Related papers: Compact expansion of a repulsive suspension
We analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too…
We use computer simulations to test a simple idea for mapping between long-time self diffusivities obtained from molecular and Brownian dynamics. The strategy we explore is motivated by the behavior of fluids comprising particles that…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
The effect of mechanical interactions between cells in the spreading of bacterial populations was investigated in one-dimensional space. A continuum-mechanics approach, comprising cell migration, proliferation, and exclusion processes, was…
Nonintersecting motion of Brownian particles in one dimension is studied. The system is constructed as the diffusion scaling limit of Fisher's vicious random walk. N particles start from the origin at time t=0 and then undergo mutually…
Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) both self-propel at fixed speed $v$ along a body-axis ${\bf u}$ that reorients either through slow angular diffusion (ABPs) or sudden complete randomisation (RTPs). We…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
The collective non-equilibrium dynamics of multi-component mixtures of interacting active (self-propelled) and passive (diffusive) particles have garnered great interest in the physics community. However, the mathematical understanding of…
Systems comprised of self-steering active Brownian particles are studied via simulations for a minimal cognitive flocking model. The dynamics of the active Brownian particles is extended by an orientational response with limited…
Single-file transport in pore-like structures constitute an important topic for both theory and experiment. For hardcore interacting particles, a good understanding of the collective dynamics has been achieved recently. Here we study how…
We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with internal energy depot and interactions inspired by the dissipative…
We consider the interplay between persistent motion, which is a generic property of active particles, and a recoil interaction which causes particles to jump apart on contact. The recoil interaction exemplifies an active contact interaction…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
We study the dynamics of the outliers for a large number of independent Brownian particles in one dimension. We derive the multi-time joint distribution of the position of the rightmost particle, by two different methods. We obtain the two…
We consider active Brownian particles that intermittently switch between active and inactive states. Such behavior is ubiquitous at all scales, from bacteria to animals and in artificial active systems. We derive exact expressions for key…
We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…
When particles move at a constant speed and have the tendency to align their directions of motion, ordered large scale movement can emerge despite significant levels of noise. Many variants of this model of self-propelled particles have…
We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the…
We investigate the time evolution of a model system of interacting particles, moving in a $d$-dimensional torus. The microscopic dynamics are first order in time with velocities set equal to the negative gradient of a potential energy term…