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We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case…
We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.
We compute the persistence for the $2d$-diffusion equation with random initial condition, i.e., the probability $p_0(t)$ that the diffusion field, at a given point ${\bf x}$ in the plane, has not changed sign up to time $t$. For large $t$,…
Incorporating boundary conditions into stochastic models of passive or active particle motion is usually implemented at the level of the associated forward or backward Kolmogorov equation, whose solution determines the probability…
A Brownian particle floating in a narrow corrugated (sinusoidal) channel with fluctuating cross section exhibits non-Gaussian normal diffusion. Its displacements are distributed according to a Gaussian law for very short and asymptotically…
We study the Brownian motion of a particle in a bounded circular 2-dimensional domain, in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional…
We analyze the mean squared displacement of a Brownian particle in a medium with a spatially varying local diffusivity which is assumed to be periodic. When the system is asymptotically diffusive the mean squared displacement,…
Fractional Brownian motion and the fractional Langevin equation are models of anomalous diffusion processes characterized by long-range power-law correlations in time. We employ large-scale computer simulations to study these models in two…
In this paper we investigate deterministic diffusion in systems which are spatially extended in certain directions but are restricted in size and open in other directions, consequently particles can escape. We introduce besides the…
The problem of the diffusion evolution of a pore filled with molecular hydrogen in a spherical granule in a hydrogen medium is solved. The initial position of the pore is displaced relative to the center of the granule. A nonlinear system…
We present results on tagged particle diffusion in a meso-scale lattice model for sheared amorphous material in athermal quasi-static conditions. We find a short time diffusive regime and a long time diffusive regime whose diffusion…
Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their…
We consider an anisotropic needle-like Brownian particle with nematic symmetry confined in a $2D$ domain. For this system, the coupling of translational and rotational diffusion makes the process ${\bf x} (t)$ of the positions of the…
We show in detail some results, outlined in a previous paper regarding the case of Brownian motion (BM), about the distribution of the $n$th-passage time of a one-dimensional diffusion obtained by a space or time transformation of BM,…
In this paper we study the time evolution of the decay process for a particle confined initially in a finite region of space, extending our analysis given recently (Phys. Rev. Lett. 74, 337 (1995)). For this purpose, we solve exactly the…
We study the dynamics of the outliers for a large number of independent Brownian particles in one dimension. We derive the multi-time joint distribution of the position of the rightmost particle, by two different methods. We obtain the two…
We investigate the dynamics of an overdamped Brownian particle moving in a washboard potential with space dependent friction coefficient. Analytical expressions have been obtained for current and diffusion coefficient. We show that the…
In this work, we study the dynamics of a single active Brownian particle, as well as the collective behavior of interacting active Brownian particles, in a fluctuating heterogeneous environment. We employ a variant of the diffusing…
The structure and dynamics of confined suspensions of particles of arbitrary shape is of interest in multiple disciplines, from biology to engineering. Theoretical studies are often limited by the complexity of long-range particle-particle…
Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…