nource

References: (1| TIIORNE, L. - MCCOHMICK, G. - DOWNING, 11. - IMUCE, ».: Fuel C2 (1983) 1053 |2] PAGE, D. - PIGGINS, T.J Dttielopmtnl of an X-ray fluorescence method for on-line determination of aulpliur in coal, Int. J. Appl. iladUt. (sot. 3G (1080) 1 |3J CLAYTON, C, C. - COLEMAN, C. K.s Currtni devtlopmenlt and applications of nuclear techniques in the coal industry, In: Gamma X-tlay and Neutron Techniques for the Coal Industry, I ABA 198G |4) SIMON, L. - CECIIAK, T, - IIAI.LY, J. - KOC, L: Rudy 36 (1988) 210

ICQ Section 4

ENGINEERING INFORMATICS AND CYBERNETICS

NEXT PAGE(S) left BLANK ENaiNEBItlNa lNFOltMATjC3 fcOYDERNCTOS GENETIC ALGORITHMS AND INVESTIGATION OF THEIR PERFORMANCE

J, LnBnrwky, J, Kubnlik, V, MnFfk, O. StCpdnkovii, M. Domlov/1, Z. Koubn, T. Vlcck, J. Koplncc

CTU, Fftculty of Electrical Engineering, Department of Control Engineering TeclmickA 2, CZ-1G0 27 I'rngita G

Key words! genetic algorithm!), discrete optimisation, state space search, artificial intelligence, planning

The Urgf t of. the project on genetic algorithms (0 A) him been ft study &tid experimental investigation of QA's pcrfortnancc in a range of optimization tanks, The main interest concerns the behaviour of GA in discrete combinatorial optimisations. These tanks have not been researched and tented in a sufficient and satisfactory extent anywhere in the world, GAa nre search algorithms baaed on principles of natural selection and genetics. They are probabilistic algorithms which maintain a population of candidate solutions (individuals). Tim individuals are reproduced in accordance to tlicir fitness values (objective (unction, goodness) and they undergo crossover and mutation operations (recombination) Each individual lias its fitness value which is value of the function according to which we want to optimize, For OA purposes, each individual is represented by a string of symbols from a finite alphabet, A simple GA is composed of three operators • reproduction, crossover and mutation. GAs work with population of individuals and by reproduction, crossover and mutation of individuals create a new, hopefully better, population. Reproduction is a process in which individuals arc selected to bo crossed later. Individ- uals are selected according to their fitneai values in the way that strings with a higher value have a higher probability of contributing one or more offspring in the next generation. The ways of doing this step form different selection strategics that arc often modified by different scaling mechanisms. Devising a good selection strategy can prevent the worst problem of GA • the premature convergence when the search process gets stuck in a local optimum due to the lack of diversity in the population. Next, pairs of selected individuals undergo crossover operation yielding new individuals. The mutation operator plays a secondary role in GAs. This way, a new set of individuals is generated. These new individuals must replace some selected individuals in the old generation. The rules for this selection form the replacement strategy. Currently, many publications and articles describing experimental results for combinatorial optimization tasks are available. However, information is very restricted. Repeating some of the published experiments, it has been even discovered that some of the results arc cither wrong or the published details arc insufficient. Generally, GA represent a large set of algorithms that can differ in many internal steps strongly influencing the global behaviour. These are namely the probabilistic parameters, scaling mechanisms, selection procedures, and replacement strategics.

163 WORKSHOP % ENG1NMHIWI INFORMATICS h CYBERNETICS

Thus, tlio primary target of our endeavour !

References: [1| MAftlK, V. - LA2ANSKY, J,: AI for Manufacturing: Some practical experience. Camarinha-Matos L.M., Afsarmancsh II. (Eds.): Balaccd Automation Systems, Proc. of the IEEE/ECLA/IF1P conf. BASYS'95, Chapman it Hall, 1995, pp. 151-158 [2] LA2ANSKY, J.: Genttic Algorithms and Discrete Optimization. Proc. of BASYS'95 accompanying seminar "Discrete Optimization Techniques and their Applications in Industry", Univ. Federal do Espfrito Santo, Vit6ria, ES, Brasil, 1995, pp. 12-25 This research has teen conducted at the Department of Control Engineering as a part of the research project "Genetic Algorithms" andhas been supported by CTUgrant No. 10038189.

