Diffusion and Reactions in Fractals and Disordered Systems

This book describes diffusion and transport in disordered media such as fractals and random resistor networks.

Daniel ben-Avraham (Author), Shlomo Havlin (Author)

9780521617208, Cambridge University Press

Paperback, published 20 January 2005

332 pages, 100 b/w illus. 128 exercises
24.6 x 18.8 x 2.3 cm, 0.59 kg

'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

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.

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.

Subject Areas: Stress & fracture [TGMD5], Materials science [TGM], Physics [PH]