Mazo R.M. — Brownian Motion: Flucuations, Dynamics, and Applications :: Электронная библиотека попечительского совета мехмата МГУ

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Mazo R.M. — Brownian Motion: Flucuations, Dynamics, and Applications

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Название: Brownian Motion: Flucuations, Dynamics, and Applications

Автор: Mazo R.M.

Аннотация:

Brownian motion - the incessant motion of small particles suspended in a fluid - is an important topic in statistical physics and physical chemistry. This book studies its origin in molecular scale fluctuations, its description in terms of random process theory and also in terms of statistical mechanics. A number of new applications of these descriptions to physical and chemical processes, as well as statistical mechanical derivations and the mathematical background are discussed in detail. Graduate students, lecturers, and researchers in statistical physics and physical chemistry will find this an interesting and useful reference work.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2009

Количество страниц: 289

Добавлена в каталог: 18.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\sigma$ -field      12 74 75
Absorbtion      76
action      79
Adelman equation      166 168
Annhilation      76
Anomalous diffusion      116n 251
Anomalous drift      65 68
Anomalous exponent      126
Attractor      253
Attractor strange      253
Autocorrelation function      see “function correlation”
Balance equation      113 115 122
Bertrand’s paradox      13
Binary shift map      252
Boltzmann distribution      58 199
Boltzmann equation      1159 160 169
Boltzmann factor      209
Boundary, absorbing      122
Boundary, reflecting      123
Broken symmetry      147
Brown, R.      1—3 46 47
Brownian dynamics      10 241 242 244 246
Brownian function      246 250
Brownian trail      246 250
Cayley Klein parameters      205
Central limit theorem      22 24 25 33 37 45 153 155 157
Chaos      253 257
Chapman — Kolmogorov equation      6 32 33 35 55 56
Characteristic function      23—25 36 94
Characteristic time      145
Cole-Cole plot      201
Collective modes      222
Collision time      240
Colloid coagulation      184 191
Compatibility      28 32 36
Completely random process      29
Concentration gradient      58
Conditional probability      14 15 216
Configuration space      183 208 226
Conservation of probability      130
Conserved quantities      144 145 147 150
Constant force field      83 92 93 115 116
Constraints      220
Continuity mean-square      38
Continuity stochastic      38
Convergence in distribution      37
Convergence mean square      37
Convergence strong      37
Convergence weak      37
Convevtive diffusion equation      194
Correlation function      28 29 44 141 147 148
Correlation function current      181
Correlation function density      150 152 234
Correlation function force      143 225 228
Correlation function velocity      61 164 166 168
Correlation function, angular displacement      172
Correlation function, electric field      234
Correlation function, random force      141 153
Correlation function, trajectory      255
Correlation time      29 60 68 98 137 140 141 225 228
Coulomb force      187 188 189 234
Current density      198
De Moivre Laplace limit theorem      21 37 112
Debye cloud      234
Debye equation      199
Debye length      189
Debye — Huckel law      189
Density function      18
Depolarization ratio      202 203
Deterministic chaos      251
Dichotomic process      44 45
dielectric constant      200
Diffusion      95 183 198 212
Diffusion coefficient      37 64 110 184 192 193 195 196 211 214 215 228—235 239 244
Diffusion coefficient mutual      228
Diffusion coefficient rotational      56 204 205
Diffusion coefficient self-      6 148 152 228 233n
Diffusion coefficient, frequency and wave number dependent      149
Diffusion coefficient, generalized      228
Diffusion constant      see “diffusion coefficient”
Diffusion control      183—185 187 190 191 244 246
Diffusion current      58 268
Diffusion equation      6 55 114 149 183 186 229
Diffusion flux,      see “diffusion current”
Diffusion mutual      269 270
Diffusion rotational      197
Diffusion self      269 270
Diffusion tensor      228 230
Dilute gas      159
Dimension box-counting      247 249
Dimension Brouwer      247
Dimension Euclidean      247 251
Dimension fractal      246 248 250 251
Dimension Hausdorff — Besicovich      247 248
Dimension topological      247 248
Dipole      199 200 202
Dipole moment      198 207
distribution      see “generalized function”
Distribution binomial      20 22 48 112
Distribution Cauchy      24 38
Distribution exponential      33 62 63
Distribution function      16 18 27—29 56 128 129
Distribution function conditional      85 91
Distribution function cumulative      16
Distribution Gaussian      20 33
Distribution Lorentz      25
Distribution multivariate      24
Distribution multivariate Gaussian      22 25 36
Distribution Poisson      22 23
Divergence-like      101
Doob’s theorem      85
Drift      67
Drift coefficient      37 67
Dumbbell      209 216 219
Dynamical variable      134 138
Einstein relation      58 229
Einstein, A.      5—7 54—59 86 215 236
Elastic collisions      160 161
Ellipsoid      201
Equation of continuity      213
Equipartition      49 52 53 59 61 91 94 171 175 179 181 218
Euler angles      205 206 264
Events compound      11
Events elementary      11 71
Events independent      6 15 16 50 52 121
Events mutually exclusive      12
Events pairwise independent      15
Excluded volume      221 222 225
Expectation      see “mean”
Exponential Brownian motion      70
External force      57 183 198 212 236
Fast modes      223
Fast variable      101
Feynman integral      71 78 79 261
Feynman Kac formula      76—78
Fick’s law      228 268
First passage time      120 121 124
Flow birefringence      204
Fluctuation-dissipation theorem      153
Fluctuations      4 59 60 127 147 170 171 178 182 195
Fluctuations current      181
Fluorescence      202 203
Fluorescence depolarization      201—204
Flux      244
Fokker — Planck equation      33—35 55 56 88 92 97 141 143 153 157 161 162 168 172 174 183 194 197 223—225 226
Fokker — Planck operator      109
Forward equation      35
Fractal      126 246 253 257
Fractional Brownian motion      250
Free draining      215