164 WORKSHOP 00 ENGINEERING INFORMATICS k CYBERNETICS GNOSTICAL NEURAL NETWORKS

P. Pntntkn

CI'U, Faculty of Klectrlcnl Engineering, Department of Control Engineering Karlovo u(w\M{ 13, 121 115 I'raha 2

Key words; ncurnl networks, back propngntion, gnostics

Introduction. Neural networks based on the gmmtlcal theory of uncertain data arc proponed. The Idea of application of this theory to the neural networks has been first published hi [2|, Neural networks. Multilayer neural networks based on the pcrccptron model [3] of the neuron are widely used. The beat known learning algorithm for such a network is the back propagation algorithm, It has been published probably first time in (0] and rediscovered in [i]. The algorithm had solved the learning of multilayer neural nets. Dack propagation algorithm has well known problems: slow convergence and achievement the global minimum is not guaranteed. There have been made many attempts to improve this algorithm especially in speeding up the convergence, They resulted in faster algorithms with ati error value of the critcrlal function which is higher then the error value of the original algorithm. Gnostlcnl theory of uncertain tlntn. Clnwiticid theory of uncertain dntn Is n. non- statistical theory of data treatment. The complete theory is described by Us author in (1], The theory derives a mathematical model of dnta disturbed by uncertainty. The guoslical theory is developed in two steps, In the first step, the theory of single datum based on two simple axioms is constructed. Laws controlling uncertainty in each individual datum arc formulated using varlational principles of the virtual kinematics and dynamics of real data, New formulae for the entropy and information of data evaluation follow, In the second step, the gnostical theory of data samples from the theory of single datum is constructed, Algorithms resulting from the gnostical theory maximize the information obtained from data and data characteristics arc robust with respect to outliers or inlicrs. The algorithms arc efficient even for small samples of corrupted data. Motivation, Methods of the gnostical theory provide an useful and robust tool for data treatment. Because of inherited robustness of the gnostical algorithms the advantages of introduction of the gnostical theory into the neural networks can be expected:

» robustness of the learning process, • speed up of the learning process, • learning on smaller training sets, • better fit of training set, • better generalization, • robustness of new models of the neuron.

Gnostical neural networks. The gnostical theory can be applied to the neural networks at two different levels. The first level implies using of the gnostical criteria! function

165 WitlMMW m jBNOjNMHINO lNl'OHMATIl'3 h CVIlMNUTIC'f)

In known )eaf/i!ftg »!g«fIISMM. Al lli* *mmt\ level new inodel* of the tiemon tan I)* f*rc>- powd, Mi'1 titil (etc) liai brfti studied flfld lliC modified standard !mrk propagation Icnfiiilift dfgofiJf'fff h*f fcwff (tfthnte h ha* Wn iwUml \n idfr* tlilfrri-iil fn^rlnirtiU. In llic fitsl rupffiwiri l(i»" «)Vi*-Olt fiuitllmi )i*t lipen lcafnci), This Irsk Is noi niiUnbli- for »iuU •>( lijuiilwilttrfi diitiU f(I tlie frsolitlkm of 10 x 10 phrlg card f(ifil«ihinf{ 1(KI digita, Tic* iMittin^ wt totiUilicil digit* Wfiltril tiy two (.rfsoni. Ttir fifsJ Ifst wl t«f*>l«fh«"«l kmiilitt dij;il» ftotn tlic sump lw« ppf«>rn. 'Mir upronil IPSI »cl totiUlftPtl digits wfittrn by tliifd pffwirt, t(««lllt* of ilmulAttali*. 'Ilie KimnUtiolii Imvc I,T(I doff* with fi«rd tcnffilfi^ Ml? 7, tnotrwtitum /< fcnd W«IP pafattiftft .«. If llif »f*l(« p»f»mrtrf it tliosrfl WPII (lifl »[rrrd lip of the iMfhitfg Jifotes* t*n I* Vrfy "lignifirniiti TIMJ |p»rk (•ni(mrstinn. Cortctu>ioh!ti 'the neural tift*i>tlt« da-wil on tli»> t,i\tmtk*1 ihroty of iinfrflflin dal* l r«ri|ti of tijuuUli'itii At? |ili>(rii«ing Hfirl furlhrr rrwarffi i« frf|i|i/r'l.

