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Illustrated Encyclopedia of Applied and Engineering Physics, Volume 1 A–G

Illustrated Encyclopedia of Applied and Engineering Physics, Volume 1 A–G

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Illustrated Encyclopedia of Applied and , Volume 1 A–G

Robert Splinter

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Publication details https://www.routledgehandbooks.com/doi/10.1201/9780203731543-4 Robert Splinter Published online on: 07 Dec 2016

How to cite :- Robert Splinter. 07 Dec 2016, C from: Illustrated Encyclopedia of Applied and Engineering Physics, Volume 1 A–G CRC Press Accessed on: 30 Sep 2021 https://www.routledgehandbooks.com/doi/10.1201/9780203731543-4

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The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 US Navy.) Class, 2nd Specialist Communication Mass Pastoric, Jayme of (Courtesy Navy. States United the by used Figure C.1 Figure C.1). (see Figure disease” 101.325 kPa, or “the “divers bends” called also or 1 atmosphere, to approximately 10 m each where corresponds of water column, water resting the applied by pressure hydrostatic external the for compensate to necessary was air 1870s. compressed The compressed air).One exampleistheuseofcaissonswhileworking ontheNew York Brooklyn Bridge inthe under caisson the in enclosed while efforts underwater from (when returning acaisson compartment, aclosed from exodus the with associated was disease the rapidly. too Originally surfacing while level, sea to the on return expeditions scuba-diving during occur can which gases, dissolved with associated pressure applied tothebodyisreduced tooquickly. Thisphenomenonisconnected toosmotic pressure, thepartial bubbles of gas release the from resulting embolisms of formation disease, Decompression general] dynamics, fluid [biomedical, disease Caisson Element: [nuclear] Cadmium of abundance integrins selectins, cadherins, receptors: of types into four divided be can which interaction, cell-to-cell is there In chemical] [biomedical, Cadherins the cadherin to bind to each other spanning the extracellular space. extracellular the spanning other to bind to each molecules cadherin the C

Decompression chamber used to mitigate and treat decompression sickness after deep-sea deep-sea after sickness decompression treat and mitigate to used chamber Decompression Ca [Cd]

2+ to provide a platform for temporary adhesion for temporary ions to provide aplatform

1 48 12 from tissue into the bloodstream, primarily nitrogen, when the external pressure pressure external the when nitrogen, primarily bloodstream, into the tissue from Cd . material. . Semiconductor immunoglobulin superfamily immunoglobulin , and . The adhesion is homotype, using using is homotype, adhesion . The . Cadherins rely on the on rely the . Cadherins diving, C

176 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Calcification Figure C.2 C.2 Figure C.2). (see Figure seepage and duepump function to regurgitation the of efficacy adiminished in resulting valves, of the into hardening evolves gradually heart on valves deposition Calcium habits. eating due to primarily thesupply chain, in adeficiency and inequilibrium due to metabolic decreases level bone calcium osteoporosis, During fracture. and for tearing fragile hence and more rigid to become material the biological causing tissues, diseased in are calcium of effects mineralization Other plaques. fatty than harder and it tougher making the of blood vessels, lumen in of theplaques formation in is ofform calcification Another organisms. biological in devices of implanted to surfaces Theadhesionof calcium [atomic, biomedical] Calcification The metal is artificially generatedasaThe metalisartificially resultofcollidingCurium[ 1950. Berkeley, the in of California, University atthe synthesized was Californium of 898 years. half-life a with Actinide of as ametalcategory elementthe in element, classified unstable [nuclear] Radioactive Californium [ ( cells between tion - communica the in as well as teeth of bone and formation the in Elementused biomedical] [atomic, Calcium processes. 1 About blood vessels. the of plaquein formation the in is of calcium implication Another muscle contraction. Gibbs free a rolethe in play also and Nernstequation by the ions calcium described . The is electropotential calcium The ions. potassium and sodium actionwith potential of combination an in creation for the charges Curium. Californium possesses a simple hexagonal crystal structure. crystal asimple hexagonal possesses Californium Curium. of of isotopes production the alpha in decay, produces results also which and neutron emission generates Californium of process radiation.disintegration The aggressive with half-life amuch shorter have isotopes % of calcium is dissolved in blood, and the remaining 99 remaining the and blood, in dissolved is of calcium Calcification of a water heater element due to “hard water” with calcium content. calcium with water” to “hard due element heater water of a Calcification [Ca] 20 40 251 Ca 98 have special calcium channels that carry the calcium ion( calcium the carry that channels calcium special cellhave ). Biological Cf ] calculations for biological cells. Calcium is a major catalyst in skeletal in amajor catalyst is Calcium cells. for biological calculations 24 96 7 Cu % is in cellular structures and muscular muscular and structures cellular in is ] withalpha particles [ 4 2 He 2 + ]. Other ]. Other Ca 2 + ) Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 wheels of an automobile or motorcycle, also called “calliper” (see Figure C.3). (see Figure “calliper” called automobile of also or an motorcycle, wheels for the successively clamp pressure moving disk-break the the caliper line to describe around used the polygon. Also of apolygon, thus defining edges the with the line” a“caliper corners aligns respectively orantipodal pairs while caliper by antipodalpoints its formingof a polygon, expressed rotating pairs and vertices.computational The Count Rumford Count until not introduced was and of heat transfer for the foundation generally intheorder of accuracy, relative with of size measurements for analog designed is that device Measuring general] [computational, Calipers incorrect. This concept was intended to replace kinetic theory intended to replace was concept This incorrect. States Sections In Nine Knowledge: of Useful Rudiments Spafford and (1778–1832) Gates Horatio Geography, General his in 1809 in by caloric, introduced afluid as of, named heat concept Hypothetical ] [general, Caloric Watt James is engine stem to the related of thesteamenginein1712with Thomas Newcomen (1663–1729).Theother, more well-known, inventor coinventor United Kingdom, the of from the modern concept and [energy, ] Calley, John concepts. of thermodynamic formulation theoretical the contributions to significant whomade United States the from Physicist thermodynamics] [computational, Babar Herbert Callen, of(Courtesy Daimler AG.) C.3 Figure that is indestructible and self-repellent and is ofindestructible is that asubsystem being of heat idea ], the propounds [ Illustrated with an Elegant Improved Plate of the Solar System. A Map of the World. A Map of the United United AMapof the World. AMapof the System. Solar of the Plate Improved Elegant an with Illustrated (a) Brake calipers on a Mercedes automobile front axle and (b) close up of disk brake calipers. calipers. brake disk of up close (b) and axle front automobile aMercedes on calipers (a) Brake (a) (1663–1717) 00 .. 10 − 05  mm (1919–1993) . In geometry this refers to a mechanism of calculating the configuration thisrefers. In toamechanismofcalculatingtheconfiguration geometry (1736–1819). (b) , the idea that atomic/molecular atomic/molecular that idea , the ( Benjamin Thompson is the the motion is Caloric

C 177

178 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Caloric theory Caloric Galileo Galilei by Galileo reaffirmed Abbreviated unit: entropy to energy: connected loosely to aconcept respect with ferent format heat and “ and heat [1753–1814]) described the equivalence of1798. workin However,ofprinciple and rising temperature the by 1 by [biomedical, general,thermodynamics] Theamountofheat toraisethetemperature of1 g ofwater necessary Calorie ( ture of abody. two systems;healsointroduced theconceptandunitofCalorieinto theprocess ofraisingthetempera- 1799) in1760.Thisconceptisbasedon Black’s theoretical interpretation oftheenergy transferbetween [general, thermodynamics]Conceptofheat value Caloric ( indestructible supposedly namedwas inquestion “caloric,” transfer the energy in involved medium caloric. The of fluidic theory energy transfers that medium concept of a The physical thermodynamics] [general, theory Caloric 1809. C.4 Figure ° C (from 14.5° motionmolecular Horatio Gates (1778–1832), Spafford engineer thermodynamics who introduced the caloric concept in cal ca ) C to15.5° lJ = 186.4 see

conservation C )underatmospheric ; kilocalorieisexpressed asCal(alsosee ” was introduced in a rudimentary form arudimentary by in introduced ” was (1564–1642) C.4). (see Figure

of

energy transfer introduced by Professor Joseph Black (1728– ) and self-repellent (this statement comes back in a dif a in back comes ) self-repellent (this and statement pressure (1atm=

heat 1.013×10

capacity (427–347 BC) later and Plato ). ). 5 Ν/m , also referred to as to as referred , also 2 = 1.013 ×10 5 Pa). - Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 the the the latent introduces andvaporization of melting process). The process Carnot the as such cooling, and heating general and (e.g., vaporization, phasemelting, transitions as well as combustion activity, of pyrotechnic consumption energy of the indication an is calorimetry applications dynamic muscle action. and thermo In celldivision, general, temperature, body metabolic for example, activity, the caloric one of form energy, specifically of converting process of heat exchange to avoid caloric value the insulated to determine of used asubstance, Device thermodynamics] [general, Calorimeter free energy obtained from cleaving bonds within ATP is applied to fix to fix applied ATP is phosphor within bonds cleaving from obtained energy free photosynthesis in pathway reactions” “dark The energy transfer. cellular biological in reaction carbon Photosynthetic thermodynamics] chemical, [biomedical, cycle Calvin polypeptide chain. a forming acids, amino to binding forbonds peptide use of the identifies nature muscle. The proteolytic eye the brain, of tissues connective the in found is of protein type This core. peptidase symmetric with calcium-dependent family, enzyme proteolytic the Proteinin chemical] [biomedical, Calpain object of energy interchange of the Indication energy, thermodynamics] [biomedical, Calorimetry C.5 Figure . The enzymes and their intermediates involved in the Calvin cycle cycle Calvin the involvedin intermediates their and order carbohydrate to in form reduce, enzymes . The latent = energy gain by colder object. Additionally, in biological applications calorimetry describes the the describes calorimetry applications biological in Additionally, byobject. colder gain energy A calorimeter. heat ofvaporization.

with the exterior media (see Figure C.5). (see Figure media exterior the with Joule’s apparatus . In this chemical reaction pathway, the reaction . chemical In this value (i.e., involved of fuel food) in : energy loss by hot loss : energy CO 2 and chemically chemically and , and skeletal lens,and heat fusion and of metabolism Calvin cycle -

C 179

180 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Camber Tx camber by the wingdescribed end of the tail the location location design the camber can also be negative (see Figure C.7). (see Figure negative be also can camber the design thickness curve can be of any formulations, for instance for instance formulations, of be any can curve thickness the Nobel Prize in in 1961 in C.6). Chemistry (see in Figure Prize Nobel the (1922–2012) (1917–), Benson Bassham James from Andrew support and received Calvin Melvin for which (1911–1997),Calvin Ellis by Melvin the characterized with was cycle metabolic This matrix. mitochondrial the to equivalent is that compartment a forms stroma The stroma. chloroplast cellular the in located are Figure C.7 Figure in object cient for the lift maximum the ensures camber of definition The equation. Bernoulli on the based (higher) thebottom(lower)the top and between difference apressure providing bottom, the under than greater be will theair-flow top over the velocity and lowersurface, the upper between camber in of adifference anaerofoil. Because of surfaces and lower the upper contours of surface asymmetric The [] Camber C.6 Figure the upper portion, upper portion, the () =− ) ( () x

ta Camber of model plane wing on profile. on wing plane model of Camber The Calvin cycle. (Courtesy of Mike Jones.) Mike of (Courtesy cycle. Calvin The r from front to rear, and for the bottom of the aerofoil, aerofoil, of the bottom for the front to from rear,and

02 . Ribulose 5-phosphate   −+ Z up 1 xb - () flight. This principle is defined numerically by the line connecting the front and the connecting line the by numerically defined is principle This flight. 12 xZ / Glyceraldehyde 3-phosphate = 11 xc ATP () xT +− + (G3P) xc () 2 12 / ADP () Regeneration of ribulose Inorganic phosphate 1 Phase 3: − () Carbon fixation Ribulose 1,5-bisphosphate x 1 Phase 1: xd , where , where 3 line + 3-Phosphoglycerate Reduction Phase 2: 1 RuBisCo x ) ( Tx NADP+ 4 Zx   () , where , where () Carbon dioxide is the “thickness function,” which varies with with varies function,” which “thickness the is to travel: for airto travel: for the length apath with NADPH 1,3-Bisphosphoglycerate t r is the thickness ratio. In supersonic supersonic In ratio. thickness the is Z lo w () ATP Central metabolic xZ 3-Phosphoglycerate = pathways ADP () xT − () 12 / () x coeffi- . The Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 hard-copy reproduction (see Figure C.8). (see Figure reproduction hard-copy and capture for both magnification on relies formation image The possibilities. capture image zoom or angle wide- uses to provide a thin lens configurations combination optical various with of lenses with a range system formation image The life. real in observed when as distribution relative same the in hues the presents this manner, asimilar in to light exposure to the to respond treated chemically is that a printon apaper of the production requires design the solid-state in process The final respectively. darken chemical the making oxidation of the increase process, an in result will more image light , since anegative in result will mechanism the photographic of thesurface covers that structure chemical afixed to form interactions silver The effect. photographic for the strips plastic coated color and tions for distor correct that imaging) (or lens,for low-end ofa simple lenses or asingle set complex only of pixel arange in and range dynamic avariable with format electronic in values (RGB) or red–green–blue elements of grayscale matrix to record on acharge-coupled device (CCD)array relied Later photography movies. for acquisition frame-rate high in images photography of still asequence and record to film photographic used cameras early The mechanism. recording format is line chamber of acurved example An well. up as curves that line achamber has wing end of the tail atthe upward curves that aerofoil An lift in-flight provide the surfaces curved respected wing.Thecamberof the of the surfaces lower curved upper and the separating line partition the indicates line camber an aerofoil the On [fluid dynamics] line Camber Figure C.8 C.8 Figure usedforcollectingstillimagesormoving[general, ]Optical instrument footageona Camera from front to rear and and front tofrom rear (a) (a) Picture of an old-fashioned Kodak camera. (b) Picture of a new age digital camera. digital age anew of Picture (b) camera. Kodak old-fashioned an of (a) Picture

aberrations resulting from diffraction. The early mode solid-state camera used silver-chloride- used camera mode solid-state early The diffraction. from resulting aberrations

a and and b are constants. are Z () xD =− (b ) 22   bx cx 2 chloride oxidizes and is later processed by chemical by chemical processed later is and oxidizes chloride 2 +− () cx 2 1 3   , which varies with location location with varies , which single still images for still for still images still single magnitudes. The camera has has camera The magnitudes. solid- . This plate. This state ordigital ) ( x Camera -

. C 181

182 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Camera obscura primarily resulting from the changes in propagation velocity with respect to long versus short waves. waves. short to long versus respect with velocity propagation in changes the from resulting primarily conditions, flow spectacular create can topography riverbed the someIn places conditions. flood ebb and the formation the wavefrontand mechanism diffraction Rayleigh on the depending pinhole of the diameter on the resolution depending optimal an The image has (see Figure C.9). deconvolution spatial inverted an provides lensthat Fourier the as apinhole using device optics] Imaging [general, obscura Camera [fluid dynamics, ] Canals have a specific tidal flow tidal havespecific a Canals geophysics] [fluid dynamics, tides of the theory Canal Goldstein 1886 by in made Eugen was particlepositive the of stream discovery The . positive atthe of number any by surrendering ions formed the hence gasand on the depends ray canal positive of the nature ray. () exact the from The direction the opposite in migrate rays canal The field. electric applied the under anode the ray. toward Thepositive ionsmigrate or ray canal anode called are and anode, the from ions released the cathode represents anodeand with this tube [nuclear] gas-filled In rays Canal C.9 Figure

Camera obscura. (1850–1930). approach. The pinhole image formation was first described byAristotle described first was formation image The pinhole approach. of a light pattern generated by a source distribution on a screen or on ascreen distribution by asource generated pattern of alight

. The image formation is based on the paraxial image image the on paraxial based is formation image . The pattern due to forced pattern oscillation by induced photographic plate photographic (384–322 BC) (384–322 BC) . Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 red red succession of tidalwaves succession a with Alaska, Girdwood, in is another and Sumatra in River Kampar the in surf the is One example system at constant temperature and the second system a heating bath to maintain the temperature in system 1. temperature in system the to maintain bath aheating system second the and temperature atconstant system components: one component a two is with arrangement Athermodynamic thermodynamics] [computational, ensemble Canonical 20 approximately stitutes bone (i.e., con blade). shoulder scapula (cranium), the Cancellous and (ilium), skull joints, pelvis ball in instance for found to ahoneycomb (“trabecular”) similar structure internal bone with Spongy [biomedical] bone Cancellous See [fluid dynamics] waves Canal Surf.) Bono of (Courtesy Alaska. (d) and wave, Bono River; (c) Kampar bore, tidal Sumatra; (b) 50 km, to up for River Kampar the of distance the travels 3 m and C.10 Figure lous bone is bonelous is Young’s of modulus blood cells. (d) (b) (a)

Canal wave examples. (a) Sumatra, Indonesia. The “Seven Ghosts” wave can have a crest of up to to up of acrest have can wave Ghosts” “Seven The Indonesia. (a) Sumatra, examples. wave Canal E Y = 1 GP

tidal E Y a , whereas the cortical the , whereas = running for 8 km along the riverbed (see Figure C.10). (see Figure riverbed the along for 8 km running %

18 waves of the bone structure in the human anatomy human the in bone structure of the GP . a . Cancellous bone is rich in bone marrow and is an essential supplier of essential an is and marrow bone in rich is bone Cancellous . found in the skeletal structure such as the tibia has a has tibia the as bone found such in the skeletal structure (c) . The cancel Young’sfor modulus Canonical ensemble Canonical - - C 183

184 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Canonical transform Canonical storage ofelectriccharge culminatinginthefinaldescription. hasmanyexperimentalobservations Two as theinsulationbetween “ where plates ( defined by defined Hamiltonian ( Hamiltonian for instancethecapacitanceof ahorsewithrespect tosoilisapproximately foraninsulatorductor willbeuniform,which doesnotholdtrue Because oftherepulsive force between likecharges, thechargedistributiononaconductor orsemicon- in Farad [ and can lag in phase. in lag Indication oftheamount charge ( can and voltage driving the to respect with current the in retardation induce will dependence The capacitance. ( current the Consider defined. singular and no linear longer are parameters the meaning properties, crossover velocity. flow,high of jets “shock” through are flow layer boundary turbulent for canonical conditions the achieving tion, the canonical transform (with operator (withoperator transform canonical tion, the number Reynolds high The upstream. no obstruction are there that mandate also conditions the layer boundary turbulent canonical or of surface the formation roughness the by wall. In not curvature affected are Reynolds number flow number Reynolds high streamlined the in gradient pressure azero in 1904, features in the published layers on boundary the work on by Ludwig Prandtl Elaborating geophysics] dynamics, fluid [computational, layer boundary turbulent Canonical (withoperator transform to Hamiltonian compared When [computational] transform Canonical inenergy ( have fluctuations still will ensemble The E complex; become current alternating under capacitance and reactance, the resistance inductance, , Specifically, tions. opera current (steady-state) to alternating current direct from capacitance the changes general of adevice in [ac]current conditions; alternating to [C] specific capacitance Electrical general] , [biomedical, Capacitance ( as system) for the ( capacitance of the into afunction of now acapacitor transforms current process this tude). For charging the on acapacitorwhenvoltage ( , or canonical energy distribution distribution energy tion, or canonical a plate capacitor the capacitance is a function of the surface areaa platecapacitorthecapacitanceisfunctionofsurface ( as expressed to aHamiltonian to conform factor additional an requires transform cal wher NV C i N ), a sinusoidal function with time ( time with function ), asinusoidal ;; == ) and the applied voltage voltage applied the ) and ), a constant volume ( ), aconstant Vd em T k // F d b tr . Note that the temperature is related to entropy ( related is temperature the . Note that ( ), is a generating or transform function. or transform agenerating is =× frequency Re F V 868 10 3806488 1 C σε ], inactualitythevalue ofcapacitorsingeneralusehasadenomination of . ρ

>− elec = = ci H 5 730 350 () [ () {} 1/ / s ε qp ) and the Entropy Entropy the ) and ( ω N = ,, CI (C) (C) ( {} − νω QA 1)A of an incompressible medium are described in apipe in described are medium incompressible of an i , which yields a new parameter identified as the reactance, the reactance, as identified parameter anew yields , which V ra − ), and at constant temperature ( temperature ), atconstant and ground ng 23 = ε ) ( /2 ]/d V indicatestheelectricfieldbetween the plates, with

   e π= ma 1 , where ) 22 , in the shear layer will be the instigator for canonical condition. One of way condition. for canonical instigator the be will layer shear the in x gsK kg/s where where ∫ V ,

∏ ” orbetter, thedielectricseparatingtwosidesofcapacitor. The Vt CV i ) isapplied, t ) ( ), ), = S = ωω s i 3 ( ε ω = N is the Boltzmann coefficient. Boltzmann the is ρ isthedielectricpermeabilityand It 1 for the ensemble is defined by a normalized Boltzmann distribu - by a normalized defined is ensemble for the angular the is ex ma ci () pe x {} ma cos, qp () C Hq x tr cos, , si () C ) implicitly does not have time as a parameter. The canoni- The aparameter. as not time have does ) implicitly {} () ω {} = () i E QV where where , where , where ). The ensemble consists of a fixed number of particles particles number of fixed of a ).consists The ensemble / {} which translates to a current–voltage relationship relationship to acurrent–voltage translates which ) dependent; and parameters that have have that parameters frequency and ) dependent; pk ib T . The value ofthecapacitance is expressed S ) as ) as ), which defines the canonicalensembleat defines ), which I {} ma qp x TH ii ( represents the maximum current (i.e., current ampli- maximum the represents 1/ , . Anyobjecthasacompleximpedance, {}    TS Q A )( xp =∂ ) that can be “steady-state” stored represent the degrees offreedom the represent ), andtheseparationbetween the −   5 200 150 / H where the flow phenomena the where ∂ si N E () − tr { thenumberofplateswhile σ ) and Lagrangian formula- Lagrangian ) and ) q . The distribution of the of distribution . The elec }}{ XC , theplatechargedensity. c p = F, pk H ib 1/ } thehooves act rt tr tr tr ω =+ pF CF (1875–1953) (1875–1953) T orμ , a derived a derived   () ∂∂ F . For - t

, Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 C dQd ε of medium, and and of medium, defined by theelectricfieldbetween thetwochargelayers ortheelectricalpotential ( of awet hand holdingthedevice,providing themeanstodischarge. illustrated thestorageandrespective dischargeofchargeinacontainer, mediatedby theconductive interface Musschenbroek (1692–1761)andEwald Jurgens von experimentsthat Kleist(1700–1748)performed ing thecollectionofwhatwasthoughttobe“electric fluid,” now known aselectriccurrent. BothPieter van concurrent butseparateevents are notableinthishistoricaldevelopment, around 1745theworldwaspursu- respective plates. The capacitance ( capacitance The plates. respective two for the but opposite value in equal be will on applied acapacitor Acharge used. also are materials polymer electrolytes, mica, as ( Farad in expressed charge, electrical releasing and of storing capable Device general] electronics, [biomedical, Capacitor electricfield( external an When design. system counting coupling capacitive for such allow can use polydimethylsiloxane of the instance, For configurations. molecular certain to responds specifically that system capacitive to provide aligand-based used be can micropillars Polarizable equipment design. diameter, put particle severe to the constraints respect on with the large relatively is diameter channel the when specifically conditions, Particle microfluidic under counting imaging] electronics, [biomedical, spectroscopy Capacitive capacitance under resistance described . As representing parameter complex of anew introduction requires charging capacitive the circuit electronic distribution in an charge current alternating under lag of time Because general] electronics, [biomedical, reactance Capacitive ( See electronics] chemical, [biomedical, Capacitance, membrane charge while the voltage applied ( applied voltage the while charge potential average over an acharge of transferring result the Theenergy is on stored acapacitor ceramics. gel), and conducting in emerged foil electrolysis metal (oxidized radiodesign), early in capacitor, used air (tuning current in the capacitive system will adhere to the equation to the adhere ofcontinuity will system capacitive the in current ( capacitance the whereas in series the total charge is equal for each capacitor and the combined capacitance equates: equates: capacitance combined the and capacitor for each equal is charge total the series whereas in capacities, individual the adding thus storage charge capacitive for the area surface the increasing as the capacitive reactance, reactance, capacitive the as spectroscopy underimpedance referenced also is technology sensing This “lab-on-a-chip.” the through fluid passing the of composition chemical the hence and spectrum plot) capacitive aBode the to derive to as referred (also aBodediagram in of frequency afunction as plotted and calculated be can (i.e., capacitance) impedance density, Ohm’s and accordingly, resulting in a time decay ( atime current in of the resulting accordingly, this , field, electric this 0 equivalent , paper, polycarbonate, polyester (PET film), polystyrene, polypropylene, PTFE or teflon, silver teflon,or PTFE polypropylene, polystyrene, film), (PET polyester , paper,glass polycarbonate, =× 85418781 8 tI . == F =+ ). The capacitor design uses two conductors that are spaced apart by an insulating medium, such such medium, insulating an by apart arespaced that conductors two uses ).capacitordesign The ) ( 12 CC / Cd 12  () V . Vd 71

