Related papers: Statistics of boundary encounters by a particle di…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
When a suspension freezes, a compacted particle layer builds up at the solidification front with noticeable implications on the freezing process. In a directional solidification experiment of monodispersed suspensions in thin samples, we…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
Fix $p>1$, not necessarily integer, with $p(d-2)<d$. We study the $p$-fold self-intersection local time of a simple random walk on the lattice $\Z^d$ up to time $t$. This is the $p$-norm of the vector of the walker's local times, $\ell_t$.…
The adsorption phenomenon of neutral particles from the limiting surfaces of the sample in the Langmuir approximation is investigated. The diffusion equation regulating the redistribution of particles in the bulk is assumed to be of…
We investigate a one-dimensional system of $N$ particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the $N$ particles do…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane…
Driven by diverse applications, several recent models impose randomly switching boundary conditions on either a PDE or SDE. The purpose of this paper is to provide tools for calculating statistics of these models and to establish a…
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…
We consider a Brownian particle, with diffusion constant D, moving inside an expanding d-dimensional sphere whose surface is an absorbing boundary for the particle. The sphere has initial radius L_0 and expands at a constant rate c. We…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
There are several inequivalent proposals in the literature for how to compute the probability distribution of the time that a detector registers for the arrival of a quantum particle. For two of these proposals, based on absorbing boundary…
Fluctuations of the local volume fraction within granular materials have previously been observed to decrease as the system approaches jamming. We experimentally examine the role of boundary conditions and inter-particle friction $\mu$ on…
In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarisation. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
The problem of diffusion in a time-dependent (and generally inhomogeneous) external field is considered on the basis of a generalized master equation with two times, introduced in [1,2]. We consider the case of the quasi Fokker-Planck…
This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…
The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this…