Dynamics of fractal dimension during phase ordering of a geometrical multifractal

Avner Peleg, Baruch Meerson
2000 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
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 t=0 represents a non-uniform recursive fractal set, and that this set is a geometrical multifractal characterized by a f(α)-curve. It is assumed that the droplets shrink according to their size and preserving their ordering. It is shown that at early times
more » ... Hausdorff dimension does not change with time, whereas at late times its dynamics follow the f(α) 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.
doi:10.1103/physreve.62.1764 pmid:11088637 fatcat:lie47gvdvje5tps2jhiv5pmgki