Related papers: A probabilistic model of diffusion through a semi-…
Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the…
As a generic model for transport of interacting fermions through a barrier or interstitials in a lattice, quantum Brownian motion in a periodic potential is studied. There is a duality transformation between the continuous coordinate or…
In this paper we consider diffusion in a domain $\Omega$ containing a partially absorbing target $\calM$ with position and occupation time resetting. The occupation time $A_t$ is a Brownian functional that determines the amount of time that…
We consider scaled Brownian motion (sBm), a random process described by a diffusion equation with explicitly time-dependent diffusion coefficient $D(t) = D_0 t^{\alpha - 1}$ (Batchelor's equation) which, for $\alpha < 1$, is often used for…
Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is still unclear. We introduce a model in which…
We study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behaviour of the Brownian particle…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim…
We construct a new random probability measure on the sphere and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the…
Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous…
A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal…
Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of…
We consider a particle transport process in a one-dimensional system with a thin membrane, described by a normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators,…
The escape of a Brownian particle over a dichotomously fluctuating barrier is investigated for various shapes of the barrier. The problem of resonant activation is revisited with the attention on the effect of the barrier shape on optimal…
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 investigate time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to whole fusion-fission dynamical process and can be…
The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…