title: Scale invariance and lack of self-averaging in fragmentation
abstract: 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, the entire range of exponents allowed by mass conservation is realized. We demonstrate that this fragmentation process is non-self-averaging as the moments Y(alpha)= summation operator(i)x(alpha)(i) exhibit significant sample to sample fluctuations.
authors.affiliation: Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.initials: PL
authors.lastname: Krapivsky
authors.initials: I
authors.lastname: Grosse
authors.initials: E
authors.lastname: Ben-Naim