ωπ C () , applying the capacitance yields yields capacitance the , applying CC C ) changes under the influence of the passage of the quantity of specific molecules. The molecules. specific of the quantity of thepassage of influence the under ) changes law 12 tC = 2 0 − QV (constitutive Ohm’s (constitutive law), = 12 ν= / of alternating applied voltage with frequency frequency with voltage applied frequency angular of alternating the F/ or or () . Next to conductors semiconductor semiconductor conductors to and board, Next . circuit , printed XC m dI plates separated by separated metal as such plates media, various with made are . Capacitors c ( Rd the absolute permittivity of of permittivity absolute the 11 = // CC () V 1/ tR equivalent C C su ω = ppl ) of the capacitor represents the ability to hold charge ( ability the represents capacitor ) of the X

) over the external resistor ( resistor external ) over the membrane c Cd . )

) () =+ () Id (ac), t 12 ; solving for the charging phenomenon or respectively the the phenomenon or respectively charging for the ; solving J

E capacitance

=+ V () () = 11 σω = I // ()

) (i.e., charge released per unit time: t time: unit per released ) (i.e., charge 12 CC () / 1/ iE ω + vacuum CV εε CI () r 0 . 2 , which introduces the parameter defined defined parameter the introduces , which . Placing capacitors in parallel equate to equate parallel in capacitors . Placing i R , with , with . A capacitor discharges its electrical electrical its discharges . Acapacitor , ) (i.e., impedance: ) (i.e., impedance: σ the conductivity per unit length length unit per conductivity the ε r , the relative the ∇ ⋅= J 0 is the current current the Jis , where V X ) and and permittivity elect associated with with associated ri c ) expressed as as ) expressed Q E ) will drop ) is applied applied ) is ) andis ν . The Capacitor

C 185

186 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Capacitor, parallel plate of precisely precisely of ), e.g., oil), tube, of the lining function of tube diameter ( diameter of tube function current current water water the current through the capacitor ( capacitor the through the current [electronics, general] See general] [electronics, Capacitor, plate parallel C.11 Figure yields of charge release time Figure C.12 Figure ( density of the afunction is liquidsurface the level to respect with tube the inside liquidsurface the of The height column. anarrow inside liquid free surrounding to the respect with height level and shape surface resulting the and liquid surface a into inserted tube hollow gauge fine a between interaction surface The thermodynamics] [fluid dynamics, Capillarity signalonly. transmitter radio on to one specific locking hence circuit, the resonance frequency receiving of the capacitordetermines the of value The receivers. analog and amradioreceiver and FM design capacitor plate early in Variable used capacitance [general] Capacitor, radio ing current ( current ing that is directly dependent on the tension( dependent on the directly is that d h = I () 30/ tV

90 Capacitor. Capillarity. I = ca ° , or alcohol () pm or π/ or () tI su ppl = , the current leading over the voltage with respect to time (see Figure C.11). (see Figure to time respect with voltage over the leading current phase, the 2 in R ax

parallel e si d −

n d h RC ) for the following liquids is as follows: mercury falls below the surface surface the below falls mercury follows: as is liquids following ) for the h ρ Q () = / ) of the liquid and the “adhesive forces.” For instance, the height height the forces.” “adhesive For the instance, and liquid ) of the = ω t . When the capacitor is charged and discharged resulting from an alternat- an from resulting discharged and charged is capacitor the . When () 16 11 4c t tC Fg ./ ), where

T =− I plate ca p os . The surface curvature will make an angle make will curvature surface . The V Water ) per unit time; there will be a lag between the voltage and the current current the and voltage the between alag be will there time; unit ) per θρ su

capacitor ppl F ω T indicating the change in direction of direction in change the frequency indicating angular the is [] d ) between the liquid and the surface material of the tube (or tube of the the material surface the and liquid the ) between , where , where e1 − RC . / t g ; or discharge, ; or discharge, is the gravitational the is ρ d θ F h T Q Mercury () tQ = acceleration C.12). (see Figure 0 e θ − with the wall the with tube of the RC / t , or for the charging charging , or for the ) ( h d h as a a as =− 10/ , Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 curved surface, surface, curved with the wall outside the liquid. The height ( The height liquid. outsidethe wall the with liquid liquid Under these circumstances the surface of the bubble can be divided in regions that are subject to specific force force to specific subject are that regions in divided be bubble of the can surface the circumstances Under these number. by a low,capillary identified be may nonzero which tube, of the wall the with contact close in hence and bubble elongated be the may conditions Under locally. certain vary bubble of the can surface the across forces lubrication by viscous ruled wall be the and will abubble between stress viscous the where conditions to describe Bond number the with together ties number tional wall μ where the formation of a flow-free layer at the vessel wall. the vessel oflayer at aflow-free formation the to attributes and ofblood cells, red to deformation leads concomitantly wall of the surface on the rate shear The wall. the near large be still can rate shear the vessels Young’smembrane diameter For large modulus. of a conduit with diameter diameter of aconduit with Flow[fluid dynamics] flowCapillary [fluid dynamics] [fluid dynamics] number Capillary force, elastic to force viscous of Ratio dynamics] fluid [biomedical, number Capillary The capillary flow vasculatureblood systemsofthecirculatory undermechanicalcontractionofthe heart flow incapillary revealing theinfluenceofforces between thewall andthemedium.One specificallynotablesituationis residual forces becomeapparent intheflow [biomedical, ,general]Small diametertubingthatresults inhemodynamicconditionswhere Capillary of the liquid in a tube with radius radius with atube in liquid meniscusof the of the curvature of radius The tube. narrow inside a rise the to fluid phenomenoncause may This liquid. of the forces Waals Van der internal the than greater attraction of apolar because surface wall to the the wets liquid adheres and Thesurface forces. or adhesive bycohesive either dominated are a that fluid a solid and capilla (Greek: [fluid dynamics] action Capillary ofbloodflow. properties tion, emphasizingtheviscoelastic mechanical contactwithhighfrictionandfrequently resulting inbothvascular andred bloodcelldeforma- vessel. Thefull-circumferencewall ofthetube,thatis,capillary contactofthe red bloodcells results inafull straighten outwiththeedgeofcircumference ofthedisk-shapedcellincross-sectional contactwiththe Rouleaux formation. In casethered bloodcellsare tiltedthere willbeagradientinforce makingthecell ent force, which entailsthatthered bloodcellslineupasstackedparachutes,resulting inwhatisknown as of a passage way ( way of apassage Q = () 24 ρ πη acceleration ): , expressed as the pressure of the column of liquid under gravitational under of liquid attraction column of the pressure the ( as , expressed / is the the is [] () 2 γ PP 12 s () L

σ Surface − ), while the velocity can be a function of the radius ( radius of the afunction be can velocity the ), while surfac isconfined by thefactthatred is expressed as the integral of the velocity of medium over the cross-sectional area area cross-sectional over the of medium velocity of the integral the as expressed is P e LR r =ρ tension, 2 , yielding , yielding ∫ R 0 R gh (Ca) (Ca) ,

(Ca =η [] . The velocity is the result of the pressure gradient ( gradient the pressure of the result is . The velocity γ  compared to the force per unit area resulting from the over the tensionover the surface the from resulting area unit per force to the compared : hair, i.e., hollow tube) Surface forces in the operational environment operational the in between forces i.e.,: hair, hollow tube) Surface is the shear rate, rate, shear the is 2 − () η rr h viscosity, viscosity, ′ = 2 2 v σθ dr /γ surfac h mechanismofactionaswell asundersteady-stateconditions ′ ) with the whichof thedensity liquid the on depends may rise , known as Poiseuille’s as , known s v ) e velocity. In the description of of velocity.description the In cos a is the radius, radius, the is . Under capillary flow transporting a bubble the a friction bubble transporting flow . Under capillary ρ bloodcellswillflow through withminimalgradi- gR . R is defined as defined is h thickness, and and membrane thickness, the is Ca law. =µ r ) to the center of the conduit, conduit, of center the ) to the γ  ah rR capillary = E , when applied to vascular vascular to applied when , P P /c 12 − os θ for a certain tension for acertain flow ) over a length ) over alength , where , where g , the capillary capillary , the the gravita the - Capillary number Capillary θ is the angle the is E is the the is .

C 187

188 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Capillary waves Capillary ψ φ x P velocity. At the crossover wavelength the phase velocity has a minimum value, approximately approximately value, aminimum has velocity the phase wavelength velocity. crossover the At the phase than greater is waves capillary for group velocity The wavelengths. decreasing with increase 0.0173 m capillary than considered be less can waves wavelength a with waves water Generally, force. as a restoring acting description, wave the on influence fluids. of two interface Under capillary instance). The driving force and force the driving The instance). associated for Hawaii, in beach atthe wave to braking corresponds this scale (on large eventually to “break” crest sharp the cause will to dispersionsubject be and will higher The frequencies. lowfrom to high ranging spectrum, a forms rather but value, is not a singular “opposite crest.” side ofwavelength the The respective radiusR are inthecrest.become discontinuousatthesurface formingcrest, Assumingtwocurves eachwith based on the velocity potential, potential, velocity on the based defined for one side respectively, defined density density In the case of negligible influence of gravity influence thevelocity of negligible case the In wave grow and extinguish rapidly when the source (i.e., wind) engages or disengages. The (i.e., or disengages. source wind) engages the when rapidly extinguish capillary and grow wave or magnitude, size of the of aliquid. Because surface on the wind from resulting ripplewave the is stance Onecircum- liquids. two between interface an at Ripplesoccurring mechanics] [energy, dynamics, fluid waves Capillary C.13 Figure Navier–Stokes the in equation reductions and mations approxi influence additionally may number capillary The to tail. tip from unique locally respectively diagrams, process isconfinedprimarily by thesurface from a fresh wind blowing over smooth water. These waves have curved crowns and v-shaped troughs. troughs. and v-shaped crowns curved have waves water. over These smooth blowing wind afresh from and result ripples, small as be recognized generally can waves Capillary interface. surface fluid water–air v ′ -direction the imposed velocity, and imposed the −= = PT Ck ′ ′ e ρ − ky . The surface deformation velocity is defined by defined is velocity deformation surface . The s [] cosc

withamplitudeinthe () The relation for the capillary number in bubble growth. bubble in number capillary the for relation The 11 RR () 12 xt i , the discontinuity in the fluid surface pressure, thediscontinuityinfluidsurface (P)canbedefinedas + () os () ψϕ + , where ϕ shift. This translates in a varying pressure under external force external under pressure varying in a translates This aphase shift. K , respectively, where where respectively, , Ey ( η Pt P =∂ /e y and and -direction () ρψ 12 f )c // e =∂ wave motion wave P () ρρ ′ tension ( ∫∫ represent the pressure at the surface on either side of the crest. oncrest. side either of the surface at the pressure the represent φ 0 λλ v φφ energy can be represented as as represented be can vv Horizontal tube d ∂ () = C T () ∂− of motion ( c s and and ). Thebreaking wave causesthefluid pressure to the surface tension has an overpowering force overpowering an tensionhas surface the (see Figure C.13). (see Figure and group velocity velocity group and velocity phase the . Both 2 ak y ψ == potential ( 0 C dx = u → ′ are constants and and constants are ky [] b Tk a ( KE 12 s os γ 3 s ) will determine the wavelength spectrum spectrum wavelength the determine ) will r () ) φ kx () φ v ′ ρρ v ) ofthewave propagation inthe 0 = + φφ si Ck vv n, ′′ e ′ () ky () ∂∂ ψϕ , cosc where where t k + () = yd xt 2 y πλ ρ in case of afluid case in / ′ 0 the density on the on the density the os x the wave number, wave the () for waves atthe for waves ψϕ 02 . + 31 m/ and and wave s in a in

- Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 k generally the crests are sharp and the troughs are rounded (see Figure C.14). (see Figure rounded are troughs the and sharp are crests the generally the respective constituents,fortherespective phase definition oftemperature astheaverage kinetic energy( system isthesumofenergyconstituentsvarious phases Capillary waves are extinguished by molecular “ by molecular extinguished are waves Capillary sucrose), and oligosaccharides (e.g., inulin, also found specifically in AB blood in specifically found (e.g., also inulin, sucrose), oligosaccharides and (e.g., glucose monosaccharides in subdivided further is designation carbohydrate The lactose. and wheat, sugars, are of carbohydrates Examples charide. sac- as to referred Also compound. an organic as oxygen including definition, macromolecular full the on depending and , of carbon, consisting principally structure Molecular chemical] [biomedical, Carbohydrate concerning themathematicaldefinitionofthermalconceptsforasystem( madestatementswithrespectematical expressions. tothesecondlawofthermodynamics Carathéodory the Pfaffian. madesignificantstrides in formulatingthermodynamiclawsproper math- Carathéodory the geometricconfigurationofaspecificdifferential equationandtheappropriate solutions, known as namics, thesolution mechanismforthesecond law ofthermodynamicsrelies onhow tointerpret significant changesinthecomputationalapproach tothermodynamicaxiomas. In axiomaticthermody- [computational, thermodynamics]Mathematician from Germany. Thework of Dr. made Carathéodory Constantin Carathéodory, C.14 Figure cells where they form a marker in cell in amarker form they where cells mechanical termsofdisplacement(i.e.,: and heat( pressure ( b =× 868 10 3806488 1 . Q P

Capillary wave. Capillary ). Eachsystemwillconsistofdifferent phases(e.g.,liquid, solid),where thetotalenergyof the =+ ∆ UW  − 23 mk

, withthechangeofinternalenergy 22 g/ sK theBoltzmannconstant. to cell communications). to cell (1873–1950) ), polysaccharides (e.g., starch), disaccharides (e.g., (e.g., lactose, disaccharides starch), ), polysaccharides viscosity i . ThishasanalogieswithLord Kelvin’s (1824–1907) mv p = E ) ofasystem, gravitational waves .” For gravitational , withmass U andthework εε = ∑ mv E m ii andvelocity = = S () Vp y () ), suchastemperature ( 12 W // ,, describedin performed), and on the membrane on the and ii m 2 k , where v () ), volume ( 32 , in contrast, contrast, , in kT b k denotes Carbohydrate , where V T ), and ) of of C 189

190 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Carbon 11 atomic weight the atomic by definition element has stable This percentage. alarge in carbon containing chains of molecular composed are organism biological tures, struc- organic in block building atomic Major fuels. organic and carbohydrates as well as diamond and element Organic imaging] chemical, [atomic, biomedical, Carbon positron emission tomography emission positron isotope carbon unstable This imaging] chemical, [biomedical, radionuclide Carbon a pencil and a diamond earring. of tip graphite (d) and form; life biological (c) achameleon, atree; (b) wood; of out completely made cabin (a) Log C.15 Figure isotopes are are isotopes available Some of the structure. biological the with integrate seamlessly will they since applications imaging in used are isotopes carbon Additionally, 6 electrons. of and 6 protons, 6 neutrons, consists C is by one is positron.

Carbon is the building block of organic structures, as well as a fundamental ingredient for construction. construction. for ingredient afundamental as well as structures, organic of block building the is Carbon 11 ( (a) (c) C 12 and and 6 C ) 14 C (see Figure C.15). (see Figure as a tracer in order to label physiological processes. Thedecay processes. physiological order to in label atracer as ( 11 C) C) of 12.00000 atomic mass units ( units mass of 12.00000 atomic (b (d ) ) . Part of molecular structures such as graphite graphite as such structures of molecular . Part has a half-life of 20.4 min and is used in in used is and of 20.4 min ahalf-life has u ). Stable carbon carbon ). Stable process of of process Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 and time range (see Figure C.16). (see Figure range time and accuracy the to limitations are however There base), such. not and stones ametabolic (primarily abase as organism’s age the to estimate used radioactivity5730 years, to decay 14C the 14C its and no begins replenish longer levels respiration nutrition and 14C removes and through adds continuously thelife it organism’s(since throughout constant are an organism The in levels 14C animals. and by plants standard ratio of ratio standard metabolism normal During structures. of organic dating tool for radioactive astandard as used is and with a half-life of ahalf-life with of the pulmonary veins from the lungs (carrying oxygen-rich blood) and the hollow vein the blood) and oxygen-rich (carrying lungs the from veins pulmonary of the by means atrium right and the left to back leading and veins, combination of venules under a flowing capillaries, and arterioles, out into of aweb arteries, branching side, ventricular right on the artery pulmonary the side and pliance as well as the fluid the as well as muscle cardiac the put ( put dating. for radioactive tools quantitative the provides ratio remaining of molecularchainscontainingcarboninalargepercentage. Thedecay process of composed are organism biological structures, organic in block Major atomic building chemical] [biomedical, radionuclide Carbon volume ejected by the contracting heart contracting by the volume ejected Blood dynamics] fluid [biomedical, output Cardiac C.16 Figure rays cosmic isotope Carbon nuclear] [general, Carbon-14 dating tures as a common “cousin” with a ratio of aratio “cousin” acommon with as tures by stroke volume ( volume stroke by CO ) is thus a function of both the volume of the ventricles and the heart rate ( heart the and ventricles volume of the the of both afunction thus ) is in the whole body circulation whole body the in

Carbon dating of human skull. . ( Note 14 SV τ 1/ C : standard carbon has has carbon : standard 2 ): ): to to = C 730 5 12 OH ,

C =× is maintained while after cell after while maintained is levels of 14C are measured and the level of decay from the original value is is value original the from of decay level the and of 14C levels measured are

years RS ( ; 14C is produced in the upper atmosphere ; 14C the in produced is radioactive isotope . Theradioactive Adolf Eugen Fick Eugen by Adolf flow principle recognized . This type of radioactive dating only applies to objects that have carbon carbon have that to objects applies only dating radioactive of type . This V 14 . The heart ejects a volume of blood based on the muscular function of of function the muscular on a volume based of blood ejects . The heart dynamic constraints resulting from the vascular resistance vascular the from resulting constraints dynamic C) C) per minute of time, expressed in liters per minute. The cardiac out cardiac The minute. per liters in expressed of minute time, per . The circulation system comprises the aorta comprises system circulation . The 1 . 31 × mass 12.) The the mass Earth drops to 14C 0 − 12 to stable carbon-12 (same as the atmospheric ratio), atmospheric the as (same carbon-12 stable to death the the death

. Using the fact that the half-life for 14C is half-life the that fact the . Using 14 C occurs in normal living carbon struc carbon living normal in occurs 14 C will start to decay. Determining the the to decay. Determining start will ). When an organism dies it can it can dies organism an ). When as 14N by as bombarded is HR 14 (1829–1901) total the as on the left ventricular ventricular left on the C (superior vena cava), cava), vena (superior ): heart rate multiplied multiplied rate ): heart isby two electrons where it is absorbed it where absorbed is Cardiac output and com and the the - - - C 191

192 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Cardiac pacemakers efficiency: efficiency: associated an andhence devices of working efficiency the with associated a reality is there ideal is process has four (4) stages in an ideal mechanism; isothermal mechanism; ideal an in (4) stages four has process The work. of performance the and heat of exchange on the relies that of aprocess description theoretical the is asset Carnot’s remarkable most of thermodynamics. essence of the founders ing up in the exact same energetic point in pressure and volume (PV plot) as where it left off. Work plot) volume it where (PV and left as pressure in point energetic same exact the in up 2. of stage expansion adiabatic the as well 1as performed of stage during the expansion isothermal exchange (i.e., loss) atlow exchange heat compression, with isothermal temperature, third-stage followed the by adiabaticexpansion, with applications of the second of the applications practical on the insight essential provided who French physicist thermodynamics] [computational, (1796–1832) Sadi Léonard Nicolas Carnot, See [biomedical] pacemakers Cardiac individual. the of health general and training the on depending fivefold, by more than increase output can cardiac the exercise During respectively. blood, oxygen-depleted carrying operates based on internal temperature ( temperature on internal based operates engine by the entropy generated the and source heat external the both from entropy received of the disposal the and system external on the components: work performed two in divided the energy of distribution the for parameter Identification [thermodynamics] coefficient Carnot C.17 Figure ing the Carnot coefficient, coefficient, Carnot the ing ible process as as ible process (see Figure C.17). heating 70% Examples oftheefficiencyspecificdevices areasfollows: electricmotor or other stored energy stored or other e

c –85% Nicolas Léonard Sadi Carnot (1796–1832). = S ou ir

rC pacemaker ; hydrogen–oxygen fuel tput = η ofusefulenergy arnot () η temperature heat ( heat temperature

QT Car law . ou o ou not

ti

mechanism provides for the stroke in stage 3. Since the described Carnot Carnot described the 3. Since stage in stroke for the provides mechanism of thermodynamics of =−

n () TT , where , where ti deliveredenergyfortheproces T cell 60% in ) and the external temperature that drives the process ( process the drives that temperature external the ) and no Q Q ou T t L represents the energy transferred out system. of the transferred energy the represents ut ); and the fourth phase adiabatic phase fourth ); the and ; nuclearpower-plant 30% . This provides the entropy provides . This in 1824 and may be credited as one cultivat of the as 1824 in credited be may and expansion during delivery ofheat( duringdelivery 50% s === –95% WQ –35% Carnot engine . TheCarnot / “consumption” of a system, “consumption” of asystem, ( ; gas furnacefordomestic S ; incandescentlamp5% ) generated by an irrevers by an ) generated () QQ

compression HL − Q H Q T ) athigh ( H primarily W ou , ending ending , . t ), yield ), ) is ) is - - - Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 of energy exchange processes andresulting work were firstdescribedin1824(see Figure C.18). Carnot, aFrench (1796–1832).Theprinciplesofthethermodynamicsandassociatedefficiency able order. TheCarnotcycle andCarnot engineprinciple were conceived Léonardby Nicolas Sadi where agasisexpandedandcontractedintwoisothermalstagesisentropic stagesininterchange- [energy, general,thermodynamics](syn.:work) {use:cooling,heating,thermodynamics}Afour-stageprocess cycle Carnot [general] Electromagnetic or acoustic wave or acoustic Electromagnetic [general] wave Carrier systemisclassifiedasfacilitateddiffusion , anactive process. Thistransport molecules totransport. at specific receptor sites.The respective individualized protein chains are highlyspecialized intheselectionof [biomedical] Protein ofmolecules through thebiologicalcellmembrane chainsthatfacilitatethetransport Carrier 1973). Togetherwith adapted andincorporatedinthefirstheart–lung machinedeveloped by Dr. John Heysham Gibbon(1903– human [biomedical] Vascular surgeonfrom France, whoinvented themechanismofblood oxygen exchange outsideofthe (1873–1944) Alexis Carrel, expansion periodic the in results ing) (cooling/heat exchange heat the Alternating process. exchange aheat in resulting temperature loweither or high gas with filled is the piston off by sealed compartment apiston, the and cylinder a of consists engine Carnot The thermodynamics} heating, work) (syn.: cooling, {use: [energy, thermodynamics] engine Carnot C.18 Figure has been removed by a demodulation scheme. In electromagnetic In scheme. removed by a demodulation been has wave carrier the after of action mechanism of spectral some kind with analyzed be can that arange in or range audible the in be can modulation to promote the chosen long distance whereas propagation, be can wave stations).carrier The channels/television respective for wave the carrier same (using the ing encod to digital modulation frequency from changed has countries other various in (inand 2009) States United the in mechanism transfer the For television bit notmodulation. in in is rate, of transfer nism mecha the format digital In location. to aremote receiver for transmission information to encrypt lated (a) body forwhichhereceived theNobel Prize inPhysiology andMedicinein1912.Thismechanismwas Pressure μ

