Related papers: Diffusion-Limited Aggregation Processes with 3-Par…
We develop a unified approach to the problem of clustering in the three different fields of applications, as indicated in the title the paper. The approach is based on Khintchine's probabilistic method that grew out of the Darwin-Fawler…
We discuss contemporaneous aggregation of independent copies of a triangular array of random-coefficient AR(1) processes with i.i.d. innovations belonging to the domain of attraction of an infinitely divisible law W. The limiting aggregated…
We consider a continuum aggregation model with nonlinear local repulsion given by a degenerate power-law diffusion with general exponent. The steady states and their properties in one dimension are studied both analytically and numerically,…
We consider the homogenisation of a coupled reaction-diffusion process in a porous medium with evolving microstructure. A concentration-dependent reaction rate at the interface of the pores with the solid matrix induces a…
The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are…
Let A(t) denote the cluster produced by internal diffusion limited aggregation (internal DLA) with t particles in dimension d > 2. We show that A(t) is approximately spherical, up to an O(\sqrt{\log t}) error.
Wet granular materials are characterized by a defined bond energy in their particle interaction such that breaking a bond implies an irreversible loss of a fixed amount of energy. Associated with the bond energy is a nonequilibrium…
A large number (~10,000) of uniform stainless steel balls comprising less than one layer coverage on a vertically shaken plate provides a rich system for the study of excited granular media. Viewed from above, the horizontal motion in the…
The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase…
We study the kinetics of diffusion-limited coalescence, A+A->A, and annihilation, A+A->0, in random media consisting of disconnected domains of reaction. Examples include excitons fusion and annihilation in porous matrices and along polymer…
We consider a reaction-diffusion model incorporating the reactions A -> 0, A -> 2A and 2A -> 3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order…
Coupled aggregation and sedimentation processes were studied by means of three dimensional computer simulations. For this purpose, a large prism with no periodic boundary conditions for the sedimentation direction was considered.…
We show that various surface parameters in two-dimensional diffusion limited aggregation (DLA) grow linearly with the number of particles. We find the ratio of the average length of the perimeter and the accessible perimeter of a DLA…
Diffusion-limited aggregation is consistent with simple scaling. However, strong subdominant terms are present, and these can account for various earlier claims of anomalous scaling. We show this in detail for the case of multiscaling.
We study a class of reaction-diffusion model extrapolating continuously between the pure coagulation-diffusion case ($A+A\to A$) and the pure annihilation-diffusion one ($A+A\to\emptyset$) with particles input ($\emptyset\to A$) at a rate…
Neutral grains made of the same dielectric material can attain considerable charges due to collisions and generate long-range interactions. We perform molecular dynamic simulations in three dimensions for a dilute, freely-cooling granular…
We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case…
In this paper, we analyze the scaling behavior of \emph{Diffusion Limited Aggregation} (DLA) simulated by Hastings-Levitov method. We obtain the fractal dimension of the clusters by direct analysis of the geometrical patterns in a good…
We draw an analogy between droplet formation in dilute particle and polymer systems. Our arguments are based on finite-size scaling results from studies of a two-dimensional lattice gas to three-dimensional bead-spring polymers. To set the…
We study diffusion-limited coalescence, A+A<-->A$, in one dimension, and derive an exact solution for the steady state in the presence of a trap. Without the trap, the system arrives at an equilibrium state which satisfies detailed balance,…