Brownian motion : fluctuations, dynamics, and applications

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Brownian motion : fluctuations, dynamics, and applications / Robert M. Mazo

資料種別:: 図書
出版情報:: Oxford : Clarendon Press, 2002
形態:: xii, 289 p. ; 24 cm
シリーズ名:: The international series of monographs on physics ; 112 <BA00185191>
Oxford science publications <BA00281843>
著者名:: Mazo, Robert M. <DA10051369>
ISBN:: 9780198515678 [0198515677]
書誌ID:: BA56701375

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注記:

Includes bibliographical references (p. 271-284) and index

言語:

英語

目次情報:

Historical Background / 1：

Robert Brown / 1.1：

Between Brown and Einstein / 1.2：

Albert Einstein / 1.3：

Marian von Smoluchowski / 1.4：

Molecular Reality / 1.5：

The Scope of this Book / 1.6：

Probability Theory / 2：

Probability / 2.1：

Conditional Probability and Independence / 2.2：

Random Variables and Probability Distributions / 2.3：

Expectations and Particular Distributions / 2.4：

Characteristic Function; Sums of Random Variables / 2.5：

Conclusion / 2.6：

Stochastic Processes / 3：

Distribution Functions / 3.1：

Classification of Stochastic Processes / 3.3：

The Fokker-Planck Equation / 3.4：

Some Special Processes / 3.5：

Calculus of Stochastic Processes / 3.6：

Fourier Analysis of Random Processes / 3.7：

White Noise / 3.8：

Einstein-Smoluchowski Theory / 3.9：

What is Brownian Motion? / 4.1：

Smoluchowski's Theory / 4.2：

Smoluchowski Theory Continued / 4.3：

Einstein's Theory / 4.4：

Diffusion Coefficient and Friction Constant / 4.5：

The Langevin Theory / 4.6：

Stochastic Differential Equations and Integrals / 5：

The Langevin Equation Revisited / 5.1：

Stochastic Differential Equations / 5.2：

Which Rule Should Be Used? / 5.3：

Some Examples / 5.4：

Functional Integrals / 6：

The Wiener Integral / 6.1：

Wiener Measure / 6.3：

The Feynman-Kac Formula / 6.4：

Feynman Path Integrals / 6.5：

Evaluation of Wiener Integrals / 6.6：

Applications of Functional Integrals / 6.7：

Some Important Special Cases / 7：

Several Cases of Interest / 7.1：

The Free Particle / 7.2：

The Distribution of Displacements / 7.3：

The Harmonically Bound Particle / 7.4：

A Particle in a Constant Force Field / 7.5：

The Uniaxial Rotor / 7.6：

An Equation for the Distribution of Displacements / 7.7：

Discussion / 7.8：

The Smoluchowski Equation / 8：

The Kramers-Klein Equation / 8.1：

Elimination of Fast Variables / 8.2：

The Smoluchowski Equation Continued / 8.4：

Passage over Potential Barriers / 8.5：

Concluding Remarks / 8.6：

Random Walk / 9：

The Random Walk / 9.1：

The One-Dimensional Pearson Walk / 9.2：

The Biased Random Walk / 9.3：

The Persistent Walk / 9.4：

Boundaries and First Passage Times / 9.5：

Random Remarks on Random Walks / 9.6：

Statistical Mechanics / 10：

Molecular Distribution Functions / 10.1：

The Liouville Equation / 10.2：

Projection Operators--The Zwanzig Equation / 10.3：

Projection Operators--The Mori Equation / 10.4：

Stochastic Equations from a Statistical Mechanical Viewpoint / 10.5：

The Langevin Equation A Heuristic View / 11.1：

The Fokker-Planck Equation--A Heuristic View / 11.2：

What is Wrong with these Derivations? / 11.3：

Eliminating Fast Processes / 11.4：

The Distribution Function / 11.5：

Two Exactly Treatable Models / 11.6：

Two Illustrative Examples / 12.1：

Brownian Motion in a Dilute Gas / 12.2：

The Particle Bound to a Lattice / 12.3：

The One-Dimensional Case / 12.5：

Brownian Motion and Noise / 12.6：

Limits on Measurement / 13.1：

Oscillations of a Fiber / 13.2：

A Pneumatic Example / 13.3：

Electrical Systems / 13.4：

Diffusion Phenomena / 13.5：

Brownian Motion in Configuration Space / 14.1：

Diffusion Controlled Reactions / 14.2：

The Effect of Forces / 14.3：

The Coagulation of Colloids / 14.4：

Taylor Diffusion / 14.5：

Rotational Diffusion / 15：

Fluorescence Depolarization / 15.1：

Non-Spherical Brownian Particles / 15.3：

Polymer Solutions / 15.4：

A Model for Dilute Solutions of Polymers / 16.1：

Hydrodynamic Interaction / 16.2：

The Equation of Motion / 16.3：

Diffusion and Intrinsic Viscosity / 16.4：

Historical Remarks and Additional Reading / 16.5：

Interacting Brownian Particles / 17：

Effects of Concentration / 17.1：

The Multiparticle Smoluchowski Equation / 17.2：

The Diffusion Coefficient / 17.4：

The Viscosity / 17.5：

Dynamics, Fractals, and Chaos / 17.6：

Brownian Dynamics / 18.1：

Brownian Paths as Fractals / 18.2：

Brownian Motion and Chaos / 18.3：

The Applicability of Stokes' Law / 18.4：

Functional Calculus / B：

An Operator Identity / C：

Euler Angles / D：

The Oseen Tensor / E：

Mutual Diffusion and Self-Diffusion / F：

Mutual Diffusion / F.1：

Self-Diffusion / F.2：

Relation between D[subscript m] and D[subscript s] / F.3：

References

Index

Historical Background / 1：

Robert Brown / 1.1：

Between Brown and Einstein / 1.2：

Albert Einstein / 1.3：

Marian von Smoluchowski / 1.4：

Molecular Reality / 1.5：

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