1 |l) KOVANIC, I ,; Grw,tlrk

|'J] I'At.ATKA, I'.i tf/ifiti-nrifnf fn/lifmrtff MHtnhnvymi tit/mi. t'!"vmttk tptktit, CVUT f Kt. t'f»fva ('//}. [:ij KOfillNtlLAff, Ffof Vnp| WKUIIO9, I'.: ///JIKI<< /ffjff««l»n: AW Tnnb for I'ntitlinn nnd Antttyii* in H,t II" hmnnr»lScitntr/i. Ph.D. Th~K ll*f»»»r( lfni»-t.itjr, I'l7i.

W, WORKSHOP S6 ENGINEERING INFORMATfCS k CVBEKNKT1CS MULTI-AGENT SYSTEM FOR CIM PURPOSES

V, Mutlk, O, flle'pn'nkovii,J . f.nHiinik^ M. Dwdw*, U I, PteutU, T. Vlfek, 2. Koulm, M, Fentfnv*1, J. T- ll/Kilm, J. Kcrnt, O, Hek, I

C'tU, Fae, of Mectrlcal KIIK,, Dept, u( Control Crriri TeehnlckA U, 100 27 I'/ah* 0

Kty wordsl CIM, mufli-ageni architecture, dil'il'iilrd cfedsfon-makfnj; lyiteiiii

The problems which are expected to \>e solved by computer* are growing fapii'ly In their extend, xl«iiHj{ "i«Unil«" of well-workl/)£ nl^orlltuti* Into moie robust floM nyilntM. tint inulll< Aftrnl Icclmolo^y (roii/icctcil with 00 ityle of projtMfnmlnj;) Is tuntldeicd to be xiltnlile fot rrr*tl)ijt 0|K-n, ll"»llilf rtivtrnnmrtit M? to ltilrj;jntr wiftwarp plcrm of ilivrtue imlilrc l In «HfTr>rrnl l»itgit»g«» MU\ running on ilKfi't'iirl tyjicn of rtitnputiw, T1i« itiiittl- ppfuAcIt ttclnihg from the thfoty of agency, ftuin LcliAviowial lno

1. The agent* are independent, autonomous entitle* communicating in the peerlo-peer way among thrmvlvr*. The aaynchronou* message pajsing/broadcaaltng In UNIX/IN- TKItNKT environment Is used lo perform this communication. 2. Each agent consists of a functional body (usually a stand-alone program with a well- defined functionality) and * wrapper responsible fof Involvement of the agent Into the agents community. The wrapper contains a model of the. agent behaviour (in the form of live list of messages which the agent can teceiw/nend out). It translates the Inter-agent communication Into Instructions fof the activity of the functional body and mediates the result! of the body activity back to the agenta' community. 3. The limpfait typical model of an agent behaviour is deKtibed in |l). The agent Is usually Initialled (included Into the age«t«' community). Then it ot»er*e* the meaugn btouicaiteiJ Id the community, la the use, I he knowledge conUirv-d in the agent i* rec|«iired hy wtive metnl>ef of tfc* agentt' community, the agent »end» out

