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General Aspects of Pattern Formation 1 Alexander A Self-Assembly, Pattern Formation and Growth Phenomena in Nano-Systems NATO Science Series A Series presenting the results of scientific meetings supported under the NATO Science Programme. The Series is published by IOS Press, Amsterdam, and Springer (formerly Kluwer Academic Publishers) in conjunction with the NATO Public Diplomacy Division Sub-Series I. Life and Behavioural Sciences IOS Press II. Mathematics, Physics and Chemistry Springer (formerly Kluwer Academic Publishers) III. Computer and Systems Science IOS Press IV. Earth and Environmental Sciences Springer (formerly Kluwer Academic Publishers) The NATO Science Series continues the series of books published formerly as the NATO ASI Series. The NATO Science Programme offers support for collaboration in civil science between scientists of countries of the Euro-Atlantic Partnership Council. The types of scientific meeting generally supported are “Advanced Study Institutes” and “Advanced Research Workshops”, and the NATO Science Series collects together the results of these meetings. The meetings are co-organized by scientists from NATO countries and scientists from NATO’s Partner countries – countries of the CIS and Central and Eastern Europe. Advanced Study Institutes are high-level tutorial courses offering in-depth study of latest advances in a field. Advanced Research Workshops are expert meetings aimed at critical assessment of a field, and identification of directions for future action. As a consequence of the restructuring of the NATO Science Programme in 1999, the NATO Science Series was re-organized to the four sub-series noted above. Please consult the following web sites for information on previous volumes published in the Series. http://www.nato.int/science http://www.springeronline.com http://www.iospress.nl Series II: Mathematics, Physics and Chemistry – Vol. 216 Self-Assembly, Pattern Formation and Growth Phenomena in Nano-Systems edited by Alexander A. Golovin Northwestern University, Evanston, IL, U.S.A. and Alexander A. Nepomnyashchy Israel Institute of Technology, Haifa, Israel Published in cooperation with NATO Public Diplomacy Division Proceedings of the NATO Advanced Study Institute on Self- Assembly, Pattern Formation and Growth Phenomena in Nano- System s St. Etienne de Tinee, France August 28– September 11, 2004 A C.I.P.Catalogue record for this book is available from the Library of Congress. ISBN-10 1-4020-4353-8 (PB) ISBN-13 978-1-4020-4353-6 (PB) ISBN-10 1-4020-4354-6 (HB) ISBN-13 978-1-4020-4354-3 (HB) ISBN-10 1-4020-4355-4 (e-book) ISBN-13 978-1-4020-4355-0 (e-book) Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com Printed on acid-free paper All Rights Reserved © 2006 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands. This book is dedicated to the memory of Lorenz Kramer v Contents Dedication v Contributing Authors xi Foreword xiii Preface xv Acknowledgments xvii General Aspects of Pattern Formation 1 Alexander A. Nepomnyashchya and Alexander A. Golovinb 1 Introduction 1 2 Basic models for domain coarsening and pattern formation 3 3 Pattern selection 11 4 Modulated patterns 22 5 Beyond the Swift-Hohenberg model 41 6 Wavy patterns 43 7 Conclusions 50 8 Acknowledgement 52 References 52 Convective patterns in liquid crystals driven by electric field 55 Agnes Buka, Nándor Éber, Werner Pesch, Lorenz Kramer Introduction56 1 Physical properties of nematics 57 2 Electroconvection 61 Acknowledgements 79 References 80 Dynamical phenomena in nematic liquid crystals induced by light 83 Dmitry O. Krimer, Gabor Demeter, and Lorenz Kramer Introduction83 1 Simple setups - complicated phenomena 84 2 Theoretical description 85 3 Obliquely incident, linearly polarized light 91 4 Perpendicularly incident, circularly polarized light 98 5 Perpendicularly incident, elliptically polarized light 107 6 Finite beam-size effects and transversal pattern formation 115 Acknowledgments 120 vii viii PATTERN FORMATION IN NANO-SYSTEMS References 120 Self-Assembly of Quantum Dots from Thin Solid Films 123 Alexander A. Golovin, Peter W. Voorhees, and Stephen H. Davis 1 Introduction 123 2 Mechanisms of morphological evolution of epitaxial films 124 3 Elastic effects and wetting interactions 127 4 Surface-energy anisotropy and wetting interactions 139 5 Conclusions 156 Acknowledgment 157 References 156 Macroscopic and mesophysics together: the moving contact line problem revisited 159 Yves Pomeau References 166 Nanoscale Effects in Mesoscopic Films 167 L. M. Pismen Introduction167 1 Hydrodynamic Equations 169 2 Thermodynamic Equations 173 3 Fluid-Substrate Interactions 178 4 Dynamic Contact Line 184 5 Mobility Relations 186 Acknowledgements 192 References 192 Dynamics of thermal polymerization waves 195 V.A. Volpert 1 Introduction 195 2 Mathematical model 198 3 Gasless combustion 202 4 Analysis of base FP model 230 5 Other thermal FP studies 238 6 Conclusion 239 References 239 Spatiotemporal Pattern Formation in Solid Fuel Combustion 247 Alvin Bayliss Bernard J. Matkowsky Vladimir A. Volpert 1 Introduction. 