Diffusion and Reactions in Fractals and Disordered Systems

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Januar 2005



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.


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.


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 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.


'This book explains how fractals and scaling relationships are useful in understanding anomalous diffusion in disordered media. Definitions and explanations are clear and concise. There is a careful balance between text, equations and pictures. This is a well organised book. Illustrations are especially appealing and free from unnecessary elaboration. My guess is that its pedagogical and challenging style will indeed inspire many students to tackle problems with increased confidence.' Eric Dickinson, Chemistry in Britain '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.' Zentralblatt MATH
EAN: 9780521617208
ISBN: 0521617200
Untertitel: 100 b/w illus. 128 exercises. Sprache: Englisch.
Verlag: Cambridge University Press
Erscheinungsdatum: Januar 2005
Seitenanzahl: 332 Seiten
Format: kartoniert
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