167 WORKSHOP WKNaiuEFAum wonM/vncsk C

A conflri;irtllofl message (Informs tlm others timt it is rendy to nofve, tlm given add- problem) MU\ Initializes Us own body, If the: lioily requires some piece of Information from llie others In the community! the wrApper broadcasts (lie re(|ii!t<(ilienl, Tlifi agrnb \h*ft W»ll» {for a j>ri>-set time) for Any confirmation iiiefisnge from »om« of the agent*, If there Id no connrmntion messRgn occured wtlfiht tlic pio-wC (due diCcfvai, tlie original Hfi-ut replace* the ir(|iilri'il pl«i' of diilA Uy ft dcfftull value, Tlifl morlcl of bdmvlour describe* only lite re-ncl'ivr part of licliavlodr, Tlic dcllficfntlvt l>cli«viour (l(tri|iilic(l) in KXfjfct'rd to lie Implemented m n nnturid |mrt of Ilir ogrdt'* l/wly. 4. TlintP l» no cctitrnl pftrl of inciiKiry or control in llir «Rrnt A Illifury of »tnnd»rd inciungrs (written In t(i<; OOorleiilcd proKmiinnlng langatige I'ilfrl) ftvaiUliIc for lli<* environment tucr (=flpplirntlon diîglicr), 't'lik 11- lielpn lilin/lier to trrate its own nftriiln by very fnil iigentlzAtloii of (ir)iltr«ry -alone program*. 0. T.W interface )ms Wn (Icaigtieil M nnrpftnite nênl in llie coiniiitinity. Tlie mobility of tills ngrnt is AH lin|>ortmil fenttire proviiling liigli system (Irx'iility from tlm end ihrr'd point of view. 7. 'Die bAolc types of Agents currently developed and tented lire: (n) «ri expert nyntefn *ênt (bflxed on A FKIv-HXI'Klt't' like rnlcltAmd dinftiimtic iynlein)i (b) A lb ap-nt (M « body of wbii li Lit** I'OSTOKES OO-diitftbusu (a considered), (c) it ( ttvi' sliiml«lloi» dgent (rxpturiiiK tlie (JUAHIMOI)O ('2| nyntetn for (|iinlitntlve lion), ami (J) k usct intetf.uc ac.eiit. 'Hie nctir»( ndw/fk tifmt it wt'l'- tk

Tlie ctucUl |irobtein of (lie environment ItnpleiicritAtloii w,v tlie problem liow to ensure tli« inter-Agent peer-tu-peer cuiiiinunicnlioti in (lie UNIX/lfileni/-l environment. Finally, it WAS decided tu explore1 (lie /nlvniitn^e* of the I'VM (I'uMllel Virtual Machine) system. t'VM rimy be Implementeil on it liArdw«re b«e eom'nling of dilferelit innrliine nrcliiteclures Interconnected by one or more network* of different types. As follows from the rest of this puragniph the v«ri«-ty of prN/l»iij(|i'>/{«'n/»yiiterns involved U renlly very wide And document* the versatility of the Approach: Tlie inr»siigr<» transferred by tlie I'VM support (nil he written either in Kilfrl or C f+• The user lulerfnce Kgent U iriiplemente

|l| MAftJK, V. - STftl'ANKOVA, O. - KI,KK, 0.: Malli-Agtnl Srl"» ui(A QunUlatitt .Simulation Unit submitted to the XIII. Ktiropean Meeting on Cybernetic* And b'ysl«nis HrwAtth, Vienna, Austria, April 19% |V) MAItVAN, I.: QunhMm Simulation ami iU Languagt. I'h.l). Thesis, FEL CVUT,

hat trtn conduettj at Me Departmtnl of Control t'ngintrring at a part of tin- iiMilith projrrt "Multi-agrnt $y«rVm.«/or CIS!" and hat ittn tupporttJ by CTU gnat No. ll WOnKSilOPOO ENGINEERING INFORMATICSk CVnEflNKTICg A MULTI-AGENT SYSTEM IN TRANSPORT MANAGEMENT

L. HronkovA'DiotakA, T, VWek, Z. Koubn, I, Vhuiti, i. LnUmty, O. SUpAnknvH, V, Mnflk, J, Klemn, T. Hnzdrn

CTU, Fflc. of Electrical Eng,, Dcj.t, of Control Engineering TechnlckA 2, lCfl 27 IWi* 0

