TY - JOUR
T1 - Multifractal fluctuations in the dynamics of disordered systems
AU - Havlin, S.
AU - Bunde, A.
AU - Eisenberg, E.
AU - Lee, J.
AU - Roman, H. E.
AU - Schwarzer, S.
AU - Stanley, H. E.
N1 - 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.
PY - 1993/3/15
Y1 - 1993/3/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=43949171007&partnerID=8YFLogxK
U2 - 10.1016/0378-4371(93)90361-7
DO - 10.1016/0378-4371(93)90361-7
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AN - SCOPUS:43949171007
SN - 0378-4371
VL - 194
SP - 288
EP - 297
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 1-4
ER -