Diffusion

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. '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 MATHPreface; 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.