Key wordu distributed »ftlfldnl Intelligence, Irftiiijujft iii/wingerrieiit, multi-agent system*, natural language promising, communication

At present, there exist both dntabuc And first generation expert systems M practically Applicable »y«tcms. Si hoc these classical »y§lcm» have a lot of disadvantages, the scientific community liiu concrntrntrd on the prolilcrrn of «o-c«lle«l open nyslemi, umially dcilgneiJ AS dlatributcd, The niin it to crr.itfl lyntcttit of » new gerieratlun which enable to utilize more heterogeneous knowledge lotirces, more declsioti-timkin^ methods, intelligent Information retrieval In Iftrgc-acala ny»lruu with full-text Information. It hfu been ahowed thnt Intelligent retrieval In vnry rnirrJi Conner led with natural language (jrorrnnlrig which l« iwnally l«ngu«gto]er of words which Are usually not declared aa key words but they have significant lemantic relationship to certain key words and Are frequently used by the users. In order to develop a user-friendly nystem reacting In queries to such word! it ha* been necessary to embody natural-language, understanding techniques Into the system. Also determining what texts are about, and indicating their eivutial meaning, implies language understanding. Similarly, relating one text to Another, whether that of one doc*

1R9 WORKSHOPOO BNCWBEHINO INFORMATICS k CVBEItNETlCS uinent to another, or of a document to a request, l,e, searching lor information, implies language-based reasoning. Oitc possibility liow to find Miruifltlc relationship between words is to ((»« machine /earning mclhwU, 'T)m ptnhhm w* )>av« tiM to solve has been to follow up relations IM?IWj>licAtion» solving "real- watlcl" crr>Mirmi, The main rrwon for the efficiency of constraint-based search Is that It allows early detection of dead-ends, Cl-l' U cotmidcriMl to be a ptomUaltig tool for t)m iwAifh of solutions ol some optimisation problem* (

References! fll IIAJEK, P. - IIAVKANEK, T. - CIIYTIL, M.: Shtoda GUIIA, aulamatuka tporba hypottt. Acadtmia PrnAn t9S3 [2] KLEMA, J. - LIIOTSKA, L: Machine Ltarning Method* in Natural language Pro- ttmng. I'rneniinqi of AIVM, Brno, 1995. |3j tfttr Manual Ectipie litkaie 3.9, Shy IS93, pr A'n» OS (t.O.'J. or hinhtr), Interna- tional Computer* Limited and ECtlC GmbH 1992.

This rttearch hat httn con&utltd at the Department of Control Engineering at part of the mtareh project 'Distributed Stineilttnct and Control of Truck Trantportalhn in the Cztch Republic" and hat been tupported by CTU grant No. 10038155.

170 WORKSHOP 00 ENGINEERING INFORMATICS k CYIUSUNETICS IMAGE-BASED SCENE REPRESENTATION FOUND AUTOMATICALLY

V. lUav&l, A. Lconnrdli*, T. Werner

CTU, I'nc, of Electrical Hfig., Dcpt. of Control Engineering Karlovo nam. 13,121 3.11'rnlm 2 •Technical University Vienna, Dcpt, of Pattern Recognition snd Irnngo Processing Trcltlstrassc 3, A-1010 WIcti, Austria

Key words: Image-based representation, selection of optimal views, minimizing the number of views, reference views, view interpolation

The problem addressed in our research Is related to displaying « real 3-D a scene from any viewpoint. Todispiayascene, arelativclysparscs«tof2-D reference viewt is stored. The linages that arc In-between tlic reference views arc obtained by interpolation of coordinates and brightness (colour). This approach it ftlilo to generate llio scene representation and render litiAges Automatically and efficiently even for complex scenes of 3-D objects. This is possible since the proo-ming time dor* not depend on tfie complexity

171 WORKSHOP 1)0 KNCHNKERINO INFORMATICS k CYURRNETiCS

Fig. 1: Examplo of eonitructlon a new view (b) liy Interpolation between two ruferonrn views (a,c), (<1) is the result of th« step 1 of tho process (alt acceptable viewing Intcrvnl*). ((•) Is the result of tho itep 1 (optimal subnet of viewing Intern!*), In (•!}, (oj, tho top view of the object l» superimposed for tlia easier orientation.

