Related papers: Impulse Response Function for Brownian Motion
Active Brownian motion with intermittent direction reversals are common in a class of bacteria like {\it Myxococcus xanthus} and {\it Pseudomonas putida}. We show that, for such a motion in two dimensions, the presence of the two time…
We consider a Brownian particle with diffusion coefficient $D$ in a $d$-dimensional ball of radius $R$ with reflecting boundaries. We study the maximum $M_x(t)$ of the trajectory of the particle along the $x$-direction at time $t$. In the…
Let $\tau$ be the first hitting time of the point 1 by the geometric Brownian motion $X(t)= x \exp(B(t)-2\mu t)$ with drift $\mu \geq 0$ starting from $x>1$. Here $B(t)$ is the Brownian motion starting from 0 with $E^0 B^2(t) = 2t$. We…
Brownian motion with stochastic resetting-a process combining standard diffusion with random returns to a fixed position-has emerged as a powerful framework with applications spanning statistical physics, chemical kinetics, biology, and…
We study the dynamics of a chirality reversing active Brownian particle, which models the chirality reversing active motion common in many microorganisms and microswimmers. We show that, for such a motion, the presence of the two…
The transport of interacting Brownian particles in a periodic asymmetric (ratchet) substrate is studied numerically. In a zero-temperature regime, the system behaves as a reversible step motor, undergoing multiple sign reversals of the…
The dynamics of macroscopically homogeneous sheared suspensions of neutrally buoyant, non-Brownian spheres is investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics. We show that the complex dynamics of…
In this paper, we investigate a Brownian motion (BM) with purely time dependent drift and difusion by suggesting and examining several Brownian functionals which characterize the lifetime and reactivity of such stochastic processes. We…
Let $\{B_{t}\}_{t\geq0}$ be a fractional Brownian motion with Hurst parameter $\frac{2}{3}<H<1$. We prove that the approximation of the derivative of self-intersection local time, defined as \begin{align*} \alpha_{\varepsilon} &=…
We determine the nonlocal stress autocorrelation tensor in an homogeneous and isotropic system of interacting Brownian particles starting from the Smoluchowski equation of the configurational probability density. In order to relate stresses…
We consider motion of an underdamped Brownian particle in a washboard potential that is subjected to an unbiased time-periodic external field. While in the limiting deterministic system in dependence of the strength and phase of the…
Dynamic particle-scale numerical simulations are used to show that the shear thickening observed in dense colloidal, or Brownian, suspensions is of a similar nature to that observed in non-colloidal suspensions, i.e., a stress-induced…
Consider branching Brownian motion in which we begin with one particle at the origin, particles independently move according to Brownian motion, and particles split into two at rate one. It is well-known that the right-most particle at time…
We investigate theoretically and experimentally the first passage-time properties of a spherical Brownian particle that is harmonically trapped at thermal equilibrium in a fluid at constant temperature. By using the overdamped version of…
The narrow escape problem is a first-passage problem concerned with randomly moving particles in a physical domain, being trapped by absorbing surface traps (windows), such that the measure of traps is small compared to the domain size. The…
We investigate the time average mean square displacement $\overline{\delta^2}(x(t))=\int_0^{t-\Delta}[x(t^\prime+\Delta)-x(t^\prime)]^2 dt^\prime/(t-\Delta)$ for fractional Brownian and Langevin motion. Unlike the previously investigated…
We extend generalized isoperimetric-type inequalities to iterated Brownian motion over several domains in $\RR{R}^{n}$. These kinds of inequalities imply in particular that for domains of finite volume, the exit distribution and moments of…
We study subdiffusive overdamped Brownian ratchets periodically rocked by an external zero-mean force in viscoelastic media within the framework of non-Markovian Generalized Langevin equation (GLE) approach and associated multi-dimensional…
Despite extensive progress in characterizing the emergent behavior of active matter, the microscopic origins of self-diffusion in interacting active systems remain poorly understood. Here, we develop a framework that quantitatively links…
We analyze \emph{fractional Brownian motion} and \emph{scaled Brownian motion} on the two-dimensional sphere $\mathbb{S}^{2}$. We find that the intrinsic long time correlations that characterize fractional Brownian motion collude with the…