Free particle      83 100
Friction      209
Friction coefficient      see “friction constant”
Friction constant      52 57 58 127 143 156 159 152 169 172 174 205 211 226 227 229 243
Friction constant force      100 193 198 210
Friction constant kernel      136
Friction constant linear      83
Friction constant rotational      69 93 198
Friction constant tensor      220
Function space      71
Functional      72 73 76 154 260—262
Functional derivative      261
Functional integral      71 73 76—78
Generalized function      18
Generating function      113 118 121
Gibbs Duhem relation      268
Green’s function      104 202 205 206 266
Harmonically bound particle      83 88
Hermitian operator      131
High frequency limit      100
Hookean springs      209 212
Hurst exponent      250
Hydrodynamic interaction      209—215 218 219 222 225 227 228 230 232 236 243
Hydrodynamic modes      223
Independence      14—16
Independent increments      33 35 55 56 242 250 251
Infinitesimal rotation      264
Integral, of random process      39
Intermolecular force      243
Intrinsic viscosity      214 215 218 235
Irrelevant part      132 224
Ito equation      64 65 70
Ito’s rule      66 70 242
Johnson noise      178
Kinetic theory      8 47 54 221 216
Koch curve      248 249
Kolmogorov — Sinai entropy      254—256
Kolmogorov’s theorem      75
Kramers — Klein equation      97 98 99 101 103 104 212
Lagrangian      79
Laminar flow      192
Langevin equation      59—61 67 84 100 137 138 141 172 180 241—243
Langevin equation generalized      135 156 157
Levy walk      116 126
Lifetime      203
Light scattering      239
Linear restoring force      87
Liouville equation      129—131 142 169 213
Liouville operator      131—133 138—140 223 224
Liouville theorem      255
Long time tail      144 168 169
Longitudinal mode      145 147
Lorentz, H.A.      59 152 258 259
Lyapunov exponent      253—256
Macromolecules      see “polymers”
Macroscopic, definition      49
Markov chain      55
Markov process      6 22 30—33 38 55 85 128 169 173 251
Markov process dichotomic      30
Markov process Gaussian      85
Mass ratio      68 139 144
Master equation      68
Maxwell distribution      96 98 100 105 154 162
Maxwell — Boltzmann distribution      156 160
Mean      28 112
Mean free path      50 53 160 162 163 174
Mean square amplitude      94
Mean square angular displacement      94
Mean square dispacement      6 51 52 57 86 177 242
Mean square end to end distance      112
Mean square length      216 218
Measure      12 16 71
Measure invariant      255
Measure Lebesgue      13n 74 75
Measure Wiener      75
Median      19
Memory      29
Memory function      135 139 140 148
Mesoscopic      56 62 208
Mesoscopic, definition      49
Microscopic      56
Microscopic, definition      49
Mirror      93 171 172
MODE      19
Mode-mode coupling      148
Molecular Dynamics      11n 240
Moments      20 24 28
Moments central      19
Monte Carlo method      81
Mori equation      133—136 139 147 148
Motional narrowing      195
Multifractal      17
Navier Stokes equations      163 210 236—238 258n 266
Noise      10 41 67 170 251 478
Noise additive      64 70 84
Noise Gaussian white      45 68 69
Noise multiplicative      64 69 70 242 243
Noise shot      44
Noise thermal      43—45 181
Noise white      30 62—64 173 178 180
Non Markovian process      32 117 126 169 251
Non-differentiable function      9
Normal stress      216
Nyquist’s theorem      178
O-U process      see “Ornstein — Uhlenbeck process”
Onsager length      189
Onsager relations      270
Ornstein — Uhlenbeck process      85 86 149
Oseen approximation      229
Oseen tensor      210—214 227 228 230 266 267
Osmotic pressure      6
Osmotic second virial coefficient      230 232
Path      71
Pattern entropy      255 256
Pearson walk      112 120
Persistence of velocity      8
Phase space      129 130
Poisson bracket      63 130
Poor solvent      233
Potential barrier      106
Power spectrum      42—44 172
Principal axes      205 218
Probability current      123
Probability current convective      124
Probability current diffusive      124
probability density      55
probability distribution      134
Probability, conditional      14—16 28—30
Process continuous      38
Process diffusion      35
Process Gaussian      36 45 63 83 84
Process homogeneous      33 35 41 55
Process Poisson      33
Process scaled Poisson      33
Projection operator      131—133 136 138 139 141 142 146
Quasiinterval      75
Random error      170
Random force      83 98 139 140 241 243
Random frequency modulation      69
Random function      see “stochastic process”
Random torque      93 172 197
Random variable      16 26 27
Random variable Cauchy      25
Random variable Gaussian      153 157 249
Random variable independent      18 24
Random variable Poisson      33
Random variable sum of      111
Random walk      54 111 193
Random walk biased      114—116
Random walk correlated      112

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