Reaction–Transport Systems

Mesoscopic Foundations, Fronts, and Spatial Instabilities

  • Vicenç Méndez
  • Sergei Fedotov
  • Werner Horsthemke

Part of the Springer Series in Synergetics book series (SSSYN)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. General Concepts

    1. Front Matter
      Pages 1-1
    2. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 3-31
    3. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 33-54
    4. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 55-120
  3. Front Propagation

    1. Front Matter
      Pages 121-121
    2. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 123-153
    3. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 155-181
    4. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 183-208
    5. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 209-244
    6. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 245-266
  4. Spatial Instabilities and Patterns

    1. Front Matter
      Pages 267-267
    2. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 269-286
    3. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 287-331
    4. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 333-344
    5. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 345-364
    6. Vicenç Méndez, Sergei Fedotov, Werner Horsthemke
      Pages 365-420
  5. Back Matter
    Pages 421-456

About this book

Introduction

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.

Keywords

anomalous diffusion biomedical applications cells pattern formation reaction-diffusion systems reactive mixtures transport equations turing instabilities

Authors and affiliations

  • Vicenç Méndez
    • 1
  • Sergei Fedotov
    • 2
  • Werner Horsthemke
    • 3
  1. 1.Dept. de Física Grup de Física EstadísticaUniversitat Autònoma de BarcelonaBellaterra Edifici CcSpain
  2. 2.School of MathematicsUniversity of ManchesterManchesterUK
  3. 3.Department of ChemistrySouthern Methodist UniversityDallasUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-11443-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-642-11442-7
  • Online ISBN 978-3-642-11443-4
  • Series Print ISSN 0172-7389
  • About this book
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