Scale invariance and lack of self-averaging in fragmentation
Scale invariance and lack of self-averaging in fragmentation
We derive exact statistical properties of a recursive fragmentation process. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution, P(x) approximately x(-2p), in one dimension. In d dimensions, the volume distribution diverges algebraically in the small fragment limit, P(V) approximately V-gamma, with gamma=2p(1/d). Hence, …