Related papers: An interesting track for the Brachistochrone
We consider the degenerate Einstein's Brownian motion model for the case when the time interval ($\tau$) of particle Jumps before collision (free jumps) reciprocal to the number of particles per unit volume $u(x,t) > 0$ at the point of…
We study the long-time tails of the survival probability $P(t)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $\rho$ of traps $B$ that move sub-diffusively, such that the mean square displacement…
We discuss the approximate phenomenological description of the motion of a single second-class particle in a two-species totally asymmetric simple exclusion process (TASEP) on a 1D lattice. Initially, the second class particle is located at…
We investigate the first-passage properties and extreme-value statistics of an overdamped Brownian particle confined by an external linear potential $V(x)=\mu |x-x_0|$, where $\mu>0$ is the strength of the potential and $x_0>0$ is the…
We remove a small disc from the flat two-dimensional torus and consider a point-like particle that starts moving from the center of the disc with linear trajectory. We provide asymptotic estimates for the moments of the first exit time,…
In this paper we derive and discuss the time it takes for a force to turn a velocity. More precisely, we derive the formula for the time $\tau$ it takes a constant force that makes an angle $\alpha$ with the initial velocity $\vec{v}(0)$ to…
We study the properties of least time trajectories for particles moving on a two dimensional surface which consists of piecewise homogeneous regions. The particles are assumed to move with different constant speeds on different regions and…
Many studies on microscopic systems deal with Brownian particles embedded in media whose densities are different from that of the particles, causing them either to sink or float. The proximity to a wall modifies the friction force the…
We consider the movement of a particle advected by a random flow of the form $\vv+\delta \bF(\vx)$, with $\vv\in\R^d$ a constant drift, $\bF(\vx)$ -- the fluctuation -- given by a zero mean, stationary random field and $\delta\ll 1$ so that…
A particle moves randomly over the integer points of the real line. Jumps of the particle outside the membrane (a fixed "locally perturbating set") are i.i.d., have zero mean and finite variance, whereas jumps of the particle from the…
We present a numerical scheme for simulating the dynamics of Brownian particles suspended in a fluid. The motion of the particles is tracked by the Langevin equation, whereas the host fluid flow is analyzed by using the lattice Boltzmann…
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…
Consider a tagged particle in zero-range dynamics on the integer lattice in dimension d with rate g whose finite-range jump probabilities p possess a drift. We show, in equilibrium, that the variance of the tagged particle position at time…
We consider a version of random motion of hard core particles on the semi-lattice $ 1, 2, 3,...$, where in each time instant one of three possible events occurs, viz., (a) a randomly chosen particle hops to a free neighboring site, (b) a…
How long does it take to fall down a tunnel through the center of the Earth to the other side? Assuming a uniformly dense Earth, it would take 42 minutes, but this assumption has not been validated. This paper examines the gravity tunnel…
Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape…
Minimising movements are investigated for an energy which is the superposition of a convex functional and fast small oscillations. Thus a minimising movement scheme involves a temporal parameter $\tau$ and a spatial parameter $\epsilon$,…
A uniform, flexible and frictionless chain falling link by link from a heap by the edge of a table falls with an acceleration $g/3$ if the motion is nonconservative, but $g/2$ if the motion is conservative, $g$ being the acceleration due to…
In this article, results have been presented for the two-time correlation functions for a free and a harmonically confined Brownian particle in a simple shear flow. For a free Brownian particle, the motion along the direction of shear…
Given two probability measures $\mu, \nu$ on $\mathbb{R}^d$, in subharmonic order, we describe optimal stopping times $\tau$ that maximize/minimize the cost functional $\mathbb{E} |B_0 - B_\tau|^{\alpha}$, $\alpha > 0$, where $(B_t)_t$ is…