Stochastic Dynamics

Nico G. van Kampen (auth.), Lutz Schimansky-Geier, Thorsten Pöschel (eds.)3540628932, 9783540628934

Stochastic Dynamics, born almost 100 years ago with the early explanations of Brownian motion by physicists, is nowadays a quickly expanding field of research within nonequilibrium statistical physics. The present volume provides a survey on the influence of fluctuations in nonlinear dynamics. It addresses specialists, although the intention of this book is to provide teachers and students with a reliable resource for seminar work. In particular, the reader will find many examples illustrating the theory as well as a host of recent findings.

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Table of contents :
Probability in physics….Pages 1-4
From stratonovich calculus to noise-induced phase transitions….Pages 6-14
Generalized langevin equations: A useful tool for the perplexed modeller of nonequilibrium fluctuations?….Pages 15-22
Colored noise in dynamical systems: Some exact solutions….Pages 23-31
On the operator method of variable contraction for stochastic processes….Pages 32-41
Recurrence time statistics in low-dimensional dynamical systems….Pages 42-54
The boltzmann equation for the gas of partly inelastic balls with regard to random interaction forces….Pages 55-66
Ratchets driven by colored gaussian noise….Pages 68-80
A motor protein model and how it relates to stochastic resonance, feynman’s ratchet, and maxwell’s demon….Pages 81-87
A diffusion-limited reaction….Pages 88-100
Stochastic localization in soft anharmonic oscillators….Pages 101-115
Quantum transition state theory for multidimensional dissipative systems….Pages 116-126
Surmounting fluctuating barriers: Basic concepts and results….Pages 127-139
Some problems of cluster dynamics of biological macromolecules….Pages 140-152
Stochastic synchronization….Pages 154-166
Stochastic analysis of limit cycle behavior….Pages 167-178
Symbolic dynamics approach to stochastic processes….Pages 179-192
Stochastic resonance (for beginners)….Pages 193-209
Dynamics of globally coupled noisy oscillators….Pages 210-219
Cluster statistics and traffic on a lattice….Pages 220-231
Phase synchronization in noisy and chaotic oscillators….Pages 232-244
A glauber-dynamics approach to coupled stochastic resonators….Pages 245-258
Stochastic aspects of the force network in a regular granular piling….Pages 260-272
Burgers’ turbulence and dynamical scaling….Pages 273-284
Quantum mechanics simulated by diffusion and branching processes….Pages 285-293
Markov chain models for spatially-distributed reacting systems….Pages 294-305
Macromechanical modeling of the surface flow of granular systems….Pages 306-318
Novel pattern formation in granular matter….Pages 319-333
Self-motion in physico-chemical systems far from thermal equilibrium….Pages 334-345
Synthetic random flows: Generation and applications….Pages 346-357
Active brownian particles: Artificial agents in physics….Pages 358-371
Planetary rings — nonequilibrium systems in space….Pages 372-386