Related papers: Fluid limit for the coarsening phase of the conden…
Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a…
We survey our recent articles dealing with one dimensional attractive zero range processes moving under site disorder. We suppose that the underlying random walks are biased to the right and so hyperbolic scaling is expected. Under the…
We consider the evolution of a connected set on the plane carried by a periodic incompressible stochastic flow. While for almost every realization of the random flow at time t most of the particles are at a distance of order sqrt{t} away…
The Zero-Range Process, in which particles hop between sites on a lattice under conserving dynamics, is a prototypical model for studying real-space condensation. Within this model the system is critical only at the transition point. Here…
We study a system of particles in the interval $[0,\epsilon^{-1}] \cap \mathbb Z$, $\epsilon^{-1}$ a positive integer. The particles move as symmetric independent random walks (with reflections at the endpoints); simultaneously new…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
We study condensation in several particle systems related to the inclusion process. For an asymmetric one-dimensional version with closed boundary conditions and drift to the right, we show that all but a finite number of particles condense…
We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its…
Condensation occurs in nonequilibrium steady states when a finite fraction of particles in the system occupies a single lattice site. We study condensation transitions in a one-dimensional zero-range process with a single defect site. The…
Zero-range processes with decreasing jump rates exhibit a condensation transition, where a positive fraction of all particles condenses on a single lattice site when the total density exceeds a critical value. We study the onset of…
It is difficult to derive the solid--fluid transition from microscopic models. We introduce particle systems whose potentials do not decay with distance and calculate their partition function exactly using a method similar to that for…
We derive reduced finite dimensional ODE models starting from one dimensional lubrication equations describing coarsening dynamics of droplets in nanometric polymer film interacting on a hydrophobically coated solid substrate in the…
In this article, we investigate the condensation phenomena for a class of nonreversible zero-range processes on a fixed finite set. By establishing a novel inequality bounding the capacity between two sets, and by developing a robust…
We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites…
We argue that the coarse-grained dynamics of the zero-range process in the condensation regime can be described by an extension of the standard hydrodynamic equation obtained from Eulerian scaling even though the system is not locally…
We establish the zero-diffusion limit for both continuous and discrete aggregation models over convex and bounded domains. Compared with a similar zero-diffusion limit derived in [44], our approach is different and relies on a coupling…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
How finite-sized material lines stretch in chaotic (mono-scale) and turbulent (multi-scale) flows remains a central but unresolved problem that governs mixing, transport and reaction. We show elongation is controlled by a finite-sampling…
We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site $k$ hops to its nearest neighbour with a quenched rate $w(k)$. These rates are chosen randomly from the…
We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at…