Related papers: Universality in diffusion-controlled nucleation an…
This paper is devoted to the analysis of the uniform null controllability for a family of nonlinear reaction-diffusion systems approximating a parabolic-elliptic system which models the electrical activity of the heart. The uniform, with…
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
The continuum random cluster model is a Gibbs modification of the standard boolean model of intensity $z > 0$ and law of radii $Q$. The formal unormalized density is given by $q^{N_{cc}}$ where $q$ is a fixed parameter and $N_{cc}$ is the…
In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…
The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is…
We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at…
Nucleation, commonly associated with discontinuous transformations between metastable and stable phases, is crucial in fields as diverse as atmospheric science and nanoscale electronics. Traditionally, it is considered a microscopic process…
We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a non-diffusive…
The aggregation of particles in the free molecular regime is determined approximately for situations with a high degree of translational energy equilibration. The mean particle sizes develop linearly in time. Scaling relations are used to…
Nucleation phenomena are ubiquitous in nature and the presence of impurities in every real and experimental system is unavoidable. Yet numerical studies of nucleation are nearly always conducted for entirely pure systems. We have studied…
Using state-of-the-art rare-event sampling simulations, we precisely characterize the nucleation of liquid droplets from a supersaturated Lennard-Jones gas and uncover a key physical feature: critical clusters nucleate with a density that…
In the framework of Gibbs statistical theory, the issue of the distribution of particle sizes forming the statistical system and the moments of this distribution are considered. This task is relevant for a wide variety of applications. The…
The theory of false vacuum decay in a thermal system may have a cross-over from predominantly thermal transitions to quantum transitions as the temperature is decreased. New numerical methods and results are presented here that can be used…
We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a…
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…
We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually…
We consider the behavior of the Gaussian concentration bound (GCB) under stochastic time evolution. More precisely, we consider a Markovian diffusion process on $\mathbb{R}^d$ and start the process from an initial distribution $\mu$ that…
We study the nucleation of crystalline cluster phases in the generalized exponential model with exponent n=4. Due to the finite value of this pair potential for zero separation, at high densities the system forms cluster crystals with…
Nucleation is an out-of-equilibrium process, which can be strongly affected by the presence of external fields. In this letter, we report a simple extension of classical nucleation theory to systems submitted to an homogeneous shear flow.…
For high- pressure nucleation experiments in upward diffusion cloud chamber, there is the great deviation of predictions of classical nucleation theory from experimental results; the discrepancy is more than 10 orders of magnitude of…