SCALING BEHAVIOR IN EXTENDED COALESCING RANDOM WALKER MODEL

A simple aggregation model on one-dimensional lattice is presented to study the scaling behaviour. The model is an extended version of the coalescing random walker model to take into account the dependence of transition probability upon mass s of particle. A particle moves ahead one step with transition probability T and is stopped with probability 1 - T where T = a + bs(-alpha) (alpha > 0, a, b greater-than-or-equal-to 0 and a + b less-than-or-equal-to 1). It is shown that the mean mass [s] of particle scales as [s] almost-equal-to t(beta) where t is time. The scaling relation beta = 1/(1 + alpha) is satisfied for a = 0.0. For a > 0, the scaling relation beta = max[0.5, 1/(1 + alpha)] is satisfied. We discuss the relation between our model and the extended KPZ equation.