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In this note, we connect two seemingly unrelated objects: On the one hand is a two-dimensional drift-diffusion process $X$ with divergence-free and time-independent drift $b$. The drift is given by a stationary Gaussian ensemble, and we…

Probability · Mathematics 2025-11-24 Peter Morfe , Felix Otto , Christian Wagner

We examined the Brownian motion of point defects in a two-dimensional hexagonal colloidal crystal, going beyond the conventional treatment that assumes constant diffusion coefficients. By extracting the spatially varying drift vector and…

Soft Condensed Matter · Physics 2026-05-18 Huang Xicheng , Liu Zefei , Chen Yong-Cong , Yang Guohong , Ao Ping

Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion…

We derive the Virial theorem appropriate to the generalized Smoluchowski-Poisson system describing self-gravitating Brownian particles and bacterial populations (chemotaxis). We extend previous works by considering the case of an unbounded…

Statistical Mechanics · Physics 2014-10-13 Pierre-Henri Chavanis , Clement Sire

Active particles (i.e., self-propelled particles or called microswimmers), different from passive Brownian particles, possess more complicated translational and angular dynamics, which can generate a series of anomalous transport phenomena.…

Soft Condensed Matter · Physics 2022-01-05 Ze-Hao Chen , Zhi-Xi Wu

We consider a diffusion process in $\mathbb{R}^d$ with a generator of the form $ L:=\frac 12 e^{V(x)}div(e^{-V(x)}\nabla ) $ where $V$ is measurable and periodic. We only assume that $e^V$ and $e^{-V}$ are locally integrable. We then show…

Probability · Mathematics 2016-01-13 Moustapha Ba , Pierre Mathieu

We consider the setting of multiscale overdamped Langevin stochastic differential equations, and study the problem of learning the drift function of the homogenized dynamics from continuous-time observations of the multiscale system. We…

Numerical Analysis · Mathematics 2024-11-12 Max Hirsch , Andrea Zanoni

The drift diffusion model (DDM) is a model of sequential sampling with diffusion (Brownian) signals, where the decision maker accumulates evidence until the process hits a stopping boundary, and then stops and chooses the alternative that…

Econometrics · Economics 2022-10-12 Drew Fudenberg , Whitney K. Newey , Philipp Strack , Tomasz Strzalecki

In the diffusive hydrodynamic limit for a symmetric interacting particle system (such as the exclusion process, the zero range process, the stochastic Ginzburg-Landau model, the energy exchange model), a possibly non-linear diffusion…

Probability · Mathematics 2017-05-01 Makiko Sasada

We present an extensive direct numerical simulation of statistically steady, homogeneous, isotropic turbulence in two-dimensional, binary-fluid mixtures with air-drag-induced friction by using the Cahn-Hilliard-Navier-Stokes equations. We…

Fluid Dynamics · Physics 2016-11-16 Nairita Pal , Prasad Perlekar , Anupam Gupta , Rahul Pandit

The celebrated Sutherland-Einstein relation for systems at thermal equilibrium states that spread of trajectories of Brownian particles is an increasing function of temperature. Here, we scrutinize diffusion of underdamped Brownian motion…

Statistical Mechanics · Physics 2020-04-22 J. Spiechowicz , J. Luczka

We study the dynamics of a Brownian motion with a diffusion coefficient which evolves stochastically. We first study this process in arbitrary dimensions and find the scaling form and the corresponding scaling function of the position…

Statistical Mechanics · Physics 2023-01-30 Ion Santra , Urna Basu , Sanjib Sabhapandit

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…

Analysis of PDEs · Mathematics 2012-04-17 José A. Cañizo , José A. Carrillo , Maria E. Schonbek

The diffusion type is determined not only by microscopic dynamics but also by the environment properties. For example, the environment's fractal structure is responsible for the emergence of subdiffusive scaling of the mean square…

Statistical Mechanics · Physics 2021-10-26 Piotr Kubala , Michał Cieśla , Bartłomiej Dybiec

An interesting feature of the Davies-Unruh effect is that an uniformly accelerated observer sees an isotropic thermal spectrum of particles even though there is a preferred direction in this context, determined by the direction of the…

General Relativity and Quantum Cosmology · Physics 2012-11-29 Sanved Kolekar , T. Padmanabhan

Diffusion and rectification of Brownian particles powered by a rotating wheel are numerically investigated in a two-dimensional channel. The nonequilibrium driving comes from the rotating wheel, which can break thermodynamical equilibrium…

Statistical Mechanics · Physics 2017-07-24 Bao-quan Ai

In the present work, we explore homogenization techniques for a class of switching diffusion processes whose drift and diffusion coefficients, and jump intensities are smooth, spatially periodic functions; we assume full coupling between…

Probability · Mathematics 2025-07-01 Chetan D. Pahlajani

In this paper we study the diffusion approximation of a swarming model given by a system of interacting Langevin equations with nonlinear friction. The diffusion approximation requires the calculation of the drift and diffusion coefficients…

Numerical Analysis · Mathematics 2015-05-08 V. Bonnaillie-Noël , J. A. Carrillo , T. Goudon , G. A. Pavliotis

In this paper we study a parametric class of stochastic processes to model both fast and slow anomalous diffusion. This class, called generalized grey Brownian motion (ggBm), is made up off self-similar with stationary increments processes…

Mathematical Physics · Physics 2009-11-13 Antonio Mura , Gianni Pagnini

Langevin simulations provide an effective way to study collective effects of Brownian particles immersed in a two-dimensional periodic potential. In this paper, we concentrate essentially on the behaviour of the tracer (DTr) and bulk (DB)…

Statistical Mechanics · Physics 2015-05-13 S. Zayzoune , M. Mazroui , Y. Boughaleb , A. Kara