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We study the statistical properties of many Brownian particles under the We study the statistical properties of many Brownian particles under the influence of both a spatially homogeneous driving force and a periodic potential with period…
We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion we introduce a basis that…
We consider driven systems where the driving induces jumps in energy space: (1) particles pulsed by a step potential; (2) particles in a box with a moving wall; (3) particles in a ring driven by an electro-motive-force. In all these cases…
This article deals with transport properties of one dimensional Brownian diffusion under the influence of a correlated quenched random force, distributed as a two-level Poisson process. We find in particular that large time scaling laws of…
Two deterministic models for Brownian motion are investigated by means of numerical simulations and kinetic theory arguments. The first model consists of a heavy hard disk immersed in a rarefied gas of smaller and lighter hard disks acting…
We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models that are applicable…
The fundamental solutions of diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences…
A knowledge of the particle escape time from the acceleration regions of many space and astrophysical sources is of critical importance in the analysis of emission signatures produced by these particles and in the determination of the…
We consider the overdamped motion of Brownian particles, interacting via particle exclusion, in an external potential that varies with time and space. We show that periodic potentials that maintain specific position-dependent phase…
We present an experimental investigation of the statistical properties of spherical granular particles on an inclined plane that are excited by an oscillating side-wall. The data is obtained by high-speed imaging and particle tracking…
We treat the problem of particle pushing by growing ice as a free diffusion near a wall that moves with discrete steps. When the particle diffuse away from the surface the surface can grow, blocking the particle from going back. Elementary…
We consider two different models for colloidal particles. In the first model, we consider their free motion to be diffusion while in the second model we take it to be integrated Ornstein-Uhlenbeck process. In both models, we derived…
We investigate motility-induced phase separation of active Brownian particles, which are modeled as purely repulsive spheres that move due to a constant swim force with freely diffusing orientation. We develop on the basis of power…
We study here the small time dynamics of $N$ electrons on the circle with Coul;omb repulsive interaction and study the series for the velocities (initially zero). The main result is the estimates of the convergence radius from below. We…
Understanding the spread of infectious diseases requires integrating movement, physical constraints, and spatial configurations into epidemiological models. In this study, we investigate how particle diffusivity, hardcore interactions, and…
We investigate the dynamics of two interacting diffusing particles in an infinite effectively one dimensional system; the particles interact through a step-like potential of width b and height phi_0 and are allowed to pass one another. By…
Based on Brownian dynamics simulations we study the collective behavior of a twodimensional system of repulsively interacting colloidal particles, where each particle is propelled by a repulsive feedback force with time delay $\tau$.…
The dynamics of individual colloidal particles in random potential energy landscapes were investigated experimentally and by Monte Carlo simulations. The value of the potential at each point in the two-dimensional energy landscape follows a…
We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the…
We analyse qualitative properties of the solutions to a mean-field equation for particles interacting through a pairwise potential while diffusing by Brownian motion. Interaction and diffusion compete with each other depending on the…