Related papers: Anomalous diffusion in comb-shaped domains and gra…
We address the problem of diffusion on a comb whose teeth display a varying length. Specifically, the length $\ell$ of each tooth is drawn from a probability distribution displaying the large-$\ell$ behavior $P(\ell) \sim…
This work analyses the homogenization of a linear elliptic equation with Neumann boundary conditions in a comb/brush domain, composed of a fixed base and a family of thin teeth. The teeth are defined as rescalings of order less than or…
We study the second-order asymptotics around the superdiffusive strong law~\cite{MMW} of a multidimensional driftless diffusion with oblique reflection from the boundary in a generalised parabolic domain. In the unbounded direction we prove…
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…
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…
The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x-direction are allowed only when the y coordinate of…
Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) which converges back to a Brownian motion with reduced diffusion coefficient at long times, after the anomalous…
Anomalous diffusion is discussed in the context of quantum Brownian motion with colored noise. It is shown that earlier results follow simply and directly from the fluctuation-dissipation theorem. The limits on the long-time dependence of…
We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…
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…
It is well known that on long time scales the behaviour of tracer particles diffusing in a cellular flow is effectively that of a Brownian motion. This paper studies the behaviour on "intermediate" time scales before diffusion sets in.…
Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic…
We propose to model the stochastic dynamics of a polymer passing through a pore (translocation) by means of a fractional Brownian motion, and study its behavior in presence of an absorbing boundary. Based on scaling arguments and numerical…
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…
We study the asymptotic behavior of a diffusion process with small diffusion in a domain $D$. This process is reflected at $\partial D$ with respect to a co-normal direction pointing inside $D$. Our asymptotic result is used to study the…
We quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction, with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the…
This short note is motivated by a recently discovered connection between a drift-diffusion process in $n$-dimensional Euclidean space with a divergence-free drift sampled from a stationary and isotropic Gaussian ensemble of critical scaling…
In this paper we study the discrete approximation to Brownian motion with varying dimension (BMVD in abbreviation) introduced in [4] by continuous time random walks on square lattices. The state space of BMVD contains a $2$-dimensional…
We study a transport of impurity particles on a comb structure in the presence of advection. The main body concentration and asymptotic concentration distributions are obtained. Seven different transport regimes occur on the comb structure…
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with…