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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
Kronecker delta $\delta_{ij}$      10
Lagrange multipliers      37 250
Lagrange multipliers, comments on SmC      266-267
Layer compression constant      see smectic layer compression constant
LCD      see liquid crystal displays
Lehmann, O.      2
Leslie angle      see flow alignment angle
Leslie coefficients      146
Leslie viscosities      146 151
Leslie viscosities, in terms of Miesowicz viscosities      158
Leslie viscosities, restrictions      146
Light scattering      236-246
Light scattering, displacements of director in      238
Light scattering, domination by slow modes      243 246
Light scattering, effective viscosities      245
Light scattering, experimental set-up      237
Light scattering, fast modes      242
Light scattering, governing dynamic equations      241- 242
Light scattering, in an electric field      246
Light scattering, in smectics, references to      300 306
Light scattering, in-plane mode      237 241
Light scattering, integrated intensities      245 246
Light scattering, line defects in SmA and SmC      268 272
Light scattering, line widths      245 246
Light scattering, Lorentzian lines      245
Light scattering, orientational fluctuations      236
Light scattering, out-of-plane mode      237 242
Light scattering, periodic disturbances      238
Light scattering, power spectrum      244
Light scattering, response functions      244
Light scattering, slow modes      242
Line singularities      see disclinations line
Line width (in light scattering)      245
Liposomes      268
Liquid crystal displays      8 72 101 108 109
Liquid crystals      1
Liquid crystals, classification of      2
Local angular velocity      134
Lorentzian lines      245
Lyotropic liquid crystals      2 6
Magnetic anisotropy      29 31 329
Magnetic anisotropy, conversion rule      31
Magnetic anisotropy, measurements of in nematics      see Table D.3
Magnetic anisotropy, negative      30
Magnetic coherence length      68 69 71 122
Magnetic energy density      30 32
Magnetic fields      26 28-31 258-259
Magnetic induction      29
Magnetic potential      42 168 219 225
Magnetic torque      42
Magnetisation      28 29 32 42 149
Magnitude of a vector      11
Mandelstam's condition      232
Material time derivative      135 325
Maximum distortion angle      79 85
Maxwell equations      28 31 89 90
MBBA      4 64 67 159 164-166 169- 171 175 187 228 232 233 236 330
Measurements of      see Table D.3
Melting point      2
Mesogenic      2
Mesomorphic phases      2
Mesophases      2
Miesowicz viscosities      155 156 158
Miesowicz viscosities, in terms of Leslie viscosities      158
Miesowicz viscosities, principal      155 156
Misalignment      84
Molecular length      4
Moving domain wall      317
Natural boundary condition      47 54
Natural orientation      14
Negative magnetic anisotropy      30
Nematic energy      20 21
Nematic energy, one-constant approximation      23
Nematic liquid crystals      3 7-8
Nematic viscosities      151 154-159
Nematic viscosities, canonical set      158
Nematic viscosities, measurements of      see Table D.3
Nematic viscosities, physical interpretation      154
Nematic viscosities, restrictions      146
Newtonian fluid      157 170 176 177 180 212 213
Newtonian viscosity      170 176-177 180 213
No-slip boundary condition      150 167
Non - Newtonian fluid      177
Non - Newtonian properties in nematics      177
Non-contemporaneous variations      34
Non-flow-aligning      166
Non-flow-aligning, instability in oscillatory shear      196
Normal stress      139
Normal stress differences      177
Notation and conventions      9-12 35
Null Lagrangian      38-39
Objective      136
Objectivity      see principle of material frame-indifference
Oersted (Oe)      32
One-constant approximation      22-23 79 81 110
Orientational fluctuations      236
Orthogonal vectors      11
Oscillatory shear flow      187-197
Oscillatory shear flow, flow-aligning nematics      191
Oscillatory shear flow, non-flow-aligning nematics      191
Oscillatory shear flow, stability and instability      191-197
Oseen, C.W.      7
Out-of-plane mode      237
Out-of-plane surface tilt angle in SmC      275 280
PAA      4 7 67 159 165 166 171 175 216 217 228 330
Parabolic cyclides      272-275
Parabolic cyclides, Cartesian equation for      273
Parabolic cyclides, cross-sections of      274
Parabolic cyclides, illustrations      272 274
Parabolic cyclides, parametrisation of      273
Parodi relation      146 151
Patents      108
Penetration length in smectics      284- 286
Permeability of free space      29 329
Permeation in smectics      319
Permittivity of free space      27 329
Perpendicular disclinations      118
Physical components      198
Physical components, in cylindrical coordinates      325-327
Pieranski - Guyon instability      166
Pitch, cholesteric      5 23 24
Pitch, SmC*      307 308
Planar alignment      47
Planar alignment, in SmC      302
Plane of shear      155 163
Point defect      115 127
Point defect at a surface or interface      127-131
Point form      139
Poiseuille flow      209-217
Poiseuille flow, anisotropic fluid      210-213
Poiseuille flow, between coaxial cylinders      217
Poiseuille flow, isotropic viscoelastic fluid      217
Poiseuille flow, nematic liquid crystal      213-217
Polar fluids      134 140
Polarisation vector      236
Polariser      102
Polymorphism      7
Power      33
Power spectrum      244
Pressure gradient      209
Pretilt      82 85 109
Pretilt at the boundaries      82-84
Pretilt, advantage of      84
Principle of material frame-indifference      136
Principle of virtual work      33 35 259
Proper orthogonal matrix      15 136
Rapini - Papoular weak anchoring en-ergy      49
Rate of strain tensor      133 135 151 293 326
