Related papers: Condensation-Driven Aggregation in One Dimension
In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…
In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…
We present a simple non-equilibrium model of mass condensation with Lennard-Jones interactions between particles and the substrate. We show that when some number of particles is deposited onto the surface and the system is left to…
Selected theoretical developments in modeling of deposition of submicrometer size (submicron) particles on solid surfaces, with and without surface diffusion, of interest in colloid, polymer, and certain biological systems, are surveyed. We…
We study the large deviations behavior of systems that admit a certain form of a product distribution, which is frequently encountered both in Physics and in various information system models. First, to fix ideas, we demonstrate a simple…
We discuss a cosmological model where the universe shrinks rather than expands during the radiation and matter dominated periods. Instead, the Planck mass and all particle masses grow exponentially, with the size of atoms shrinking…
Diffusion-limited aggregation (DLA) assumes that particles perform pure random walk at a finite temperature and aggregate when they come close enough and stick together. Although it is well known that DLA in two dimensions results in a…
We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random…
A microscopic model of the effect of unbinding in diffusion limited aggregation based on a cellular automata approach is presented. The geometry resembles electrochemical deposition - ``ions'' diffuse at random from the top of a container…
We prove the following results. (i) One-dimensional Bose gases which interact via unscaled integrable pair interactions and are confined in an external potential increasing faster than quadratically undergo a complete generalized…
We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass…
Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the…
We consider a constrained version of the HL$(0)$ Hastings--Levitov model of aggregation in the complex plane, in which particles can only attach to the part of the cluster that has already been grown. Although one might expect that this…
We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as…
Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring,…
We study mass fluxes in aggregation models where mass transfer to large scales by aggregation occurs alongside desorption or fragmentation. Two models are considered. (1) A system of diffusing, aggregating particles with influx and outflux…
We study domain growth properties of two species of particles executing biased diffusion on a half-filled square lattice, consisting of just two lanes. Driven in opposite directions by an external ``electric'' field, the particles form…
We introduce a lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics. This model roughly corresponds to placing the irreversible…
We study classical particles on the sites of an open chain which diffuse, coagulate and decoagulate preferentially in one direction. The master equation is expressed in terms of a spin one-half Hamiltonian $H$ and the model is shown to be…
We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the Coordinate Bethe Ansatz. The chosen deformation of the…