Description
Book SynopsisThis book first discusses fractals, percolation theory, regular random walks and diffusion, continuous time random walks and Lévy walks and flights. It then moves on to cover anomalous diffusion in fractals and disordered media, and then introduces the kinetics of diffusion-limited reactions. Finally, it discusses the problem of diffusion-limited coalescence in one dimension.
Trade Review'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
Table of ContentsPreface; 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.
