Nematics : Mathematical and Physical Aspects Proceeding of the NATO Advanced Research Workshop on Defects, Singularities and Patterns in Nematic Liquid Crystals: Mathematical and Physical Aspects Orsay, France May 28-June 1, 1990

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. Front Matter....Pages i-xiii An Energy-Decreasing Algorithm for Harmonic Map....Pages 1-13 A Cohomological Criterion for Density of Smooth Maps in Sobolev Spaces Between Two Manifolds....Pages 15-23 On the Mathematical Modeling of Textures in Polymeric Liquid Crystals....Pages 25-36 A Result on the Global Existence for Heat Flows of Harmonic Maps from D 2 into S 2 ....Pages 37-47 Blow-Up Analysis for Heat Flow of Harmonic Maps....Pages 49-64 Taylor-Couette Instability in Nematic Liquid Crystals....Pages 65-91 On a Class of Solutions in the Theory of Nematic Phases....Pages 93-105 Rheology of Thermotropic Nematic Liquid Crystalline Polymers....Pages 107-112 Cartesian Currents and Liquid Crystals Dipoles, Singular Lines and Singular Points....Pages 113-127 Heat Flow for Harmonic Maps....Pages 129-140 The Motion of Defects in Convective Structures of the Elliptical Shear Instability of a Nematic....Pages 141-171 Fiber Evolution in the Heat Flow of Harmonic Maps....Pages 173-178 Axially Symmetric Harmonic Maps....Pages 179-187 Defects of Stationary Convective Structures in a Nematic....Pages 189-194 An approach to the construction of Morse flows for variational functionals....Pages 195-199 An Example of Frustration in a Ferromagnetic Material....Pages 201-221 Flow-Induced Instabilities in Nematic Liquid Crystals....Pages 223-232 Defects in Macroscopic Structures: Ginzburg-Landau Approach....Pages 233-246 Nematic Liquid Crystals with Variable Degree of Orientation....Pages 247-259 Field-Induced Instabilities in Nematic Liquid Crystals....Pages 261-278 Variational Problems with Obstacles and Harmonic Maps....Pages 279-290 Weakly Nonlinear Analysis of Pattern Formation in Nematic Liquid Crystals....Pages 291-301 Dynamics of Defects....Pages 303-326 Defects of Nonlinear Waves in the Convection of a Nematic Liquid Crystal....Pages 327-340 Projection Methods for Solving Nonlinear Systems of Equations....Pages 341-355 Regularity results for harmonic maps of Minkowski space....Pages 357-369 Defects in Nematic Liquid Crystals with Variable Degree of Orientation....Pages 371-390 External Forcing of Liquid Crystal Instabilities....Pages 391-400 On Travelling Waves in Electrohydrodynamic Convection in Nematics....Pages 401-426 Back Matter....Pages 427-428