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Stochastic Dynamics
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.
Nonlinear Dynamics of Chaotic and Stochastic Systems
We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. W...
Collective Dynamics in Complex Networks of Noisy Phase Oscillators
This work aims to contribute to our understanding of the effects of noise and non-uniform interactions in populations of oscillatory units. In particular, we explore the collective dynamics in various extensions of the Kuramoto model. We develop a theoretical framework to study such noisy systems and we show through many examples that indeed new insights can be gained with our method. The first step is to coarse-grain the complex networks. The oscillatory units are then characterized solely by their individual quantities, so that identical units can be grouped together. The second step consists of the ansatz that in all these groups the distributions of the oscillators' phases follow time-dependent Gaussians. We apply this analytical two-step method to oscillator networks with correlations between coupling strengths and natural frequencies, to populations with mixed positive and negative coupling strengths, and to noise-driven active rotators, which can perform excitable dynamics. We calculate the rich phase diagrams that delineate the emergent rhythms. Extensive numerical simulations are performed to show both the validity and the limitations of our theoretical results.
Stochastic Dynamics Of Reacting Biomolecules
This is a book about the physical processes in reacting complex molecules, particularly biomolecules. In the past decade scientists from different fields such as medicine, biology, chemistry and physics have collected a huge amount of data about the structure, dynamics and functioning of biomolecules. Great progress has been achieved in exploring the structure of complex molecules. However, there is still a lack of understanding of the dynamics and functioning of biological macromolecules. In particular this refers to enzymes, which are the basic molecular machines working in living systems. This book contributes to the exploration of the physical mechanisms of these processes, focusing on critical aspects such as the role of nonlinear excitations and of stochastic effects. An extensive range of original results has been obtained in the last few years by the authors, and these results are presented together with a comprehensive survey of the state of the art in the field.
Stochastic Climate Models
A collection of articles written by mathematicians and physicists, designed to describe the state of the art in climate models with stochastic input. Mathematicians will benefit from a survey of simple models, while physicists will encounter mathematically relevant techniques at work.
Stochastic Processes in Physics, Chemistry, and Biology
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...
Analysis And Control Of Complex Nonlinear Processes In Physics, Chemistry And Biology
Nonlinear dynamics of complex processes is an active research field with large numbers of publications in basic research, and broad applications from diverse fields of science. Nonlinear dynamics as manifested by deterministic and stochastic evolution models of complex behavior has entered statistical physics, physical chemistry, biophysics, geophysics, astrophysics, theoretical ecology, semiconductor physics and -optics, etc. This field of research has induced a new terminology in science connected with new questions, problems, solutions and methods. New scenarios have emerged for spatio-temporal structures in dynamical systems far from equilibrium. Their analysis and possible control are i...
Active Matter and Nonequilibrium Statistical Physics
From molecular motors to bacteria, from crawling cells to large animals, active entities are found at all scales in the biological world. Active matter encompasses systems whose individual constituents irreversibly dissipate energy to exert self-propelling forces on their environment. Over the past twenty years, scientists have managed to engineer synthetic active particles in the lab, paving the way towards smart active materials. This book gathers a pedagogical set of lecture notes that cover topics in nonequilibrium statistical mechanics and active matter. These lecture notes stem from the first summer school on Active Matter delivered at the Les Houches school of Physics. The lectures covered four main research directions: collective behaviours in active-matter systems, passive and active colloidal systems, biophysics and active matter, and nonequilibrium statistical physics—from passive to active.
Physics of Self-Organization and Evolution
This thoroughly updated version of the German authoritative work on self-organization has been completely rewritten by internationally renowned experts and experienced book authors to also include a review of more recent literature. It retains the original enthusiasm and fascination surrounding thermodynamic systems far from equilibrium, synergetics, and the origin of life, representing an easily readable book and tutorial on this exciting field. The book is unique in covering in detail the experimental and theoretical fundamentals of self-organizing systems as well as such selected features as random processes, structural networks and multistable systems, while focusing on the physical and theoretical modeling of natural selection and evolution processes. The authors take examples from physics, chemistry, biology and social systems, and include results hitherto unpublished in English. The result is a one-stop resource relevant for students and scientists in physics or related interdisciplinary fields, including mathematical physics, biophysics, information science and nanotechnology.
Stochastic Dynamics
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.
