Multifractal fluctuations in the dynamics of disordered systems

S. Havlin, A. Bunde, E. Eisenberg, J. Lee, H. E. Roman, S. Schwarzer, H. E. Stanley

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We review recent developments in the study of the multifractal properties of dynamical processes in disordered systems. In particular, we discuss the multifractality of the growth probabilities of DLA clusters and of the probability density for random walks on random fractals. The results for multifractality in DLA are based mainly on numerical studies, while the results for random walks on random fractals are based on analytical results. We find that although a phase transition in the multifractal spectrum occurs for d = 2 DLA, there seems to be no phase transition for d = 3 DLA. This might be explained by the topological differences between d = 2 and d = 3 DLA clusters. For the probability density of random walks on random fractals, it is found that multifractality occurs for a finite range of moments q, qmin < q < qmax. The approach can be applied to other dynamical processes, such as fractons or tracer concentration in stratified media.

Original languageEnglish
Pages (from-to)288-297
Number of pages10
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-4
StatePublished - 15 Mar 1993

Bibliographical note

Funding Information:
We are gratefult o A. Aharony, M. Araujo, A.B. Harris, P. Meakin and S. Russ for discussions,a nd to NSF, ONR and DFG for financial support.


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