Nematics: Mathematical and Physical Aspects

ISBN-13: 9789401055161 / Angielski / Miękka / 2012 / 428 str.

Jean-Michel Coron; Jean-Michel Ghidaglia; Frederic Helein

Opis

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.

Spis treści

An Energy-Decreasing Algorithm for Harmonic Maps.- A Cohomological Criterion for Density of Smooth Maps in Sobolev Spaces Between Two Manifolds.- On The Mathematical Modeling Of Textures In Polymeric Liquid Crystals.- A Result on the Global Existence for Heat Flows of Harmonic Maps from D2 into S2.- Blow-Up Analysis for Heat Flow of Harmonic Maps.- Taylor-Couette Instability in Nematic Liquid Crystals.- On a Class of Solutions in the Theory of Nematic Phases.- Rheology of Thermotropic Nematic Liquid Crystalline Polymers.- Cartesian Currents and Liquid Crystals Dipoles, Singular Lines and Singular Points.- Heat Flow for Harmonic Maps.- The Motion of Defects in Convective Structures of the Elliptical Shear Instability of a Nematic.- Fiber Evolution in the Heat Flow of Harmonic Maps.- Axially Symmetric Harmonic Maps.- Defects of Stationary Convective Structures in a Nematic.- An Approach to the Construction of Morse Flows for Variational Functionals.- An Example of Frustration in a Ferromagnetic Material.- Flow-Induced Instabilities in Nematic Liquid Crystals.- Defects in Macroscopic Structures: Ginzburg-Landau Approach.- Nematic Liquid Crystals with Variable Degree of Orientation.- Field-Induced Instabilities in Nematic Liquid Crystals.- Variational Problems with Obstacles and Harmonic Maps.- Weakly Nonlinear Analysis of Pattern Formation in Nematic Liquid Crystals.- Dynamics of Defects.- Defects of Nonlinear Waves in the Convection Of A Nematic Liquid Crystal.- Projection Methods for Solving Nonlinear Systems of Equations.- Regularity Results for Harmonic Maps of Minkowski Space.- Defects in Nematic Liquid Crystals with Variable Degree of Orientation.- External Forcing of Liquid Crystal Instabilities.- On Travelling Waves in Electrohydrodynamic Convection in Nematics.