Intervals, the subset In selected, which minlmi/is mi objective Junction, taking Into Recount (dings lilec (lie number of view* and ihe lu-cutvr.y of um»'

References:

[I] WERNER, T. - IIERSCII, II. D. - HLAVAC, V.: tendering Rtal-World Objrclt U,ina View Interpolation. I'roc. of International Conference on Computer Vision, Boston, 109\ pp. 057-0C2. |2) WERNER,T.-IIEItSCII,R.D.-IILAVAC,V.: Rendering[ttal-World Objectt without 3-D Model. CTU Workshop 1995, Czech Technical University, Zikov* 4, 1GC35 I'mgiie, Czech Republic, pp. 179-180. [3] IILAVAC, V. - LEONARDIS, A. - WERNER, T.: Automatic Selection of Reference Viewt for Imagc-battd Scene Representation,

172 WORKSHOP 00 BNfllNIWItINO INFORMATICS k CY1IKRNETICS LASER PLANE RANGE FINDER

T. Pnjdln, V. HlnvM

CTU, I'M. of Electrical Eng., Dept. of Control Engineering Knrlo"o n/mi. Ill, 121 35 1'rnlia 2

Key words! computer vision, range iinngn Acquisition, surface modelling Tliln work describes ft 3-D scunner - llic I,n*<:r I'lnnc Range Kinder. Tim nctuor bullila on tlic trinngnlntlnn mid active Illumination lining User light plane. It delivers 3-D coordinate* of points In the volume of »lz

Ughl Plane Tranilnllon Piojcclor Fig. 1; The picture of the LPRF range finder nnd its Illustrative chart.

The use uf an active controlled Illiimliiallon (structured liglit) can remove correspon- dence problem. Usually, one cAinera is rcplsccd by ft source of light rays. For instance, the most trivial setup would use just one ray at a time «o tiiat the Image had contained maximally one bright point. Such a tctup leads to very trivial solution to the matching of projections. However, it turns out to be very impractical since tfic whole image lias to be captured and processed to measure one 3-D point. Faster uchcrnc projects planar pencil of rays at a time, so that an intersection curve, light trace, can lie «ccn in each image, Fig. 1. H»y identification is still unique albeit much fastc. extraction is enabled, sec (1], Our sensor utilize* the iJea of active illuination by a light plane. The light plane is generated by a special light projector that delivers planar pencil of rays emanating from

173 WORKSHOP 00 KNOINKKHINO INFORMATICS it CYWJJtNBTICS ono foeiin point. In our »cttij>, the /( tli« fixed holder, forming tlic cimicrii'projector rig, to that the projector center lira on the Una of intersection of nil the plnnet ptumiiig through rows hi the Imdgc and llm camera projection tenter. The rig Itself l» then mounted OH the plAtform allowing A translation along tho x »xi» of tho world coordinate aystern, sec Figi I, 'f Jio liitcHCcllon curve of tlio tight iilntifl with « Mutate, lliu ll^ht trnee, i« captured by tho camera liwldug ftt tho sutkec. Due to the «pccl«I nrrsng^tiwrit of <;«inpr«-|>f(jj«lor r!#, msxltnnlly otic intnwocllon per row i» drtcctwl M tho brightest pixel in Hie row. Imngc coofdinaten, («,«), of each «tich pixel nlttgntlicr with tht* position of the light plane in space provide dnU fur the Dmling npathtl coordinnlcs of the point by the trlasigulation. .'1-1) dntn totna from the scruor In the world coonthmtc »y»t<'ii) attached to thu rotary plntfonii.