Aggregates with biased random walks on a square lattice.

Abstract

Irreversible stochastic models for the growth of clusters on a square lattice are formulated and studied by Monte Carlo simulation in which diffusing particles are biased globally and locally. In the case of global bias, the preferred directions of incoming particles are diagonal. Contrary to the biased walks on continuum space, the lattice anisotropy is enhanced and results in diagonally elongated clusters. With the local biased walk controlled by a parametric \ensuremath{\zeta}, it seems that there is a crossover length L(\ensuremath{\zeta}). For the region rL(\ensuremath{\zeta}), the cluster is more or less compact while for the region r>L(\ensuremath{\zeta}) the shape of the clusters becomes similar to that of the ordinary diffusion-limited aggregation. The comparison of clusters of our model is made with those of the model considered recently by Meakin, Feder, and Jo/ssang [Phys. Rev. A 43, 1952 (1991)].