Related papers: Birth, death and diffusion of interacting particle…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the…
We study conditions under which carbon clusters of different sizes form and stabilize. {We describe an approach to equilibrium by simulating tenuous carbon gas dynamics to long times.} First, we use reactive molecular dynamics simulations…
Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening phenomena in a simple driven diffusive system. The model is reminiscent of vehicular traffic on a two-lane ring road. At sufficiently high density,…
Groups of cells, including clusters of cancerous cells, multicellular organisms, and developing organs, may both grow and break apart. What physical factors control these fractures? In these processes, what sets the eventual size of…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how…
The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is…
The diffusion of active microscopic organisms in complex environments plays an important role in a wide range of biological phenomena from cell colony growth to single organism transport. Here, we investigate theoretically and…
The dynamics of dispersal-structured populations, consisting of competing individuals that are characterized by different diffusion coefficients but are otherwise identical, is investigated. Competition is taken into account through…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
We present a generic mechanism by which reproducing microorganisms, with a diffusivity that depends on the local population density, can form stable patterns. It is known that a decrease of swimming speed with density can promote separation…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
Originally motivated by the morphogenesis of bacterial microcolonies, the aim of this article is to explore models through different scales for a spatial population of interacting, growing and dividing particles. We start from a microscopic…
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…
A simple model accounting for the ejection of heavy particles from the vortical structures of a turbulent flow is introduced. This model involves a space and time discretization of the dynamics and depends on only two parameters: the…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
Colloidal systems present exciting opportunities to study clusters. Unlike atomic clusters, which are frequently produced at extremely low density, colloidal clusters may interact with one another. Here we consider the effect of such…
Active matter deals with systems whose particles consume energy at the individual level in order to move. To unravel features such as the emergence of collective structures several models have been suggested, such as the on-lattice model of…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…