Scaling of Aggregation with Creation

Abstract

A simple aggregation model with creation is presented to study the scaling behavior. The model is an extended version of the coalescing random walker model to take into account creation and the mass-dependent transition probability. The mass s of a particle is created at the rate s^μ (μ <1), moves ahead one step with transition probability T=a+bs^-α (α >0, a, , b>0 and a+b≤ 1), and is stopped with probability 1-T. The aggregation shows an interesting scaling behavior in competition with creation. It is shown that the mean mass ‹ s› of particle scales as ‹ s› ≈ t^β where t is time. The scaling relation β =max, [1/(1+α ), , 1/(1-μ )] is found for a=0.0. For a>0, the scaling relation β =max, [1/2, , 1/(1+α ), , 1/(1-μ )] is satisfied. The scaling relation is consistent with that derived from a simple scaling argument.