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Stewart I.W. — The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction
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Название: The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical IntroductionАвтор: Stewart I.W. Аннотация: Stewart (Math, U. of Strathclyde, Glasgow) prepared this text for graduate students of applied mathematics, theoretical physics, and engineering. Introductory material sets the scene for later chapters which cover, in turn, the features and applications of the static theory and dynamic theory of nematics, including extensive derivations as a way to communicate to readers how to apply the results from continuum theory to practical problems. The final chapter, an introduction to the theory of smectic C liquid crystals, does not give as many detailed computations; as the author explains, "smectic liquid crystals have some uniquely different mathematical problems..." and detailed coverage is beyond the scope of this volume.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1st editionГод издания: 2004Количество страниц: 360Добавлена в каталог: 20.09.2009Операции: Положить на полку |
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Acceleration of free fall 329 Alternator 10 anchoring 46 291 Anchoring, conical 46 48 55 Anchoring, no anchoring 46 54 Anchoring, simplifications 54-56 Anchoring, strong 46 47 54 Anchoring, weak 46 49-50 55 Angstrom 4 Angular velocity 134 Angular velocity tensor 135 Angular velocity, local 134 Angular velocity, regional 134 Angular velocity, relative 133 134 Anisotropic 2 Anisotropic axis 3 Anisotropic fluid 152 197 201 210 Apparent viscosity 156 185 217 Asymmetric stress tensor 33 204 Atkin scaling laws 217 Axial disclinations 110 Axial vector 11 134 Backflow 162 218 223 233 236 Backflow, in bend geometry 234-236 Backflow, in MBBA 233 Backflow, in splay geometry 224-229 Backflow, in twisted nematic device 234 Backflow, reason for name 233 Backflow, reduction in switch-on time 228 Backflow, schematic representation of 229 Balance laws 138 Balance of angular momentum 140 Balance of couple condition 50 Balance of linear momentum 140 Balance of mass 140 Bend 15 16 21 Bend geometry 78 Bend viscosity 158 235 Bend, measurement of 78 Body forces 148-149 Body forces, connection with energy 39 42 Body moment 41 138 147-149 264 Boltzmann constant 244 329 Bookshelf SmC 275 276 305 308 310 313 315 boundary conditions 46 150 Boundary conditions, and weak anchoring 50 150 Boundary conditions, simplification 53-56 Boundary disclination lines 120 Boundary layer phenomenon 182 184 Capillary 209 213 CBOOA 209 cgs units 31-33 329 Change of coordinates 53 Characteristic length in nematics 71 Characteristic length in SmC* 318 Characteristic times 218 Chiral 4 Chiral nematic 2 5 Cholesteric energy 23 26 Cholesteric liquid crystals 4 23 Cholesteric liquid crystals, helical axis 4 Cholesterol 5 Cholesteryl benzoate 2 Cholesteryl myristate 7 Classical Freedericksz transitions 72- 82 Classification of phases 2 Clearing point 2 3 Co-rotational time flux 135 151 293 Coherence length see magnetic coherence length Comments on fields 31 Cone of easy directions 48 Conical anchoring 48-49 55 121 125 Conservation law for angular momentum 138 Conservation law for linear momentum 138 Conservation law for mass 138 Conservation laws 138 Conservation of mass 36 Constant solution 43 Constitutive equations 133 142 Constitutive relations 133 Continuum theory, development of 7- 9 Contraction rule for alternators 10 Conversion factors see Table D.2 Coordinate transformations 53 Core 113 Core radius 113 Couette flow 197-209 Couette flow, anisotropic fluid 197-202 Couette flow, nematic liquid crystal 202-209 Couple stress tensor 41 139 142 151 264 292 Couple stress vector 41 138 264 Critical electric field in a nematic 89 Critical electric field in SmC 280 Critical field strength 8 72 89 Critical field strength, in SmC 279 Critical field strength, in twisted nematic device 105 Critical field strength, obtained by linearisation 81-82 Critical voltage 89 Critical voltage, in twisted nematic device 107 Curl 11 Curvature strains 15 Curvilinear coordinates 53 Cylindrical coordinates, physical components 325-327 Cylindrical solution 43 45 Decay time 222 defects 8-9 109-131 Density, measurements of in nematics see Table D.3 Derivative, notational convention 35 Development of continuum theory 7-9 Diamagnetic susceptibilities 29 Dielectric anisotropy 27 329 Dielectric biaxiality, neglection of 311 Dielectric constants 27 Dielectric constants, measurements of in nematics see Table D.3 Dielectric permittivities 27 Dielectric tensor 27 Direct stress 139 Director 4 Director inertial term 147 Director reorientation in SmC* 313- 319 Discharge 217 Disclinations 4 109 Disclinations, axial (wedge) 110 Disclinations, boundary 120 125 Disclinations, Frank index 111 114 Disclinations, line 110 Disclinations, perpendicular (twist) 118 120 Disclinations, point at a surface or interface 127 Disclinations, strength (order) 111 114 Discontinuity at initial time 232 Discovery of liquid crystals 1-2 Dissipation function 140-142 145 147 153 193 218 224 Dissipation function, general form for nematics 145 147 Dissipation function, in reformulated equations 153-154 Dissipation function, in SmC 292 293 294 304 Distorted surface 121 Divergence 11 Divergence theorem 12 DOBAMBC 284 307 DOBPC 300 Domain