A

JT (a,b) Pressure–volume diagram for a Carnot cycle at a specific temperature. aspecific at cycle aCarnot for diagram (a,b) Pressure–volume μ =0 D JT >0 μ JT =0 Q Charles Lindbergh (1902–1974)Carrel machinein1935. developed thefirstheart–lung

Q Two-pha L H

Volume B St ate: ide se st μ JT C = ate: liquid– al ga Tv h fg fg and contraction of the sealed-off gas, moving the piston up and down. the up piston moving gas, sealed-off of the contraction and s h =Const va in analog format that can be frequency or amplitude modu frequency be can that format analog in Critical po po int r (b

) Pressure μ μ Sa JT JT turation dome =0 >0 amplitude modulation is is radiation modulation amplitude μ Sp JT =0 Two-pha eci fic entropy and the reservoir is exposed to to exposed is reservoir the and μ Rankin JT se st =

→ Tv h ate: liquid– fg fg h =Const va po Carrier waveCarrier r - - -

- C 193

194 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Cartesian coordinates {} completed the work of the Jeancompleted Picard He Italy, geophysicist. from and engineer astronomer, and [astronomy, geophysics] Mathematician, general, Giovanni (1625–1712) Domenico Cassini, x,y,z]). [coordinates: (three-dimensional planes orthogonal or three dimensional) René Descartes after named system Coordinate mechanics] [general, coordinates Cartesian radio of the part is which decoder,in a is recombined signal converted multiplexed The ratio. low signal-to-noise and consumer) to the (reproduction input of signal the transfer frequency in for accuracy 1966 standards in the to set introduced was standard HiFi The high-fidelity. HiFi, as or 15 kHz, defined and 30 Hz between is transmission radio air the across transmission the for encoding audio the perform Radiostations stereo. in transmitted is 108 MHz). radio FM General am in used oval shapes are sometimes referred to as cassinoids. to as referred sometimes are shapes oval contracted These eight. of figure outline general the in shapes irregular and oval, primarily loop shapes, Cassini astronomer, son and of [astronomy, mathematician, French physicist, general] (1677–1756) Jacques Cassini, C.19 Figure C.19). (see Figure spacecraft Cassini by the powered Administration, Space and Aeronautics National by the investigation situ in the as well as (to for the to Saturn, used date) 10mission also year 1789. was in name son, Cassini’s by his continuation the 1670, in after of France set out map as well grandson, a topographical by his completed to be ( management on water worked Cassini engineer an As Division. honor: Cassini his in (not named belt), acontinuous are of Saturn which rings of the division the discovered also Saturn orbiting . Cassini satellites four of discovery the system, specifically solar of our description on the contributions for his known is Cassini Giovanni planets. of several period rotation the as well Moon as of of the rotation axis of precision the of the description theoretical athorough presented He him. after named aptly was which Saturn’s split in the ring he discovered addition In for cartography. globe opposite world. side the of from the ionospherereflection the ranging from due to distances extreme travel can waves short into very reaching waves modulated frequency whereas up to 200 km, range, ashort have generally waves radio modulated Amplitude pleasure. listening for the frequencies: audio rate 09 .s () [] () νν (1625–1712). Cassini provided a detailed mathematical description of curvature of various closed closed various of curvature of description (1625–1712). mathematical adetailed provided Cassini left + (150 kHz–26 MHz), whereas frequency modulation is used in FM radio (87.5 MHz– radio FM in used is modulation radio (150 kHz–26 MHz), frequency whereas

Giovanni Domenico Cassini (1625–1712). Cassini Giovanni Domenico ri gh tl 22 flow +− ν [ left () () unit, and the output is transferred to an amplifier and relayed to speakers speakers to and relayed amplifier to an output transferred is the and receiver unit, and and νν control for rivers; specifically the river Po in Italy, known for its devastating flooding) as flooding) river forthe devastating known in its Po Italy, specifically for rivers; control ef tr modulation is obtained at two sepa attwo obtained is Thestereo modulation audience. to the ways ν ri gh angular division scale of the of the scale (1620–1682) division latitude and longitude angular on the ight t (i.e., multiplexing) with respect to the pilot tone to the respect with (i.e., multiplexing)

in () 40 πν p t ] + .s 1 i nn2 () πν (1596–1650), (two- planes two using p t × 75 kHz. Giovanni Domenico Domenico Giovanni in FM FM signalin Theaudio ) ( ν p , expressed as as expressed -

Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 processes to the mean orientation of a synchronously locked satellite locked of orientation asynchronously mean to the processes as a function of location. These laws are known as the Cassini’sas known are laws These of location. afunction as Sun the around plane orbital to the normal by the described plane the with Earth the around plane elliptic rotational to the normal the from intersect the by carved the plane that was observations Cassini’s fromconclusion third The orbit acircle. as elliptic precession the that he found by Giovanni observation On second Domenico Earth. the Cassini faces Moon always the planes. two the other by confined is plane lunar ecliptic the describing vector the that amanner such in orientated are that vectors coplanar three form plane lunar ecliptic to the normal to the addition in Moon,of the and following three laws. TheMoon laws. three following in compliance when is it state Cassini in a as residing [astronomy, defined is geophysics] Asystem state Cassini Casson model 1959, Casson the as known in behavior viscous of model his whopublished engineer behavior fluidic unknown Relatively [fluid dynamics] N. Casson, C.20 Figure winter in of Polaris left to the pivots [ earth of the axis rotational the as seasons the with change will dipper) Star (Polaris) the North to in reference found is constellation Cassiopeia the of The location [astronomy, general] , Cassiopeia as plane angle fixed the a moon’ssubtends (2)to plane The normal equatorial Earth. the faces Moon side ofalways the same the meaning rate; rotation orbital mean its matches that rate uniform follows: as (1) a at TheMoon constrained spins is laws these to according rotation The moon’s well. axial as orbits Moon Cassini (1625–1712) orientation and position of the derivations geometric 1693,of in mathematical the with [astronomy, astrophysics, geophysics]Three setsof laws Cassini’s for earth’s satellites. With modifications these laws also appear to apply to the obliqueness theof Venus apply to obliqueness to appear also laws these modifications With satellites. for earth’s with respect to Earth respect with , with ursa major (big dipper) to one side and Cassiopeia of the lower other side (the relative position lowerside position (the of other the relative (big to Cassiopeia one major side dipper) and ursa , with θ= 15 Outline of the constellation Cassiopeia. constellation the of Outline (Polaris is fixed in our view of the northern sky), which is part of the ursa minor (little minor (little ursa the of part is sky), which the northern of view in our fixed is (Polaris 9. ° (twentieth century) (twentieth . (3) The normal to the moon’s equatorial orbital plane, the normal to general orbital plane plane orbital general to the normal the moon’s. (3) to plane, orbital The normal equatorial

. The same rules have been applied in setting the configuration of geostationary geostationary of configuration the setting in applied been have rules same . The . The shape of Cassiopeia is more or less a flattened “W” (see Figure C.20). “W”Figure (see flattened a is more or less Cassiopeia of shape . The of the moon, describing a cone, is executed in a plane that intersects the the intersects that aplane in executed is acone, moon, of describing the revolves the Earth the revolves Cassiopeia , or the fluids as Casson fluids. Casson as fluids , or the will contain the orientation of the rotational axis of the Moon of the axis rotational of orientation the the contain will planetary in a 1:1 spin-orbit ratio, meaning that the same side of same the a1:1 that in spin-orbit meaning ratio, motion described by rules Giovanni Domenico laws precession . This applies in the scope of the of thescope in applies . This as well. as with the normal to the ecliptic ecliptic to the normal the with ]); to the right in summer in ]); right to the (1625–1712) (1625–1712) Casson, N. Casson, with the the with and and

C 195

196 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Casson model where of flow ratethrough acapillary tube(alsosee planeseparatedby aliquid plate;andmeasurestationary thickness;rotating conewithrespect tostationary mechanisms inusetodeterminetheviscosity:twoconcentricrotating cylinders;rotating diskwithrespect to is afunctionofthedeviceandmethodsusedtoderive theviscosity. Specifically there device are fourprimary constant. Note thatbasedontheFåhraeus–Lindqvist effectthedeterminationofapparent viscosity distribution peakorthatare sharplydistinguishedfrom theneighboringvolumes (seeFigure C.21). zenith angularorientationsinorder toidentifyregions withX-raydensitythatisdifferent from thenormal program thatrenders avisualization.Thevisualizationcanbeselected by choosingslicesatazimuthaland scans aswell asaxialincrements, athree-dimensional byreconstruction meansofacomputer isperformed that are stackedinascanningbelt.Once allthemeasurements have beenacquired from 360°circumferential array intheaxialdirection by discrete stages,orthrough theuseofmultipleX-raysources anddetector arrays anatomical features fortheimagereconstruction. Theaxialcomponentisadded by moving thescanning dimensional dissectionplanethathave equalattenuation,providing thetriangulationforlocationof intersects oflinesfrom anglesforidentificationofpointsinthetwo- various (multipleandincongruent) angles completinga360°circumferential scan.Thecomputationalcomponentisinthecalculationof reconstruction resulting from multiplesequentialorparalleltransmissionmeasurements atincremental [general] Computerized axialtomography, alsoknown asCTscanorX-ray tomography. X-rayimage scan CAT dough, andchocolateunderlow isdefinedas shearrate.Theviscosity [biomedical, fluiddynamics,general] Non-Newtonian flow model Casson solution ofacid, salt the Greek word for“the direction inwhichtheSunsets.” Both thecathodeandanodesubmergedina positively chargedanode,asintroduced by MichaelFaraday (1791–1867).Theword “cathode” comesfrom [biomedical, chemical,electronics, general]Negatively chargedelectrode, usuallyaccompaniedby the Cathode C.21 Figure (e.g., and anodeundertheinfluence oftheappliedelectricfield resulting from an externalelectricalpotentialsource of thecharge.Thepositive (cation) andnegative (anion)chargedionswilldiffuse respectively tothecathode battery σ s ,0 isthematerialyieldstress,

CT scanner X-ray machine. , chemicalreaction), which isrequired inorder toinduce theionicmigration. tobestationary

, orbasewilldividetheconstituents oftherespective electrolyte(s) basedonthesign

γ  theshearrate,and viscosity

model k C modelofcolloidsuspensionssuchasblood, theCassonconstantorrheological ). It isalsoknown asCassonequation. η visc = () γσγ σγ sC ,, 00  + () kk sC + , Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 ( m electron chargeequivalence, with current density cathode willemitelectrons, formingcathode rays. Theelectron emissionwillprovide afree spacecurrent, negative electrical potential,withrespect totheanodewhichisatapositive electricalpotential.Aheated electrolysis willgreatly dependonthestrength oftheacid(acidity)expressed inpH. willbeat by theaddition ofanacid, suchascarbonicacid,sulfuricnitricorperchloric acid.Thespeedofthe the time-dependentMaxwell andformoxygen ( respective anodeandcathode,therespective cationandanionwilllosetheirchargeinexchange withthe the polarized watermoleculeandthehydrogen ionwithpositive coefficient for the material surface ( coefficient forthematerialsurface conductor charge gradientbetween thecathodeandanodewillresult inionization ofthewater When (consistingofelectrons) between theelectrodes isappliedtopure watertheelectric The Crookes tube was the predecessor to the modern neon light signs. light neon the modern to the predecessor was tube Crookes The Crookes tube. the electrode tube, investigational the glow, introduced and cathode of the description Picard glow [atomic, Low-pressure nuclear] glow Cathode C.22 Figure defined asafunctionoftemperature T involved. Additionally due to the electronics Additionally involved. and of glass amount large due to the heavy and bulky are CRT screens CRT screens. to as referred are screen display, LED and flat-panel screen, the The monitors oscilloscope predating screens. and old-fashioned in component elementary the was CRT screen. a fluorescent impacts before it electrodes by deflected be can that (electron gun) electron [biomedical] Vacuum tubewithacathode thatemitselectrons andahollow anodetoprovide aprojectile ray tube Cathode J 42 e =− HO =× () 22 14 03 10 10939 9 .  (1620–1682). (1832–1919) Crookes It wasn’t 1870 William Sir until that aformal provided re  ()

. Theformationofthe . HO π mk eb −+ − ++ 31 23 kg; 22 J hT HH , whichcanbecalculatedwiththeuseofRichardson’s law,

h =× 2 e 209710 62606957 6 eC O − . =× () (CRT) (CRT) φ 2 equations (seeFigure C.22). elec OH ) andhydrogen molecules( 16 . kT 275 10 0217657 ) ( r  HO , alsoreferred toasdriftcurrent densityordisplacementcurrent density; ≅ Jean in 1675described astronomerthe Jean discharge first by French 22 3 , usingBoltzmanncoefficient 05 () . + fortungsten).Theconceptofdisplacementcurrent alsoappliesto 3

OH ion istemporary, andisduetotheinherent attractionbetween − 34 + mk ++ − 19 2 g/ ; OO s φ thePlanck’s constant,and elec −−  thework function;electron mass, H 48 2 ). Theelectrolysis ofwatercanbeenhanced 2 charge (cation).Upon reaching the k b HO =× + 868 10 3806488 1 ↔+ . e 48 22 r  themeanreflection H ) − , which is a poor , whichisapoor 23 m Cathode ray tube ray Cathode 22 kg/s K;

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198 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Cathode rays Cathode cathode the from avacuum in emitted Sir beam, Crookes tubeor tube(after [atomic, Electron nuclear] rays Cathode C.23 Figure energy electrical a consuming amountsignificant are of devices these of action CRT mechanism of the construction Figure C.24 Figure solution methodbasedontheresidues ofthedeveloped serieswithrespect toafunction(see Figure C.24). priorin1676.Anothermathematicalcontributionby Cauchyisthe Hooke (1635–1703)more thanacentury description ofstress andstrainonmicroscopic scalebasedontheinitialmacroscopic definitions by Robert [general] Mathematician, physicist,andengineerfrom France. Cauchyprovided significant detailsonthe Cauchy, Augustin-Louis to electrolysis air atmospheric and coronas. particular of in ion diffusionapplies process positive anet charge. The cathode to the carrying , hence attracted is Ionthat electronics] [chemical, Cation

Drawing of Augustin-Louis Cauchy (1789–1857). Cauchy Augustin-Louis of Drawing CRT computer monitor to attached a cameramounted on an optical microscope. , with inherent generation of heat (see Figure C.23). (see of heat Figure generation inherent , with [1832–1919]).

(1789–1857)

Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 ) ( Res the deformation or flow deformation the where the coefficientof solution canbewrittenwiththeuseof a Bessel function ofzeroth order ( rotational displacement, wavedisplacement, rotational with curve of radius at anypoint analytic in the points inside the curve withinthecomplexdomain analytic inthepointsinsidecurve outbyoftheclosedintegralpath,butisnot theintegralloopaswellcarved asonthepointsofcurve ary conditionsthedisplacementpressureary willsatisfy closely related tothemach numberandisoftenexpressed astheMach numbertothesecondpower. (see Figure C.25). residues isdescribedby thealgorithm: velocity (i.e., singularpoints).Thefunctioncanbedeveloped inaLaurent seriesas: complex domain.Considerafunction Louis Cauchy (1789–1857). The “residue” theorem appliestosolvingintegrals inthe over closedcurves [computational, fluiddynamics,general] Mechanism ofcomplexfunctionanalysisnamedafter Augustin- method ofCauchy residues pressible) liquid withfinitedepth atthesurface, (1789–1857) andSiméonDenisPoisson (1781–1840)regarding thewave [computational, fluiddynamics] Mathematical problem introduced in1815 by Augustin-Louis Cauchy wave problem Cauchy–Poisson [fluid-dynamics, tensor strain Cauchy forces tothecompressiblethe ratioofinertial forces. TheCauchy numberisafunctionofthefluiddensity ber describestherelativeandelasticforces undercompressible ofinertial importance flow conditions;infact factorofinfluence,namedafteracontributorinthefield Augustin-Louis Cauchy (1789–1857).Thisnum- [engineering, fluiddynamics]Thisnumberidentifies regimesinfluid number Cauchy C.25 Figure ( and density g fz ρ thegravitational () , [] aswell astheflow velocity( fz =+ , 12 01 potential ( = () z The Cauchy residue method. a 12 ρ − j is 11 ) as . For instancetheLaurent functionfor !( mechanics] Res P / // zz acceleration, and [] φ ρ= )! fz ) equalszero ++ , velocity (solid respectively fluid). (solid respectively velocity 22 a () (C =ρ j ∂∂ − 1 φ () withrespect to . ThisisalsotiedtotheCauchyintegral 11

ε= y tg v Z ∇+ ) andtheelasticmodulusoffluidmedium( −+ 1 23

vv  = ∇ C C zF 2 v 2 1 ) ( ∫ φ 23 () C 2 Z f ∇ Ft / 2 fz () E that is analytic and holomorphic inside the curve ofthedomain thatisanalyticandholomorphicinsidethecurve 0 () () () t , T ) z 1 the time-perturbed influencefunction (e.g.,storm).Asbound- thetime-perturbed , ! the vertical displacement, thevertical dz ∼

undertheconditionthatLaplace derivative of the z () ) ( 3 Z zz h r E = 3 , respectively − is the Lagrangian the finitestraintensor Eis , where + . Thedisplacementfollows from thelocalpressure ( ξ= 2 C  π 3 0 if with ∑ istheresidual ofthefunction 1 fz /gt () k n = Z [] 1 ∂∂ n−1 Re Res C = φ r z n−1 e s, =− [] iz [] / fz around the point z z ,. = z jj cos 0 C 01 j , aswell as fa =+ n flow () , where theresidue ofthefunction == xi θ x a Z ), usingthewave number k J and − = n 0 propagation ona(slightly com- x () where compressibility isa 12 y Cauchy–Poisson wave problem wave Cauchy–Poisson j ϖ 2 : π y excluded points fz ∂∂ E The Cauchy method of TheCauchymethodof thepropagation directions, if ξ () , ). The Cauchy number is ). TheCauchynumberis  / ∫ = ϖ z tt =− 0 () =− canbewrittenas zz r ∑ fz si / n ∞ () () n [] =− ∂∂ θ ∞ φ − in ; the surface ; thesurface az ad nj () z z k 0 1 z z , ; = =

z 0 . The . The z 2 2 P , …, and and πλ ) / n ,

f , z v 

n

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200 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Cauchy–Riemann equations [] ( Cauchy–Riemann equationsare expressed as published in1779,andwithfinishingtouches by Augustin-Louis Cauchy (1789–1857)in1814.The work by Jean leRond d’Alembert (1717–1783)publishedin 1752,Leonard Euler(1707–1783) by the German mathematicianGeorg Friedrich Bernhard Riemann(1826–1866)in1851,basedonthe the factthatholomorphic functions are analyticitfollows arbitrary disk(D)withintheclosureC) oftheintegranditcanbeshown ( arbitrary for to thecomplexnumber current day accepted standard, standard, accepted day current can bedescribedby pressure inaseries,whilethedisplacementsatisfies Cauchy–Riemann equationswithrespect totwovariables, for theintegrationconstraintstocomplexfunction.Thelatterintegralprovides thetoolstosolve the material intended for consumption or processing. for intended consumption material solid orliquid transport to used vacuole or of vesicles theformation in results The process processes. 1728 in as constant gravitational universal the derived Cavendish days. men of his one wealthiest of French of the nobleman origin, British and physicist, chemist, Scientist, [general] Henry, (1731–1810) Lord Cavendish, [computational, fluiddynamics] Based ontheCauchyintegral equations Cauchy–Riemann where Generally theformationof bubbleprogresses ataslower ratethanthecollapse, providing aunique mechanism deformation orvapor bubble; [biomedical, fluiddynamics,general] Sudden decrease in volume (collapse)ofexpansion (e.g.,mechanical Cavitation cell the in invagination formed of actively Location [biomedical] Caveolae C.26 Figure fi () gt () gt χπ /c 2 23 4 λ = πθ

) represents thewavelength, provided 12 ϖ {} [] Pr −

1 Lord Cavendish Henry (1731–1810). (Courtesy of George Wilson.)  () ∫∫ DD os }

[] , whichfor

fz () rt /! = 22 () z zd − () =+ − gh () ) ( χπ xi gt gt nucleation) thatexerts forces onthesurrounding mediaandmaterials. . 2 66 / / . 21 zi y as ϖ 2910 7259 +∂ [] 12 25  fx !c Pr () × 2 yields: () + ∫ φϖ os − iy 11 =− =∂ , θ Nm ()

gt = // ξπ vx /e fz ux ξπ 23 () 32 = () 22 () π =− /kg () + , ∫ tg −∞ gt ∞ /! [] yy ∂ yi () 21 3 {} (see Figure C.26). (see Figure /s z gt kg 24 ′ ∂ + ρ 72 [] ux fa ϖϖ zd z dz dz vx and nn 2 () () 3 () () { ρϖ ∧− tk , !! 22 fa , !/! /! y ∂ [] () = y 42 to support the endocytosis the membrane to support 3 ux [] ′ and ni () , aholomorphicfunction. () 13 PPr () in !/ = 3 2 22 ,, () 67 () () + π () cos/ v yy . 12 gt () χ [] 51  () xy ∫ / ∂= × π θ gt , fz , where if 52 ϖ 2 () χ∈ 0  ∫ , asexpressed inthe thesis − 2 [] −∂ 11 . Note thatthewavefront 4 () 5 DC () Nm () za t vx zz , 2 ⊂ kJ ∧ ()

− after developing the after developing the / 3 isthe “logical” “and” 22 () − yx , forwhich kg/  − + 1 dz ad + ∂ , compared to to , compared . For an () kz 13 , withrespect z 222 , and 0 () 59 kd ! } k

≈

Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 KE heat ( heat exchange ofthebubbletosurrounding liquid mediumisprimarilysubjecttotheNusselt where respect totheinitialradius entirely different. entirely is functionality the number Euler the resemble may this Even propeller in though action. velocity angular pipe parameter withthedimensionsofvelocity) insecond-order derivative by the surface ofthebubblecapturedby thesurface by incremental deltainradius(Δ from which the top layer has been removed which makes the charge layer light sensitive and can be used in in used be can and sensitive light layer charge the makes removed which been top has layer the which from semiconductor structure device Charge-coupled solid-state] quantum, optics, dynamics, fluid [electronics, camera CCD See solid-state] quantum, electronics, [computational, CCD pressure, local density,KE the where Pis to in relation gradient pressure” of Ratio “static [energy, dynamics] fluid number Cavitation ( function of therateofchangeover time( chemical changes. Thecollapseofasphericalbubblecanbeassociatedwithkinetic the wave can becriticallydampedrangingtoundamped.Cavitationcanprovide mechanicaleffectas well as that willobeythewave laser ablation(i.e.,initiatedby thermal can bedescribedresulting from durationevents, thermalablationprocesses, suchaspulsed specificallyshort materials (i.e.,initiatedby mechanicalforces), specificallybiologicalmedia. Additional occurrences ofcavitation of mechanicalinteraction.Cavitationmayresult from interactionofultrasound pressure wave withsoft Figure C.27 C.27 Figure expansion/collapse therateofchangeiscaptured velocity by equivalent asurface (i.e., change inbubblediametercanbedescribedasawave phenomenon.Assumingthespecialcaseofadiabatic and henceotherconservation occurs duringthesize reduction ofthebubble.During condensationthedensityofvapor bubblechanges involving created ionized duringanablationprocess plasma (e.g.,laservaporization) orwhencondensation of thesystem.Theforce ( proportional to the momentary changeinkineticenergy( tothemomentary proportional rarefaction vs.expansionprocesses), whichtiespressure anddensitytogetheras == flow, especially in a curved vessel, this will also be very useful in determining the impact of shape and shape of impact the determining in useful be very also will this vessel, curved in a flow,especially 24 γ Q πρ a

represents theadiabaticfactor(definedasratioofspecific ) required tochangethetemperature ( P rr v 32 the fluid vapor fluid pressure the ,  Cavitation process for bubble generated by laser heating resulting from nanosecond laser pulse. () / 3

