DISTRIBUTION OF THE NUMBER OF FRAGMENTATIONS IN CONTINUOUS FRAGMENTATION

The continuous fragmentation equation is generalized to include the nu mber of fragmentations as a variable. The fragmentation rate alpha(n,x ) and the probability for the production of progeny size y from parent size x, B-n, (x --> y), are both made dependent on the number n of fr agmentations experienced by the fragment during its history. An interp retation where n is the number of impacts experienced by the fragment is possible by also allowing a single progeny equalling the parent in size. Solutions for the cases where alpha(n) does not depend on x are studied. The theory is adapted to model clustering in fragmentation-ge nerated cellular structures.