Related papers: Comparison Techniques for Competing Brownian Parti…
We consider the collective motion of finite-sized, overdamped Brownian particles (e.g., motor proteins) in a periodic potential. Simulations of our model have revealed a number of novel cooperative transport phenomena, including (i) the…
We consider a system $x(t)=(x_{1}(t),...,x_{N}(t))$ consisting of $N$ Brownian particles with synchronizing interaction between them occurring at random time moments $\{\tau_{n}\}_{n=1}^{\infty}$. Under assumption that the free Brownian…
The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is…
In many physical or biological systems, diffusion can be described by Brownian motions with stochastic diffusion coefficients (DCs). In the present study, we investigate properties of the diffusion with a broad class of stochastic DCs with…
The lateral diffusion coefficient of a Brownian particle on a two-dimensional random surface is studied in the quenched limit for which the surface configuration is time-independent. We start with the stochastic equation of motion for a…
We study the motion of an overdamped particle connected to a thermal heat bath in the presence of an external periodic potential in one dimension. When we coarse-grain, i.e., bin the particle positions using bin sizes that are larger than…
We consider both the effect of particle inertia on stochastic Stokes' drift, and also a related process which could be considered as a crude model of stochastic Stokes' drift driven by an eddy diffusivity. In the latter, the stochastic…
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…
Sufficient and necessary conditions are presented for the order-preservation of stochastic functional differential equations on $\R^d$ with non-Lipschitzian coefficients driven by the Brownian motion and Poisson processes. The sufficiency…
We consider a (one-dimensional) branching Brownian motion process with a general offspring distribution having at least two moments, and in which all particles have a drift towards the origin where they are immediately absorbed. It is…
An important question in the field of active matter is whether or not it is possible to predict the phase behavior of these systems. Here, we study the phase coexistence of binary mixtures of torque-free active Brownian particles, for both…
Simultaneous diffusive and inertial motion of Brownian particles in laminar Couette flow is investigated via Lagrangian and Eulerian descriptions to determine the effect of particle inertia on diffusive transport in the long-time. The…
We investigate sorting Rayleigh optical particles up to several nanometers in size during Brownian motion in an tilted periodic potential with multiple deep wells. The wells are induced which by optical bound states in the continuum in a…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…
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…
We study two Brownian particles in dimension $d=1$, diffusing under an interacting resetting mechanism to a fixed position. The particles are subject to a constant drift, which biases the Brownian particles toward each other. We derive the…
We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent…
We study asymptotic properties of the system of interacting diffusion particles on the real line which transfer a mass [arXiv:1408.0628]. The system is a natural generalization of the coalescing Brownian motions. The main difference is that…
Consider n non-intersecting Brownian motions on $\mathbb{R}$, depending on time $t \in [0,1]$, with $m_i$ particles forced to leave from $a_i$ at time $t=0$, $1\leq i\leq q$, and $n_j$ particles forced to end up at $b_j$ at time $t=1$,…
We study a model of interacting random walkers that proposes a simple mechanism for the emergence of cooperation in group of individuals. Each individual, represented by a Brownian particle, experiences an interaction produced by the local…