Kinetic growth transition in a simple aggregation of charged particles with injection

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Abstract
The simple aggregation model of charged particles introduced by Takayasu (1990) is explored using computer simulations. In the Takayasu model, positive or negative charges are randomly injected at a constant fraction p (p:the fraction of positive charges) and each cluster having a positive or negative charge is conserved when two particles collide. The author finds a kinetic growth transition between cluster growth of positive charges and that of negative charges at the critical concentration pc=0.5. For p>pc (or pc), the cluster size distribution of a positive charge (or a negative charge) shows the dynamic scaling nS(t) approximately=S- tau f(S/tz) with the same exponents ( tau =4/3 and z=3/2) as the Scheidegger river model at longer timescales than the correlation time tc where nS(t) indicates the cluster distribution with a positive charge S (or a negative charge S for pc).

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