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Maugin G.A. — Nonlinear waves in elastic crystals
Maugin G.A. — Nonlinear waves in elastic crystals

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Название: Nonlinear waves in elastic crystals

Автор: Maugin G.A.

Аннотация:

The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. Students are introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.


Язык: en

Рубрика: Физика/Классическая физика/Упругие среды/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 314

Добавлена в каталог: 17.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Acceleration wave      76 215
Acoustic, emission in defective crystals      146
Acoustic, surface waves      189
Acoustic, waves emission      134
Acoustical branch      11
Action, Hamiltonian      264
Adiabatic evolution      225
Adiabatic time variation      116
Airy-function signal      172
Alloys, martensitic      156
Amorphous material      3
Amplitude-dependent dispersion relation      279
Analysis, convex      37
Anelasticity      51 52
Anelasticity in large strains      34
Anelasticity in small strains      37
Anharmonic approximation      10
Anisotropic elasticity      11
Annihilation, kink-antikink      136
Anomalous dispersion      46 165
Antikink      134
Antikink kink-      136
Antisoliton, soliton-, solution      93
Approximation, anharmonic      10
Approximation, harmonic      10
Asymptotics, intermediate      169
Atoms, interstitial      4
Austenite and martensite, kinks between      164
Austenite, solitons in      157
Axiom of local accompanying state      34
Backlund transformation      93 270
Bad Boussinesq (BaB) equation      78
Bain transformation      241
Barkhausen effect      146
Behaviour quasi-solitonic      209
Bilinear form      272
Bloch configuration      65
Bloch wall      17 109
Blow-up, nonlinear      179
Born — Karman model      41
Bound state      93
Boundaries, grain      4
Boundaries, twin      4
Boussinesq — Kortweg — de Vries system      45
Boussinesq, crystal equation      75
Boussinesq, equation      46 55 170
Boussinesq, equation, bad (BaB)      78
Boussinesq, equation, generalized (GBE)      168
Boussinesq, equation, generalized modified (GMBE)      156
Boussinesq, model      78
Boussinesq, paradigm      47 49
Branch, acoustical      11
Breaking distance      78
Breaking symmetry      142
Breather      133 213
Breather solution      93
Bremsstrahlung      146
Bright envelope, SESOL      201
Bright envelope, soliton      96 200 281
Brillouin zone, first      12
Bulk quasi- wave      191
Burgers, equation      255
Burgers, vector      16 52
Canonical equation of momentum balance      119
Chain, elastic      71
Chain, monatomic      9 72
Chaos, route to      123
Chaos, spatial      124
Chaos, transition to      123
Characteristics, theory of      277
Classification, Hadamard’s      215
CMKdV equation      144
Cnoidal type solution      45
Coating, thin film      194
Coefficients, Lame      29
Coherency condition, full      221
Coherent phase transition fronts      231
Coherent structure      129
Cole — Hopf transformation      255
Collision, head-on      85 97 180
Collision-induced fusion of subsonic solitons      214
Compactons      88
Competitive interactions      158
Condition, coherency, full      221
Condition, jump      222
Condition, orthogonality      132
Condition, secularity      76 131
Conduction, Fourier law of      252
Conduction, heat      31
Conduction, normal      70
Conductors, elastic      69
Conductors, thermoelasticity of      30
Configuration, Bloch      65
Configuration, incommensurate      124
Configuration, intermediate elastically released      35
Configuration, Neel      64
Conservation of wave action      279
Conservation, laws      165 276
Conservative difference scheme      208
Consistency geometrical      221
Constancy of angles law of      2
Construction Maxwell-line      237 240
Continua micromorphic      263
Continuum, limit      42
Continuum, mechanics      13
Continuum, quasi-      49 55 184
Convex analysis      37
Cooperative interactions      158
Coupled NLS equations      138
Coupling, electromagnetomechanical      57
Coupling, electrostatic      62
Coupling, resonance      111
Crystal momentum      11 43
Crystal, defective      4
Crystal, defective acoustic emission in      146
Crystal, elastic ferroelectric      39
Crystal, electroelastic      243 245
Crystal, equation Boussinesq      75
Crystal, ferroelastic      151
Crystal, ferromagnetic      243 246
Crystal, formation      4
Crystal, lattice theory      46
Crystal, liquid      3 43
Curie — Weiss law      153
Curves, kinetic      236
Dark, envelope solitons      200
Dark, soliton      281
Defect point      51
Defective crystal      4
Defective crystal, acoustic emission in      146
defects      15
Defects, line      4
Defects, point      4
Defects, surface      4
Density, Hamiltonian      24 135
Density, Lagrangian      39
Derivative, Euler — Lagrange      39
Difference, conservative scheme      208
Difference, five-point      47
Difference, three-point      47
Direct-motion gradient      21
Director-field theory      115
Disclination      8
Discontinuity, fronts      219
Discontinuity, surface      17
Dislocation      16 221
Dislocation of rotation      8
