Related papers: Advection-diffusion equations with density constra…
We investigate the dynamics of an overdamped Brownian particle moving in a washboard potential with space dependent friction coefficient. Analytical expressions have been obtained for current and diffusion coefficient. We show that the…
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
We study the main properties of the solution of a Fokker-Planck equation characterized by a variable diffusion coefficient and a polynomial superlinear drift, modeling the formation of consensus in a large interacting system of individuals.…
A {\em propagation-dispersion equation} is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the continuous limit of the {\em first visit equation}, an…
We investigate a model, inspired by (Johnston et al., Sci. Rep., 7:42134, 2017), to describe the movement of a biological population which consists of isolated and grouped organisms. We introduce biases in the movements and then obtain a…
We present a method how to estimate from experimental data of a turbulent velocity field the drift and the diffusion coefficient of a Fokker-Planck equation. It is shown that solutions of this Fokker-Planck equation reproduce with high…
We show that when Brownian motion takes place in a heterogeneous medium, the presence of local forces and transport coefficients leads to deviations from a Gaussian probability distribution that make that the ratio between forward and…
General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding…
This paper is interested in the description of the density of particles evolving according to some optimal policy of an impulse control problem. We first fix sets on which the particles jump and explain how we can characterize such a…
We consider a semi-linear advection equation driven by a highly-oscillatory space-time Gaussian random field, with the randomness affecting both the drift and the nonlinearity. In the linear setting, classical results show that the…
Excitonic transport in static disordered one dimensional systems is studied in the presence of thermal fluctuations that are described by the Haken-Strobl-Reineker model. For short times, non-diffusive behavior is observed that can be…
The transport of single-phase fluid mixtures in porous media is described by cross-diffusion equations for the mass densities. The equations are obtained in a thermodynamic consistent way from mass balance, Darcy's law, and the van der…
This is an attempt to address diffusion phenomena from the point of view of information theory. We imagine a regular hamiltonian system under the random perturbation of thermal (molecular) noise and chaotic instability. The irregularity of…
In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We…
We present a simple and systematic procedure to determine the effective dynamics of a Brownian particle coupled to a rapidly fluctuating correlated medium, modeled as a scalar Gaussian field, under spatial confinement. The method allows us,…
We outline a reduction scheme for a class of Brownian dynamics which leads to meaningful corrections to the Smoluchowski equation in the overdamped regime. The mobility coefficient of the reduced dynamics is obtained by exploiting the…
We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…
The Active Brownian Particle (ABP) model exemplifies a wide class of active matter particles. In this work, we demonstrate how this model can be cast into a field theory in both two and three dimensions. Our aim is manifold: we wish both to…
Motivated by the phenomenon of transport barriers in fusion plasma devices, we write a mathematical model of heat dispersion in a turbulent fluid with a transport barrier, properly idealized; in a scaling limit of the turbulence model with…
We derive the distribution of particle currents for a system of interacting active Brownian particles in the long time limit using large deviation theory and a weighted many body expansion. We find the distribution is non-Gaussian, except…