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Author: Jan A. Freund
Publisher: Springer
ISBN: 3540453962
Category : Science
Languages : en
Pages : 512
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Book Description
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.
Author: Jan A. Freund
Publisher: Springer
ISBN: 3540453962
Category : Science
Languages : en
Pages : 512
Get Book Here
Book Description
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.
Author: N.G. Van Kampen
Publisher: Elsevier
ISBN: 0080571387
Category : Science
Languages : en
Pages : 482
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Book Description
This new edition of Van Kampen's standard work has been completely revised and updated. Three major changes have also been made. The Langevin equation receives more attention in a separate chapter in which non-Gaussian and colored noise are introduced. Another additional chapter contains old and new material on first-passage times and related subjects which lay the foundation for the chapter on unstable systems. Finally a completely new chapter has been written on the quantum mechanical foundations of noise. The references have also been expanded and updated.
Author: Kurt Jacobs
Publisher: Cambridge University Press
ISBN: 1139486799
Category : Science
Languages : en
Pages : 203
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Book Description
Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.
Author: Peter Schuster
Publisher: Springer
ISBN: 3319395025
Category : Science
Languages : en
Pages : 728
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Book Description
This book has developed over the past fifteen years from a modern course on stochastic chemical kinetics for graduate students in physics, chemistry and biology. The first part presents a systematic collection of the mathematical background material needed to understand probability, statistics, and stochastic processes as a prerequisite for the increasingly challenging practical applications in chemistry and the life sciences examined in the second part. Recent advances in the development of new techniques and in the resolution of conventional experiments at nano-scales have been tremendous: today molecular spectroscopy can provide insights into processes down to scales at which current theories at the interface of physics, chemistry and the life sciences cannot be successful without a firm grasp of randomness and its sources. Routinely measured data is now sufficiently accurate to allow the direct recording of fluctuations. As a result, the sampling of data and the modeling of relevant processes are doomed to produce artifacts in interpretation unless the observer has a solid background in the mathematics of limited reproducibility. The material covered is presented in a modular approach, allowing more advanced sections to be skipped if the reader is primarily interested in applications. At the same time, most derivations of analytical solutions for the selected examples are provided in full length to guide more advanced readers in their attempts to derive solutions on their own. The book employs uniform notation throughout, and a glossary has been added to define the most important notions discussed.
Author: Zeev Schuss
Publisher: Springer Science & Business Media
ISBN: 1441916059
Category : Mathematics
Languages : en
Pages : 486
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Book Description
Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.
Author: W. Horsthemke
Publisher: Springer Science & Business Media
ISBN: 3540368523
Category : Science
Languages : en
Pages : 322
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Book Description
The study of phase transitions is among the most fascinating fields in physics. Originally limited to transition phenomena in equilibrium systems, this field has outgrown its classical confines during the last two decades. The behavior of far from equilibrium systems has received more and more attention and has been an extremely active and productive subject of research for physicists, chemists and biologists. Their studies have brought about a more unified vision of the laws which govern self-organization processes of physico-chemical and biological sys tems. A major achievement has been the extension of the notion of phase transi tion to instabilities which occur only in open nonlinear systems. The notion of phase transition has been proven fruitful in apphcation to nonequilibrium ins- bihties known for about eight decades, like certain hydrodynamic instabilities, as well as in the case of the more recently discovered instabilities in quantum optical systems such as the laser, in chemical systems such as the Belousov-Zhabotinskii reaction and in biological systems. Even outside the realm of natural sciences, this notion is now used in economics and sociology. In this monograph we show that the notion of phase transition can be extend ed even further. It apphes also to a new class of transition phenomena which occur only in nonequilibrium systems subjected to a randomly fluctuating en vironment.
Author: Grigorios A. Pavliotis
Publisher: Springer
ISBN: 1493913239
Category : Mathematics
Languages : en
Pages : 345
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Book Description
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
Author: Hong Qian
Publisher: Springer Nature
ISBN: 3030862526
Category : Mathematics
Languages : en
Pages : 364
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Book Description
This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.
Author: Radek Erban
Publisher: Cambridge University Press
ISBN: 1108572995
Category : Mathematics
Languages : en
Pages : 322
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Book Description
This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.
Author: Guo-qiang Cai
Publisher: World Scientific Publishing Company
ISBN: 9814723347
Category : Technology & Engineering
Languages : en
Pages : 552
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Book Description
Stochastic dynamics has been a subject of interest since the early 20th Century. Since then, much progress has been made in this field of study, and many modern applications for it have been found in fields such as physics, chemistry, biology, ecology, economy, finance, and many branches of engineering including Mechanical, Ocean, Civil, Bio, and Earthquake Engineering.Elements of Stochastic Dynamics aims to meet the growing need to understand and master the subject by introducing fundamentals to researchers who want to explore stochastic dynamics in their fields and serving as a textbook for graduate students in various areas involving stochastic uncertainties. All topics within are presented from an application approach, and may thus be more appealing to users without a background in pure Mathematics. The book describes the basic concepts and theories of random variables and stochastic processes in detail; provides various solution procedures for systems subjected to stochastic excitations; introduces stochastic stability and bifurcation; and explores failures of stochastic systems. The book also incorporates some latest research results in modeling stochastic processes; in reducing the system degrees of freedom; and in solving nonlinear problems. The book also provides numerical simulation procedures of widely-used random variables and stochastic processes.A large number of exercise problems are included in the book to aid the understanding of the concepts and theories, and may be used for as course homework.
