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| Mazo R.M. — Brownian Motion: Flucuations, Dynamics, and Applications |
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| Предметный указатель |
 -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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