Universal power-law and partial condensation in aggregation-chipping processes

Abstract

The asymptotic behaviour of a distribution function P(X) for X clusters is investigated in aggregation-chipping processes, where aggregation and chipping off of a finite unit of size less than L take place simultaneously. Numerical simulations show that above a certain threshold <X>c of an average cluster size, the system exhibits partial condensation where one condensed cluster coexists with a universal power-law distribution with the exponent -5/2 . The critical value <X>c is calculated and turns out to increase monotonously with L . The z-transform technique is used to analyze the case L=2 in detail. Obtained results agree well with numerical ones. Finally, universality of the asymptotic power law is discussed for general cases. It becomes evident that universality holds as long as the size of chipped off unit is finite.