Dynamics of fractal dimension during phase ordering of a geometrical multifractal

Avner Peleg*, Baruch Meerson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


A simple multifractal coarsening model is suggested that can explain the observed dynamical behavior of the fractal dimension in a wide range of coarsening fractal systems. It is assumed that the minority phase (an ensemble of droplets) at [Formula Presented] represents a nonuniform recursive fractal set, and that this set is a geometrical multifractal characterized by an [Formula Presented] curve. It is assumed that the droplets shrink according to their size and preserve their ordering. It is shown that at early times the Hausdorff dimension does not change with time, whereas at late times its dynamics follow the [Formula Presented] curve. This is illustrated by a special case of a two-scale Cantor dust. The results are then generalized to a wider range of coarsening mechanisms.

Original languageAmerican English
Pages (from-to)1764-1768
Number of pages5
JournalPhysical Review E
Issue number2
StatePublished - 2000


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