Related papers: On One-dimensional Multi-Particle Diffusion Limite…
In this article a multilayer parking system with screening of size n=3 is studied with a focus on the time-dependent particle density. We prove that the asymptotic limit of the particle density increases from an average density of 1/3 on…
We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the…
In bidisperse particle mixtures varying in size or density alone, large particles rise (driven by percolation) and heavy particles sink (driven by buoyancy). When the two particle species differ from each other in both size and density, the…
We examine the validity of the hypothesis of self-similarity in systems coarsening under the driving force of interface energy reduction in which three dimensional particles are intersected by a one or two dimensional diffusion matrix. In…
In this paper we look at the properties of limits of a sequence of real valued time inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions then the limit does not have to be a diffusion. However,…
We settle a conjecture by Bik and Marigliano stating that the degree of a one-dimensional discrete model with rational maximum likelihood estimator is bounded above by a linear function in the size of its support, therefore showing that…
We revisit the diffusive instability in dusty disks that arises when the dust mass diffusivity and/or viscosity decreases sufficiently steeply with increasing dust density. Our updated model includes an incompressible, viscous gas that…
The Large Deviations Principle (LDP) is verified for a homogeneous diffusion process with respect to a Brownian motion $B_t$, $$ X^\eps_t=x_0+\int_0^tb(X^\eps_s)ds+ \eps\int_0^t\sigma(X^\eps_s)dB_s, $$ where $b(x)$ and $\sigma(x)$ are are…
Diffusion Limited Aggregation (DLA) is a model of fractal growth that was introduced in 1981 and had since attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. Despite…
In this work, we consider a diffusive two-species d-dimensional model and study it in great details. Two types of particles, with hard-core, diffuse symmetrically and cross each other. For arbitrary dimensions, we obtain the exact density,…
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.…
Models of fractal growth commonly consider particles diffusing in a medium and that stick irreversibly to the forming aggregate when making contact for the first time. As shown by the well-known diffusion limited aggregation (DLA) model and…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
We consider incorporation of particle detachment in Smoluchowski model of colloidal growth. Two approaches are considered, utilizing phenomenological rate equation and exact large-time results. Our main conclusion is that the value of the…
We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued…
The recent theoretical prediction by Maimbourg and Kurchan [arXiv:1603.05023] that for regular pair-potential systems the virial potential-energy correlation coefficient increases towards unity as the dimension $d$ goes to infinity is…
The evolution of marginally bound supercluster-like objects in an accelerating LambdaCDM Universe is followed, by means of cosmological simulations, from the present time to an expansion factor a = 100. The objects are identified on the…
We employ the recently introduced conformal iterative construction of Diffusion Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process…
The long-time diffusion of two-dimensional dusty plasmas on a one-dimensional periodic substrate with varied widths is investigated using Langevin dynamical simulations. When the substrate is narrow and the dust particles form a single row,…
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…