Diffusion and Reactions in Fractals and Disordered Systems |

##### Daniel ben-Avraham, Clarkson University, New York, U.S.A.

and

Shlomo Havlin, Bar Ilan University,
Ramat-Gan, Israel (eds.)

#### Diffusion and Reactions in Fractals and Disordered Systems

(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.Fractals2.Percolation

3.Random walks and diffusion

4.Beyond random walks

#### Part two: Anomalous diffusion

5.Diffusion in the Sierpinski gasket6.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 reactions12.Trapping

13.Simple reaction models

14.Reaction-diffusion fronts

#### Part four: Diffusion-limited coalescence: an exactly solvable model

15.Coalescence and the IPDF method16.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*s