π

equation withassociatedpropagation ofeffects. Depending onthematerialproperties PR 10 () F rbubble R ) exerted by thecavitationprocess atanyspecificpointinthecollapseisdirectly 0 breakdown formation withassociatedinternalpressure 33 Electric Bubble − laws r σ R . The true nature. Thetrue ofthebubblecollapseismore intricate,specificallywhen c max1 needtobeincludedinthetheoretical evaluation process. Therateof = 2( v flow expansion). Thecavitationprocess isaccompanied by shearwaves t ) ofthebubbleradius the flow the t collapse1 P – Cavitation; T collapse ) ofamass( collapse velocity (average), velocity First v

charge )/ KE W t collapse2 ρ =∆ v flow R P M - max2 1 ) ( coupled , in two phases of the ) by 1 K]ofthegasintwophases collapse Second rr definedusingthedensity = 2 , i.e., thework) over thedistance traveled ) ) (  rd r () ), t = Time (μs) W ρ

expressed as device the fluid density. In addition to density. addition fluid In the 22 heat [ rd =∆ Fr t . P cQ :

sp (seeFigure C.27). rr /  P =∆ v energy (KE)thatisa += 00 s ′ rd  () = 32 = = () / ρρ mT ρρ rt () rv  () P = 22 1 /ρ , describing the , describingthe / number ( γ dt () a t . The rate of . Therateof s ′ , with , with ; “constant” CCD camera as as () Rr 0 Nu 3 γ a ) , C 201

202 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 CCT ture, measuredKelvin in ( lamp. Thecolorofsource lightis related totheemissionfrom areference tempera source heatedtoaparticular - [general, optics]Correlated color CCT C.28 Figure C.28). (see Figure format matrix resolution in of ccd number by the limited are that images to capture form array tive character, and the RGB standard. (red–green–blue) for instance, used in thedifference between dyes CMYK with (cyan–magenta–yellow–black), standard a subtrac C.29 Figure experience ofobjectcolorscanbesignificantlydifferent (alsosee illuminated by thesource. Two lampsmayvisuallyappeartobethesamecolor, whiletherespective visual not give informationonitsspecificspectral distribution, more soontheappearanceofcolorobjects

Picture of digital camerausing CCD element for registration of light and radiance. spectrum Correlated color temperature map: (a) 1931 map: CIE x temperature color Correlated K ). Thecorrelated colortemperature classificationforalight y (a) (b) 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.8 0.9 500 temperature. Thecolor 0.0 490 480 520 470 460 0.1 CMYK 10,000 0.2 380 ∞ 540 T C (K) 0.3 6,000 4,000 560 0.4 x emitted by a source, primarily a appearanceoflightemittedby asource, primarilya 3,000 , ychromaticity space. (b) Color outlining chart the 2,000 2,500 vision 0.5 580 1,500 0.6 ) (see RGB 600 0.7 Figure C.29). 620 700 0.8 unites in the array or array the in unites source, however, does - Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 ε lar concentration centripetal (tangential) force balances the gravitationally confined orbital force (see Figure C.30). force (see Figure orbital confined gravitationally the balances force (tangential) centripetal energy) where under theoperational conditions(concentration the ionsolution withthechemicalpotential half-cell potentialis temperature. At thebodytemperature° of37 tration ofaspecificion,respectively, onthe outsideorinsideofthecellmembraneandT galactic dust and stars. The escape velocity for an object from any celestial body with mass mass with body celestial any from an object for velocity escape The stars. and dust galactic [astronomy/astrophysics, general,mechanics]Anyobjectingalacticspace,rangingfrom planets(e.g.,Earth ) to bodies Celestial F Nernst half-cell the materials used, communicationsnetwork. For theelectricalpotentialthatcanbeachieved isafunctionofthe abattery structures,specialized muscles aswell cellsthatformorgans,supporting asahighlyconfigurable The ameba isanexampleofasingle-cellorganism,whereas thespeciesHomo sapienshasamultitudeof enclosure. Cellscangrow andformsemipermanentadhesionsto otherstructures andothercells. well asproviding amechanismtoactively move thecellby meansofchangingthe configurationofthe genetic informationandphysicallyadjuststoexternalshear forming thecell pump cellinabattery needstobeconsidered. Thebiologicalcellhasalipid–protein dynamicbilayer familiar withthebiologicalcompositionofsingle-andmulticellorganismssecondarilycharge [biomedical, chemical,energy, solid-state]There are several typesofcellstobedefined:primarily we are Cell C.30 Figure which provides forchlorine withrespective intracellularconcentration higher altitude (e.g., from a plane at cruising altitude) changes the radius ( radius the changes altitude) (e.g., atcruising altitude aplane from higher speed ( speed which becomes becomes which radius radius io ni =× = 453910 64853399 9 . () R v RT e ), in perpendicular direction, required to overcome the gravitational attraction of the body with with body of the attraction gravitational to overcome the required direction, ), perpendicular in and gravitational constant constant gravitational and potential equationforthespecificionsinplaceateithersideof cellmembrane: /F A full moon (celestial body) in the eastern sky. eastern the in body) (celestial moon A full ZI on G 2 represents theGibbs free energyand ln membrane thatenclosestheintercellular fluid, whichmaycontainthenucleuswith [] times the orbital equilibrium velocity( equilibrium orbital the times Cl () 4 ε [] − C/ io on ou ni mo t = = ou RT/ l t 12 istheFaraday / [] potential. In biologythehalf-cellpotentialisderived from the 50 Io Fa . n mM ln G in () and can be defined as defined be can and , where ; on ε / Cl − () =− constant PP io R n µ C, theequationyields 70 / = ii =∂ mV [] 3144621 8 0 io . () n , , whichcanbeexperimentally verified. Thegalvanic , GN where Z , pressure [ N ∂ io n i v theioniccharge, the particulates fortherespective theparticulates constituents v ta e n J/Km ): ): a = TP force andstrain,reinforcing weak spotsas io ,, r v n ta N () n =− 2 P ji ol = ≠ GM ex ], andtemperature [ (also known molar asthepartial isthegasconstant, pR ε () [] io /. GM () r n [] R µµ ) factor to the location specifics, specifics, location to the ) factor Cl =× ii − 15 61 Note that the release from from release the Note that [] Io in .l for stationary orbit, where for stationary  = n 90 / i represent the concen- . n/ () T mM ][] [] Io isthe“ T M nI , andextracellu- ]) andwith is the minimum minimum the is ou theabsolute ti activity on n , ” of

Cell C 203

204 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Cell, electrically responsive β (see Figure C.31). describing therangeofchemicalconstituentsandtheirrespective quantitiesinthereaction slow build-up before catastrophic response is achieved. Damage can be affected on the cell on affected be can Damage achieved. is response catastrophic before slow build-up may be very short (order short very of energy be of may deposition the tial dna on the and chemical solution, of thesolutionas and the electric wiring in the average household produces field strengths in the order in of strengths field produces household average the in wiring electric the Figure C.31 Figure the numberofreleased electrons isdescribedby respect toachosenstandard stateμ [biomedical, nuclear]Cellsrespond toradiation to radiation response and composition Cell as small as strengths field electric detect can that sharks certain of the head in organ thesensory is example cific in magnitude small extremely are that influences to electrical to respond cells individual the allow that configurations cellular certain are there media biological In electronics] [biomedical, responsive Cell, electrically bilities to detect muscle to detect bilities lightning an altered communication behavior, changes in the chemical responses. chemical the in behavior, changes communication altered an the type (i.e., energy) ofbe may the response radiation radiation One specific to years. minutes from ranging ondepends initialtime and in cumulativedelay the of The duration doseperiod. and may vary, depending on magnetic energy to the proportional [electron]; P 0 isthestandard pressure radiation. The biological change in specific cells as a result of radiation may occur after a latent a after occur may radiation of result asa cells specific in change The biological radiation.

10 produces approximately approximately produces Biological cell. γ [EM radiation]; etc.) and dose. Additionally, radiation exposure is cumulative, leading to a leading cumulative, is exposure radiation Additionally, radiation]; dose. etc.) and [EM − 6 , as well as total cell death. Damage may be reversible or irreversible. Although the ini- the Although or reversible irreversible. be may Damage death. cell total as well , as NC Peroxisome Mitochondria Secretory vesicle / ε P io io n . In comparison the background radiation background the comparison . In n =− is the partial pressure isthepartial oftheionicsolutionrespectively gas,expressed inPascal, endoplasmic reticulum Smooth contractions from several kilometers distance kilometers several from contractions () ∆ of the applied radiation and the mechanism of action: particle of action: mechanism the and radiation applied of the Gn Centrioles  // 10 Fn 5 P i  a − 10 , representing solutionasifitresponds thepartial asanideal . Thehalf-cellpotentialcanalsobedefinedintermsofacidity(pH) () 05916 0 4 ./  NC / n asinthechemicalprocess: . The sensory perceptionsensory . The lo dependingonthetypeofradiation( g. () {} aa 10 A reticulum Rough endoplasmic − 17 a {} s ), the large-scale implications are directly directly are implications ), large-scale the B Nucleolus Poro nuclear Membrane nuclear b {} in outer space is is outer in space aa C AbB aA c {} ++ of the shark of the . D Vacuola d Lysosome membrane Plasma Ribosomes − ne complex Golgi () [] 059 0 Nucleo −+ ~ +  31 10 hc 116

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206 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Cell membrane to shearstress ofthemembranedescribesitasanelasticsolid(seeFigure C.32). increase area insurface forthebilayer withrespect totheoriginalarea neighboring cell,nexttogrowth. Afree (nonenclosed)bodyofliquid issubjecttoLaplace morphological changes.Other externalinfluencesincludehydrostatic pressure andadhesionfrom making upactin andmyosin toformcytoskeletalcablesthatorchestrate cellularmovements as well as tensile whereas thecellmembraneformsanequilibriumby meansofbothstretch and modification. The result from fluid resulting from localosmoticpressures aswell asgravitationalinfluences. Additional external forces may External forces canbefoundresulting from high-frequency vibrations,aswell aspressure gradients scale. Themacromolecular structure provides anactive lifestyle. an elasticconfigurationthatsupports to localstress andstrainresulting from externalinfluencesonbothmicroscopic andmacroscopic through pores.gated transport Mechanically, thecellcanmodifyits cellmembranetobecomeresilient through endocytosis transport nexttofacilitatedmembrane accommodateschemicalandparticulate lenges aswell asmechanicalinfluences resulting from bothinternalandexternalforces. Thecell containing thebiologicaldna.Themembraneisalivingstructure thatcanadjusttochemicalchal- [biomedical] Lipid–proteinandinmostcasesanucleus bilayer thatenclosesthecellularplasma Cell membrane variable defined in digital format. For each cell, time progresses in incrementalin steps, progresses time cell, not each For format. continuous, digital in defined variable astate with associated cellis “cells.” the Each called are which parameters array contains that format matrix uniform into a divided is thespace approach, computational this Under confined. time and place both is which signalprocessing, in concept wavelet to the respect with drawn be may analogy Another equationsfield in concept thefield to equivalent inare generalconcepts These problem solving. discrete in used are that foundation abstract an with definitions System [computational] Cellular automata lining). abdominal the from machines ( dialysis of days early the in cellulose acetate Regenerated mechanism afiltration as [biomedical] , used Cellophane C.32 Figure expansion themembranethickness( constant (range: force (

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Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 paracrine, of the signaling processes are identified by their specific mechanism as follows: follows: as mechanism specific their by identified are processes signaling of the proteins, primarily involve soluble factors, other processes are ionic signaling Some of the in nature. Some ( membranes cell’s or neighboring own cell’s on the of ports or closing of opening hormones or the secretion involve the interact with its cellular membrane cellular its with interact which charges electronic as well as signals of chemical by secretion balance energetic and chemical natural their regulate cells the of. addition, In part integral an are they or tissue organ the with balance as well as segments are defined to be noninteractive, each with the same local and uniform sets of rules. of sets uniform and local same the with each be noninteractive, to defined are segments matter for that and , for parallel ideal mechanism this lends system the segment of finite to a respect with time in steps of for solved number afinite be can system the that fact The thestate. of definition provider for the on the a“look-up” as relies table frequently and Figure C.33 C.33 Figure β from made biocompatible, and degradable are that polymer. Polymer occurring naturally as as well constructed Artificially chemical] [biomedical, Cellulose autonomic parasympathetic and the with as well as cells neighboring with communicate cells Biological energy] chemical, [biophysics, signaling Cellular cross-linking the cellulose fibers to form paper (see Figure C.33). paper form to Figure (see fibers cellulose the cross-linking by followed or bisulfites, media of alkali aid the with reformed and bonds lignin to break treatment tissue to blood of oxygen 1950s the in 1960s asemipermeable and developed to generate devices lung artificial in used was material This cellulose. of composed material occurring naturally of example specific cell of plants matrix cellular the component forming main the is Cellulose strength. inherent its with cellulose provides configuration The long molecular cellulose. called are polysaccharides, engineering and synaptic and Raw cotton with greater than 90 than greater with cotton Raw phagocytosis in an extracorporal system. Additional applications are found in drug delivery, sutures, sutures, delivery, drug in found are applications Additional system. extracorporal an in , and bandages and wound dressings. Cellulose can be reconstituted with chemical chemical with reconstituted be can Cellulose dressings. wound and bandages , and signaling , pinocytosis

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208 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Cellulose acetate Cellulose tist Ferdinand II de’ Medici, the grand duke of Tuscany duke (1610–1670),grand the to approximately 1654. back Medici, dating de’ II Ferdinand tist expansion of liquid by means temperature principle of measuring ascentigrade 1741. in defined Celsius introduced find as format relative one still in may Sometimes Anders Celsius (1701–1744) as the total range of observable AndersCelsius(1701–1744) asthetotalrangeofobservable by molecular expressions of average defined as temperature ( temperature as defined with the Fahrenheit scale (see Figure C.34). (see Figure scale Fahrenheit the with Daniel Fahrenheit Gabriel was metrologist contemporary histemperature[Rinaldini] (1615–1698)whoperformed scale Celsius of the introduction for his known Sweden, from generally Astronomer thermodynamics] [general, (1701–1744) Anders Celsius, of cellulose treatment of the result Chemical chemical] [biomedical, nitrate Cellulose cellulose from formed ester Acetate chemical] [biomedical, acetate Cellulose [general, thermodynamics] Generally accepted measure for temperature ( for temperature measure accepted Generally thermodynamics] [general, scale Celsius C.34 Figure eye nylon and cotton as such materials, other with (oftenblends in textiles in are acetate of cellulose of applications examples Other names. commercial under available are applications emulsions). of production photographic the in Several used (one materials foundation acetate of the lulose cel- form to anhydride acetic with to react made in was produced 1865. first Cellulose was acetate Cellulose even burn under water. It is also known as nitrocellulose as known water. It under also is burn even will it flammable, highly and unstable nitrate cellulose the makes oxide, nitric as by-products such acidic age With cameras. in used roles and sheets “transparent” transparent to produce used be can nitrate Cellulose explosives. and transducer the from separated ligands chemical the with lining transducer element chemical sensing as components such active biologically artificial to encapsulate used for instance membranes, microporous thin of extremely construction the in component used Chemical glasses. Cellulose acetate can be spun into strands for weaving, for instance, acetate rayon. acetate instance, for for weaving, into strands spun be can acetate Cellulose glasses. used in temperature measurement temperature in used Painting of Anders Celsius (1701–1744). Celsius Anders of Painting Tk = () 23 E , where , where . Anders Celsius followed the inspiration of Carlos Renaldini the inspirationofCarlos Renaldini followed Celsius . Anders k b

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. The . Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 T Fahrenheit Fahrenheit second distance identified by center ofmassisformulatedas all themassesofconstituentsadevicewithvarious components and materials.Thedefinitionofthe of size andstructure; includingatomsandmolecules)orconcurrently thelocationofcombined effectof and additionally the triplet point for water is expressed with respect to the Kelvin temperature scale as as scale temperature Kelvin to the respect with expressed is point for water triplet the additionally and nation ofthemomentinertia The relative position( to liquid to the boiling point of water at 1 atmosphere pressure ( pressure point at1 atmosphere of water boiling the uses The temperature scalegenerallyusesthree pointsas reference todefinethetemperature. TheCelsiusscale frame ofchoiceassummarized over allthemasses( whereas thecenterofmassisin oftheball.Thelocationperceived single massina reference considered tobeconcentrated.Forrubber shell rubber ballallthemassisin instance,foranair-filled [general, mechanics,nuclear]Thepointinsidetheoutlineof abodyofsystemwhere allmasscanbe Center ofmass (r human entire to the reference in of foot ahuman, the for instance system, oftion atotal subsec- specific for a defined be may centergravity The of rotation. in result will atorque forms that system up, do not the line forces of acting sum and force normal the case In force. normal the with align gravity of center the through forces of the sum the that requires equilibrium in upon. Abody acting apparently are theforces convenience wherethefor volume body of a in point virtual The mechanics] [biomedical, Center of gravity “ of medicine encyclopedia of an Author medic. and scientist Egyptian [biomedical] Celsus Ferchault René-Antoinethe (definedscientist by French Réaumur exercises; past from to scales next scale, Kelvin DanielGabriel Fahrenheit by introduced scale Fahrenheit the are scales temperature Other steps. 100 in incremental subdivided are considered tobeactingontheobjectproviding theaccelerationtocenterofmass( of lowest temperature with no molecular with temperature of lowest techniques. Absolute techniques. Planck’s use temperature law of determination for the used of action mechanisms Later principles. expansion or liquid on gas based are work thermodynamics of stages early from thermometer mechanisms Other tube. gas-filled to the nected con- medium container open of the level liquid the or lowering raising hence atube; in pressure hydrostatic Galilei to Galileo attributed is invented thermometer first The definitions. Celsius to the according scale acalibrated up with lining when the linear expansion coefficient and coefficient expansion linear the extensions of certain compositionand materialsthatholdmass.Thelocation( extensions ofcertain forthatbody,the momentofinertia specificallyifthebodyisnonuniform andhas various geometric coordinate systemisdefined by thecomponents ofanobject,eachwith respective mass ( alcohol Macquorn Rankine De Tr iple Medicina t ≡ law 27 or mercury in a closed tube, relying on linear thermal on linear expansion relying tube, aclosed in or mercury toanorigin( for for 31 AD) (second century ) ( [1683–1757]) and Rankine and [1683–1757]) de Réaumur . T , i 6 ∑ F HO ) asafunctionofeachrespective location( K. .” 2 Fm and degree Celsius ( Celsius degree and The Celsius scale is the range of temperatures from melting point to boiling point pointboiling to from melting temperatures of range the is scale Celsius The = recognized as the melting the as point recognized r a  [1820–1872]). Thethermometer temperature *  cm r ) ofeachthe components( i ) inacoordinate system,defined by thetotal mass( . Thelocationofthecenter massanddimensionsofabodydirectly determine CM

rr radiation captured by optical spectroscopic spectroscopic optical by captured black-bodyradiation on rely the and (1686–1736) absolute the 1717 as in well United States) as the in used (still CM ) foranobject.Thecenterofmasswillalsobethepointwhere allforces ( (1564–1642) 1595, circa dated gas using =  ∑∑ T the length of the medium) of the medium to indicate amagnitude to indicate medium of the medium) of the length the scales C i ) is ) is ii mm motion TT /. CF are expressed in Kelvin or Rankin, both referencing the point the referencing both or Rankin, Kelvin in expressed are =− i () 59 i ∑ as the zero point. A useful conversion between degree degree conversion between Auseful point. zero the as Thecenter-of-masswilldirectly influence thedetermi- T i , also referenced as the freezing the as referenced , also i ) cannow bedefinedforaspecific subsection(k)as () boi mM (defined by the Scottish scientist William John John William scientist Scottish the (defined by i l r i = ≡ ) contributed from a system of particles (regardless) contributedfrom asystemofparticles used to express the Celsius scale uses either either uses scale Celsius the to express used 100 32/ ) (eachrespective mass[ ° . C phase transition ); phase the expansion to raise or lower the to raise expansion Mm ( R ∆ = ) ofthe centermassina  ∑ =− called the the called α i m ) as () point point TT i ] constituent m 21 body a  i R point from solid solid point from ) andrespective cm = ) ( ) inNewton’s T ∑ Center of mass , where , where me . i lt mr ≡ ii 0° / α C M is is F ; .

