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Diffusion and Reactions in Fractals and Disordered Systems


  • Date Published: January 2005
  • availability: Available
  • format: Paperback
  • isbn: 9780521617208


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About the Authors
  • 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. 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 a valuable source to graduate students studying in areas of physics, chemistry, and engineering.

    • Excellent review of the field
    • Contains over 100 figures and over 120 exercises with answers
    • Only book currently available that deals with this selection of topics
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    Reviews & endorsements

    "incredibly well-done introduction into the subject matter...takes the reader from the very basic concepts to the most recent developments...tour-de-force...I can wholeheartedly recommend this book to students and to mature scientist alike; it is beautifully written and it contains a wealth of information. Hence, if you cannot but it (price is, however, not unreasonable) then beg, borrow or steal it." CHEMPHYSCHEM 2001

    "invaluable...the best introduction to the field of diffusion-limited reactions...essential for anyone wishing to develop an understanding of anomalous diffusion in disordered medis and to be paeticularly accessible to graduate students and young researchers." amazon.cpm

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    Product details

    • Date Published: January 2005
    • format: Paperback
    • isbn: 9780521617208
    • length: 332 pages
    • dimensions: 246 x 189 x 18 mm
    • weight: 0.6kg
    • contains: 100 b/w illus. 128 exercises
    • availability: Available
  • Table of Contents

    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

  • Authors

    Daniel ben-Avraham, Clarkson University, New York
    Daniel ben–Avraham obtained his Ph.D. in Physics from Bar–Ilan University, Israel in 1985. After a 2 year Post-Doctoral position in the Center of Polymer Studies at the University of Boston, he gained a permanent position at Clarkson University where he is now Professor of Physics. Prof. ben–Avraham has spent time as Visiting Professor at various institutions including Heidelberg University, Bar–Ilan University and the European Center for Molecular Biology. He has published over 80 papers and contributed invited papers to several anthologies.

    Shlomo Havlin, Bar-Ilan University, Israel
    Shlomo Havlin obtained his Ph.D. in 1972 from Bar–Ilan University. He stayed at Bar–Ilan University progressing through the ranks of Research Associate, Lecturer, Senior Lecturer and Associate Professor until in 1984 he became Professor and Chairman of the Department of Physics. He is currently Dean of the Faculty of Exact Sciences. Since 1978 Prof. Havlin has spent time as Visiting Professor at numerous institutions including the University of Edinburgh, the National Institute of Health (NIH) and Boston University. He is currently on the editorial board of 3 journals, author of over 400 papers, editor of 10 books and has given over 40 plenary and invited talks.

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