Statistical Theory of Diffusion-Limited Growth in Two Dimensions

Statistical Theory of Diffusion-Limited Growth in Two Dimensions

Constrained diffusion-limited aggregation in 3 dimensions

Diffusion Limited Aggregation (DLA) has usually been studied in 2 dimensions as a model of fractal growth processes such as river networks, plant branching, frost on glass, electro-deposition, lightning, mineral deposits, and coral. Here the basic principles are extended into 3 dimensions and used to create, among other things, believable models of root systems. An additional innovation is a me...

Nonequilibrium cluster diffusion during growth and evaporation in two dimensions.

The diffusion of growing or evaporating two-dimensional clusters is investigated. At equilibrium, it is well known that the mean square displacement (MSD) of the cluster center of mass is linear in time. In nonequilibrium conditions, we find that the MSD exhibits a nonlinear time dependence, leading to three regimes: (i) during curvature-driven evaporation, the MSD shows a square-root singulari...

Off-lattice noise reduction and the ultimate scaling of diffusion-limited aggregation in two dimensions.

Off-lattice diffusion-limited aggregation (DLA) clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this also accounts for the apparent "multiscaling" in the DLA mass distribution. We interpret the correction to scaling in terms of r...

Spatial Structure in Low Dimensions for Diffusion Limited Two-particle Reactions

Consider the system of particles on d where particles are of two types, A and B, and execute simple random walks in continuous time. Particles do not interact with their own type, but when a type A particle meets a type B particle, both disappear. Initially, particles are assumed to be distributed according to homogeneous Poisson random fields, with equal intensities for the two types. This sys...