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210 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Centered difference Oh [ [] rr energy is tum ( velocity needs tobecorrected by meansoftheLorentz transformation, whichtranslatesinthemomen- Under relativistic conditions(approaching thespeedoflight[ . The centripetal force ( force of a centripetal influence the centripetal forceunder . The derived over incremental stepsize Δ description canbeappliedundervarious conditions,includingCompton configuration due to the complexity of the local boundary conditions. configuration duetothecomplexityoflocalboundary putational with certain tangential velocity( tangential certain with that are totheparameter orthogonal [general, mechanics] Any object with mass ( mass with object Any mechanics] [general, Center-seeking forces becomes ( [computational, fluiddynamics]Computationaltechniqueused toisolateextremes by usingthehalf-intervals Centered difference pole vault jump during the different vaulting phases. C.35 Figure this intoa Taylor seriesthederivative hasasecondcomponent: and respective accuracycanbeexpressed in(andisdirectly dependenton)theincrement stepsize. Increasing energy isdefinedas −+ −− Δ * kk () 82 h {} fx =− /2) inthefirstderivatives ofafunction ∆ fx () () mv p ii = 2 ii R () , whichusesthecentered differences around f em fluid 22 kk () ′′ ; similarlythevelocity isdefined by ∆∆ ∆∆ () = ) formulation asfollows: A high jumper is manipulating her center of mass to enhance the high jump level when performing a performing when level jump high the enhance to mass of center her manipulating is jumper A high hf xf hf // // ii dynamics, primarilysincethenumericalsolutionneedstobesolved inafinite c =+ 2 / [] ++ +− E () 168 * 1 () = xh − () xh {} [] vc  () () k () ∑ xh / ∆∆ () i 22 ep // 2 i () 22 2 and “inertial energy” and“inertial v

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∑ 23 are conserved, whiletheparallelcomponentsare are modified.Thislast conserved,  p xfx fx kk ∗ 22 12 i ()  =− − () i ff ii ∆∆  ( pe 22 01 hO c m −− / xfx fx ′ ) moving in a curved trajectory (e.g., circular, elliptic motion) (e.g., elliptic circular, trajectory acurved in ) moving () v  () . In theLorentz [] x * () () kk i γγ ii + =− cm = −− vV 

x [] kk () () // i fx 62 β {} . Thissolution methodisfrequently usedincom- cp () hh =  h −+ () ii ∑ , where + 2 Oh c mcm cm i ], which applies to nuclear conditions), the ], whichappliestonuclearconditions),the )() () fx thesecond-order difference now  () /( pc ∆∆  2 ′ {} transformation the momentum components transformation the momentumcomponents k () {} () hf ∆ ∆ () / // γβ ∆∆ hf e ii V 22 i / and F 2 / c =− isthevelocity vector forthesystem. ) is directed toward the center of the of center the the toward directed ) is 2 . The slope connecting these two points . Theslopeconnectingthesetwopoints −− ) 1 +− γ scattering (seeFigure C.35). fx 2 cm () () ()  xh + () = ⋅ x Oh  + ∑ i () () i 22 (() eE β  ∆∆ i 22 /. , where thequantum ∆∆ hf and // hh ∗ // In thisthequantum ∆∆ ++ fx hO ′′ 82 22 12 () + () i () element xh () = i

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214 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Chandrasekhar mass upper limit for the mass of a stable white dwarf. The electron density density electron The dwarf. white of astable mass for the upper limit able awhitedwarf to be produce only will star the mass Chandrasekhar constant for the star (based on its history and size). and on history its (based star for the constant interaction— for adapted tissue light in successfully purposes biomedical century twentieth end of the the toward and timereversal. quantum–mechanical situations.Thechargeconjugationfollows thepatternoutlined forspaceinversion formed intotheirrespective Theoperatorisdiscontinuousandapplies onlyto antiparticles. relativistic– [computational, relativistic, thermodynamics]Under aLorentz transformation are allparticles trans- conjugationCharge as electric Chinese documentationdatingbackwell before ChristontheChristian/western calendar. It isalsoreferred to the conceptofchargewasknown andhasbeendescribedasfarbackancientGreek philosophers andold of twodifferent chargeswasofficially introduced byBenjamin negative orpositive [electronics, general]Excess ofelectrons inan atomicormolecularsystemthatproduces orshortage either Charge [atomic, See nuclear] X-ray Characteristic collapses, energy and Fermi the overcome of astar gravitymass where will gravitational The energy,[astronomy/astrophysics, quantum] mass Chandrasekhar C.39 Figure tion oftion aneutron forma preventing the thus neutrons, to produce energy enough not possess will mass Chandrasekhar the of that star, star, of that

charge. E ( Subrahmanyan Chandrasekhar (1910–1995). equation of radiative transfer radiative of equation Fe q = ) () 53 by means of the constraints to the electron electron to the constraints star of the by means // charge. On anuclearlevel theexcess protons canprovide apositive charge.Theconcept X- () ray 1 NC , characteristics () NR MM

e 53 ~. / 14 4 , where , where  . , where , where (see Figure C.39). (see Figure R defines the equilibrium radius for the star and thestar for radius equilibrium the defines M  represents the solar mass. Stellar mass less than mass Stellar mass. solar the represents Franklin (1706/1705?–1790) in1747;however, degeneracy ) ( N e for theenergy star definesthe Fermi . This also defines the the theoretical defines also . This . At a mass less than the the than less amass . At C is a is - Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 π λ [atomic, solid-state,thermodynamics]Periodic chargedensityfluctuationsinalow-dimensional metal wave density Charge and number of moles. It is also known as the Gay-Lussac the law as known of It moles. also number is and volume to the [atomic, Gas nuclear] Charles’s law Washington, DC.) Figure C.40 pre– with gasses of ideal behavior the in work was Charles’ France. from physicist and Scientist [general] (1746–1823) César Alexandre Jacques Charles, applications. analog also are but there binary, primarily is tion ccd it next over to the transferring and information electronic the ing memory,” stor- a“bucket as temporarily acts (time concurrently delay) line and adelay to form used be can and circuitry external by controlled be can time store electricchargestorage . The to temporarily used be can that structure material semiconductor Capacitive solid-state] quantum, electronics, [computational, device (CCD)Charge-coupled length. unit per object on a“one-dimensional” evenly distributed is that Total charge [general] length unit per Charge ( area. unit per object on a“two-dimensional” evenly distributed is that Total charge [general] area unit per Charge ( Fermi wave vector. Thephononspectralpatternthat results is referred toastheKohn isassociatedwiththe superimposed,causingachargedensitywave pattern.Eachperturbation lattice distortion density structure. Because ofaninteractionbetween electron densityinfree flow perturbations areperturbations disorganized, theparticle gapoccurringattheFermi constant phase transitionsinducedby theelectron chargedensityfluctuationsgenerateawave patternwithawavelength char ge ideal gaslaw = wave , however filledelectron bands. notsowhenthelatticehasonlypartially Whenthelatticedensity k

F pattern is generated with a periodic charge density modulation that has a rhythmic intermittent patternisgeneratedwithaperiodicchargedensitymodulationthathasrhythmicintermittent Jacques Alexandre César Charles (1746–1823). (Courtesy of the United States Library of Congress, Congress, of Library States United the of (1746–1823). Charles (Courtesy César Alexandre Jacques , where ( V ) and temperature ( temperature ) and definitions. Cotemporary of Joseph Louis Gay-Lussac Louis Joseph of Cotemporary definitions. k law F istheFermi wave vector. Thewavelength maybecommensurate with thelattice Jacques Alexandre César Charles (1746–1823) respect Charles with César Alexandre by Jacques introduced σ T e ) of an ideal ) of an ) λ e ) gas expressed as as expressed . T V level willcreate aninsulator in the circuit. The stored informa- stored The circuit. the in andphononpropagation anelectron /c (1778–1850) C.40). (see Figure = onstant anomaly for constant pressure pressure for constant . The periodic . Theperiodic Charles’s law Charles’s . lattice

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216 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Charm 540 (rest energy he received theNobel Prize inPhysics, andGeorge Zweig (1937–)in1963(see and identicalrest energy. Thequark charmprinciplewasintroduced by Murray Gell-Mann(1929–),forwhich provides anotheridentification.Thecharmcanbe “up( type ofquark definesthefinal product. Nexttothefactthat variousquarks have fractionalchargethecharm antiquark, whereas abaryon mesonsconsistofaquark particles, by spin-up orspin-down. In ofrudimentary theconstruction [general] Classificationofelementary Charm Introduced by PafnutyIntroduced Chebyshev value. average the near are of data of aseries values all mostly aprobabilitydistribution In [computational] inequality Chebyshev fundamentals. probabilitytheory as well as foundations, mathematical basic ples providing theory ofand number concepts introduced basic the fluid [computational, (1821–1894) Chebyshev, PafnutyLvovich [Пафну́тийЛьво́вичЧебышёв] an situation this In constituents. of the balance chemical the as well as parameters when temperature volumesubjected and and pressure, the medium, ofto the change will affectthe other (1850–1918). Braun Ferdinand inventor Karl constituents the the of moles of number by defined Asystem French chemist Henry LouisLeChâtelier (1850–1936) and physicist German by the independently and the by introduced equilibrium chemical the to changes the of The principles thermodynamics] [chemical, principle Châtelier–Braun Figure C.41 Figure “charmed ( electron charge magnitude principle as Le Châtelier–Braunprinciple, or Châtelier Le as known also is principle This conditions. boundary ing chang the with complies that direction the in reaction chemical the force or volume will pressure in changes energy requires that direction the in proceed to encouraged be will reaction endothermic for an increase atemperature Alternatively, constant. reaction the reducing hence increased, artificially is temperature system the when reaction its to reverse forced be M eV ), “top ( . Also referred to as Châtelier–Braun to as inequalities referred . Also c

5000

)” withcharge Concept of “charm” pertaining to elementary particles, quarks in particular. in quarks particles, elementary to pertaining “charm” of Concept t M )” withcharge eV ). The respective antiquarks: - princi stochastic several described Chebyshev Russia. from Mathematician dynamics] Quarks Decay/interaction ce characteristics: : : | + willbecomposedofthree quarks. With thebroadandmesons variety ofbaryons eC |. Charge: +⅔ Charge: −⅓ () 23 =× e t / 6021765 1 : + () (rest energy 23

/ (1821–1894).

particles (rest energy 71

Down , thus increasing the equilibrium reaction constant. Similarly Similarly constant. reaction equilibrium the increasing , thus Strong 0 150 pCamTop Charm Up − , specificallyquarks. In reference, anelectron canbeidentified ud 19 , 0  u d Me , “down ( 7 000 173 u ,,,,, )” withcharge cs V , ), “strange ( Strange tb Me ekWeaker Weak d )” withcharge V , or Le Châtelier theorem. Châtelier , or Le have opposing chargetothe“regular” quark c s ), and“bottom( ue s )” withcharge : + Bottom () 23 / e d quark (rest energy : b t − () exothermic 13 b / ) withcharge ) e s (seeFigure C.41). : − (rest energy () 13 /

360 (rest energy (rest energy and an andan will reaction will M be : eV + 360 () 23 ), ), / M eV

), ), - Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 pile) wasconceived by theItalian physicistAlessandro Volta (1745–1827)in1800(seeFigure C.42). electrons, forexample,hydrogen–oxygen (voltaic andalcohol andfossilfuel-basedsystems.Thefirstbattery time. Anotherchemicalenergyapplicationisinfuelcells,relying onoxidation ofanelectrolyte intofree andthechemicalreaction isexpressed capabilityofabattery inampere-hours, orchargemultipliedby carrying materialsincludelead-acid field. Other battery ,usedinautomobilesandhospitalequipments.Thecharge ing acurrent externally;duringtherecharging process theionsare forced backby theappliedexternalelectric In thelithium-ionbattery, lithiumionsactuallymigratebetween thecathode andtheanode,henceproduc- by weight. [chemical] Pure substancecomposedoftwoormore elements compound Chemical Figure C.42 C.42 Figure rechargeable andthechemicalreaction isreversed tothepointwhere theelectromotive force ( (disposable), whereas lithium-ion(i.e.,lithium)batteries(usedinmobilephonesandlaptopcomputers)are tobatteries.Alkalinebatteriesareprinciple appliesinparticular producing nonreversible chemicalreactions form offree electrons. Theelectrochemical isadirect property result ofthehalf- [chemical, general,solid-state]Chemicalreaction thatdelivers electricalenergy withelectricalcurrent inthe energy Chemical zinc ( maintained foralongduration.Thealkalinebattery isforinstancebasedonthechemicalreaction between Zn ) andmanganesedioxide ( (a) Chemical energy expressed by voltaic pile and (b) “dry cell.” “dry (b) and pile voltaic by expressed energy (a) Chemical (a)(

Cardboard Cardboard Cardboard Cardboard Silver Silver Mn Zinc Zinc O 2 ), whereas theelectrodes are potassiumhydroxide (i.e.,thealkaline). Cell b) combinedinafixed anddefinite proportion phenomenon. This cell phenomenon.This V Chemical energy em f ) will be ) willbe

C 217

218 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Chemical gradient R chemical chemical by the described as of butane oxidation the as such reactions for chemical depicted be can situations rium Two systems in the same volume under identical conditions with the same same the with conditions identical volume under same Two the in systems ture will initiate the the initiate will ture gas/ the thus point, boiling the system undercertain (4) and relativistic in potential, be discriminated:(1) thermodynamic potential. There are fourdifferent typesofchemicalpotentialthatcan chemical same the have will librium of energy described by by described of energy molecular ( written as as written where where number and and number reverse mixture ( adistance over concentration in difference The relative [biomedical] Chemical gradient [biomedical, thermodynamics] The partial derivative change in free energyfree in change derivative partial The thermodynamics] [biomedical, potential Chemical cessation. smoking of process the in are who individuals by used C.43 Figure ponent of each respective ingredient, with with ingredient, respective ponent of each tion the mixture, mixture, the Chemical potential of solvent potential Chemical of thepure solvent inthemixture attemperature stant temperature ( temperature stant = = Nk temperature. The change in internal energy per change in unit state for each of the constituents constituents the of each for state unit in change per energy internal in change The temperature. (a) µµ A vapor ii osmosis in water purification ( purification water in osmosis reaction () gas µ pTp Tp N ii 3145 8 ,, (a) Chemical gradient in reverse osmosis water filtration. (b) Chemicalgradient for nicotine patch S k () , or solid , liquid .J ) content, respectively, of the constituent constituent of) content, the respectively, SV state in comparison with the liquid state at that specific temperature. The rise in tempera in rise The temperature. specific atthat state state liquid in the comparison with the entropy of respective state, state, entropy of respective the =× ,, =… 86 10 38066 1 . 21 T CH nU ir /mol reordering from the higher to the lower potential. Similar change of state or equilib of state change Similar lower potential. to the higher the from reordering Reverse osmosis 41 ) and constant volume ( constant ) and () conditions. For instance water will evaporate when the water temperature is above above is temperature water the when evaporate will water For instance conditions. =∂ E migrating from migrating () 02 =+ K + ,, Pressure 21 is the universal gas constant, constant, gas universal the is yy µµ 12 38 ∂ OC − ga ni 23

concepts. Thethermodynamicconceptisusedtodescribethe stateina with respect to constituent to constituent respect with - ( sC , state , J/Kmo flam SV 41 μ → H4 ,, i e 02 ) n chemical potential, (2) chemical potential, (3) electronic chemical (3) chemical potential, electronic (2) potential, chemical chemical CH , y : n- and p-structures). One specific application is in the use use of the in is application One specific p-structures). : n- and fo liquid OH see also r1 or or lecule 10 22 l concentration contaminant im + =… µ V n 10 Semipermeable Higher the number of states, and and of states, number the ii ii iii ii ii ii ii ii ii to gas to ,, ), incorporating the definition of the Gibbs free energy ( energy free the Gibbs of definition the ), incorporating 38 the Boltzmann constant. In this configuration the following following the configuration this In constant. Boltzmann the () membrane chemical 2 y Tp concentration → ga ,, contaminant O sO T , , with respective chemical potentials and the release release the and potentials chemical respective with 1 Lower state with an associated lower chemical potential in in potential lower chemical associated an with state andpressure 2 r yielding the solvent factor for constituent for solventconstituent the factor yielding OC µ , where , where = i 22 hT

N =∂ potential −+ i () () A is expressed as as expressed is µµ =× FN U ga pT (b) 60 sC is the internal energy, internal the is ∂ , . Og 210 22 − p ) (see Figure C.43).) (see Figure , and TV O within specific constituents of a constituents specific within , sT r the total number of constituents. of constituents. number total the () = 23 i GT 10 µµ th y , ( mo i ii p isthefractionalcom- () F constituent and in equi in and constituent = ) per change in atomic and atomic and in change ) per lecules/mo ,, as is the chemical potential potential chemical the is PN , HO ii 2 () Tp HHO ,l V 2 N the volume of of volume the + atthecombus- under con under l Ty RT the Avogadro Avogadro the n, i and and i

- - is is G - - ). ). Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 [] µχ µ thermoluminescence (every object with a temperature above absolute above atemperature with object (every thermoluminescence cence (e.g., (e.g., electroluminescence firefly), and (e.g., scintillation), lightning), radioluminescence a under variety light produce of that mechanisms available Other blue light. for oxidation (high-energy) oxygen and the nitrogen , producing release can that compound based amino-based derivative of an reaction with reduction a the base in and is oxygen- state of asinglet formation such just describing reaction chemical Astrictly of light. emission the with degrades and lifetime alimited has lent totheelectron negativityoftheatom potential). Since theelectronic chemicalpotentialisbasedontheelectron density, thispotentialisequiva- atom of nuclearelectrostatic potentialandtheelectricinfluencesofmagneticfieldsexternalto where hmclcompound and which identifiestheKEofelectrons inthechemical with with gas thechemicalpotentialislinkedtopressure ( isaddedunderconstantentropy (S).Forsent thechangeinenergyofsystemifoneparticle anideal variable are used: used: are variable oxidation–reduction reaction is the chemical the is reaction oxidation–reduction chemiluminescence reaction is oxidation–reduction, A more intricate fire. specifically produced a during well-known most The reaction. of achemical result the as produced Light solid-state] chemical, [biomedical, Chemiluminescence fermions, theelectricalpotentialis density. canbedescribedasagasoffermionsandbosons. particle Whenjustconsideringthe Theelementary Boltzmann equationinquantum physicsandpossessesahigherpotential,whichrelates toahigherparticle chemical potentialisassociatedwiththewave particles tomigrateoutofenergeticregions withhigherchemicalpotential.The “relativistic” elementary the systemintowhichitisintroduced orfrom whichitescapes.Thepotentialdescribesthetendencyof particleof stateforfermionsandbosons,buteachelementary contributestothetotalinternalenergyof potential butwiththefollowing inherent anduniquecharacteristicsrelativistically there willbenoenthalpy particles analogoustothethermodynamic the termchemicalpotentialrelates thestatesoffundamental potential of a genuine constituent will equal the Gibbs free energy of reaction for that particular constituent, constituent, particular for that of reaction energy Gibbs free the equal will constituent of agenuine potential energy, or h oiainpotential ( the ionization the the for abattery as theelectron density, whichisexpressed as derivativefunctional partial oftheelectrochemical densityfunctionalwithrespect tothesystemstatedefined asappliedtodensityfunctionalorenergytheory.chemistry Theelectronic chemicalpotentialisthe for theconstituentsateithersideofmembrane.Theelectronic chemicalpotentialfallsundertheoretical potential cellular membrane creating anelectricalpotentialgradientaccording totherespective Nernst ∂ ii Mulliken () () µ Tp hmclgradient chemical i ormoleculeresulting from surrounding chemicalsandoutsideinfluences,also referred toastheexternal p ,, ρ ii RT the partial pressure of constituent of constituent pressure partial the () isthedensityfunctional( 00 rr µ = =− F ∂ gT , for instance. The use in true chemical potential applies to biomedical physics to biomedical applies potential chemical true in use The , for instance. =∂ ln ii () () P Mulliken h EN T iii ii p () () = Tp () 1 . The latter can describe the conversionthe ofchemical describe can latter . The , ( . Thechemicalpotentialdescribesthedifference inchemicalconcentrationacross a // also see ∂ =− NE the specific enthalpy of system system of enthalpy specific the IP () s ) fortheatom.Thiscommodityisalso referred toasthe Mulliken potential, IP =∂ f () + rienergy ermi

E µ EA () F ρρ or = bita = kT 2 le , asamatter offactthesumelectron affinity( i ∫ () . Under chemical equilibrium ataground equilibrium . Under chemical =∂ NN nln ln µρ )() () [] mechanical description of the elementary particles by the particles mechanicaldescriptionoftheelementary i ). rV () transfer that results in an excited singlet excited an in results that energy transfer () zk EN ∂ rE () =− =∂ rd ss [] P T +∂ ) as ∂ () 3 N rF () EN () + [] e ∂ NN ii  lectrostatic F µ = and and ∂ / () i kT ρρ ρ () 0 . Lastbutnotleast,inrelativistic physics () NP transfer principles are biolumines are - principles energy transfer rV , where s 1 iii ii () ρρ () , where isthefugacity, ∂ == Tp zero re , / fr T ∂ F V = N == () ex kelvin emits light with a a with light emits kelvin energy the respective specific entropy specific respective the ρ VP t ex () , where bothtermsrepre- t istheuniversal functional ρ () rF is the combined influence isthecombinedinfluence RT/ +∂ into electrical energy energy electrical into [] state , orequivalently () Chemiluminescence  and relates to to relates and F p ∂ istheFermi 0 EA ρ the chemical chemical the state which , () r ) and ) and ρρ ef , C 219

220 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Chézy, Antoine de Antoine Chézy, tion angle tion rough channels to channels rough diving. Also used as decorative jewelry. decorative as used Also diving. C.44 Figure absolute to the proportional inversely directly range wavelength channel for flow expression Heuristic [fluid dynamics] Chézy’s formula, open channel Figure C.45 the flow on In experiments from 1769performed France. Engineer Chézy [fluid dynamics] Chézy, de Antoine C.44). (see lightbulb) Figure stovetop or, incandescent the electric indirectly, heuristic Chézy formulas. The Chézy quantity (i.e.,coefficient), quantity Chézy The formulas. Chézy heuristic the provided information This Canal. Courpalet the and Paris near River Seine the as such channels open is defined as defined is of the riverbanks, and and riverbanks, of the

Antoine de Chézy (1718–1798). Chézy de Antoine Chemiluminescence example producing light in a “glow stick,” for instance, used during deep-sea deep-sea during used instance, for a“glow stick,” in light producing example Chemiluminescence 90 m/ C v 1/ = 2 s for large smooth channels (see Figure C.45). (see Figure channels smooth for large chez (1718–1798) y () C m chez θ incl y the Chézy’s flow velocity coefficient. The Chézy’s velocity The flow coefficient. flow Chézy’s velocity the , where where velocity in an open canal. The flow velocity in anopen in Theflowvelocity canal. open an in velocity m is the mean hydraulic depth, depth, hydraulic mean the is

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temperature chez y , varies from about about from , varies ; gloving heating coil on coil heating ; gloving θ incl the inclina the 30 m resistance 1/ 2 /s - for small for small

in in Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 C n wood: wall of the surface of the (see Figure C.47).(see Figure Illumination” de International of color concept “Commission the standardized has that organization on the (1818–1894) (1818–1888)Ganguillet Kutter Rudolf Wilhelm and Emile-Oscar ( Swiss the by derived the formula by approximated be can coefficient Figure C.47 Figure color perceived of optics] Definition chemical, [biomedical, Chromaticity Figure C.46 n-type using functions semiconductor Silicon solid-state] [electronics, Chip See thermodynamics] mechanics, [fluid dynamics, transfer for mass j-factor Chilton–Colburn See thermodynamics] [fluid dynamics, for heat transfer j-factor Chilton–Colburn chez = 035 0 yi . =+ n [] = 23 to 010 0 .

