Reactions in and on fractal media

Abstract
This article deals with bimolecular chemical reactions. Whereas the dynamics under well-stirred conditions is readily described by ordinary differential equations, to account for geometrical or energetic restrictions is a much harder task. In the framework of random walks we discuss some modern approaches of treating different disorder aspects. We focus on fractals, which provide a good picture for spatial randomness, and on ultrametric spaces, which mimic energetic disorder. Furthermore, differences in waiting times can be incorporated in the general formalism in terms of continuous-time random walks. The study of the survival probability of the chemical species leads to rich temporal behaviours, as for instance to stretched exponential or to algebraic decay patterns. We point out the importance of the mean number of distinct lattice points visited in time t, and give a derivation of this quantity for regularly multifurcating ultrametric spaces.

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