Scale Invariance and Lack of Self-Averaging in Fragmentation
| dc.creator | Krapivsky, P. L. | |
| dc.creator | Grosse, I. | |
| dc.creator | Ben-Naim, E. | |
| dc.date | 1999-10-19 | |
| dc.date.accessioned | 2026-07-07T03:14:49Z | |
| dc.date.available | 2026-07-07T03:14:49Z | |
| dc.description | We derive exact statistical properties of a class of recursive fragmentation processes. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution in one dimension, P(x) ~ x^{-2p}. In d dimensions, the volume distribution diverges algebraically in the small fragment limit, P(V)\sim V^{-γ} with γ=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. Specifically, the moments Y_α=\sum_i x_i^α exhibit significant fluctuations even in the thermodynamic limit. | |
| dc.description | 4 pages, revtex | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9910281 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9910281 | |
| dc.identifier | Phys. Rev. E 61, R993 (2000) | |
| dc.identifier | doi:10.1103/PhysRevE.61.R993 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/29824 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Scale Invariance and Lack of Self-Averaging in Fragmentation | |
| dc.type | text |