00 . Chromaticity colorChromaticity chart. Chip. () 10 5 // ). nn to ++ . 00 () 13 .. and p-type and 00155 ; river with rocks imbedded in the shores and bottom as well as grass and growth: growth: and grass as well as bottom and shores the in imbedded rocks with ; river of the flow and is found listed in tables for specific materials (e.g., polished (e.g., polished materials for specific tables in listed found is and flow of the θθ nc li materials, also known as integrated circuit (see Figure C.46). C.46). (see Figure circuit integrated as known also materials, [] 12 c olburn [] 30 + ()

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222 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Chromatograph for the identification, for instance, of alkaloids, amino acids, nucleic acids, proteins, steroids, and vitamins. and steroids, proteins, acids, nucleic acids, amino alkaloids, of instance, for identification, for the are available analyses Specific for separation. used process abinding provides or antibodies) antigens identify to used matrix a biomolecular instance, (for matrix usechemical ofa the chromatography affinity In sieves. diffusion respective the with associated process retardation the influence described the mechanisms Specifically, tion. separa of molecular mechanism own its with chromatography,phy, each partition gel chromatography, and adsorption for instance, are, analysis chromatographic the involvedin action of mechanisms Different atomicingredients. and chains molecular define can Chromatography applications. for specific are available techniques chromatography Different chemical constituents. C.48). (see Figure chromatography permeation gel and chromatograph, gas Figure C.48 C.48 Figure chromatography called process a in of composition media of the analysis the in to assist device Analytical solid-state] general, [electronics, Chromatograph medium observed or measured with optical devices. The chromophore is either a separate molecule or a molecule chromophoreseparate a The either is devices. optical with or measured observed medium of color essence the provides that constituent optics] Dye general, [biomedical, Chromophore different of diffusion process the blood or drawn analysis urine during for instance ted submit specimen of biological analysis foras as well diagnostics therapeutic in and flavor) water andquality, (e.g., food- safety, (“fragrance”), cosmetics pharmaceuticals, environmental, of petrochemical, analysis from range chromatography of applications The analysis. to chemical applied is Chromatography mixture. of a constituents composing the to resolve designed process Analytical solid-state] general, [electronics, Chromatography a column. In gas In a column. in arranged is process separation The mixture. of the phase stationary the to as referred is process, separation of resolution degree high components with respective of the on the chromatography “wave numbers,” chromatography on the one relies chromatography in (actually wavelengths at representative peaks absorption representative specific providing light, transmitted from attenuation spectral the optical on relies analysis The components. volatile solute processes. For instance gel chromatography uses polyacrylamide and other types of gels to act as as to act of gels types other and polyacrylamide uses chromatography gel For instance processes. Gas chromatograph equipment for analytical processing based on spectral attenuation profile of profile attenuation spectral on based processing analytical for equipment chromatograph Gas molecule sizes. The resin is generally arranged in a column, analyzing the mobile phase analyzing column, in a arranged generally is The resin sizes. molecule chromatography the mobile unit is in gas form. Gas chromatography is more popular for for more is popular chromatography Gas form. gas in is mobile unit the chromatography

when subjected to a bed of resin particles, with different diffusion coefficients for coefficients diffusion different with particles, of resin to abed subjected when

. Also used as gas– as used . Also chromatography, affinity chromatography, ion chromatography, affinity k ′ = 1/ λ ; note that the regular wave regular the ; note that liquid , next to forensics. Chemical chromatography uses uses chromatography Chemical to forensics. , next chromatograph, or liquid–gas chromatograph, chromatograph, or liquid–gas chromatograph, . The “steady-state” medium, affecting the affecting medium, . The “steady-state” number is defined as defined is number of a molecular composite of amolecular -exchange chromatogra k = 2 πλ /

- ). ). - - Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 spectrum distribution (see Figure C.49). (see Figure distribution spectrum scattering of shallow by means band(s) re-emitted are spectral white light by band abroad color irradiated when gains and molecule component of alarger A black object inherently absorbs all incident light, a white object reflects all incident light. The full spectrum is is white. as spectrum full perceived The light. incident all reflects object awhite light, incident all absorbs inherently object object. A black the of (surface) the in inclosed chromophores the by absorbed is spectrum of part remaining light; white of the chemical compound paraben. (c) color specific ofofportion based the the on object backscattered/back-reflected incident for lines Absorption (b) light. white incident the of scatter Raleigh of result the is water the of color “blue” the Whereas light. white incident the of band color “orange” the but all absorbing used, paint the in C.49 Figure (a) light

(a) The orange color on the hull of the supply boat for oil rigs is the result of the choice in chromophores chromophores in choice the of result the is rigs oil for boat supply the of hull the on color orange (a) The . The chromophore will absorb selected ranges of the source bandwidth, while the remaining the remaining while bandwidth, thesource of ranges selected absorb chromophorewill . The (c) White light White light White light White surface Black surface Red surface Black surface Red light reflected reflected White light No light reflected (b) Absorption (A, AU) 0.5 1.0 190 λ max-1 210 l = 3 5 7 290 270 250 230 0 e processes, which yields the visible color visible the yields which processes, −εCl λ Wavelength (λ,nm) max-2 A =l g =εCl l l 0 1 330 310 O source OH chromophores O Chromophore , ideally , ideally 5 370 350 CH 3 C 223

224 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Chromosphere analyzing thecolorofteethby adentist for color space,yieldingthethree axes. Thisscientificanalysis overcomes subjectivity. Forinstance,when numerical night rest, for etc.;colorblindness).TheCIEanalysisusesspectrophotometric instrumentation light colortemperature, willinfluencethe chromosphere is best investigated during a full total eclipse, exposing just the chromosphere (see Figure C.50). (see chromosphere Figure the just exposing eclipse, total afull during investigated best is chromosphere Sun for our athickness and 4200 K, photosphere the above layer geophysics][astronomy/astrophysics, Solar Chromosphere defined in“brightness” ( [general, optics]Graphical representation ofthehuesandradiancecolor space color CIE ( Illumination ofcolor optics]definition The general, [biomedical, CIE 1931 space color Austria. in Vienna, seated is committee The institute. standardization international an as for Standardization) Organization by (International ISO recognized is CIE basis, on avoluntary operating Although standardization. on advice providing independently 1913acts that anonprofit is and organization nescence related exchange tolight, information and standards implementing organization scientific technical, Illumination; on Commission International The l’Eclairage; de Internationale optics] Commission [general, CIE C.50 Figure S, M, and L responses of the human eye human of the Lresponses and M, S, red to equivalent roughly Zare Xand if even (RGB) coneresponses red–green–blue with confused be can XYZ cones of the curve red of the representation interpreted an Xis and to blue stimulation, proportional Zis brightness, oftion color and blue, respectively. However, in the CIE XYZ color space, these values are not equal or similar to the to the or similar not equal are values these color space, XYZ However, blue, CIE respectively. and the in

, color and spectrophotometry, vision spectrophotometry, and color , determination. The color determination. The Layers of the Sun, including the chromosphere. spaces associated with the virtual XYZ color space as introduced. In the color space, Y means Ymeans color space, the In introduced. as color space XYZ virtual the with associated spaces cie ) initially released in 1931. in released defini CIE ) initially The 1931 colormathematically a provides space of the human eye. The XYZ color space is also referred to as the tristimulusas values to referred also is color space XYZ The eye. human of the L

), hueandchrome ( is approximately 2000 km, containing primarily helium and hydrogen. The The hydrogen. and helium primarily containing 2000 km, approximately is representation in Euclidean in representation Layering oftheSun , but can be considered derived values ( values derived considered be , but can observations, as will the personal history for the observer (good for theobserver as willthepersonalhistory observations, reconstructive dentalwork theambient light,orexamination a and imaging as well as photobiology. CIE was founded in in founded was photobiology.CIE as well as imaging and : red-green; perception by the International Commission on Commission International by the perception b : yellow-blue), expressed inthecie

space Convection zone Subsurface flows Chromosphere Corona Photosphere Radiative zone Inner core , with a temperature greater than than greater atemperature , with is defined based on the respective respective the on based defined is inathree-dimensional space, see also vision

). La ** sensitivity sensitivity lumi b -

. - Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 vortex have no viscous forces (no boundary layers) and hence the circulation is zero. is circulation the hence layers) and (no forces boundary no viscous have vortex wing-tip and wake The volume of space. enough alarge encompassing is loop integral the assuming wake, vortex the describes also which circulation, zero has awing around airstream the instance, tion tion circula- the for yields This processes. andtermination initiation consider not will This place. at agiven a Cartesian system ( system a Cartesian enced in flow velocity in enced of “rotation” degree the experi- is vorticity the Where, path. enclosed the within vorticity of the integral measurements and and measurements around an object, object, an around the flow loop over closed Arbitrarily [fluid dynamics] function Circulation (i.e., fluid The average [fluid dynamics] Circulation ( path to the perpendicular flowpattern (e.g., wing flow The average [fluid dynamics] Circulation C.51 Figure flow velocity path. path. tion the wings create avortex create wings the of edges the outerfinite, (i.e., be horizontal) thewill phenomena of boundary the at circulation The place. wing  is displayed (two-dimensional graph), the space is defined as defined is graph), space the (two-dimensional displayed is ∫∫ Γ Cc ϖ ci rc () ), and can be represented as the closed loop integral of the vorticity of the loop integral closed the as represented be ), can and rt =

,, CIE color charts and related tools for spectral identification and standardization. and identification spectral for tools related and charts color CIE  ∫∫ Cc ( ds ϖ v  ) as a function of location ( of location afunction ) as () =∇ ( rt x plotted according to the “E-value” as as “E-value” to the plotted according ,, ,, Γ yz circ ds ( ), where flow against the path direction has a negative value and flow directions directions and flow value a negative has direction thepath ),against flow where × ) with flow velocity flow velocity ) with v  vr =∇ ) that is at the edge of the wake of the edge atthe is that ) as a function of location ( of location afunction ) as () s  ) are not considered. Circulation is defined as the steady-state closed loop closed thesteady-state as defined is Circulation not considered. ) are td × 400 nm s vr

flow . A flow at rest will have circulation zero. Thewake circulation have will . Aflow at rest velocity (i.e., wind velocity) on a path looping around the object in a in object the around looping (i.e., on velocity) apath velocity wind () γ td velocity (i.e., wind velocity) on a path looping around the perturbation perturbation the around looping (i.e., on velocity) apath velocity wind s x v  . Where the vorticity is the degree of “rotation” experienced in in of “rotation” degree the experienced is vorticity the . Where r  = ) and time ( time ) and VI WT AM TV MW IF UV () vv xy ,, r  v z ) and time ( time ) and over aloop E . t ), which is the “curl” of the velocity at a given atagiven velocity of the “curl” the is ), which = () Lb 22 t  ++ ∫ S ), which is the “curl” of the velocity velocity of the “curl” the is ), which S with path steps steps path with [] C vd 700 nm xy ab () c =+ xd 2 // ( . In case only hue only and case In sv () ϖ  ab ++ () 22 rt CMYK  RGB , s () tangential to the loop. to the tangential yds dy ) within the enclosed enclosed the ) within of the flow in,for flow of the (see Figure C.51).(see Figure Circulation function at the tip of the of tip the atthe vd z () zd / satura sd s , in in - C 225

226 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Circulatory system branching vessels. The circulatory system is defined byconservation defined is system circulatory The vessels. branching flow in reduction with impedance growing the in pressure) amplitude the dampens side that arterial on the heart) of the rhythm pumping by the component (induced oscillatory an has system circulatory The to hearts. back and veins, venules, capillaries, Blood general] dynamics, fluid [biomedical, system Circulatory thermodynamics and defined many conditions as a pioneer in the new field of thermodynamics. Clapeyron Clapeyron thermodynamics. of field new the in as a pioneer conditions many defined and thermodynamics recommendations for made several Clapeyron France. from engineer and Physicist [thermodynamics] Paul Émile Benoît Clapeyron, C.52 Figure circulation to maintain exercise easy An of time. periods for extended still perfectly standing when faint people will Theskeletal muscles. fromskeletal encapsulation by supported is that aflow have mechanism veins the heart, of the mechanism

Blood circulation diagram. Venous blood in blue and arterial (oxygen rich blood) blood in red. in the veins of the leg of the veins the in muscle

function is important, especially when considering that a large number of number alarge that considering when especially important, is function is to periodically flex and release the leg muscles (see Figure C.52). Figure (see the leg muscles and release flex to periodically is flow loop in a biological system; heart system; in a flow biological loop (1799–1864) lumen associated with increasing number of number increasing with associated lumen

of mass . In addition to the pumping pumping to the addition . In , arteries, arterioles, arterioles, , arteries, (both velocity and and velocity (both Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 relation water boiling and steam instance, for mixture, two-phase the defined Figure C.54 C.54 Figure of James Prescott Joule (1818–1889)and Lord Kelvin (a.k.a. [general, mechanics,thermodynamics]German physicistandscientist.Clausius’ fatherwasacontemporary RudolfClausius, Julius Emanuel C.53 Figure inspired Clausiustoformulatehisown interpretation ofheat Léonard ofNicolas Sadi Carnothe himselfwasacontemporary (1796–1832).Thework ofCarnot Lord Kelvin inthesecond Clausius introduced theconceptofentropy (seeFigure C.54). losses duetothework itself(generatingheatofitsown), whiletransferringheatagainstagradient.In 1865 multiple processes atastagetoaccomplishonegoal,intherefrigeration with thisequatestowork performed the transferofheatfrom abodyatlow temperature toabodyathighertemperature. Meaning thatthere are ) (see Figure C.53).) (see Figure Benoît Paul Émile Clapeyron (1799–1864). Clapeyron Émile Paul Benoît Rudolf Julius Emanuel Clausius (baptized name: Rudolf Gottlieb; 1822–1888). Gottlieb; Rudolf name: (baptized Clausius Emanuel Julius Rudolf law of thermodynamics (1822–1888) as:There isnosingleisolatedprocess that results in transfer William ( , different from thatexpressed by also see c see also

Thomson Clausius, Rudolf Julius Emanuel Clausius, Julius Rudolf lausius : 1824–1907),while –c lapeyron

C 227

228 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Clausius–Clapeyron relation Clausius–Clapeyron dQ the path of inclement weather (see Figure C.55). (see Figure of inclement weather path the perature, perature, lower part of earth lower part geophysics] Field of physics general, [energy, dynamics, fluid Climatology [thermodynamics] relation Clausius–Clapeyron Figure C.55 in the liquid phase ( phase liquid the in Note the derivative is not simply as in the equation the in not is simply as derivative Note the vaporization coexist. Generally we can assume that the gas the phase that assume we can Generally coexist. N g the heat added to the system), and and system), to the added heat the the number of molecules or atoms in the gas state, respectively. state, gas the or in atoms of molecules number the ρ V Climatological tools:(a)coldandwarmfront migrationinthree dimensions the density of the vapor phase, phase, vapor of the density the ( (a) LS ≡− dPd v

’s ’s τ a Tg  atmosphere ) and ) and () ττ TT =− 997 L 969 L ∆ LL Sd vv  aa =− = () ρρ directly related to the weather and providing warnings for people in warnings providing and weather to the related directly ag Q VL , where , where v −− a 11 vv the volume occupied by one volume atom occupied the  ≅= ρ S L ag the density of the liquid of the density the i

gas gas entropy of the the = VN gg of L of an atomic gas ( atomicgas of an τ 977 Ta state ∆ L v , 990 with with , where , where for the gas, but assumes the gas and liquid to to liquid and gas the assumes but gas, the for dealing with physical phenomena physical in with the dealing V g P the gas volume of the constituent and and constituent volume of the gas the 1029 H is the vapor the is v and liquid phases, respectively, and and respectively, phases, liquid and ag phase, phase, ) occupies a greater volume than volume than agreater ) occupies or molecule of the constituent. constituent. of the or molecule 982 L

L pressure the latent the , τ T of heat the tem the ( Continued)

- Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 background light(blocks betterthan90%)atanazimuth inthe“southern” oftheMilky portion Recent discoveries show thattheinterstellar“dust” all issodensethatitblocksvirtually cloudofparticles Yáñez Pinzón [1462–1514]),nexttoAustralian Aborigines approximately 40,000years ago(wall drawings). documented by theInca’s andearlyEuropean (documentedin1499 by Spanish observers explorer Vicente [astrophysics] Dark “cloud” inthebandofMilky observed Way galaxy, datingbacktomillennia, Nebula Coalsack carrier Cthe and frequency modulator the whereMis synthesis, modulation frequency in used Expression [] C/M CO.) Denver, KCNC-TV CBS of (Courtesy station. meteorological (c) mobile and University ofIllinois,DepartmentAtmosphericSciences,IL.) Figure C.55 (Continued) Ratio

(c)

Climatological tools: (b) drawing of isobars on a section a of the on global map. (Courtesy of isobars of drawing (b) tools: Climatological (b 1004 mb ) Isobar

1008 mb frequency. Frequency modulation synthesis is a tool used in spectral analysis. spectral in atool used is synthesis frequency. modulation Frequency 1000 mb 996 mb Wi paralle nds flowroughly l toisobars around high Wi counterclo cl oc around lows nds flow Wi kwis nds flow e ck s wise Coalsack Nebula Way . C 229

230 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Coefficient of drag of Coefficient Also defined as the ratio of shearstressratio the ( as defined Also (see Figure C.56). was thegodAtaguchu whokickedaholeinthebandofstars(now known astheMilky Way) inafitofanger tion ofAustralia describedit as theheadofanemu.The Incas inthatit South Americacirculated thestory remote stars.Thedark spothasbeenknown anddescribedforaconsiderabletime.Theaboriginalpopula- in Chile.Thedustspread-out inthenebulaprovides significantattenuationfortransmittedlight from as well as extremely remote, ofLaSerena oftheAtacama located150 kmnortheast Desert ontheperiphery European Southern Observatory’s inChile,whichisoneofthedriestareas intheworld LaSilla Observatory acquired over theyears, andmostrecently madeby bytheMPG/ESO2.2-mtelescope observations at light scattering introduced by KarlSchwarzschild (1873–1916),basedoncumulative information episode (1968).TheconfigurationoftheCoalsack Nebulacanbederived from theequationsongalactic Nebula isalsofeatured intheoriginalsciencefictiontelevisionseriesStar Trek , the“Immunity Syndrome” (“The Southern Cross”) andspansapproximately 50light-years atitswidestexpansion. TheCoalsack The Coalsack Nebula islocatedbetween 610and790light-years distance, intheconstellation Crux stress stress shear Surface mechanics] [fluid dynamics, friction of Coefficient FD friction and from resulting effects retarding of the influence the defining Coefficient mechanics] [fluid dynamics, drag of Coefficient Gandhi.) Dr. of Poshak (Courtesy across. of shape the in right, the to C.56 Figure force ( the drag to force correlated is and conditions andsurface for fluids tables in found be can and and drag A = the effective cross-sectional area of the object in motion.the object of area cross-sectional effective the over the kinetic energy the over flow ρ “Coalsack” in the constellation Crux, depicted by the dark “hole.” The Crux constellation is up and and up is constellation Crux “hole.” The dark the by depicted Crux, constellation the in “Coalsack” Av . The coefficient of drag ( of coefficient afluidThe . through moving to abody respect with viscosity () 2 2 , with , with v the velocity of the object in the fluid fluid the in (e.g., object water, of the velocity air), the

density, where (C f =σ σ s ) with respect to normal stress ( respect ) with s ρ /(1/2) the density the expressed as dimensionless number defined by the by defined number dimensionless as expressed ρ v 2 of the fluid of the ) , v velocity σ n ), ), C f ρ =σ the fluid density, density, fluid the , and , and sn σ . σ F s drag the stress. stress. the ) as as ) D flow ) Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 angle with the normal to the surface) for an object at rest. This would apply to an automobile tire on the an automobileon tire apply would to This atrest. object for an surface) to the normal the angle with kinetic friction, such as a sled sliding down a snowy hill (see Figure C.57). (see Figure hill asnowy down sliding asled as kineticfriction,such experience will over asurface dragged being object motion. in An object for an surface) to the normal the angle with (see Figure C.58). Figure velocity(see motion atuniform rolling uniform be maintain overcometo to motion in force needs object . Thefriction for an surface) to the normal the with force ( the frictionforce of ratio The [mechanics] kinetic friction, of Coefficient ( force ( the frictionforce of ratio The [mechanics] static friction, of Coefficient room for deformation. (Courtesy Daimler AG, Germany.) Stuttgart, C.58 Figure ( the friction force of ratio The [mechanics] rolling friction, of Coefficient C.57 Figure

Sliding down a ski slope with limited kinetic friction. kinetic limited with slope aski down Sliding Deformation of an automobile tire resulting in rolling friction. Rear axle with tire cut open illustrating illustrating open cut tire with axle Rear friction. rolling in resulting tire automobile an of Deformation F F F f f f ) to the normalforce ( ) to the (μ ) to the normalforce ( ) to the ) to the normalforce ( ) to the ( μ stat μ rol kin ) ) ) Fm Fm Fm n n n = = = g g g cos cos cos Coefficient of friction, static of friction, Coefficient () () () θ θ θ , where , where , where , where , where , where θ θ θ is the angle the is is the the is is the the is C 231

232 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Coefficient of friction kinetic Coefficient parallel component of the force does not exceed the frictional force ( force frictional the not exceed component does force of the parallel the long as on. As rests body the surface free to the acomponent parallel with aforce experiencing while on, uniform rest, rest, experience static friction (see Figure C.59). (see Figure friction static experience on aslopewill abox resting slip. without Also acceleration and velocity steady-state normal under road [general, mechanics] Relation between the resistive force ( force resistive the between Relation mechanics] [general, friction static of Coefficient ( See [mechanics] friction static of Coefficient ( out asphalt rolling or awaltz surface road on the for atire instance, for observed, deformations from resulting force dissipative the Frictionfor coefficient [general] Coefficient of rolling friction ( See [mechanics] friction of rolling Coefficient ( force resistive the between Relation mechanics] [general, friction kinetic of Coefficient ( See [mechanics] friction kinetic of Coefficient C.59 Figure FF FF KK Ss =µ ≤µ while experiencing a force with a component parallel to the free surface the body rests rests body the surface free to the acomponent parallel with aforce experiencing motion while

Person standing in fixed location on Lombard Street incline in San Francisco due to static friction. static to due Francisco San in incline Street Lombard on location fixed in standing Person N N . .

coefficient coefficient coefficient

of of of

friction friction friction , , , static rolling kinetic μ . . μ . S μ ) K R ) ) F F see S K ) and normalforce ( ) and ) and normalforce ( ) and

coefficient FF fs =µ

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friction ) the body will remain at remain will body ) the F F N N ) for a body at rest atrest ) for abody ) for a body in in ) for abody , rolling ). Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 thermal conductivity, (either flow the specific heat underconstantpressure, coefficient, with and resenting theratiooffrictionforces todiffusionforces, where the local temperature in Kelvin, Kelvin, in temperature local the s StPr coefficient, tubes, with under certain specificcircumstances toflatplatesandinsidestraightconduits. under certain transfer j-factor, whichisonlythecasewhenthere isnoformdrag. Theconditionsofnoformdrag apply In casethere istransferofmomentum,theColburnmassj-factorwillbeequalto heat to macroscopic applies adhesion, which entities. to Contrast of asubstance. molecules between force Binding thermodynamics] solid-state, [general, Cohesion visible to the human to the visible colors other all form blue can and green, red, constituents Basic on mass. acts which force gravitational force the electromagnetic with comparison in This as: red referenced g, b as states: r, (also “color,”three defined has on aproperty which acts Forces the Four with associated is label This color force. as referenced Also thermodynamics] solid-state, relativistic, nuclear, quantum, energy,[computational, general, Color idealgaslaw by the expressed solution. the The as osmotic be can temperature pressure volume and same the agaswith be would tion particle the of asolution if as solu osmotic Thepressure thermodynamics] chemical, [biomedical, pressure osmotic Colloid time ( perturbations space-time gravitational as referenced time ripples in Generate relativistic] [astrophysics, holes black Colliding [fluid dynamics,mechanics,thermodynamics] Colburn j-factor, transfer mass Reynolds number, where [fluid dynamics,thermodynamics] Dimensionless numberillustratingtheratioofheattransfertocrossflow j-factor,Colburn heattransfer ) or canceling or subtractive (e.g., paint; a mixture of all three colors yields black). yields colors three of all (e.g., amixture orpaint; subtractive white light) or form canceling three of of atrail leaving solids, and medium of frozen consisting object Celestial [astronomy/astrophysics, mechanics] Comet and tarling and charged particles, the comet’s tail. The tail emanates from the head, or coma of the comet. comet. the coma of or the head, from emanates tail The comet’s the tail. particles, charged gas and Sc Pr

perturbation theSchmidtnumber. Sometimes alsoreferred toasChilton–Colburn j-factor formasstransfer thePrandtl number. Sometimes alsoreferred toasChilton–Colburn j-factor forheat transfer. 2/3

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GW

W law ordiffusion), ms s themassflow rateatthewalland = and

A thearea, , v colliding S eye an m themassvelocity, tothefree specificallypertaining flow area bridgingadjacent ’ . Depending on the mechanism the colors can be additive (e.g., light, where all (e.g., all where additive be light, can colors the mechanism on the . Depending t η h D s the viscosity ofthefluid, theviscosity describestheconditionsofflow t dif off time, diffusioncoefficient,

, black

Π n law is the number of of moles number solution, the and is os [] m a ).

== holes theconcentrationofconstituent“ nR TR c p ; η thespecificheatunderconstantflow atwallfriction, VC gravitational jv mm ( S = m j [] theminimumfree flow through eithercrossflow areas, H ( () ρ

κη thedensity, j = m s that act on charges (positive and negative) and the the and negative) and (positive on charges act s that η T ( =St w , where , where theviscosityatwall, h () . Designation in the strong the in . Designation nuclear 0

ontheshellorwall, wave / ρ c D p κ m R dif G St m ; and Sc = m =× m = 135 8 theStanton masstransfernumber, mo . ) 2/3 tSc St e s ( a m c instein le [] ,” ,” ) C p J/mo v At η 23 the velocity of mass transport thevelocity ofmasstransport the concentration ( concentration the / / , dimensionlessnumberrep- κ lK

equations × h ) St is the gas constant, constant, gas the is [] 2/3 s 0 a thefilmheat-transfer theStanton number, isthemasstransfer ( η , green, and blue). and , green, w ). /η) 0.14 s see also force that that force = = κ the - Comet T see

c

p .