wall 317 Dupin cyclides 268-272 Dupin cyclides, Cartesian equation for 269 Dupin cyclides, circular tori special case 269 Dupin cyclides, cross-sections of 271 Dupin cyclides, illustrations 269 271 Dupin cyclides, parametrisation of 269-270 Dyadic product 11 Dynamic equations for nematics, simplifications 151-152 Dynamic theory of nematics 133-159 Dynamic theory of nematics, experimental confirmation of 217 Dynamic theory of nematics, summary of equations 150-152 Dynamic theory of SmC 291-306 Dynamic theory of SmC 296 Dynamic theory of SmC* 312-313 Dynamic theory of SmC, summary of equations 295-296 Dynamics 134 Dynamics of the Freedericksz transition 158 218-236 Dynes in terms of newtons 329 Easy axis 48 Easy direction 48 Effective viscosities 245 Effective viscosity 228 235 236 Efflux 217 Eigenfrequencies 242 Eigenmodes 236 Elastic constants, cholesteric 26 Elastic constants, nematic 22 Elastic constants, SmC 251 Elastic energy 13 14 Elastic energy, cholesteric 23 26 Elastic energy, nematic 20 21 Elastic energy, SmA 256 Elastic energy, SmC 250-258 320 Elastic energy, SmC 258 Elastic energy, SmC* 309-310 Elastic energy, SmC, surface terms 251 Electric displacement 27 Electric energy density 27 28 33 Electric energy density, in SmC* 310-312 Electric field effects 89-94 Electric fields 26-28 258-259 Electric susceptibility tensor 26 Emu (electromagnetic units) 31 Enantiomorphy 4 23 Energy 14 33 329 Energy density 14 33 329 Equation of continuity 139 Equilibrium equations, nematic 38 33-42 Equilibrium equations, nematic, simplification 39 50-53 Equilibrium equations, SmC 262 259-267 Equilibrium equations, SmC, Remarks 263-265 Equilibrium equations, SmC, simplification 263 Equilibrium solutions 57 58 Equilibrium solutions, tilt and twist 60-68 Erg in terms of joules 329 Ericksen - Leslie dynamic equations, derivation of 134-150 Ericksen - Leslie dynamic equations, experimental confirmation of 217 Ericksen - Leslie dynamic equations, simplifications 151-152 Ericksen - Leslie dynamic equations, summary of 150-152 Ericksen number 188-189 Ericksen's inequalities 22 Escape into the third dimension 118 Escape solution 115-118 Esu (electrostatic units) 31 Euler - Lagrange equation 37 59 110 Euler - Lagrange equation, a general form for higher derives tives 284 Euler equation 58 61 Experimental confirmation of dynamic theory 217 External body moment 138 147 292 295 Fast modes (in light scattering) 242 Fergason, J.L. 108 Ferroelectric smectic C liquid crystals see SmC* liquid crystals First variation 91 flat panel displays 101 Flexoelectric effect, references for 320 Flow alignment angle in nematics 164 166 200 Flow alignment angle in SmC 305 Flow-aligning 166 Flow-aligning, stability in oscillatory shear 196 Fluid inertial term 190 Flux lines 112 114 120 Focal conic defects 267-275 Frame-indifference 14 136-138 Frank - Oseen elastic energy 13 14 20 Frank elastic constants 21-23 79 Frank index 111 114 Frank, F.C. 7 Free energy 13 14 Free energy density, nematic or cholesteric 14 Freedericksz threshold 8 72 Freedericksz threshold, obtained by linearisation 81-82 Freedericksz threshold, SmC 279 Freedericksz threshold, weak 98 Freedericksz transition 8 72 90 276 279 Freedericksz transition, classical transitions 72-82 Freedericksz transition, dynamics in bend geometry 234- 236 Freedericksz transition, dynamics in splay geometry 223- 234 Freedericksz transition, dynamics in twist geometry 218- 223 Freedericksz transition, dynamics of 218-236 Freedericksz transition, electric field effects 89 Freedericksz transition, in bend geometry 78 Freedericksz transition, in bookshelf SmC 275-281 Freedericksz transition, in splay geometry 72-77 Freedericksz transition, in twist geometry 77-78 Freedericksz transition, one-constant approximation 79-80 Freedericksz transition, pretilt at boundary 82 Freedericksz transition, tilted fields 85 Freedericksz transition, twisted nematic device 106 Freedericksz transition, weak 95-100 Friedel, G. 2 Fundamental constants 329 Gattermann, L. 4 Gauss (G) 32 Gaussian units 31 329 General equilibrium solutions for Frank- Oseen energy 42 Gradient of a Scalar Field 11 Gradient of a vector field 12 Gravitational field 148 Gravitational potential 148 197 210 Gravity 120 122 123 Gray, G.W. 4 Hagen - Poiseuille law 217 HBAB 209 Helfrich - Hurault transition 287 311 319 Helfrich - Hurault transition, boundary conditions 286 Helfrich - Hurault transition, in SmA 289 Helfrich - Hurault transition, in SmC 286-291 Helfrich notation 155 Helfrich, W. 101 108 Hemitropic function 143 Homeotropic alignment 47 Homogeneous alignment 47 In-plane mode 237 In-plane surface twist angle in SmC 275 276 279 Incident light beam 236 Incompressible 14 33 36 139 Index notation 9 Inertial constant 148 Inertial term, director 147 149 232 Inertial term, fluid 190 232 Inhomogeneous Bessel equation 129 Instabilities see stability and instability Instability 196 Integrated intensities 245 Inter layer distance in smectics 6 248 249 284 Isothermal 2 138 248 Isotropic 2 Isotropic fluids 140 212 213 Isotropic fluids, symmetric stress tensor in 140 Isotropic viscoelastic fluid 187 217 Joule (J) 33 329 Joule (J), in terms of erg 329 Kelker, H. 4 Kickback 162 233 Kickback effect 218 223 230 233 Kickback effect, in MBBA 233 Kickback effect, in splay geometry 230-234 Kickback effect, in twisted nematic device 234 Kinematics 134
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