Scaling and Multiscaling in Models of Fragmentation

We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For d>1, the volume of the fragments is characterized by a single scale 1/t, while other geometric properties such as the length are characterized by an infinite number of length scales and thus exhibit multiscaling.

P. L. Krapivsky, E. Ben-Naim · 1994