C 233

234 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Communicating vessels have been identified in our solar system. The direction of the gas/vapor tail is indicative of the solar of indicative is tail gas/vapor the of direction The system. solar in our identified been have of 10 atotal comets far So Hyakutake. of 2537 years, and aperiod has and to millennia back dating described C/1995 O1, Comet (astronomy 1995), nomenclature: in been Hale–Bopp has is comet which “discovered” notable Another Sun. orbitthe our in around observation to the respect with position own on our depending 1986III) moves on its orbit around the Sun 1986III) on moves orbitthe its around carry information about the history of the creation of the solar system (see Figure C.60). (see Figure system solar of the creation of the history the about information carry to bound are hence system; solar of our formation of the constituents essential to be considered are Comets comets is Halley’s is comets anasteroid from different is This charged particles has a different angle adifferent has particles charged the nucleus in found contentsupposedly is comet the of The principal [biomedical, general, mechanics] ( mechanics] general, [biomedical, Compliance C.61 Figure at equallevel underequilibrium,independentoftheshapeandsize oftherespective vessels (seeFigure C.61). [general, fluiddynamics]The ofopenvessel thatare surface connectedby free-flowing passageswillbe vessels Communicating C.60 Figure nomenon is in particular applicable for an distensible tube, in which case the tube expands with increasing increasing with expands tube the case which in tube, distensible for an applicable nomenon particular in is filler). “solid” The phe- and or mash/webbing multilayer of as multiple components such amalgamation

Communicating vessels. A comet.

comet

, last seen in 1986. Halley’s comet (initially Comet 1982i; Comet Comet 1986. (initially renamed in comet seen Halley’s , last , which has no tail and consists of solids only. of solids One of consists the more and noted no tail has , which C comp to the comet’s trajectory than the vapor the than comet’s to the trajectory l ) indication of elastic nature of a material or (e.g., composition of amaterial nature of elastic ) indication , traveling to the edges or our solar or our edges to the , traveling P 1 R 1 P 0 R P 2 2 of the coma. Note that the tail of tail the Note that coma. of the

system cloud tail; forming two tails. tails. forming two cloud tail; , every 75–76 years, 75–76 years, , every

wind . Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 37 P B density. For earthquake tion velocity at the water surface at certain wavelength and temperature is approximately approximately is temperature and wavelength atcertain surface water atthe velocity tion the change in pressure: pressure: in change the the speed of propagation in solids is defined by defined is solids in of propagation speed the first-order approximation as approximation first-order while at a depth of atadepth while applied pressureapplied direction forms condensation (cooling during expansion), expressedby parallel rows of clouds. C.62 Figure ( condensations and rarefactions alternating by identified is medium oscillatory The of propagation. direction the also is mode oscillation compression the general In wave. the wave and in solids than differently responds the medium fluids In atomic level. oscillation a(damped-) in culminates which modulus, bulk on the based relaxation in resulting force, external an , or gas liquid Anysolid, geophysics] dynamics, fluid biomedical, atomic, [, wave, Compression propagation acoustics both see fluids in waves compression geophysics] wave Transfer dynamics, fluid biomedical, atomic, [acoustics, waves Compression gas dissolved in volume ofa change rate of The [fluid dynamics] fluid in of gas Compressibility of factor, compressibility The conditions. gas law, ideal and gas ideal the from deviation the indicating Parameter [thermodynamics] factor Compressibility greater. Compression waves are also used in ultrasonic in used also are waves Compression greater. propagation or modulus of tissue constituents in organs (see Figure C.62). (see Figure organs in constituents of tissue or modulus propagation gas, and and gas, propagation ( propagation .m g

=∝ state /s γ and an increase in salinity by salinity in increase an and ). ∝ , with , with the volume fraction of the undissolved gasses. undissolved of the volume fraction the Example of atmospheric compression wave. The expansion (lowering the local pressure) in a linear alinear in pressure) local the (lowering expansion The wave. compression atmospheric of Example in the form of a longitudinal elastic compression wave. This compression wave can be at the be at can compressionwave This wave. compression elastic of form alongitudinal the in v ) in sea water is a direct function of depth, salinity, and temperature and can be defined in defined be can and temperature and salinity, of depth, function adirect is water sea ) in P ( the externally applied pressure (in Pascal), (in Pascal), pressure applied externally the P 5 ), making the compliance a direct function of the change in volume in change of the function adirect compliance the ), making km C this becomes becomes this comp compression Z B v co l =∆ m = = VP PV /ρ ∆ 1% (Z , where , where 1 n RT . . 51 , wave propagation velocity propagation , wave is increases the speed of wave propagation by of propagation wave speed the increases com × ideal gas ideal 1 for an equal , will 0 B ) 3 Y v m/ is the bulk modulus and and modulus bulk the is and sound. and = s while an increase of 1 increase an while /

ρ imaging , where , where γ= , relying on the differences in speed of speed in differences on the , relying under compression of the solvent of compression the fluid under Y cc pv is the Young’s the is and modulus l see also 1 the ratio of the specific heats of the of heats specific of the ratio the . 31 ρ ( × ° in in For gasses. and solids, liquids, C results in an increase of increase an in C results the local density. The propaga- local the v see also Compression wave, propagation 0 amb 4 m/

s wave , approximately , approximately is called an acoustic acoustic an called is an 2 1 can be compressed by compressed be can .m

der ). of speed The 1 ( /s w . V 41 . In comparison comparison . In × ) as a result of aresult ) as aals ρ 0 the local local the 3

10 equation m/ × s

, :

C 235

236 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Compton, Arthur Holly Arthur Compton, momentum of the scattered photon scattered of the momentum respect to the incident direction and Δλ and incident direction to the respect which can be written as as written be can which momentum of the incident photon of the momentum ( explained by the Compton effect (see Figure C.63). Figure Compton(see by the effect energy explained effect aphoton generates electrons of acolliding conservation prevailing the and laws observations energy on the 1922. in published Based electromagnetic of radiation with particles, to that energy next phenomena as associated well as tum proofmomen- of the empirical provided who United States the from Scientist nuclear] [atomic, biomedical, Holly Arthur Compton, Figure C.64 conservation on the based E follows: photons as re-emitted of the wavelength the of thedetermination of thebasis forms of momentum conservation The electrons. free with acollision in of energy aphoton of loss the matter, energy, Description nuclear] condensed [atomic, biomedical, effect Compton C.63 Figure incident photon with wavelength incident photon wavelength with incident incident elec = . Arthur Compton received the in 1927 for atomic in of the Physics in description his Prize Nobel the Compton received . Arthur mc electromagnetic e 2 , however the electron needs to be considered in relativistic terms which yields yields which terms , however relativistic in theelectron needstobeconsidered

Arthur Holly Compton (1892–1962). (Courtesy of Noble Foundation, Stockholm, Sweden.) Stockholm, Foundation, Noble of (1892–1962). Compton (Courtesy Holly Arthur Compton effect. The angular deflection of a beam of alpha particles nearing an . atomic an nearing particles alpha of beam of a deflection angular The effect. Compton ∆ λλ =− with energy radiation energy with of is energy λ λθ i Alpha particledeflection to the emitted photon with wavelength photon wavelength with emitted to the h p s =− =× , photon : (1892–1962) hm represents the Compton the represents 626075 6 E . ie ,, photon , with momentum oftheelectron as momentum , with e with the energy balance at hand as described by the Compton by the described as athand balance energy the with c () 1c +=  51 p is mc os , photon h E i 2 , 0 photon , where , where − 34 =+ EE Atomic nucleus Js  s pp =ν photon elec the Planck’s constant, constant, Planck’s the θ with scattering angleof the with represents , wavelength (see Figure C.64). + ν ), the radiation of the the ), frequency the , photon elec . The increase in wavelength from the the from wavelength in increase . The  , where where λ s is due to the collision loss, loss, collision due to the is p elec h p i , photon λ = the wavelength of the of the wavelength the mc e E =λ withrest energy: elec / 22 the energy loss loss energy the =+ is the the is

pc ee involved involved 22 mc

4 , Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 1  tion: which canbewrittenas the tensor operator;theintrinsic spin canalsobecharacterized as the release ofapion (“π with respect totheincidentdirection. In molecularphysics theinteractionbetween twoprotons with See c matter, energy, See nuclear] condensed [atomic, biomedical, Compton scattering tions for heattions (1881–1953) FryRichardson work by the Lewis 1910 on in are More examples recent equa Laplace (e.g., periods solutions. out months) the spent on lengthy working with problem statements extensive and complex to extended approach theoretical the of The intricacy dynamics. fluid to experimental contrast in dynamics, fluid theoretical to as referred century, eighteenth to the back dating by hand attempted were on (prior to computers) Early numericalsolutions analysis. mathematical extensive and advanced Fluid thermodynamics] dynamics, fluid computational, [biomedical, dynamics fluid Computational photon [atomic, biomedical,condensedmatter, energy, nuclear]Theincrease inwavelength from theincident wavelength Compton century) in 1976 and 1978 solving Navier–Stokes and Euler algorithms (see Figure C.65). algorithms 1976 and Euler in and century) 1978 solving Navier–Stokes (twentieth R.F. Warming and century) (twentieth Beam M. work of the Richard and century), (twentieth 1960s 1970s and 1973 work McDonald by H. the shown and of century) W. (twentieth Briley Roger the in computers of availability widespread the more with to flourish came efforts of these culmination and nucleonic interspacingdistance, Figure C.65 C.65 Figure respective nucleons µ = c h Hans Lewy Hans == /2 V  π withwavelength =⋅ mc , where ττ   π ab A computational analysis of fluid flow in a tube. ina flow fluid of analysis A computational   Richard Courant Richard transfer and 14 . gm h (1904–1988) in 1928 for their work on hyperbolic partial differential equations. The equations. (1904–1988) differential 1928 for in partial work on hyperbolic their ππ 2 =× fm a () 2010 6260 6 and isthepionComptonwavelength ( . // ∆ 21 b ”) (i.e.,π Mr λλ λ , τ   i =− totheemittedphotonwithwavelength a [

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238 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Condensation number η relative intensity will generate virtually infinite number of color number infinite virtually generate will intensity relative electrons. free with of action the populating hence conduction band, conduction the overlapping is band mechanism valence the tion by aforbidden separated and gap unpopulated insulator an In two. these in than more energetic tor for asemiconduc band) conduction and band valance between gap (energy energy gap the comparison In eration established. electrical conduction electrical of phenomenon the band conduction energy thermal the When atoms. copper neighboring between to move freely electrons allowing band, valence the overlaps band conduction the for instance, copper and . In comparison with either insulator either with comparison . In shells orbit or levels energy allowed specific in electrons with model atomic Bohr to the according arranged electrons force external an of Under influence the general] [atomic, electronics, band Conduction capacitor for terminology Old general] [electromagnetism, Condenser whereΔ surface, the with contact [thermodynamics] The ratio ofin molecular of molecules number thecondensation total to surface on a number Condensation of electromagnetic of eye the in feature optics] Anatomical chemical, [biomedical, Cones of elements made Materials [atomic, general] Conductor temperature room afree electron as force binding energy trons viscosity such as germanium or silicon is approximately approximately is or silicon germanium as such can be moved to a higher energy orbit, removed from the valence the removed orbit, from band energy moved to be ahigher can ) to an energy ) to an , L

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- - . Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Figure C.66 C.66 Figure and the moment the of inertia and total exchange of energy exchange tion with conservation with tion combina- direct in for transitions, rules selection and conditions boundary setting atomic transitions, and to nuclear applies also momentum of angular Conservation structure. initial for the as momentum angular definitions are, for instance, defined by the cie by defined instance, for are, definitions momentum illustrated by ball rolling down incline, which will continue its rolling path when a level plane is reached. is plane alevel when path rolling its continue will which incline, down rolling ball by illustrated momentum C.67 Figure the angular the of product is momentum angular The nuclear] general, [fluid dynamics, momentum of angular Conservation location. respective atthe outlined be principle will conservation Each mass–energy of conservation of mass, conservation momentum, of linear conservation of energy, conservation energy, oftion leptons, conservation conservation momentum, angular of servation con distinguished: be can principles/laws conservation following The thermodynamics] [atomic, general, laws Conservation (see Figure C.66). (see Figure

angular

Conservation ofConservation energy (conversion of potential energy to kinetic energy) and of conservation angular Cones (color vision) and rods (radiance vision) in the retina of the eye. the of retina the in vision) (radiance rods and vision) (color Cones

momentum ), the sum of the angular momentum as vectors will combine to provide the same same to combine provide the will vectors as momentum angular of the ), sum the of ( energy of a system will be conserved. When a rotating system disintegrates (without (without disintegrates system arotating When conserved. be will of asystem I iner

of , conservation of mechanical , conservation ti a ) of the object ( object ) of the charge (see Figure C.67). (see Figure Pigment epithelium conservation of electromagnetic electromagnetic of conservation of current, , conservation To opticnerve system and described in greater detail under chromaticity under detail greater in described and system Amacrine cell Horizontal cell Bipolar cell Ganglion cell Choroid LI Sclera Rod Cone = of atomic nuclei, conservation of baryons of atomic nuclei, conservation Structure oftheretina iner ti a ω ), when no external forces are involved the involved the are forces external no when ),

energy Light Nerve fibers , and conservation of momentum. of momentum. conservation , and Conservation of angular momentum angular of Conservation velocity , conserva , ( ω ) - -

C 239

240 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Conservation of charge Conservation of theenclosedspace,and where where different set of objects, or adding object to the motion to object adding or of set objects, different of theelectromagnetic ( universe the in energy friction no specifically forces, net external (no collisions to lossless applying Specifically mechanics] [general, momentum of linear Conservation energythat The principle [general] of energy Conservation [energy, general,optics]Based ontheMaxwell energy of electromagnetic Conservation particle. combined the will as particles, two for the charge net the system negative with aparticle and charge positive with aparticleCombining altered. or destroyed be cannot Charge nuclear] general, [atomic, dynamics, fluid of charge Conservation [thermodynamics] In principle, mass In [thermodynamics] of mass Conservation balls. billiard the of action rolling the during involved losses friction are there however; ciple C.68 Figure the energy mass mass Poynting vector, mass can be converted into energy converted be can mass radiation see

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Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 conservation of mass principle (see Figure C.69). principle (see Figure of mass conservation the of example conceptprimary isaof flow The atoms. residue and of molecules or dissociation forming the in lost no are atoms equation; reaction by the represented is of mass conservation the reactions chemical and liquids, where the mass is captured by the density by the captured is mass the where liquids, and toward the earth’s earth’s the toward flow that masses air by accompanied is air rotation).rising The earth’s the from resulting of awall consists CCKW kilometers. of thousands for extend can that to,equatorclose the centered or on primarily effect, chimney nondispersive Atmospheric meteorology] mechanics, [fluid dynamics, Kelvin coupled waveConvectively of number Knudsen a instance For [fluid dynamics] Continuum conservation laws: conservations general The nuclear] general, [fluid dynamics, equation Continuity equation: the with accordance in interchangeable are mass and energy ciple that and energy mass both that The principle mechanics] [general, of mass–energy Conservation C.69 Figure fusive slip-flow in the continuum. the in slip-flow fusive temperature fluid flow energy, energy, of momentum, and conservation of and momentum, conservation m is the mass, and and mass, the is

can be treated as a continuous medium, with the macroscopic the with medium, acontinuous as treated be can Conservation of mass illustrated. mass of Conservation , volume of charge.

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ρ ≤ (CCKW) (CCKW) ) multiplied by the volume by the ) multiplied 0.1 sets the boundary conditions where the the where conditions boundary 0.1 the sets combined are conserved based on the prin- on the based conserved are combined wave of Convectively coupled Kelvin wave angular parameters such as pressure as such parameters feature, resembling a resembling feature, 00 mc E of <≤ Kn = mass momentum ( V 2 , where , where ), ), , conservation , conservation . 1 mV , describing dif- , describing =ρ E , next to , next is the the is . In . In , C 241

242 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Convectively coupled Kelvin wave kilometers (see Figure C.70). (see Figure kilometers over adistance weeks, as fast as (e.g., storms) arise may pattern tropical migration the with associated anomalies However,the east. to from west Ocean Pacific the to traverse CCKW the for to 2 months days approximately 45 takes is that fact the by exemplified is waves Kelvin with a with travel generally waves These pattern. astanding under only related, aphenomenon is is that Oscillation [1938–] Madden A. Julian Roland Rowland Paul and oscillation Madden–Julian the with associated phase convective active the to as referred also is CCKW cyclones. of tropical generation for the mechanism provide the can CCKW migrating eastward an with clashing Ocean Atlantic the across pattern spin to cyclonic data. (Courtesy of Paul Roundy.) Paul of (Courtesy data. radiation longwave outgoing OLR, (d) Ventrice.) Michael of (Courtesy spectrum.” frequency Wave number; Zonal phenomenon ason observed land in Dubai. (c) CCKW diagram at 40 C.70 Figure storms are reinforcing the effect combined with divergencewith combined effect the reinforcing are rainstorms These acirculation generating surface, 20 40 (a) (c) 20 S phase N N

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244 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Coriolis, Gaspard-Gustave de Coriolis, Gaspard-Gustave Figure C.72 Figure introduced thedisplacementdistance ( motion affectsthedirection ofthepathanobjectas well astheflow [fluid dynamics,general,mechanics] Physicist from France. In 1835Coriolis recognized thatthe rotational de Gaspard-Gustave Coriolis, of an object as well as the flow the as well as object of an path the of direction the that principle The thermodynamics] mechanics, dynamics, fluid [computational, Coriolis effect Coriolis de by Gaspard-Gustave described was frame reference of a rotating influence under object of moving acceleration The present. is force external real no apparent while redirection, resulting and acceleration (see Figure C.72). Pacific ocean;between the180° hurricanes (“Atlantic Ocean”) andtyphoons(cyclonic Pacific actioninthenorthwest basin: western North hemisphere willbeforced tomove incounterclockwise direction, whichisclearlyvisiblewhenobserving the airflow onthenorthern effect of Coriolis because Alternatively, force. wind as such forces, external due to other be recognized may andnever be negligible, will they that small so are effects but these boat, sail apply toa will same The tendstarboard. to also will hemisphere the northern on river sphere. The itself hemi southern on river the for asimilar riverbank western on the and hemisphere north northern on the to south running sideriver of a east the on water level higher in a result instance for will effect Coriolis position (seeFigure C.73). (1792–1843)as Coriolis force . The 1835. to in referred also The phenomenonstill is however

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246 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Coriolis force Figure C.74 Figure with respect tothenormalearth’s thatis,thelatitude surface, ontheglobe(seeFigure C.74). electric field anelectric generates thus difference potential The or natural. man-made of factors, variety electron charge are accelerated ( accelerated are charge electron radius of curvature, smaller radius higher field due to the higher surface charge density. The electrons density. electrons The charge surface higher the field due to higher radius smaller curvature, of radius electrons image of an for transfer to hold ink surfaces nonconducting machines to charge copying in used also are partially influenced by the radius of curvature ( curvature of radius the by influenced partially its movement with velocity with movement its ( componentoftheangularvelocity [computational, fluiddynamics,mechanics,thermodynamics]The vertical frequency Coriolis ( Fm mass with an object on exerted Force thermodynamics] mechanics, dynamics, fluid [computational, force Coriolis difference of apotential influence the under asurface from charges flux of excess Electric general] [electromagnetism, Corona conductor of the oxygen ( oxygen of the aplasma creates which lighting, is example Another light. in a neon discharge glowing the is example One specific opposite charge. with locations the gas between the in aplasma creates charges of discharge the and field electric The points. charged the between space the fill gas(es)that the ionizes electron excess the from resulting field electric The ratio. exceeding with greater are arc for discharged acorona conditions the points opposite charged the between distance separation electrons collide with the resident neutral molecules at a high frequency of of frequency high a at molecules electrons collide with neutral the resident 60 humidity relative with pressure air standard In arc. discharge conductor, to of the the contributing surface the from escape will of electrons number alimited energy. Only inelastic by the limited still is electrons of the flowing river to be higher than the opposite side with respect to sea level due to the earth’s rotation. earth’s the due to level sea to respect thewith opposite side than higher be river to flowing motion to the perpendicular ily ω ), alsoreferred toastheplanetary vorticity, definedas =− *2 ω are drawn into the electric field in the conductor in field electric into the drawn are 

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248 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Cosmic raysCosmic have anenergyofapproximately particles ( velocity ing law the interpretation). At thelower endofthescale,gammarays released intheproduction ofπ nuclei (1.3% heavy stars inourmilkyway aswell rangeinenergy asemissionfrom othergalaxies.Theparticles from radiation. Thestream ofparticles andelectromagnetic radiation reaching from the Sun, the Earth effects nexttoscattering , whichallresult in(cascadeof;dependingontheincidentenergy)secondary interaction ofcosmicrayswithatomsintheupperatmosphere ofEarth generateexcitation anddecay alpha emergingfrom outerspaceaswellparticles asfrom theSun.Cosmicraysconsistofgammarays,protons, [astronomy/astrophysics, atomic]Radiation consistingofbothelectromagnetic raysCosmic gravitational of the description the asteroids), additionally, and description orbits and (applying to comets of satellite Figure C.77 Figure C.77). Figure (see program flight space “Russia”) Federation, Russian now (USSR; Republics Union Socialist the of Soviet under Astronaut [astronomy/astrophysics, general] Cosmonaut of excess by energybound is in concept theoretical The strings. cosmic to as referred are sion that or discontinuities defects hypothetical are there breakdown of symmetry description quantum theoretical relativistic the In theoretical] nuclear, quantum, computational, [astrophysics, string Cosmic to inexcess of Schriefer unified theory. unified in Schriefer captured is theory concept string of general The loops. closed vibrating as well as infinity to extend that networks string open oscillating of configurations of string theorypart is string cosmic physics. The dimensional short very in jE () >= bubble–

E particles, neutrinos,andelectrons nexttoaminorcontributionfrom isotopesofheavynuclei.The ≥ 10 . The particle flux. Theparticle (“j KE cosmic G He

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, where

) aswell as electrons ( leon . At thehighestrangeenergeticcontentisdominatedby protons atincreasing andare composedofprotons ( . K cosmic ”) forparticle inexcess ofaspecificthreshold energy( 10 and 5 e V δ , higherenergiesare inelectrons andpositrons, increasing toalpha are positive constantsintheenergyregime describedby thepower ~ 1 % ) andatrace ofelectromagnetic radiation(dependingon ~ 86% ), helium nuclei (alpha particles; 12.7% helium nuclei(alphaparticles; graviton.” , in this case relating energy energy relating case this , in energy aswell as E in linear dimen- linear in ) isexpressed as 0 eV mesons eV 10 ∼ Te 6 ), ), e V V

Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 The laminar Couette flow, with average flow velocity flow velocity flow, Couette average with laminar The zero flow velocity on the central dividing plane (see Figure C.78). Figure plane (see dividing central the on flow velocity zero and distance, separation of function as a flow velocity in gradient gradual only with again object, moving two the between line central the to respect with flow backward and forward spin is in velocity the where develop can flow Couette turbulent aplane rotation, vorticity. Under of spanwise conditions constant has and stratified is flow not Couette fluid. by aviscous other, separated to each respect with plates two of velocity translational low under low flow velocity, found alternatively or primarily isof flow type This separation. on plate dependence of quadratic maximum yield a only will flow Couette where power fourth the to radius tube the to havedependency a will tube flow magnitudein a Poiseuille the comparison, In plates. two the between plane midpoint to the dependence aquadratic has plates stationary two between the flow flow Couette in Similarly, tube. of the length the along gradient pressure applied an under tube the of radius the on location the to dependence quadratic has a flow,the Poiseuille flowvelocity In between two rotating concentric cylinders, with with cylinders, concentric rotating two between Reynolds number. automobile acritical Theflowvelocity below only for engine,however an crankshaft the and the rod piston between connection the in flow, found as such stress-dependent shear describes generally flow Couette opposite in direction. moving of plates case aspecial with available, solutions are Poiseuilleto flow velocity. Couette flow obeys the simplified Navier–Stokes equation, equation, Navier–Stokes the simplified flow obeys velocity. Couette fluid flow Laminar [fluid dynamics] flowCouette the direction of flow direction the described with respect to the center plane at plane center to the respect with described and “X-direction” the in planes to the parallel velocity and and between two plates at separation atseparation plates two between distance of function asa Theflowvelocity plates. stationary motion fluid between the describe can flow the and cylinders, of concentric case for the curved be can other, plates the to each respect move with The moving (sliding)platessolution forrelative velocity potential Couette flow. Couette potential C.78 Figure ω angular relative the

