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Brownian motion : fluctuations, dynamics, and applications

Author: Robert M Mazo
Publisher: Oxford : Clarendon Press ; New York : Oxford University Press, 2002.
Series: Oxford science publications.; International series of monographs on physics, v. 112.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:

Describes the theory of how processes on the unobservable molecular scale give rise to observable effects, such as diffusion and electrical noise on the macroscopic or laboratory scale. This title  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Robert M Mazo
ISBN: 0198515677 9780198515678
OCLC Number: 48753074
Description: xii, 289 p. : ill. ; 25 cm.
Contents: 1 Historical Background 1 --
1.1 Robert Brown 1 --
1.2 Between Brown and Einstein 3 --
1.3 Albert Einstein 5 --
1.4 Marian von Smoluchowski 7 --
1.5 Molecular Reality 8 --
1.6 The Scope of this Book 10 --
2 Probability Theory 11 --
2.1 Probability 11 --
2.2 Conditional Probability and Independence 14 --
2.3 Random Variables and Probability Distributions 16 --
2.4 Expectations and Particular Distributions 18 --
2.5 Characteristic Function; Sums of Random Variables 23 --
3 Stochastic Processes 26 --
3.1 Stochastic Processes 26 --
3.2 Distribution Functions 27 --
3.3 Classification of Stochastic Processes 29 --
3.4 The Fokker-Planck Equation 33 --
3.5 Some Special Processes 35 --
3.6 Calculus of Stochastic Processes 37 --
3.7 Fourier Analysis of Random Processes 40 --
3.8 White Noise 43 --
4 Einstein-Smoluchowski Theory 46 --
4.1 What is Brownian Motion? 46 --
4.2 Smoluchowski's Theory 48 --
4.3 Smoluchowski Theory Continued 52 --
4.4 Einstein's Theory 54 --
4.5 Diffusion Coefficient and Friction Constant 57 --
4.6 The Langevin Theory 59 --
5 Stochastic Differential Equations and Integrals 62 --
5.1 The Langevin Equation Revisited 62 --
5.2 Stochastic Differential Equations 64 --
5.3 Which Rule Should Be Used? 67 --
5.4 Some Examples 69 --
6 Functional Integrals 71 --
6.1 Functional Integrals 71 --
6.2 The Wiener Integral 72 --
6.3 Wiener Measure 74 --
6.4 The Feynman-Kac Formula 76 --
6.5 Feynman Path Integrals 78 --
6.6 Evaluation of Wiener Integrals 79 --
6.7 Applications of Functional Integrals 82 --
7 Some Important Special Cases 83 --
7.1 Several Cases of Interest 83 --
7.2 The Free Particle 83 --
7.3 The Distribution of Displacements 85 --
7.4 The Harmonically Bound Particle 87 --
7.5 A Particle in a Constant Force Field 92 --
7.6 The Uniaxial Rotor 93 --
7.7 An Equation for the Distribution of Displacements 94 --
8 The Smoluchowski Equation 97 --
8.1 The Kramers-Klein Equation 97 --
8.2 The Smoluchowski Equation 98 --
8.3 Elimination of Fast Variables 101 --
8.4 The Smoluchowski Equation Continued 104 --
8.5 Passage over Potential Barriers 105 --
9 Random Walk 111 --
9.1 The Random Walk 111 --
9.2 The One-Dimensional Pearson Walk 112 --
9.3 The Biased Random Walk 114 --
9.4 The Persistent Walk 117 --
9.5 Boundaries and First Passage Times 120 --
9.6 Random Remarks on Random Walks 125 --
10 Statistical Mechanics 127 --
10.1 Molecular Distribution Functions 127 --
10.2 The Liouville Equation 129 --
10.3 Projection Operators --
The Zwanzig Equation 131 --
10.4 Projection Operators --
The Mori Equation 133 --
11 Stochastic Equations from a Statistical Mechanical Viewpoint 138 --
11.1 The Langevin Equation A Heuristic View 138 --
11.2 The Fokker-Planck Equation --
A Heuristic View 141 --
11.3 What is Wrong with these Derivations? 144 --
11.4 Eliminating Fast Processes 146 --
11.5 The Distribution Function 153 --
12 Two Exactly Treatable Models 159 --
12.1 Two Illustrative Examples 159 --
12.2 Brownian Motion in a Dilute Gas 159 --
12.4 The Particle Bound to a Lattice 163 --
12.5 The One-Dimensional Case 167 --
13 Brownian Motion and Noise 170 --
13.1 Limits on Measurement 170 --
13.2 Oscillations of a Fiber 171 --
13.3 A Pneumatic Example 174 --
13.4 Electrical Systems 178 --
14 Diffusion Phenomena 183 --
14.1 Brownian Motion in Configuration Space 183 --
14.2 Diffusion Controlled Reactions 183 --
14.3 The Effect of Forces 187 --
14.4 The Coagulation of Colloids 191 --
14.5 Taylor Diffusion 192 --
15 Rotational Diffusion 197 --
15.1 Rotational Diffusion 197 --
15.2 Fluorescence Depolarization 201 --
15.3 Non-Spherical Brownian Particles 204 --
16 Polymer Solutions 208 --
16.1 A Model for Dilute Solutions of Polymers 208 --
16.2 Hydrodynamic Interaction 210 --
16.3 The Equation of Motion 212 --
16.4 Diffusion and Intrinsic Viscosity 214 --
16.5 Historical Remarks and Additional Reading 219 --
17 Interacting Brownian Particles 222 --
17.1 Effects of Concentration 222 --
17.2 The Fokker-Planck Equation 223 --
17.3 The Multiparticle Smoluchowski Equation 226 --
17.4 The Diffusion Coefficient 228 --
17.5 The Viscosity 235 --
18 Dynamics, Fractals, and Chaos 240 --
18.1 Brownian Dynamics 240 --
18.2 Brownian Paths as Fractals 246 --
18.3 Brownian Motion and Chaos 251 --
A The Applicability of Stokes' Law 258 --
B Functional Calculus 260 --
C An Operator Identity 263 --
D Euler Angles 264 --
E The Oseen Tensor 266 --
F Mutual Diffusion and Self-Diffusion 268 --
F.1 Mutual Diffusion 268 --
F.2 Self-Diffusion 269 --
F.3 Relation between D[subscript m] and D[subscript s] 269.
Series Title: Oxford science publications.; International series of monographs on physics, v. 112.
Responsibility: Robert M. Mazo.
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