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.
Includes supplementary material: sn.pub/extrasKlappentext
The theory of stochastic processes provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. Noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for as yet open problems (information transmission in the nervous system and information processing in the brain, processes at the cell level, enzymatic reactions, etc.), or pave the way to novel technological applications. Noise can play a prominent role in structure formation in physics, chemistry and biology, e.g. current filaments in semiconductors, catalytic reactions on surfaces, complex dynamics of the heart, brain, or of ecosystems. The book reviews those aspects of applied stochastics addressing researchers as well as students.Inhalt
Stochastic Transport and Brownian Motion.- Directed Current Without Dissipation: Reincarnation of a MaxwellLoschmidt Demon.- Molecular Motors and Stochastic Models.- Nonlinearly Coupled Chemical Reactions.- Thermodynamics of Isothermal Brownian Motors.- Rocking Ratchets at High Frequencies.- Defect Dragging in Periodic Structures.- Conduction in an Inhomogeneous Medium.- Theory and Control of Multiple Hopping in Activated Surface Diffusion.- Brownian Motion in a d-Dimensional Space with Fluctuating Friction.- Active Motion of Brownian Particles.- Diffusion in Granular Gases of Viscoelastic Particles.- Stochastic Resonance and Phase Synchronization.- Scaling of Noise and Constructive Aspects of Fluctuations.- Stochastic Resonances in Underdamped Bistable Systems.- Stochastic Resonance in a System of Coupled Asymmetric Resonators.- Optimizing Information Transmission in Model Neuronal Ensembles: The Role of Internal Noise.- Stochastic Resonance with Images and Spatially Correlated Stochastic Patterns.- Adiabatic and Non-adiabatic Resonances in Excitable Systems.- The Lighthouse Model of a Neural Net with Delay.- Noise-enhanced Phase Coherence in Ensembles of Stochastic Resonators.- Estimation of Synchronization from Noisy Data with Application to Human Brain Activity.- Nonequilibrium Thermodynamics and Dynamical Complexity.- Noise-Induced Phase Transitions and Reactive Processes.- Noise-Induced Order in Extended Systems: A Tutorial.- Linear Instability Mechanisms of Noise-Induced Phase Transitions.- Parametric Resonance Revisited.- On Noise-Induced Transitions in Nonlinear Oscillators.- The Kramers Oscillator Revisited.- Reactive Processes in Low Dimensions: Statistical and Dynamical Aspects.- On-Off Intermittency and Stochastic Stability in Nematics Driven by Multiplicative Noise.- Effect of Boundary Condition Fluctuations on Smoluchowski Reaction Rates.- Experimental Studies of NoiseInduced Phenomena in a Tunnel Diode.- Quantum Mechanical Model of Proton Transfer in a Fluctuating Potential Field of the Active Site of ?-Chymotrypsin.- Large Fluctuations and Noise in Chaotic Systems.- A Gentle Introduction to the Integration of Stochastic Differential Equations.- Controlling Large Fluctuations: Theory and Experiment.- Fluctuational Escape from a Chaotic Attractor.- Problems of a Statistical Ensemble Theory for Systems Far from Equilibrium.- Stochastic Approach to Lyapunov Exponents in Coupled Chaotic Systems.- Peculiarities of Nonhyperbolic Chaos.- Information of Open Systems.- Structure Formation.- Nonlinear Spatiotemporal Patterns in Globally Coupled Reaction-Diffusion Systems.- Segregation Effects in Randomly Mixed Diffusion-Controlled Binary Reactions.- Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia.- Stochastic Field Equation for Amorphous Surface Growth.- Epitaxial Growth with Elastic Interaction: Layer and Cluster Growth.- Stochastic Evolution of a Discrete Line: Numerical Results.- Structures in Planetary Rings Stability and Gravitational Scattering.