Couette flow: (a) comparison between Couette and Poisseuille flow and (b) example of locations for locations of example (b) and flow and Poisseuille Couette between comparison (a) flow: Couette and will develop into Poiseuille flow for larger flow velocity. Additional combination combination flowvelocity. Additional flowforlarger into Poiseuille develop will and x can be described under two conditions: (1) moving plate or (2) stationary plates. (1) conditions: plates. two under or plate (2) moving stationary described be can (b (a) Gudgeon pin Gudgeon ) Crankshaft Conne velocity Couett Piston cting L h viscosity with for afluid e , as a function of radius ( of radius afunction , as ro between plates with a gradual, and frequently linear, gradient in flow in gradient linear, frequently and agradual, with plates between d h h /2 y =0 in the form form the in R 1 the inner cylinder radius, radius, cylinder inner the Cylinder uh Flywhe av y g : the plates can distance can plates : the separation plate the is u =− 0 yields el uu η r () with respect to apressure ( respect with ) is ) is =− Po 2 32 iseuille 8 uy ur η L () θ d () () av 22 Pdx dP ud g Couett =+ [] = flow 14 uy Couett y () 0 ω flow () () = Rr e R R between stationary plates is is plates stationary between // 1 0 yh 2 2 hd e , where , where the outer cylinder radius, radius, outer cylinder the / 22 / [] () () 12 rRR Rr , which has similarity similarity has , which 2 u 22 η represent the flow the represent −− () P Pd ) gradient is in in is ) gradient / () xy Couette flow Couette 2 () 2 2 − 1 2 hy . . C 249

250 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Coulomb, Charles-Augustin de well as (see Figure C.79). (see Figure as well electrostatic force willbeequaltotheforce appliedtothearmofsuspendedrod, expressed astorque. are balanced,basedonNewton’s third law, andthechargecanbederived. Based onCoulomb’s law the and willrepel. Theballswillmove awayfrom eachothertothepointwhere thetorque touched by achargedrod, bothwillbeloadedwiththesameelectrostatic charge(bothinsign andmagnitude) dimensional spaceby anonconductinggeometricdevice. When thetwoballsare incontact,andiftheballsare same horizontal planewithaballofidenticalmaterialandsize asthesuspendedballisfixedthe inthree- in has anelectricchargeapplied,forinstance,aglass silver wire, counterbalancedby aloopwithpaperdisk. Thesuspendedballwillbecharged by a rod that static force between electriccharges. Agoldleaf-covered ballattachedtoarod issuspendedfrom a l’Académiede Sciences des Royal 1785 in attraction ( of electric publication whose [energy, French scientist general] de Coulomb, Charles-Augustin [general] apparatus Coulomb where of 1 ampere, acurrent conducting wires parallel Electric electronics] [chemical, Coulomb, unit C.79 Figure [atomic, condensed matter, energy] matter, energy] [atomic, condensed potential Coulomb , and apositive charge to protons, and applies as also this 1 coulomb across the cross-sectional area of the wire per second per wire of the area cross-sectional the across 1 coulomb Torsion

Charles-Augustin de Coulomb (1736–1806).Charles-Augustin balanceusedby Charles- ) “Coulomb’s Law” opened the doors for the Bohr for the doors the opened ) “Coulomb’s Law” charge unit, defined indirectly from the between two between force Lorentz the from indirectly defined unit, charge V Co ul om b Augustin deCoulomb (1736–1806)toderive theelectro- = er 2 / rod that has been rubbed by rod silk.Thesuspended thathasbeenrubbed rod is , where , where (76–1806) (1736 r the separation between the protons. the between separation the 1 1  AC e = =− 16 / .C . s defines the flow defines × 10 − 19 is the electron charge, however, charge, electron the is of an of charge electric of an

Histoire et Mêmoires atomic andelectrostatic force

model as as Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 star is merely 25 km, but has the mass of our Sun of our mass the but 25 km, merely has is star neutron pulsating this of size estimated The of 30 Hz. frequency pulsating steady with beam, ioned lighthouse maintain invariance, continuumthespace-time to independence The antiparticles. respective ( gation Science Institute, Baltimore, Telescope MD.) Space NASA/STScI, of (Courtesy core. its in star neutron pulsar astrong has Nebula Crab The 1054 AD. by the equation equation by the constants and complex daytime. At the center of the nebula is a pulsating neutron apulsating is nebula of center the At the daytime. the during also was of this weeks three years, for two visible was explosion the documentation, to the According [chemical, electronics, mechanics] The force of attraction or repulsion ( or repulsion force of attraction The mechanics] electronics, [chemical, Coulomb’s charge law, electrostatic elastic behaviordescribedasa functionofstress ( [general, mechanics]Anelastic deformationofasolidmedium.Anelasticcreep isdefined by anonlinear Creep C.80 Figure Earth from 2000 parsecs atapproximately is Nebula Crab distance the and time atthe available tools rudimentary the mind in (keeping astronomers by Chinese of asupernova Remnants [general] pulsar Nebula, Crab to time invariant is theory Lagrangian the Additionally transformation “proper” Lorentz standard under theory Lagrangian of the Invariance theorem. Charge–space–time thermodynamics] [computational, theorem CPT with theappliedstress. For acyclically (angular charges, charges, to theconstants as and strain( C Q compliance ), space and 1 and and

 Crab Nebula, part of the constellation Taurus. Remnant of a supernova that supposedly exploded in in exploded supposedly that asupernova of Remnant Taurus. constellation the of part Nebula, Crab strain τ therelaxation Q FQ =∆ e 2 , respectively, with adistance with , respectively, = J LL 1 () Λ Λ

14 () inversion / , ωω ζζ J πε * 0 ; =+ == L GG JJ  () thelength): uR strain = 12 δ [] Qs (

() time σ P that presumably exploded in 1054 AD, based on documented observations observations documented on 1054 AD, in based exploded presumably that Kronecker delta function delta aKronecker , yielding stress charge conjugation, ). charge In − 2 withrespect todeformation.Thematerialcanbedefined by a J . Introduced by Charles-Augustine . Introduced u Ji J 12 Ru () + 1 στ + +∂ J (see Figure C.80). , where thereal ofthecompliance( part , 22 Jt σ s

τ frequency , separated by a medium of dielectric by amedium , separated () stress , specifically pertaining to quantum pertaining , specifically σ and reversal (in either direction) ( (in direction) either reversal // = ∂=

FA

star ( 13 / J 2 . pa  ()

, spinning in similar fashion to an old-fash to an fashion similar in , spinning , theforce ωω ω +∂ rsec all particles are transformed into their into their transformed are particles all ) appliedstress thecomplianceisrelated τ( =− == () JJ F Ru ∂ e 26 ) exerted between two two between ) exerted t requires the following condition to to condition following the requires ) , where F  light-years actingparalleltothearea for the matrix for the de Coulomb de τω () J 1 R + T , ), ), J u 31 22 , and conju charge τ .

field value, value, J 1 × ) isinphase (known as (1736–1806). multiplication. 10 τ electrostatic electrostatic are material

16 theory ε m , is given given , is ) . ). The - - Creep A .

) C 251

252 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Crick, Francis Harry Compton Harry Francis Crick, cient: periods oftime(see Figure C.81). biomedical context,thiscanrelate tohearinglossesresulting from excessively loudmusicforextensive also appliestophononpropagation and“dislocated” lattice vibrations(vibrationaldamage).In function oftheactivation energy required fortheprocess andthetemperature assumed underconstantstress, whichprovides specific typesofcreep: anelastic,secondary, creeps. andtertiary For instance,anelasticcreep canbe the Figure C.82 Figure aone-way flow as correlation DNA–RNA–protein the published and code, genetic of the mystery the work to unraveling his of dna structure doublethe helix of codiscoverer England, biophysicist from and neuroscientist, biologist, Molecular general] [biophysics, Compton Francis Harry Crick, C.81 Figure Debye equations). The relaxation process underelasticdeformationadheres to k b =× 868 10 3806488 1

. The creep phenomenon. Francis Harry Compton Crick (1916–2004). Crick Compton Harry Francis of genetic information (see Figure C.82). (see Figure information of genetic ε − = 23 ΔL mk L Primary creep 22 primary creep Δ James Dewey Watson Dewey James with = L g/ ε Strain, ε 0

L0 sK Primary creep L ). Applying specific boundary conditionsthiswillprovide). Applying specificboundary three 0 A 0  strain (1916–2004) Δε ε = t Time t () 1 Δt tJ Δε Δt σ Secondary stress creep Anelastic creep , 0 (1928–), 1953. in published He dedicated A =+ uR t () f Tertiary JJ creep − B u [] 1 T − (Boltzmanncoeffi- e − () t / ττ τ = . Thisprocess 0 e Ek Ab / T , asa Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 [general] Angle [general] ( angle Critical [nuclear] The minimum amount of a fissionable material that will support achain support will that material fissionable amount of a [nuclear]minimum The size Critical C.84 Figure critical ( constituents the of two phases the out separate will which fluids, polarization exhibiting ferroelectrics magnetization, spontaneous experiencing ferro- superconductors, point are critical atthe operating of media Examples transition. phase order liquid of the density the and reached vapor between density in difference The temperature. boiling in increase aproportional in result will pressure in correlated tothedirectly is pointpressure.liquids An of increase boiling The thermodynamics] [general, point Critical ( C.83 Figure fiber in importance of particular is angle critical reflectiontotal and fluid and

pressure Critical angle for refraction/reflection. Dependence of of a the medium conductivity to with respect the critical temperature. of incidence at an interface between two media of different index of refraction index of different media two between interface atan of incidence phase diminishes with increasing pressure and temperature until the critical point is point is critical the until temperature and pressure increasing with diminishes phase occurs. The critical angle is based on the refracted angle of 90 of angle the refracted on based is angle critical The occurs. [ P c ]) (see Figure C.84). ]) (see Figure c θθ

Pressure “c”), subscript: c )

d o S T << i l

solid c and Liquid

Liquid

and vapor phases become equal. This phenomenonis asecond- This equal. become phases vapor and Vapor/gas and solid and Vapor/gas

T < Volume c Critical state

T = T >

Triple line Triple Vapor and liquid and Vapor - optic θ c c c P > θ transmission (see Figure C.83). (see Figure transmission θ refr refl Constant temperature Constant pressure c Gas P << Vapor/gas see c

critical P < c TemperatureT c

temperature under Snell’s° under reaction , and binary binary , and [ T . c and ] and law Critical size Critical at which atwhich . The C 253

254 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Critical temperature contrast, carbon dioxide is a substance that will expand upon melting. upon expand will that asubstance is dioxide carbon contrast, Figure C.85 C.85 Figure C.85). (see Figure superconductive resistance its relinquishes amaterial Temperature which below thermodynamics] [general, temperature Critical ( Figure C.86 C.86 Figure Crookes the tube, electrode investigational the introduced who Britain Great from Physicist nuclear] [atomic, electronics, SirCrookes, William, Critical point in a phase diagram for a substance that contracts when melting, for instance, water. In In water. instance, for melting, when contracts that asubstance for diagram aphase in point Critical Vanity Fair Vanity Ward, (1832–1919). Leslie of Crookes William (Courtesy Sir tube in 1870 in C.86). tube (see Figure

− Resistance 10 6 Ω 100 10 20 30 40 50 60 70 80 90 0 0 (1832–1919) T c ) 246 T C Temperature (K) Superconductor Nonsuperconductive 81 material 01 , 1903.) , 2 and becomes becomes and

Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 an applied external electric field, that is, superconductivity.is, that field, electric external applied an of influence the under electrons free of migrating probabilityfor collision of the areduction in resulting with liquid with require will for instance, bodies, perfusion Freezing human question. entire in object of the capacity heat reaction, that is, the reaction probability measured in units of area. units in measured probability reaction the is, that reaction, [atomic, electronics, nuclear] Vacuum nuclear] [atomic, electronics, Crookes tube superconductivity. Most cryogenic processes take place at temperatures below below attemperatures place take processes cryogenic Most superconductivity. in are cryogenics in applications known The most of amaterial. properties physical in changes the observe to low temperature extremely of producing Mechanism nuclear] general, electronics, [atomic, biomedical, Cryogenics see also Freeze-drying, energy, general] [biomedical, Cryodesiccation an atom subtended by area The nuclear] mechanics, [atomic, general, section Cross Figure C.87 Figure freeze quick cold storage. cold quick freeze of deep- by of means water removal the facilitate as well as processes chemical the to slow down used media decreasing temperature. At lower temperatures, the molecular mobility will reduce ( reduce will mobility molecular the lower At temperatures, temperature. decreasing with size in or reduce expand either materials most that fact due to the outer solid shell of the cracking the solid “dry-ice”) provide themechanismforquickreduction oftemperature by submersion.Themelting pointof Infor invitro fertilization. biological applications,generally, theuseoffrozen carbondioxide (alsoknown as ofsperm preservation the for instance, extreme, not that are requirements temperature the applications cal barometer vacuum in a observations earlier the on based was tube Crookes The signs. neon light modern sor to the CO

by the French physicist Jean French by physicist the Picard 2 Crookes tube and mechanism of operation. of mechanism and tube Crookes CO is − ∼° 2 + , otherwise the core will remain too warm for too long a period and there will be risk for risk be will there and for long too aperiod warm too remain will core the , otherwise −

9C 79 Cathode and onlargeobjectsisprimarily limitedby. Attempts theheatdiffusionand ofcryogenics

Anode (1832–1919), predeces (1832–1919), Crookes William by Sir CRT introduced (1620–1682) C.87). (see Figure − + lyophilization . Preservation mechanism for biological for biological mechanism . Preservation Magnetic field:B Electric field:E or molecule for the probability for the or molecule 2 150 123 KC see ∼° −

temperature . In biomedi- . In Cryogenics ) of a - C 255

256 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Crystalline lens Crystalline lens equation the lens by defined as length, thefocal increasing out, flattens lens the On contraction lens. the from 24 mm approximately retina on at the image “near point” the of the focused with rounded most is lens the relaxed are muscles point ( point near ashorter have children whereas adult, 25 cm average distance for the approximately eye the from length focal [biomedical, general, optics] Adaptive optics optics] general, [biomedical, lens Crystalline desensitization ofinterference (i.e.,band-blockfilteror“jammer”) (alsoseev cubic) withoutsignificantlossinaccuracy. Thepolynomialtermscanincorporatethehigherharmonicsand profile thatcanmathematicallybedescribed gain performance by apolynomialuptothethird order (i.e., [computational, electromagnetism, general,theoretical] Nonlinearity inelectricamplifier. Amplifierwitha amplifierCubic C.88 Figure ing by the brain. the by ing see

accommodation Crystalline lens of the human eye forming an image on the retina for signal acquisition and process- and acquisition signal for retina the on image an forming eye human the of lens Crystalline by contraction and relaxation of the muscle in the eye the musclein of the relaxation and by contraction ) (see Figure C.88). ) (see Figure , to the point of focusing “infinity” on the retina. The near isat point near The the retina. on “infinity” point of focusing , to the Graded index

Cortex Nucleus instrument in the human eye that can be adjusted for adjusted be can that eye human the in instrument Zonula ciliaris Watery Cornea liquid Lens Iris Pupil Corpus ciliare muscle Ciliary attached to the lens. When the the lens.When to the attached an

der p ol

equation ). Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 cancer (see Figure C.89). (see Figure cancer to radiation exposure of the FrenchBecause Sorbonne. atthe studies her doctoral of Poland her to homeland start left who physicist, and Scientist nuclear] [atomic, general, Curie, Manya (Marie) Skłodowska Figure C.90 Figure quartz were investigation under structures 1880. in crystalline deformation Some of the under structures of crystalline activity piezoelectric of the discovery for the responsible France from Ascientist nuclear] [atomic, general, Curie, Paul-Jacques general scientific audience in 1912, the to open upon peer review. became conference The Quanta.” the and “Radiation day: the of topic popular avery was conference the of 1911. of part subject The latter the in Brussels in held was conference (b). The in shown Belgium, from (1838–1922) chemist Solvay Joseph Gaston Ernest only. invitation by Solvay Ernest industrialist the by organized C.89 Figure (a)

Paul-Jacques Curie (1856–1941). Curie Paul-Jacques (a) Manya (Marie) Skłodowska Curie (1867–1934) at the 1911 Solvay conference: “Conseil Solvay,” (1867–1934) “Conseil Curie 1911 the at conference: Skłodowska Solvay (Marie) (a) Manya , tourmaline, and Rochelle salt Rochelle and , tourmaline, (b) W Nernst R Goldschmidt (1856–1941) (1856–1941) M Brillouin M Planck Pierre Curie of. Brother Pierre H Rubens E Solvay A Sommerfeld H Lorentz (1867–1934) (1867–1934) E Warburg F Lindemann M Knudsen M deBroglie J Perrin M Skodowska-Curie W Wien Marie Curie eventually died of died eventually Curie Marie (1859–1906) C.90). (see Figure E Hasenöhrl E Herzen J Jeans H Poincaré E Rutherford H KamerlinghOnnes Curie, Paul-Jacques Paul-Jacques Curie, A Einstein P Langevin

C 257

258 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Curie, Pierre is material specific, for instance, for magnetite is it 575magnetite for instance, for specific, material is Curie by Pierre discovered identity. phenomenon was This indicates a very powerful radioisotope powerful avery indicates the Curie is independent of the particle of independent the is Curie the of alpha emittance radium the resembles closely disintegrations Henri in Physics a Prize Nobel couple shared research The behavior. husband–wife piezoelectric magnetism and work work on on crystals his to his polonium, next Curie Marie wife work on for radioactivity his known mostly France from Scientist nuclear] [atomic, general, Curie, Pierre and wiferesearch team:Marie (Manya) Skłodowska Curie(1867–1934)andPierre Curie (1859–1906). [atomic, nuclear]Radioactive isotope Curium a permanent in domains) called (also structures magnetic the which at temperature The nuclear] [atomic, general, temperature Curie the magnetic 1906).law relates The Curie Curie by Pierre described devices/materials of paramagnetic Behavior nuclear] [atomic, general, law Curie disintegrations, [atomic, Unit nuclear] of radioactive Curie, unit C.91 Figure inverse proportionality with respect to temperature ties in with thermal agitation disrupting alignment. disrupting agitation thermal with in ties to temperature respect with proportionality inverse MC Bc = () BT /

( Pierre Curie (1859–1906). 2 96 47 , where , where

Cm) Cm) (Cu) (Cu) (1867–1934). Exemplary contributions of Pierre Curie are the discovery of radium and (1867–1934).and of radium discovery the are of Pierre Curie contributions Exemplary (1852–1908) 1903 in work on radiation for their (1859–1906) are disrupted by the kinetic motion kinetic by the disrupted are C c is the material constant and and constant material the is intheactinideseries.Theelement isnamedafter Curie husband : disintegration and particular particles emitted. The value of value The emitted. particles particular and disintegration 7 .( dipole 41 ×− 02 4 [] moment βµ 1 Cu T ° pa C and for hematide 675 for hematide C and the absolute the rticle =× and the magnet relinquishes its magnetic magnetic its relinquishes magnet the and 37 ( (1859–1906) 1894. in temperature The Curie . M 01 sC particles B ) ) to the applied magnetic applied ) to the = , specifically the formal description of description theformal , specifically 0 10 (see Figure C.91). (see Figure temperature disintegrations u/ . per second per ° C, respectively. C, /s (in The Kelvin). . from 1 g; however, 1g; from The number of The number Antoine Antoine with field with his his with (1859–

B as as 1 C u

Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 space ( space an area ( area an limit zero when the phenomenon comprises all of free space with the vector field rapidly decreasing. rapidly field vector the with space of free phenomenon all the when zero comprises limit The curl is expressed as expressed is curl The space. three-dimensional the in location the through passing lines possible upon all vector ofprojection the of electrons relies on a gradient in applied electrical potential (voltage) with an inherent electric field gradient. field electric inherent (voltage) an with potential electrical applied in on agradient relies of electrons ( function “rotation”describing operator or of a vector vector mathematical The [computational] ( Curl Figure C.92 Figure C.92). (see Figure rainfall heavy and thunderstorms with associated generally is cyclone A meteorological flow that Earth the as direction same the in volume rotating afluid generating system, Low-pressure meteorology] geophysics, [fluid dynamics, Cyclone tive posi that assumption the on based was flow current The of electrons. displacement of the opposite direction the in is direction current the of “holes,” since the flow morespecifically flow; Electron general] [electromagnetism, Current ( field vector (curl-free) field vector irrotational of an one components, consisting of two “orthogonal” sum into the decomposed be tors can vec- decaying rapidly smooth, sufficiently of composed field vector the space, three-dimensional In culus. component of Helmholtzfundamental decomposition A dynamics] fluid [computational, field vector Curl-free product. A vector field with with field Avector product. direction defined by unit direction vector vector direction unit by defined direction particle V A ) as ) as ∇ ∇× counterclockwise on the northern hemisphere and clockwise on the southern hemisphere. hemisphere. southern on the clockwise and hemisphere northern on the counterclockwise ) at a location ( ) atalocation

× V Image from satellite showing the cyclone off Florida coast. C ( where involved, before the analysis of the atomic structure was performed or understood. The flow Theflow or understood. performed was atomicstructure of the analysis the before involved, where 

  ). The formulation of this series is defined as a function of location ( location offunction asa defined is series this ). of The formulation I = ) (1 ) /) 41 ππ ∇ ∫ VS Ω ×⋅ r  ∇⋅ and the second segment composed of rotational (divergence-free) or solenoidal (divergence-free)or solenoidal of rotational composed segment the second and ); defining the rotation of the vector in infinitesimal steps, hence describing the describing hence steps, infinitesimal in the vector theof rotation ); defining   ′ cu . The pressure gradients associated with the cyclonic action generates winds winds generates action cyclonic the with associated gradients . The pressure Vr rl n  () = =  ′ 0 A lim is considered “irrotational.” considered is → rr 0 () − 1  n ′′  Ad dV which is the axis of vector rotation. It is also referred as cross- as referred It also rotation. of is vector axis the is which  ∫ C   − ⋅ () r /  4 , observed as the closed integral over aloop ( integral closed the as , observed ∫ S Ω Vr ()  ′ ⋅ dS ′ rr −  ′ , the second term will have have will term second , the r  within a volume in avolume in ) within in vector cal- vector in   C ) within ) within ), with ), with Cyclone - C 259

260 C Downloaded By: 10.3.98.104 At: 18:00 30 Sep 2021; For: 9780203731543, chapter3, 10.1201/9780203731543-4 Cyclotron accelerator and gain velocity with increasing radius (spiral path) as a result of an applied magnetic applied of an aresult as path) (spiral radius increasing with velocity gain and accelerator [atomic, Particle nuclear] accelerator Cyclotron Colorado, Boulder, CO.) Lab, and(c)DavidLindat26 MeVcyclotron beamguideduringthe1962construction.(Courtesy ofUniversity Figure C.93 velocity (angular frequency resonance the matches ofthat 19391.52 m. in applied is built field adiameter has magnetic Ablock-wave periodic 345 MeV energy of acceleration reach can cyclotron of 3.8 T.RIKEN strength The field magnetic amaximum with operate can and high, of diameter a 19 m,with 8 m in Japan, RIKEN the is cyclotron largest The meters. to several ameter than from less in size the in range generated be 1930s. Cyclotrons could field magnetic enough alarge until use (1901–1958) Lawrence for practical not feasible 1920s, was the in and Orlando invented by Ernest was elements new andcreate of atomic nuclei thestructure investigate to used is cyclotron The field ( field B ) and the magnitude the ) and (b) (a) conditions to induce acceleration, based on the orbital period of the charge. The cyclotron cyclotron The charge. of the period orbital on the based acceleration, to induce conditions Cyclotron: (a)mechanismofactionforparticleacceleration,(b)1.52 mloopatArgonne National ω of the charge ( charge of the cyclot ensures particleacceleration per atomic mass unit. The cyclotron designed by Ernest Lawrence was was Lawrence Ernest by designed cyclotron The unit. atomic mass per ro Square waveelectricfield n ; frequency ; frequency at eachgapcrossing . Charged particles are released from the center of a circular of center acircular the from released are particles . Charged q ) on the mass ) on the ν yltncyclot cycloton = ωπ (c) ( m ro n ) as ) as yield curvedpath applies torqueto 2 Magnetic field ω ) is a function of the applied magnetic applied of the afunction ) is cyclot ro n = qB m (see Figure C.93). (see Figure . The cyclotron cyclotron . The field .

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