MULTIFRACTALITY AND THE SHATTERING TRANSITION IN FRAGMENTATION PROCESSES

We consider two simple geometric models that can describe the kinetics of fragmentation of two-dimensional particles and stochastic fractals . We find a hierarchy of independent exponents suggesting the existenc e of multiple-phase boundary for the shattering transition when two or thogonal cracks are placed randomly on a fragment (model A). At the sa me time we find a unique exponent suggesting a single phase boundary w hen four equal-sized fragments are produced at each fragmentation even t (model B). We invoke the multifractal formalism to further support t he existence of multiple phase boundaries. In model A, for each choice of homogeneity index, the resultant fragments' distribution exhibits multifractality on a unique support when describing fragmentation proc esses and on one of infinitely many possible supports when describing stochastic fractals. Model B obeys simple scaling and produces self-si milar fractals when fragments are removed from the system at each time step.