Diffusion and reactions in fractals and disordered systems

著者

書誌事項

Diffusion and reactions in fractals and disordered systems

Daniel ben-Avraham and Shlomo Havlin

Cambridge University Press, 2004

  • : pbk

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注記

"First published 2000. First paperback edition 2004" -- T.p. verso

"Paperback Re-issue" -- Back cover

Includes bibliographical references and index

内容説明・目次

内容説明

Fractal structures are found everywhere in nature, and as a consequence anomalous diffusion has far reaching implications in a host of phenomena. This book describes diffusion and transport in disordered media such as fractals, porous rocks and random resistor networks. Divided into four Parts, Part I contains material of general interest to statistical physics: fractals, percolation theory, regular random walks and diffusion, continuous time random walks and Levy walks and flights. Part II covers anomalous diffusion in fractals and disordered media, while Part III serves as an introduction to the kinetics of diffusion-limited reactions. Part IV discusses the problem of diffusion-limited coalescence in one dimension. This book will be of particular interest to researchers requiring a clear introduction to the field. It will also be of interest to graduate students studying in areas of physics, chemistry, and engineering.

目次

  • Preface
  • Part I. Basic Concepts: 1. Fractals
  • 2. Percolation
  • 3. Random walks and diffusion
  • 4. Beyond random walks
  • Part II. Anomalous Diffusion: 5. Diffusion in the Sierpinski gasket
  • 6. Diffusion in percolation clusters
  • 7. Diffusion in loopless structures
  • 8. Disordered transition rates
  • 9. Biased anomalous diffusion
  • 10. Excluded-volume interactions
  • Part III. Diffusion-Limited Reactions: 11. Classical models of reactions
  • 12. Trapping
  • 13. Simple reaction models
  • 14. Reaction-diffusion fronts
  • Part IV. Diffusion-Limited Coalescence: An Exactly Solvable Model: 15. Coalescence and the IPDF method
  • 16. Irreversible coalescence
  • 17. Reversible coalescence
  • 18. Complete representations of coalescence
  • 19. Finite reaction rates
  • Appendix A. Fractal dimension
  • Appendix B. Number of distinct sites visited by random walks
  • Appendix C. Exact enumeration
  • Appendix D. Long-range correlations
  • References
  • Index.

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