title: Double power-law in aggregation-chipping processes.
abstract: Temporal evolution of a distribution function P(X,t) for X clusters is analyzed in aggregation-chipping processes, which is a model incorporating simultaneously aggregation and the chipping off of a monomeric unit from a randomly chosen aggregate. Numerical simulations show that P(1,t) exhibits the singular time dependence P(1,t)-P(1,infinity) proportional, t(-2)3 . Using this time dependence, we find a notable double power-law distribution of P(X,t) with universal exponents -5/2 and -3/2 at a sufficiently large t . In finite systems, clusters in the second power law with the exponent -3/2 eventually coagulate into one "monopolized" cluster. These analyses are in good agreement with the results of the simulation.
authors.affiliation: Division of Science, International College of Arts and Science, Yokohama City University, 22-2, Seto, Kanazawa-ku, Yokohama, Japan. hirobrd@abox.so-net.ne.jp
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Yamamoto
authors.forename: Toshiya
authors.initials: T
authors.lastname: Ohtsuki
authors.forename: Akihiro
authors.initials: A
authors.lastname: Fujihara