Related papers: Diffusion limited aggregation in the Boolean latti…
We consider first-passage percolation on the $d$ dimensional cubic lattice for $d \geq 2$; that is, we assign independently to each edge $e$ a nonnegative random weight $t_e$ with a common distribution and consider the induced random graph…
Two-dimensional dendritic growth due to solute precipitation was simulated using a phase-field model reported earlier [Z. Xu and P. Meakin, J. Chem. Phys. 129, 014705 (2008)]. It was shown that diffusion-limited precipitation due to the…
In this paper, we introduce the stationary harmonic measure in the upper half plane. By bounding this measure, we are able to define both the discrete and continuous time diffusion limit aggregation (DLA) in the upper half plane with…
The problem of the lattice diffusion of two particles coupled by a contact repulsive interaction is solved by finding analytical expressions of the two-body probability characteristic function. The interaction induces anomalous drift with a…
Single-file diffusion refers to the Brownian motion in narrow channels where particles cannot pass each other. In such processes, the diffusion of a tagged particle is typically normal at short times and becomes subdiffusive at long times.…
We study the relation between stochastic and continuous transport-limited growth models, which generalize conformal-mapping formulations of diffusion-limited aggregation (DLA) and viscous fingering, respectively. We derive a nonlinear…
Deposits of dipolar particles are investigated by means of extensive Monte Carlo simulations. We found that the effect of the interactions is described by an initial, non-universal, scaling regime characterized by orientationally ordered…
We develop the skeleton algorithm to define the number of main branches $N_b$ of diffusion-limited aggregation (DLA) clusters. The skeleton algorithm provides a systematic way to remove dangling side branches of the DLA cluster and has…
We describe a criterion for particles suspended in a randomly moving fluid to aggregate. Aggregation occurs when the expectation value of a random variable is negative. This random variable evolves under a stochastic differential equation.…
We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
The Lorentz gas describes an ensemble of noninteracting point particles in an infinite array of spherical scatterers. In the present paper we consider the case when the scatterer configuration P is a fixed union of (translated) lattices in…
We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of…
In this article, we study a type of a one dimensional percolation model whose basic features include a sequential dropping of particles on a substrate followed by their transport via a pushing mechanism (see [S. N. Majumdar and D. S. Dean,…
We consider a synchronous process of particles moving on the vertices of a graph $G$, introduced by Cooper, McDowell, Radzik, Rivera and Shiraga (2018). Initially, $M$ particles are placed on a vertex of $G$. In subsequent time steps, all…
The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of…
We study a continuous-time branching random walk on the lattice $\mathbb{Z}^{d}$, $d\in \mathbb{N}$, with a single source of branching, that is the lattice point where the birth and death of particles can occur. The random walk is assumed…
We study driven particle systems with excluded volume interactions on a two-lane ladder with periodic boundaries, using Monte Carlo simulation, cluster mean-field theory, and numerical solution of the master equation. Particles in one lane…
We present dla-ideal-solver, a high-performance framework for simulating two-dimensional Diffusion-Limited Aggregation (DLA) using Numba-accelerated Python. By leveraging just-in-time (JIT) compilation, we achieve computational throughput…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…