dispersion      38
Dispersion, anomalous      46 165
Dispersion, dispersion relation      280
Dispersion, nonlinear dispersive      199
Dispersion, numerical      55
Dispersion, parameter      158
Dispersion, pseudo- relation      114 157 274
Dispersion, relation      42 50
Dispersion, relation, amplitude-dependent      279
Dispersion, relation, dispersive      280
Dispersive nonlinear dispersion relations      199
Dissipation, inequality intrinsic      40
Dissipation, potential      234
Dissipation, pseudo-potential of      36
Dissipation-induced evolution      206
Distance, breaking      78
Distance, shock-formation      78
Distributions      223
Domain      15
Domain, magnetic wall      7 109
Double SG equation (DSG)      65 273
Drain boundaries      4
Driving force      19
Driving force, viscous, on soliton      207
Driving pseudo-force      179
Dynamical processes, quasi-linear      71
d’Alembertian, operator      196 280
d’Alembertian, wave operators      56
Effect, Barkhausen      146
Effect, shape-memory      150
Einstein equation      92
Elastic chains      71
Elastic conductors      69
Elastic crystals ferroelectric      39
Elastic energy potential      20
Elastic ferromagnets      39 66
Elastic models with internal variables      251
Elastic potential      20
Elastic superconductors      70
Elastic surface waves, classification      189
Elastic waves      11
Elastically released configuration, intermediate      35
Elasticity, anisotropic      11
Elasticity, energy based      20
Elasticity, linear      43
Elasticity, nonlinear      195
Elasticity, pseudo-      150
Elastoplasticity      224
Electroelastic crystal      243 245
Electroelasticity in ferroelectrics      63
Electroelasticity, nonlinear      61
Electromagnetic potentials      57
Electromagnetomechanical coupling      57
Electrostatic couplings      62
Electrostatics, quasi-      61
Electrostriction      62
Elliptic integral      45
Emission of acoustic waves      134
Emission, acoustic in defective crystals      146
Emitted radiation      212
Energy, based elasticity      20
Energy, Hamiltonian      69 87
Energy, momentum tensor      266
Energy, potential elastic      20
Energy, pseudo-      171
Enneper’s equation      94
Enneper’s equation, generalized      273
entropy      34
Envelope, bright, SESOL      201
Envelope, bright, solitons      137 200
Envelope, dark solitons      200
Envelope, solitary waves      100
Envelope, surface      201
Equal areas, rule of      237
Equation, Boussinesq      46 55 179
Equation, Boussinesq, bad (BaB)      78
Equation, Boussinesq, generalized, (GBE)      168
Equation, Burgers      255
Equation, canonical, of momentum balance      119
Equation, CMKdV      144
Equation, crystal, Boussinesq      75
Equation, double SG (DSG)      65 273
Equation, Einstein      92
Equation, Enneper’s      94
Equation, Enneper’s, generalized      273
Equation, evolution      146
Equation, evolution, diffusion      251
Equation, Gibb’s      23 30
Equation, Ginzburg — Landau      188
Equation, integro-differential evolution      256
Equation, jump      247
Equation, Kadomtsev — Petiashvili (KP)      104 185
Equation, KdV      85
Equation, Klein — Gordon      274
Equation, Korteweg — de Vries (KdV)      47 170 269
Equation, Maxwell’s      57
Equation, MKdV      144
Equation, modified, Kadomtsev — Petiashvili (MKP)      144
Equation, modified, KdV      100
Equation, modified, Korteweg — de Vries (KdV)      256
Equation, NLS coupled      138
Equation, nonlinear, evolution      253
Equation, nonlinear, Schrodinger      95 281
Equation, one-dimensional linear-elastodynamic      42
Equation, pendulum      91
Equation, Rankine — Hugoniot      163
Equation, Schrodinger      137 268
Equation, SG perturbed      66
Equation, sine-Gordon (SG)      52
Equation, stiff      175
Eshelby, stress      23 83 119 245
Euler — Lagrange derivative      39
Euler’s identity      235
Evolution, adiabatic      225
Evolution, diffusion equation      251
Evolution, dissipation-induced      206
Evolution, equations      146
Evolution, integro-differential, equation      256
Evolution, long-time      167
Evolution, nonlinear, equation      253
Evolution, of pulse, long-time      181
Evolution, system      84 130
Exactly integrable      56 80
Experiment, numerical      55
Factor, stress intensity      258
Far-field solution      75
Far-field study      73
Fault, stacking      51
Ferroelastic crystals      151
Ferroelectric elastic crystals      39
Ferroelectric electroelasticity in      63
Ferromagnet elastic      39 66
Ferromagnetic crystal      243 246
Field, director-, theory      115
Field, theory      264
Film thin      68
Film thin, coating      194
Finite difference, forward first-order      183
Finite difference, schemes      54
First Brillouin zone      12
First integral      112
First order finite differences, forward      183
Five-point differences      47
Flow, plastic      51
Forbidden window      206
Force, driving      19
Force, driving, viscous, on soliton      207
Force, Heisenberg      66
Force, pseudo-, driving      179
Form, bilinear      272
Form, Piola — Kirchhoff      21
Form, wave      260
Formation of surface envelope shock wave      201
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