Stochastic Processes in Physics, Chemistry, and Biology

Igor Goychuk, Peter Hänggi (auth.), Jan A. Freund, Thorsten Pöschel (eds.)3540410740, 9783540410744

The theory of stochastic processes originally grew out of efforts to describe Brownian motion quantitatively. Today it provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. The credit for acquiring all the deep insights and powerful methods is due ma- ly to a handful of physicists and mathematicians: Einstein, Smoluchowski, Langevin, Wiener, Stratonovich, etc. Hence it is no surprise that until – cently the bulk of basic and applied stochastic research was devoted to purely mathematical and physical questions. However, in the last decade we have witnessed an enormous growth of results achieved in other sciences – especially chemistry and biology – based on applying methods of stochastic processes. One reason for this stochastics boom may be that the realization that noise plays a constructive rather than the expected deteriorating role has spread to communities beyond physics. Besides their aesthetic appeal these noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for so far open pr- lems (information transmission in the nervous system and information p- cessing in the brain, processes at the cell level, enzymatic reactions, etc.). They may also pave the way to novel technological applications (noise– hanced reaction rates, noise-induced transport and separation on the na- scale, etc.). Key words to be mentioned in this context are stochastic r- onance, Brownian motors or ratchets, and noise-supported phenomena in excitable systems.

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Table of contents :
Directed Current Without Dissipation: Reincarnation of a Maxwell—Loschmidt Demon….Pages 7-20
Molecular Motors and Stochastic Models….Pages 21-31
Nonlinearly Coupled Chemical Reactions….Pages 32-37
Thermodynamics of Isothermal Brownian Motors….Pages 38-49
Rocking Ratchets at High Frequencies….Pages 50-60
Defect Dragging in Periodic Structures….Pages 61-68
Conduction in an Inhomogeneous Medium….Pages 69-74
Theory and Control of Multiple Hopping in Activated Surface Diffusion….Pages 75-84
Brownian Motion in a d -Dimensional Space with Fluctuating Friction….Pages 85-96
Active Motion of Brownian Particles….Pages 97-106
Diffusion in Granular Gases of Viscoelastic Particles….Pages 107-117
Scaling of Noise and Constructive Aspects of Fluctuations….Pages 121-130
Stochastic Resonances in Underdamped Bistable Systems….Pages 131-138
Stochastic Resonance in a System of Coupled Asymmetric Resonators….Pages 139-149
Optimizing Information Transmission in Model Neuronal Ensembles: The Role of Internal Noise….Pages 150-159
Stochastic Resonance with Images and Spatially Correlated Stochastic Patterns….Pages 160-171
Adiabatic and Non-adiabatic Resonances in Excitable Systems….Pages 172-181
The Lighthouse Model of a Neural Net with Delay….Pages 182-189
Noise-enhanced Phase Coherence in Ensembles of Stochastic Resonators….Pages 190-201
Estimation of Synchronization from Noisy Data with Application to Human Brain Activity….Pages 202-211
Nonequilibrium Thermodynamics and Dynamical Complexity….Pages 212-231
Noise-Induced Order in Extended Systems: A Tutorial….Pages 235-246
Linear Instability Mechanisms of Noise-Induced Phase Transitions….Pages 247-256
Parametric Resonance Revisited….Pages 257-267
On Noise-Induced Transitions in Nonlinear Oscillators….Pages 268-279
The Kramers Oscillator Revisited….Pages 280-291
Reactive Processes in Low Dimensions: Statistical and Dynamical Aspects….Pages 292-303
On-Off Intermittency and Stochastic Stability in Nematics Driven by Multiplicative Noise….Pages 304-315
Effect of Boundary Condition Fluctuations on Smoluchowski Reaction Rates….Pages 316-326
Experimental Studies of Noise—Induced Phenomena in a Tunnel Diode….Pages 327-337
Quantum Mechanical Model of Proton Transfer in a Fluctuating Potential Field of the Active Site of α-Chymotrypsin….Pages 338-349
A Gentle Introduction to the Integration of Stochastic Differential Equations….Pages 353-364
Controlling Large Fluctuations: Theory and Experiment….Pages 365-377
Fluctuational Escape from a Chaotic Attractor….Pages 378-389
Problems of a Statistical Ensemble Theory for Systems Far from Equilibrium….Pages 390-399
Stochastic Approach to Lyapunov Exponents in Coupled Chaotic Systems….Pages 400-410
Peculiarities of Nonhyperbolic Chaos….Pages 411-421
Information of Open Systems….Pages 422-433
Nonlinear Spatiotemporal Patterns in Globally Coupled Reaction-Diffusion Systems….Pages 437-451
Segregation Effects in Randomly Mixed Diffusion-Controlled Binary Reactions….Pages 452-462
Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia….Pages 463-472
Stochastic Field Equation for Amorphous Surface Growth….Pages 473-483
Epitaxial Growth with Elastic Interaction: Layer and Cluster Growth….Pages 484-495
Stochastic Evolution of a Discrete Line: Numerical Results….Pages 496-506
Structures in Planetary Rings— Stability and Gravitational Scattering….Pages 507-516