Related papers: Flooding dynamics of diffusive dispersion in a ran…
The problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d. We consider the case where the traps are initially randomly distributed in space, with uniform density rho, and derive upper and…
Diffusion in a confining potential offers a minimal setting to understand the interplay between random motion and deterministic forces driving a particle towards a focal point or potential minimum. In continuous space and time, two…
Turbulent wall flows offer the most direct means for understanding the effects of boundaries and viscosity on turbulent fluctuations. Available data on mean-square fluctuations in these flows show apparent contradiction with classical…
Giant diffusion, where the diffusion coefficient of a Brownian particle in a periodic potential with an external force is significantly enhanced by the external force, is a non-trivial non-equilibrium phenomenon. We propose a simple…
We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…
The statistical theory of certain complex wave interference phenomena, like the statistical fluctuations of transmission and reflection of waves, is of considerable interest in many fields of physics. In this article we shall be mainly…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time…
Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an…
We examine diffusion-limited aggregation generated by a random walk on Z with long jumps. We derive upper and lower bounds on the growth rate of the aggregate as a function of the number moments a single step of the walk has. Under various…
Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…
We consider the general problem of the first passage distribution of particles whose displacements are subject to time delays. We show that this problem gives rise to a \emph{propagation-dispersion equation} which is obtained as the…
We propose a simple equation for predicting self-diffusivity of fluids embedded in random matrices of identical, but dynamically frozen, particles (i.e., quenched-annealed systems). The only nontrivial input is the volume available to…
In this article, we obtain properties of the law associated to the first hitting time of a threshold by a one-dimensional uniformly elliptic diffusion process and to the associated process stopped at the threshold. Our methodology relies on…
We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second…
The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of…
In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first…
The statistics of the slowest first-passage time among a large population of $N$ searchers is crucial for determining the completion time of many stochastic processes. Classical extreme-value theory predicts that for diffusing particles in…
This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the…
We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e.,…