Related papers: A model of individual clustering with vanishing di…

We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry.…

We study a one-dimensional spatial population model where the population sizes at each site are chosen according to a translation invariant and ergodic distribution and are uniformly bounded away from 0 and infinity. We suppose that the…

We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…

We are interested in the long-time behavior of a diploid population with sexual reproduction, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with…

A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk…

We introduce a traffic flow model that incorporates clustering and passing. We obtain analytically the steady state characteristics of the flow from a Boltzmann-like equation. A single dimensionless parameter, R=c_0v_0t_0 with c_0 the…

We examine a family of microscopic models of plasmas, with a parameter $\alpha$ comparing the typical distance between collisions to the strength of the grazing collisions. These microscopic models converge in distribution, in the weak…

We prove that multidimensional diffusions in random environment have a limiting velocity which takes at most two different values. Further, in the two-dimensional case we show that for any direction, the probability to escape to infinity in…

We consider a two-species simple exclusion process on a periodic lattice. We use the method of matched asymptotics to derive evolution equations for the two population densities in the dilute regime, namely a cross-diffusion system of…

An integro-differential equation on a tree graph is used to model the evolution and spatial distribution of a population of organisms in a river network. Individual organisms become mobile at a constant rate, and disperse according to an…

We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…

One-dimensional reaction-diffusion models A+A -> 0, A+A -> A, and $A+B -> 0, where in the latter case like particles coagulate on encounters and move as clusters, are solved exactly with anisotropic hopping rates and assuming synchronous…

We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes random and assortative mating of individuals. By increasing the number of individuals to infinity we obtain a nonlinear transport…

We propose a model to describe an evolution of a bubble cluster with rupture. In a special case, the equation is reduced to a single parabolic equation with evaporation for the thickness of a liquid layer covering bubbles. We postulate that…

The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time…

In this two--part study, we present the development and analysis of a stochastic theory for characterizing the relative positions of monodisperse, low-inertia particle pairs that are settling rapidly in homogeneous isotropic turbulence. In…

Starting from an age-structured diffusive population growth law for single species in a discrete and periodic habitat, we formulate a stage structured population model with spatially periodic dispersal, mortality and recruitment. With a KPP…

We show that in a hierarchical clustering model the low-order statistics of the density and the peculiar velocity fields can all be modelled semianalytically for a given cosmology and an initial density perturbation power spectrum $P(k)$.…

Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A…

This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…