Rate of viscous dissipation      141-143 145
Rate of work hypothesis      140
Reaction time      221
Reduced viscosity      223
Reformulation of dynamic equations      153- 154
Reformulation of equilibrium equations      50-56
Reformulation of equilibrium equations, boundary conditions      53
Reformulation of equilibrium equations, bulk equations      51
Reformulation of equilibrium equations, in SmC      265
Regional angular velocity      134
Reinitzer, F.      2
Relative angular velocity      133 134
Relative shear velocity      187
Relaxation time      222
Response functions      244
Response time      316
Response time in SmC*      316-317
Reynolds number      188 189
Reynolds' transport theorem      139 141 324
Rigid body motion      143
Rise time      221
Ritschke, A.      4
Rod-like molecules      2-3
Rotating magnetic field      171
Rotational viscosity      157 158
Rotational viscosity, direct measurement of      175
Saddle-splay      21 38
Scalar product      11
Scalar triple product      11
Scaling properties      185-187 217
Scattered beam      236
Scattering angle      236
Scattering plane      236
Scattering vector      236
SCE13      312
SCE3      312
Schadt      101 108
Scheurle, B.      4
Secondary flow      170
Secondary flow component      170
Secondary flow, cellular      209
See cholesteric liquid crystals chiral smectic C      see SmC*
Shear      155
Shear flow      162 176-187
Shear flow, between parallel plates      182-185
Shear flow, in bookshelf SmC      305-306
Shear flow, in planar aligned SmC      302-305
Shear flow, key equations      180
Shear flow, near a boundary      180-182
Shear flow, oscillatory      187-197
Shear plane      see plane of shear
Shear stress      139 156 182 184
SI units      31 329
Sign convention for spontaneous polarisation      307
Simple flow alignment      162
Simple shear flow in SmC      301-306
Simple shear flow, steady solutions      164
Slow modes (in light scattering)      242
SMA      5 6 249 256 267 268 272 281 284 297 319
SmA elastic energy      256
SMC      5 6 9 249 267 268
SmC constraints      248-249
SmC elastic constants      251
SmC elastic constants, inequalities      255-256
SmC elastic constants, measurements and estimates      257
SmC elastic constants, Orsay notation      252
SmC elastic constants, physical interpretation      253
SmC elastic energy      250-258 320
SmC Freedericksz transition      275-281
SmC viscosities      296-301
SmC viscosities, classification of      297-299
SmC viscosities, measurements of in DOBCP      301
SmC viscosities, physical considerations      301
SmC viscosities, restrictions      299-300
SmC${}_{M}$, elastic energy      258
SmC${}_{M}$, viscosities      296
SmC*      6 9 247 308 306-319
SmC* elastic energy density      310
SmC* electric energy density      311
SmC* material parameters      312
SmC* viscosities, identification with SmC viscosities      312
SmC* viscosities, measurements of in ZLI-3234, ZLI-3488, ZLI-3489      301
SmC, in-plane surface twist angle      275 276 279
SmC, mathematical description      249
SmC, out-of-plane surface tilt angle      275 280
Smectic A      see SmA
Smectic C      see SmC
Smectic C liquid crystals      see SmC
Smectic cone angle      6 248 249 257 312
Smectic interlayer distance      6 248 249 284
Smectic layer compression      281-291 319
Smectic layer compression constant      281 284
Smectic layer dilation      282 319
Smectic layer thickness      6
Smectic layer undulations, reference to SmC experiment      283
Smectic layer undulations, references to SmA experiments      282
Smectic liquid crystals      5
Smectic tilt angle      see smectic cone angle
Soliton-like solution      317
Specific driving force      212 213 215
Specific volume, measurements of in nematics      see Table D.3
speed of light      329
Spherical solution      43 44
Spin tensor      135
Splay      15 16 21
Splay geometry      73
Splay viscosity      158 228
Splay, measurement of      77
Spontaneous polarisation      248 307 308
Spontaneous polarisation, contribution to SmC* energy      310
Spontaneous polarisation, sign convention for      307
SSFLC device      308 313 316
Stability      196
Stability and instability      165 191 196
Static theory of SmC      248-281
Static theory of SmC*      312-313
STN      101
Strength of a disclination      111
Stress tensor      37 139 151
Stress tensor, normal stress      139
Stress tensor, normal stress differences      177
Stress tensor, physical interpretation of      139
Stress tensor, shear stress      139
Stress vector      139
Strong anchoring      see anchoring strong
Suffix notation      see index notation
Summation convention      9 10
Supertwisted nematic device      101
Surface at an interface      123
Surface force      138 139
Surface moment      138 139
Surface tension      120 122 123 329
Surface tension, measurements of in nematics      see Table D.3
Surface tilt angle in SmC      275 280
Surface traction      174 206
Surface twist angle in SmC      275 276 279
Surface viscosity      150
Switch-off time      218 222
Switch-off time, in bookshelf SmC      280
Switch-off time, in twisted nematic device      223
Switch-on time      218 221 224 228 234
Switch-on time, in bend geometry, $H \gg H_{c}$      235
Switch-on time, in bend geometry, $V \gg V_{c}$      236
Switch-on time, in bookshelf SmC      280
Switch-on time, in splay geometry, $H \gg H_{c}$      228
Switch-on time, in splay geometry, $V \gg V_{c}$      229
Switch-on time, in twisted nematic device      223
Switch-on time, reduction of (via backflow)      228 236
Switching      72 223 228 308 317
Tables, conversion from Gaussian cgs to SI      329
Tables, fundamental constants      329
Tables, material constants for nematics      330
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