Related papers: Stochastic self-assembly of incommensurate cluster…
We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…
The asymptotic shape of randomly growing radial clusters is studied. We pose the problem in terms of the dynamics of stochastic partial differential equations. We concentrate on the properties of the realizations of the stochastic growth…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
The nucleation and growth of clusters in a progressively cooled vapor is studied. The chemical-potential of the vapor increases, resulting in a rapidly increasing nucleation rate. The growth of the newly created clusters depletes monomers,…
The classical nucleation theory for homogeneous nucleation is formulated as a theory for a density fluctuation in a supersaturated gas at a given temperature. But Molecular Dynamics simulations reveal that it is small cold clusters which…
This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic…
The paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete, and the binary aggregation alone governs the time evolution of the systems. By considering the growth…
The problem of the onset and growth of solid tumour in homogeneous tissue is regarded using an approach based on local interaction between the tumoral and the sane tissue cells. The characteristic sizes and growth rates of spherical…
We introduce an extended Smoluchowski equation describing coagulation processes for which clusters of mass s grow between collisions with $ds/dt=As^\beta$. A physical example, dropwise condensation is provided, and its collision kernel K is…
We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is…
Starting from configurations having homogeneous spatial density, we study kinetics in a two-dimensional system of inelastically colliding hard particles, a popular model for cooling granular matter. Following an initial time period, the…
Two-dimensional cluster-cluster aggregation is studied when clusters move both diffusively and sediment with a size dependent velocity. Sedimentation breaks the rotational symmetry and the ensuing clusters are not self-similar fractals: the…
We present stochastic homogenization results for viscous Hamilton-Jacobi equations using a new argument which is based only on the subadditive structure of maximal subsolutions (solutions of the "metric problem"). This permits us to give…
We investigate an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters. We assume that each cluster is composed of identical units (monomers) and we allow mass to be lost, gained or…
The homogeneous Boltzmann equation for inelastic Maxwell mixtures is considered to study the dynamics of tracer particles or impurities (solvent) immersed in a uniform granular gas (solute). The analysis is based on exact results derived…
The formation history of rich clusters is investigated using a hybrid N-body simulation in which high spatial and mass resolution can be achieved self-consistently within a small region of a very large volume. The evolution of three massive…
We study a stochastic model of urban growth generating spatial distributions of population densities at an intermediate mesoscopic scale. The model is based on the antagonist interplay between the two opposite abstract processes of…
Brownian particles that are replicated and annihilated at equal rate have strongly correlated positions, forming a few compact clusters separated by large gaps. We characterize the distribution of the particles at a given time, using a…