Diffusion and Reactions in Fractals and Disordered Systems

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Daniel ben-Avraham (Clarkson University, New York) Shlomo Havlin (Bar-Ilan University, Israel)

Diffusion and Reactions in Fractals and Disordered Systems

Daniel ben-Avraham (Clarkson University, New York), Shlomo Havlin (Bar-Ilan University, Israel)

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English

Cambridge University Press
21 March 2005

Physics; States of matter; Materials science; Stress & fracture

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 Lévy 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.

By: Daniel ben-Avraham (Clarkson University New York), Shlomo Havlin (Bar-Ilan University, Israel)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 246mm, Width: 188mm, Spine: 23mm
Weight: 590g
ISBN: 9780521617208
ISBN 10: 0521617200
Pages: 332
Publication Date: 21 March 2005
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Reviews for Diffusion and Reactions in Fractals and Disordered Systems

'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