Related papers: An interesting track for the Brachistochrone
The L\'evy walk process for a lower interval of an excursion times distribution ($\alpha<1$) is discussed. The particle rests between the jumps and the waiting time is position-dependent. Two cases are considered: a rising and diminishing…
Consider the circle $C$ of length 1 and a circular arc $A$ of length $\ell\in (0,1)$. It is shown that there exists $k=k(\ell) \in \mathbb{N}$, and a schedule for $k$ runners along the circle with $k$ constant but distinct positive speeds…
Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, one of the coordinate processes gets a…
We determine the globally minimum time $T$ needed to translate a thin submerged flat plate a given distance parallel to its surface within a work budget. The Reynolds number for the flow is assumed to be large so that the drag on the plate…
We investigate the motion of a suspended non-Brownian sphere past a fixed cylindrical or spherical obstacle in the limit of zero Reynolds number for arbitrary particle-obstacle aspect ratios. We consider both a suspended sphere moving in a…
We investigate the motion of an inert (massive) particle being impinged from below by a particle performing (reflected) Brownian motion. The velocity of the inert particle increases in proportion to the local time of collisions and…
We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…
Our model consists of a Brownian particle $X$ moving in $\mathbb{R}$, where a Poissonian field of moving traps is present. Each trap is a ball with constant radius, centered at a trap point, and each trap point moves under a Brownian motion…
We establish asymptotic upper and lower bounds for the Wasserstein distance of any order $p\ge 1$ between the empirical measure of a fractional Brownian motion on a flat torus and the uniform Lebesgue measure. Our inequalities reveal an…
A straightforward analytical scheme is proposed for computing the long-time, asymptotic mean velocity and dispersivity (effective diffusivity) of a particle undergoing a discrete biased random walk on a periodic lattice amongst an array of…
We consider a few thought experiments of radial motion of massive particles in the gravitational fields outside and inside various celestial bodies: Earth, Sun, black hole. All other interactions except gravity are disregarded. For the…
The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are…
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…
Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einstein's theory of Brownian motion, however, is only applicable at long time scales. At short…
We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By…
We prove the sharpness of the phase transition for speed in the biased random walk on the supercritical percolation cluster on Z^d. That is, for each d at least 2, and for any supercritical parameter p > p_c, we prove the existence of a…
Motions of a material point along a set of parabolas are studied, taking into account the forces of Coulomb friction. The obtained results are compared with similar motions along the cycloid. The analysis is carried out using numerical…
We study analytically the order and gap statistics of particles at time $t$ for the one dimensional branching Brownian motion, conditioned to have a fixed number of particles at $t$. The dynamics of the process proceeds in continuous time…
Given a standard Brownian motion $B^{\mu}=(B_t^{\mu})_{0\le t\le T}$ with drift $\mu \in \mathbb{R}$ and letting $S_t^{\mu}=\max_{0\le s\le t}B_s^{\mu}$ for $0\le t\le T$, we consider the optimal prediction problem: \[V=\inf_{0\le \tau \le…
We investigate the persistence probability $p(t)$ of the position of a Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the probability that a stochastic variable has not changed it's sign…