Nonlinear Dynamics of Field Induced Pattern Formation in Nematic Liquid Crystals PDF Download

Author: Chun Zheng
Publisher:
ISBN:
Category : Liquid crystals
Languages : en
Pages : 111

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Author: Agnes Buka
Publisher: Springer Science & Business Media
ISBN: 146123994X
Category : Science
Languages : en
Pages : 344

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Book Description
In the last 20 years the study of nonlinear nonequilibrium phenomena in spa tially extended systems, with particular emphasis on pattern-forming phenomena, has been one of the very active areas in physics, exhibiting interesting ramifi cations into other sciences. During this time the study of the "classic" systems, like Rayleigh-Benard convection and Taylor vortex flow in simple fluids, has also been supplemented by the study of more complex systems. Here liquid crystals have played, and are still playing, a major role. One might say that liquid crystals provide just the right amount and right kind of complexity. They are full of non linearities and give rise to new symmetry classes, which are sometimes actually simpler to deal with qualitatively, but they still allow a quantitative description of experiments in many cases. In fact one of the attractions of the field is the close contact between experimentalists and theorists. Hydrodynamic instabilities in liquid crystals had already experienced a period of intense study in the late 1960s and early 1970s, but at that time neither the ex perimental and theoretical tools nor the concepts had been developed sufficiently far to address the questions that have since been found to be of particular interest. The renewed interest is also evidenced by the fact that a new series of workshops has evolved. The first one took place in 1989 in Bayreuth and united participants from almost all groups working in pattern formation in liquid crystals.

Author: Patricia E. Cladis
Publisher: Westview Press
ISBN:
Category : Computers
Languages : en
Pages : 720

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The purpose of the NATO Advanced Research Workshop, upon which this book is based, was to bring together experimentalists and theorists from many different fields, ranging from applied mathematics to materials science, but unified by their intrigue with nonlinear phenomena, in search of a deeper understanding of patterns in complex systems. To meet this goal, the participants made the effort to build bridges across canonical disciplinary boundaries by sharing what they thought was significant and relevant in search of the “truly significant simplicity of the basic laws of nature embedded in the amazing complexity of natural phenomena.” Spatio-Temporal Patterns in Nonequilibrium Complex Systems is one of the most exciting and fastest-growing branches of physics that impacts fields as diverse as new technologies and processes, economics and biology. Virtually every structure in our world, including ourselves, can be considered the result of a long sequence of successive symmetry-breaking instabilities due to nonlinear processes under nonequilibrium conditions of a complex system. While a scientific description of the spontaneous appearance of patterns in nature was first made by Johannes Kepler (1611), it has only been during the past twenty years that pattern formation, epitomized by the beautiful snowflakes that Kepler studied, has emerged as a science. Concepts and methods resulting from this dynamic new field will surely influence future developments in many disciplines.Complex systems, as studied in this book, are a good first step toward a description of the variety of phenomena included under the rubric “physics of complex systems.” Even the simplest of those presented here, liquid crystals, is still complex, but provides hints of essential ingredients needed to forge a fundamental understanding of nonequilibrium, nonlinear processes in the large. Fluid dynamics and turbulence, interface motion during solidification, autocatalytic chemical reactions, and pattern formation in biological systems play similar roles in other systems far from equilibrium.

Author: Pierre Coullet
Publisher: Springer
ISBN: 9781468474817
Category : Mathematics
Languages : en
Pages : 368

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Book Description
The basic aim of the NATO Advanced Research Workshop on "New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena: The Geometry of Nonequilibrium" was to bring together researchers from various areas of physics to review and explore new ideas regarding the organisation of systems driven far from equilibrium. Such systems are characterized by a close relationship between broken spatial and tempo ral symmetries. The main topics of interest included pattern formation in chemical systems, materials and convection, traveling waves in binary fluids and liquid crystals, defects and their role in the disorganisa tion of structures, spatio-temporal intermittency, instabilities and large-scale vortices in open flows, the mathematics of non-equilibrium systems, turbulence, and last but not least growth phenomena. Written contributions from participants have been grouped into chapters addressing these different areas. For additional clarity, the first chapter on pattern formation has been subdivided into sections. One of the main concerns was to focus on the unifying features between these diverse topics. The various scientific communities repre sented were encouraged to discuss and compare their approach so as to mutually benefit their respective fields. We hope that, to a large degree, these goals have been met and we thank all the participants for their efforts. The workshop was held in Cargese (Corsica, France) at the Institut d'Etudes Scientifiques from August 2nd to August 12th, 1988. We greatly thank Yves Pomeau and Daniel Walgraef who, as members of the organising committee, gave us valuable advice and encouragements.

Author: S Kai
Publisher: World Scientific
ISBN: 9814555339
Category :
Languages : en
Pages : 596

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Book Description
In this volume, the problems of pattern formation in physics, chemistry and other related fields in complex and nonlinear dissipative systems are studied. Main subjects discussed are formation mechanisms, properties, statistics, characterization and dynamics of periodic and nonperiodic patterns in the electrohydrodynamics in liquid crystals, Rayleigh-Benard convection, crystallization, viscous fingering and Belouzov-Zhabotinsky chemical reaction. Recent developments in topological and defect-mediated chaos, chaos in systems with large degrees of freedom and turbulence-turbulence transitions are also discussed.