248 2 Mathematical Model 254 3 Analytical Results 257 4 Computational Results 267 References 280 Contents ix Self-organization of microtubules and motors 283 Igor S. Aranson, Lev S. Tsimring Introduction283 1 Maxwell Model and Orientational Instability 285 2 Spatial Localization 288 3 Aster and Vortex Solutions 291 4 Conclusion 293 Acknowledgments 294 References 294 Physics of DNA 295 Maxim D. Frank-Kamenetskii 1 Introduction 295 2 Major structures of DNA 296 3 DNA functioning 300 4 Global DNA conformation 303 5 The DNA stability 317 6 Conclusion 322 References 322 Topic Index 327 Contributing Authors Dr. Igor S. Aranson, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA Prof. Alvin Bayliss, Department of Engineering Sciences and Applied Mathe- matics, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA Prof. Agnes Buka, Research Institute for Solid State Physics and Optics of the Hungarian Academy of Sciences, Konkoly-Thege Miklos u. 29-33, H-1121 Budapest, Hungary Prof. Stephen H. Davis, Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA Dr. Gabor Demeter, Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, Konkoly-Thege Miklos ut 29-33, H-1121 Budapest, Hungary Prof. Nandor Eber, Research Institute for Solid State Physics and Optics of the Hungarian Academy of Sciences, Konkoly-Thege Miklos u. 29-33, H-1121 Budapest, Hungary Prof. Maxim D. Frank-Kamenetskii, Department of Biomedical Engineer- ing, Boston University, 36 Cummington St., Boston, MA 02215, USA Prof. Alexander A. Golovin, Department of Engineering Sciences and Ap- plied Mathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA xi xii PATTERN FORMATION IN NANO-SYSTEMS Prof. Lorenz Kramer (deceased). Dr. Dmitry Krimer, Physikalisches Institut der Universitaet Bayreuth, D- 95440 Bayreuth, Germany Prof. Bernard J. Matkowsky, Department of Engineering Sciences and Ap- plied Mathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA Prof. Alexander A. Nepomnyashchy, Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel Prof. Werner Pesch, Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany Prof. Leonid M. Pismen, Department of Chemical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel Prof. Yves Pomeau, Laboratoire de Physique Statistique de l’Ecole normale sup«erieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France Dr. Lev S. Tsimring, Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093-0402, USA Prof. Vladimir A. Volpert, Department of Engineering Sciences and Ap- plied Mathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA Prof. Peter W. Voorhees, Department of Materials Science and Engineering, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA Foreword Lorenz Kramer, who was the main driving force behind the PHYSBIO pro- gram, died suddenly on 5 April 2005. This was a shock to his numerous friends who were not aware that this strong, vigorous and buoyant man struggled for many years with a deeply rooted decease which all of a sudden went out of control. Lorenz has always been an innovator working with enthusiasm and persua- sion on the leading edge of scientific exploration. The three main subjects of his work: superconductivity from 1968 to 1981; pattern formation out of equi- librium starting from 1982 ; biophysics from 1975 to 1980 and again from the start of this century – were intertwined and supplied each other with ideas and techniques. One example will suffice here: a direct interpretation of superflow solutions as saddle points in transitions between different patterns – thereby connecting two opposites: conservative and gradient systems. He was one of the principal players in the field of nonlinear science during its acme in 1990s, and one who directed this field, when it came of age, to new applications, in particular,
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