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Stewart I.W. — The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction
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 Introduction

Автор: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2004

Количество страниц: 360

Добавлена в каталог: 20.09.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Acceleration of free fall      329
Alternator $\epsilon_{ijk}$      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${}_{M}$      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${}_{M}$      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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