Author: Daniel Walgraef
Publisher: Springer Science & Business Media
ISBN: 1461218500
Category : Science
Languages : en
Pages : 310

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Book Description
Spatio-temporal patterns appear almost everywhere in nature, and their description and understanding still raise important and basic questions. However, if one looks back 20 or 30 years, definite progress has been made in the modeling of insta bilities, analysis of the dynamics in their vicinity, pattern formation and stability, quantitative experimental and numerical analysis of patterns, and so on. Universal behaviors of complex systems close to instabilities have been determined, leading to the wide interdisciplinarity of a field that is now referred to as nonlinear science or science of complexity, and in which initial concepts of dissipative structures or synergetics are deeply rooted. In pioneering domains related to hydrodynamics or chemical instabilities, the interactions between experimentalists and theoreticians, sometimes on a daily basis, have been a key to progress. Everyone in the field praises the role played by the interactions and permanent feedbacks between ex perimental, numerical, and analytical studies in the achievements obtained during these years. Many aspects of convective patterns in normal fluids, binary mixtures or liquid crystals are now understood and described in this framework. The generic pres ence of defects in extended systems is now well established and has induced new developments in the physics of laser with large Fresnel numbers. Last but not least, almost 40 years after his celebrated paper, Turing structures have finally been ob tained in real-life chemical reactors, triggering anew intense activity in the field of reaction-diffusion systems.

Author: Hayel M. Shehadeh
Publisher:
ISBN:
Category : Electrohydrodynamics
Languages : en
Pages : 356

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Author:
Publisher: Springer Science & Business Media
ISBN: 9781402043536
Category :
Languages : en
Pages : 360

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Author: Jean-Michel Coron
Publisher: Springer Science & Business Media
ISBN: 9401134286
Category : Science
Languages : en
Pages : 426

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Book Description
This volume (>Ie) NEMATICS Mathematical and Physical aspects constitutes the proceedings of a workshop which was held at l'Universite de Paris Sud (Orsay) in May 1990. This meeting was an Advanced Research Workshop sponsored by NATO. We gratefully acknowledge the help and support of the NATO Science Committee. Additional support has been provided by the Ministere des affaires etrangeres (Paris) and by the Direction des Recherches et Etudes Techniques (Paris). Also logistic support has been provided by the Association des Numericiens d'Orsay. (*) These proceedings are published in the framework of the "Contrat DRET W 90/316/ AOOO". v Contents (*) FOREWORD v INTRODUCTION 1. M. CORON, 1. M. GHIDAGLIA, F. HELEIN xi AN ENERGY-DECREASING ALGORITHM FOR HARMONIC MAPS F. ALOUGES 1 A COHOMOLOGICAL CRITERION FOR DENSITY OF SMOOTH MAPS IN SOBOLEV SPACES BETWEEN TWO MANIFOLDS F. BETHUEL, 1. M. CORON, F. DEMENGEL, F. HELEIN 15 ON THE MATHEMATICAL MODELING OF TEXTURES IN POLYMERIC LIQUID CRYSTALS M. C. CAmERER 25 A RESULT ON THE GLOBAL EXISTENCE FOR HEAT FLOWS OF HARMONIC MAPS FROM D2 INTO S2 K. C. CHANG, W. Y. DING 37 BLOW-UP ANALYSIS FOR HEAT FLOW OF HARMONIC MAPS Y. CHEN 49 T AYLOR-COUETTE INSTABILITY IN NEMATIC LIQUID CRYSTALS P. E. ClADIS 65 ON A CLASS OF SOLUTIONS IN THE THEORY OF NEMATIC PHASES B. D. COLEMAN, 1. T. JENKINS 93 RHEOLOGY OF THERMOTROPIC NEMATIC LIQUID CRYSTALLINE POLYMERS M. M. DENN, 1. A.

Author: Alexander A. Golovin
Publisher: Springer Science & Business Media
ISBN: 9781402043543
Category : Mathematics
Languages : en
Pages : 356

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Book Description
Nano-science and nano-technology are rapidly developing scientific and technological areas that deal with physical, chemical and biological processes that occur on nano-meter scale – one millionth of a millimeter. Self-organization and pattern formation play crucial role on nano-scales and promise new, effective routes to control various nano-scales processes. This book contains lecture notes written by the lecturers of the NATO Advanced Study Institute "Self-Assembly, Pattern Formation and Growth Phenomena in Nano-Systems" that took place in St Etienne de Tinee, France, in the fall 2004. They give examples of self-organization phenomena on micro- and nano-scale as well as examples of the interplay between phenomena on nano- and macro-scales leading to complex behavior in various physical, chemical and biological systems. They discuss such fascinating nano-scale self-organization phenomena as self-assembly of quantum dots in thin solid films, pattern formation in liquid crystals caused by light, self-organization of micro-tubules and molecular motors, as well as basic physical and chemical phenomena that lead to self-assembly of the most important molecule on the basis of which most of living organisms are built – DNA. A review of general features of all pattern forming systems is also given. The authors of these lecture notes are the leading experts in the field of self-organization, pattern formation and nonlinear dynamics in non-equilibrium, complex systems.