Related papers: Dynamical density functional theory for interactin…
Active Brownian particles, even without attractive and anisotropic inter-particle interactions, can form a high-density phase featuring structure-ordered domains as well as collective motion regions under thermal noise. However, the…
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…
A fundamental assumption of the dynamical density functional theory (DDFT) of colloidal systems is that a grand-canonical free energy functional may be employed to generate the thermodynamic driving forces. Using one-dimensional hard-rods…
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
We consider stochastic dynamics of a particle on a plane in presence of two noises and a confining parabolic potential - an analog of the experimentally-relevant Brownian Gyrator (BG) model. In contrast to the standard BG model, we suppose…
The Dean-Kawasaki (DK) equation, which is at the basis of stochastic density functional theory (SDFT), was proposed in the mid-nineties to describe the evolution of the density of interacting Brownian particles, which can represent a large…
Using the scheme of mesoscopic nonequilibrium thermodynamics, we construct the one- and two- particle Fokker-Planck equations for a system of interacting Brownian particles. By means of these equations we derive the corresponding balance…
Distribution of a Brownian motion conditioned to start from the boundary of an open set $G$ and to stay in $G$ for a finite period of time is studied. Characterizations of such distributions in terms of certain singular stochastic…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
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…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
For a system of Brownian particles interacting via a soft exponential potential we investigate the interaction between equilibrium crystallization and spatially varying shear flow. For thermodynamic state points within the liquid part of…
In this paper we study a stochastic differential equation driven by a fractional Brownian motion with a discontinuous coefficient. We also give an approximation to the solution of the equation. This is a first step to define a fractional…
We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but…
We analyze a system of stochastic differential equations describing the joint motion of a massive (inert) particle in a viscous fluid in the presence of a gravitational field and a Brownian particle impinging on it from below, which…
We derive quantitative criteria for the existence of density for stochastic line integrals and iterated line integrals along solutions of hypoelliptic differential equations driven by fractional Brownian motion. As an application, we also…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
Motivated by the goal of understanding the evolution of populations undergoing selection, we consider branching Brownian motion in which particles independently move according to one-dimensional Brownian motion with drift, each particle may…
Aiming to understand the distribution of fitness levels of individuals in a large population undergoing selection, we study the particle configurations of branching Brownian motion where each particle independently moves as Brownian motion…
We investigate the nonequilibrium dynamics of spherical active Brownian particles in three spatial dimensions that interact via a pair potential. The investigation is based on a predictive local field theory that is derived by a rigorous…