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Brownian motion Fluctuations, dynamics, and applications-[2002]-[djvu]-[Robert M. Mazo]

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书籍信息:
书名: Brownian motion: Fluctuations, dynamics, and applications
语言: English
格式: djvu
大小: 2.7M
页数: 301
年份: 2002
作者: Robert M. Mazo
系列: ISMP112
出版社: OUP

简介

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.


目录
Title ......Page 3
Copyright ......Page 4
Preface ......Page 5
Contents ......Page 8
1.1 Robert Brown ......Page 12
1.2 Between Brown and Einstein ......Page 14
1.3 Albert Einstein ......Page 16
1.4 Marian von Smoluchowski ......Page 18
1.5 Molecular Reality ......Page 19
1.6 The Scope of this Book ......Page 21
2.1 Probability ......Page 22
2.2 Conditional Probability and Independence ......Page 25
2.3 Random Variables and Probability Distributions ......Page 27
2.4 Expectations and Particular Distributions ......Page 29
2.5 Characteristic Function; Sums of Random Variables ......Page 34
2.6 Conclusion ......Page 36
3.1 Stochastic Processes ......Page 37
3.2 Distribution Functions ......Page 38
3.3 Classification of Stochastic Processes ......Page 40
3.4 The Fokker-Planck Equation ......Page 44
3.5 Some Special Processes ......Page 46
3.6 Calculus of Stochastic Processes ......Page 48
3.7 Fourier Analysis of Random Processes ......Page 51
3.8 White Noise ......Page 54
3.9 Conclusion ......Page 56
4.1 What is Brownian Motion? ......Page 57
4.2 Smoluchowski's Theory ......Page 59
4.3 Smoluchowski Theory Continued ......Page 63
4.4 Einstein's Theory ......Page 65
4.5 Diffusion Coefficient and Friction Constant ......Page 68
4.6 The Langevin Theory ......Page 70
5.1 The Langevin Equation Revisited ......Page 73
5.2 Stochastic Differential Equations ......Page 75
5.3 Which Rule Should Be Used? ......Page 78
5.4 Some Examples ......Page 80
6.1 Functional Integrals ......Page 82
6.2 The Wiener Integral ......Page 83
6.3 Wiener Measure ......Page 85
6.4 The Feynman-Kac Formula ......Page 87
6.5 Feynman Path Integrals ......Page 89
6.6 Evaluation of Wiener Integrals ......Page 90
6.7 Applications of Functional Integrals ......Page 93
7.2 The Free Particle ......Page 94
7.3 The Distribution of Displacements ......Page 96
7.4 The Harmonically Bound Particle ......Page 98
7.5 A Particle in a Constant Force Field ......Page 103
7.6 The Uniaxial Rotor ......Page 104
7.7 An Equation for the Distribution of Displacements ......Page 105
7.8 Discussion ......Page 106
8.1 The Kramers-Klein Equation ......Page 108
8.2 The Smoluchowski Equation ......Page 109
8.3 Elimination of Fast Variables ......Page 112
8.4 The Smoluchowski Equation Continued ......Page 115
8.5 Passage over Potential Barriers ......Page 116
8.6 Concluding Remarks ......Page 119
9.1 The Random Walk ......Page 122
9.2 The One-Dimensional Pearson Walk ......Page 123
9.3 The Biased Random Walk ......Page 125
9.4 The Persistent Walk ......Page 128
9.5 Boundaries and First Passage Times ......Page 131
9.6 Random Remarks on Random Walks ......Page 136
10.1 Molecular Distribution Functions ......Page 138
10.2 The Liouville Equation ......Page 140
10.3 Projection Operators—The Zwanzig Equation ......Page 142
10.4 Projection Operators—The Mori Equation ......Page 144
10.5 Concluding Remarks ......Page 147
11.1 The Langevin Equation A Heuristic View ......Page 149
11.2 The Fokker-Planck Equation — A Heuristic View ......Page 152
11.3 What is Wrong with these Derivations? ......Page 155
11.4 Eliminating Fast Processes ......Page 156
11.5 The Distribution Function ......Page 164
11.6 Discussion ......Page 168
12.2 Brownian Motion in a Dilute Gas ......Page 170
12.3 Discussion ......Page 173
12.4 The Particle Bound to a Lattice ......Page 174
12.5 The One-Dimensional Case ......Page 178
12.6 Discussion ......Page 180
13.1 Limits on Measurement ......Page 181
13.2 Oscillations of a Fiber ......Page 182
13.3 A Pneumatic Example ......Page 185
13.4 Electrical Systems ......Page 189
13.5 Discussion ......Page 192
14.2 Diffusion Controlled Reactions ......Page 194
14.3 The Effect of Forces ......Page 198
14.4 The Coagulation of Colloids ......Page 202
14.5 Taylor Diffusion ......Page 203
15.1 Rotational Diffusion ......Page 208
15.2 Fluorescence Depolarization ......Page 212
15.3 Non-Spherical Brownian Particles ......Page 215
15.4 Concluding Remarks ......Page 218
16.1 A Model for Dilute Solutions of Polymers ......Page 219
16.2 Hydrodynamic Interaction ......Page 221
16.3 The Equation of Motion ......Page 223
16.4 Diffusion and Intrinsic Viscosity ......Page 225
16.5 Historical Remarks and Additional Reading ......Page 230
17.1 Effects of Concentration ......Page 233
17.2 The Fokker-Planck Equation ......Page 234
17.3 The Multiparticle Smoluchowski Equation ......Page 237
17.4 The Diffusion Coefficient ......Page 239
17.5 The Viscosity ......Page 246
17.6 Concluding Remarks ......Page 249
18.1 Brownian Dynamics ......Page 251
18.2 Brownian Paths as Fractals ......Page 257
18.3 Brownian Motion and Chaos ......Page 262
18.4 Concluding Remarks ......Page 268
A The Applicability of Stokes' Law ......Page 269
B Functional Calculus ......Page 271
C An Operator Identity ......Page 274
D Euler Angles ......Page 275
E The Oseen Tensor ......Page 277
F.1 Mutual Diffusion ......Page 279
F.3 Relation between Dm and Ds ......Page 280
References ......Page 282
Index ......Page 296
Cover ......Page 301

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