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Titlebook: Reaction-Transport Systems; Mesoscopic Foundatio Vicenç Méndez,Sergei Fedotov,Werner Horsthemke Book 2010 Springer-Verlag Berlin Heidelberg

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书目名称Reaction-Transport Systems
副标题Mesoscopic Foundatio
编辑Vicenç Méndez,Sergei Fedotov,Werner Horsthemke
视频video
概述Introduces the reader to reaction-diffusion systems beyond the classical Brownian diffusion process.Derives the physically and mathematically correct basic phenomenological equations by examining the
丛书名称Springer Series in Synergetics
图书封面Titlebook: Reaction-Transport Systems; Mesoscopic Foundatio Vicenç Méndez,Sergei Fedotov,Werner Horsthemke Book 2010 Springer-Verlag Berlin Heidelberg
描述.This book is an introduction to the dynamics of reaction-diffusion systems, with a focus on fronts and stationary spatial patterns. Emphasis is on systems that are non-standard in the sense that either the transport is not simply classical diffusion (Brownian motion) or the system is not homogeneous. A important feature is the derivation of the basic phenomenological equations from the mesoscopic system properties...Topics addressed include transport with inertia, described by persistent random walks and hyperbolic reaction-transport equations and transport by anomalous diffusion, in particular subdiffusion, where the mean square displacement grows sublinearly with time. In particular reaction-diffusion systems are studied where the medium is in turn either spatially inhomogeneous, compositionally heterogeneous or spatially discrete...Applications span a vast range of interdisciplinary fields and the systems considered can be as different as human or animal groups migrating under external influences, population ecology and evolution, complex chemical reactions, or networks of biological cells. Several chapters treat these applications in detail..
出版日期Book 2010
关键词anomalous diffusion; biomedical applications; cells; pattern formation; reaction-diffusion systems; react
版次1
doihttps://doi.org/10.1007/978-3-642-11443-4
isbn_softcover978-3-642-26376-7
isbn_ebook978-3-642-11443-4Series ISSN 0172-7389 Series E-ISSN 2198-333X
issn_series 0172-7389
copyrightSpringer-Verlag Berlin Heidelberg 2010
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Reaction Kineticsf ordinary differential equations. Systems may be homogeneous because the system is small enough and transport is efficient enough to eliminate spatial gradients. Or the spatial homogeneity may be imposed from the outside, for example by stirring in chemical reactors. In the following we collect som
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Reactions and Transport: Diffusion, Inertia, and Subdiffusion, particles or individuals can move randomly, undergo velocity jump processes or spatial jump processes [333]. The steps of the random walk can be independent or correlated, unbiased or biased. The probability density function (PDF) for the jump length can decay rapidly or exhibit a heavy tail. Simi
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RandomWalks and Mesoscopic Reaction–Transport Equationsxample of a . reaction–transport equation that can be obtained in the long-time large-scale limit of . equations. Recall that the . approach is based on the idea that one can introduce mean-field equations for the particle density involving a detailed description of the movement of particles on the
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Reaction–Transport Fronts Propagating into Unstable Statesnt the general formalism for the asymptotic analysis of traveling fronts. The method relies on the hyperbolic scaling procedure, the theory of large deviations, and the Hamilton–Jacobi technique. A generic model that describes phenomena of this type is the RD equation (2.3) with appropriate kinetics
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Ecological Applicationsvelocity is a quantity that can be obtained from observational data. In this chapter we review some recent reaction–transport models and compare the theoretical predictions with the observed values for the rate of population invasions.
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