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Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject…
We consider a model of Non-Brownian self-propelled particles with anti-alignment interactions where particles try to avoid each other by attempting to turn into opposite directions. The particles undergo apparent Brownian motion, even…
Standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during to the integration timestep. This in not the case for hard-body systems, where there is no clearcut between the…
Theory and simulation of Brownian colloids suspended in an implicit solvent, with the hydrodynamics of the fluid accounted for by effective interactions between the colloids, are shown to yield a marked and hitherto unobserved discrepancy…
We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…
The Schr\"{o}dinger problem of deducing the microscopic dynamics from the input-output statistics data is known to admit a solution in terms of Markov diffusions. The uniqueness of solution is found linked to the natural boundaries…
Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of…
We present a new Eulerian framework for the computation of turbulent compressible multiphase channel flows, specifically to assess turbulence modulation by dispersed particulate matter in dilute concentrations but with significant mass…
The non-Newtonian behavior of a monodisperse concentrated dispersion of spherical particles was investigated using a direct numerical simulation method, that takes into account hydrodynamic interactions and thermal fluctuations accurately.…
Diffusive transport of particles or, more generally, small objects is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions transport is controlled both by the…
We present a technique to investigate the stationary states of a system of a collisionless system confined by an external potential and coupled to boundary reservoirs through prescribed reinjection rules. We consider a family of boundary…
We provide a mathematical study of the modified Diffusion Monte Carlo (DMC) algorithm introduced in the companion article \cite{DMC}. DMC is a simulation technique that uses branching particle systems to represent expectations associated…
The bulk properties of convection in stellar and giant planet interiors are often assumed to be independent of the molecular diffusivities, which are very small. By contrast, simulations of this process in rotating, spherical shells, which…
The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion bridges for modeling…
We study the stochastic motion of an intruder in a dilute driven granular gas. All particles are coupled to a thermostat, representing the external energy source, which is the sum of random forces and a viscous drag. The dynamics of the…
An implicit Euler finite-volume scheme for a degenerate cross-diffusion system describing the ion transport through biological membranes is analyzed. The strongly coupled equations for the ion concentrations include drift terms involving…
We develop the kinetic theory of the flux-carrying Brownian motion recently introduced in the context of open quantum systems. This model constitutes an effective description of two-dimensional dissipative particles violating both…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
A stochastic dynamics $({\bf X}(t))_{t\ge0}$ of a classical continuous system is a stochastic process which takes values in the space $\Gamma$ of all locally finite subsets (configurations) in $\Bbb R$ and which has a Gibbs measure $\mu$ as…
In this paper, the first microscopic approach to the Brownian motion is developed in the case where the mass density of the suspending bath is of the same order of magnitude as that of the Brownian (B) particle. Starting from an extended…