Lebowitz J.L., Montroll E.W. — Nonequilibrium phenomena I. The boltzmann equation :: Электронная библиотека попечительского совета мехмата МГУ

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Lebowitz J.L., Montroll E.W. — Nonequilibrium phenomena I. The boltzmann equation

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Название: Nonequilibrium phenomena I. The boltzmann equation

Авторы: Lebowitz J.L., Montroll E.W.

Аннотация:

The objective of statistical mechanics is to explain and predict the properties of macroscopic matter from the properties of its microscopic constituents. The subject is traditionally divided into an equilibrium and a nonequilibrium part. This volume of the Studies is the first of several planned volumes devoted to a thorough review of the current state of the art of nonequilibrium theory.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1983

Количество страниц: 254

Добавлена в каталог: 20.03.2006

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Предметный указатель

Alaoglu theorem      25
Angular cutoff      22—23 197
Approximating sequence      11—14 16—17
Asymptotic behavior      210—212
BBGKY hierarchy      233 243—245
Benard problem      247—248
BGK model      153—159 164 179—182
BKW-mode      56 57 63 65ff. 72 75
Bobylev symmetry      62
Boltzmann equation for hard spheres      6
Boltzmann equation hierarchy      233—234 245—246
Boltzmann equation in shock layers      201
Boltzmann equation linear      198—199 207—210 240—241
Boltzmann — Grad limit      7 236—238 240
Boundary condition and initial conditions      124—130 138 149—152 168 173
Boundary layers      195 200—202
Cauchy problem      24
Cauchy — Kowalewski theorem      213
Chapman — Enskog expansion      138—143 195 196 202—210 221
Characteristic function      generating function
Chemical kinetics      57 87
Cluster      89
Coagulation      57 87 89 98
Collision frequency      134
Collision invariant      23 133 197
Collision operator      21—22 40—41 130—133 152—153 196—199
Collision operator, linearized      132—133 155 159
Collision rate      56 58 59
Conservation law      54ff. 61 64 68 79 81 88 99 101
Correlation functions      12 16 236 242—243
Depolymerization      102 107
Detailed balance      125
Deterministic scattering model      54 19
Distribution function isotropic velocity      61 68 78
Distribution function most probable      57 85 91 93 97 100 103 108 112 115
Distribution function size      89 97
Distribution function velocity      53
Dunford — Pettis theorem      25
Eigensolutions      167 170
entropy      218
Euler equation      195 196 204 209 214—215
Existence of global solutions (spatially homogeneous) for cut-off potential      27—31
Existence of global solutions (spatially homogeneous) for hard spheres      26—27
Existence of global solutions (spatially homogeneous) for Maxwell molecules      27
Existence of global solutions near equilibrium      39—47
Existence of local solutions (spatially dependent) for cut-off hard potentials      38
Existence of local solutions (spatially dependent) for general interactions      39
Existence of local solutions (spatially dependent) for Maxwell molecules      38
Existence theory for Boltzmann equation with mollifier      32—38
Extent of reaction      92 102 107 112
F-theorem      57 90 92 99 101ff.
Flows external      182—186
Flows internal      175—182
Fluctuation field      238
Fluctuation force      231
Fluctuations      227—228 230—231 238—244
Fragmentation      87 89 92 101 103 106
Free energy      57 91ff. 96 102 104 115
Gelation      89 90 95
Generating function      62 68 71 87 105 111
Grad inequality      41 44
Hard interaction      56 58

Hard spheres      59 78
Hilbert expansion      136—139 195 196 202—216
Hilbert space      60 68 72
Hilbert theorems      F-theorem) 23 55 79 90 99 102 126—127 194 218
Hydrodynamic approximations      248—250
Initial layer      195 200—201
Jensen's inequality      93 104
Killing-off property      26 40 43 45
Knudsen layers      173 180
Knudsen number      134—135
Krook — Wu conjecture      56ff. 63 74 76 100 111
Laguerre series      60 70 71 73 75 79
Levi properties      25
Linearized Boltzmann equation      67 69 72 76 86 147—152
Linearized Boltzmann equation, S-matrix      172
Linearized Boltzmann equation, spectrum      168—175
Linearized Boltzmann equation, variational methods      160—164
Mach number      135 182 184—185
Macroscopic correlations      233—234
Maxwell distribution      23 55 62 64 128—132 197 198
Maxwell distribution, wall      125—126
Maxwell model      56 58 59 72 78
Maxwell molecules      22 56ff. 63 69 113
Mean free path      7 134 173 199—202
Mean free time      134
Mild solution      24 40
moment      68 70 83 92 95 108 116
Moment factorial      95 103 106 112
Moment Laguerre      70 71
Moment polynomial      68
Monodisperse initial distribution      99 103 106
Monotonicity      25
Navier — Stokes equation      195 196 206 209 216
Percolation      89
Perturbation methods      41—47 130—133
Perturbation methods, expansion in large Knudsen number      144—147
Perturbation methods, expansion in small Knudsen number      135—143
Perturbation methods, spurious solutions      141—143
Polymerization      57 76 87 90 92 96 98 102 108ff. 114
Rankine — Hugoniot condition      177 216 218
Rate equation      57 87 90 91 93 103
Reynolds number      135
Scattering angle      53 58 77
Scattering cross section      54 56ff. 61
Shock waves      176—180 195 196 200 201 216—221
Similarity solution      59 63 67
Similarity transformation      63 65
Slip coefficient      164—166
Sobolev space      42 44
Soft interaction      56 58
Sound propagation      174—175
Sound speed      218
Spectral problem      207—212 220
Stochastic scattering model      54 77
Strouhal number      134—135
Time reversibility      8—9 15
Transition rate      54 11
Umqueness (non-)      57 81 87 99
Variational methods      159—167
Variational methods, for Kramers problem      164—166
Variational methods, for least squares      166
Variational methods, for linear Boltzmann equation      160—164
Very Hard Particles (VHP)      77 100 111 116

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