Dynamics of fractal dimension during phase ordering of a geometrical multifractal

A simple multifractal coarsening model is suggested that can explain the ob served dynamical behavior of the fractal dimension in a wide range of coars ening fractal systems. It is assumed that the minority phase (an ensemble o f droplets) at t=0 represents a nonuniform recursive fractal set, and that this set is a geometrical multifractal characterized by an f(alpha) curve. It is assumed that the droplets shrink according to their size and preserve their ordering. It is shown that ar early times the Hausdorff dimension do es not change with time, whereas at late times its dynamics follow the f(al pha) curve. This is illustrated by a special case of a two-scale Canter dus t. The results are then generalized to a wider range of coarsening mechanis ms.