Diffusion and reactions in fractals and disordered systems

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. 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 a valuable source 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

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On Order

Summary

Summary

Table of Contents