Ebook: Nematics: Mathematical and Physical Aspects

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.

---

---

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