Diffusion and Reactions in Fractals and Disordered Systems

Daniel ben-Avraham, Clarkson University,New York,U.S.A.
Shlomo Havlin, Bar Ilan University, Ramat Gan, Israel

Cambridge University Press, 2000

Fractal structures are found everywhere in nature, and as a consequence anomalous diffusion has far-reaching implications for a host of phenomena. This book describes diffusion and transport in disordered media such as fractals, porous rocks, and random resistor networks.
Part one 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 two covers anomalous diffusion in fractals and disordered media,while
Part three serves as an introduction to the kinetics of diffusion-limited reactions.
Part four discusses the problem of diffusion-limited coalescence in one dimension.
This book, written in a pedagogical style,is intended for upper-level undergraduates and graduate students studying physics, chemistry, and engineering. It also will be of particular interest to young researchers requiring a clear introduction to the field.

Contents:

Part one:Basic concepts
1.Fractals
2.Percolation
3.Random walks and diffusion
4.Beyond random walks

Part two: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 three:Diffusion-limited reactions
11.Classical models of reactions
12.Trapping
13.Simple reaction models
14.Reaction-diffusion fronts

Part four: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 The fractal dimension
Appendix B The number of distinct sites visited by random walks
Appendix C Exact enumeration
Appendix D Long-range correlations