Abstract
Statistical properties of random transport models defined on discrete space-time are investigated both numerically and analytically. As an extreme limit we first consider aggregation limit of massive particles. With the presence of permanent injection we have a nontrivial steady state where the mass distribution follows a power law. It is shown that the steady state is universal and very robust. Next, we analyze the cases of imperfect aggregation that a finite portion is transported at a time. We have a Gaussian fluctuation governed by the ordinary diffusion equation in the nonaggregation limit, while the system converges to the power law steady state in the aggregation limit even without injection. In the intermediate cases the fluctuations are always between Gaussian and the power law. Underlying relations to the exponential-like distributions in fluid turbulence are also discussed.
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