Quasicontinuum variants of diffusion-limited aggregation

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Abstract
Two diffusive-growth models with an indefinite range of local densities are studied, and their fractal scaling properties are compared with those of diffusion-limited aggregation (DLA). The first model, ‘‘penetrable DLA,’’ differs from standard DLA in that each diffusing particle interacts arbitrarily weakly with an aggregated particle. We derive an analytic expression for the growth rates and find by simulation that the weak interaction leaves the DLA scaling properties unmodified. We explain the observed dependence of the density on the interaction strength. Our second model is a stochastic differential equation, without discrete particles. Simulations of this equation show fractal scaling properties consistent with those of DLA. The scaling of this model shows new subtleties; the average density and the spatial correlations are controlled by different exponents. We describe the reasons for this novel behavior.