Related papers: Accelerating and Retarding Anomalous Diffusion
Anomalous short- and long-time self-diffusion of non-overlapping fractal particles on a percolation cluster with spreading dimension $1.67(2)$ is studied by dynamic Monte Carlo simulations. As reported in Phys. Rev. Lett. 115, 097801…
In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equations on cylindrical domains. In particular, we use a…
Recent investigations call attention to the dynamics of anomalous diffusion and its connection with basic principles of statistical mechanics. We present here a short review of those ideas and their implications.
The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…
In the present work, we investigate the potential of fractional derivatives to model atmospheric dispersion of pollutants. We propose simple fractional differential equation models for the steady state spatial distribution of concentration…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
Constant flux atom deposition into a porous medium is shown to generate a dense overlayer and a diffusion profile. Scaling analysis shows that the overlayer acts as a dynamic control for atomic diffusion in the porous substrate. This is…
The onset of the Rayleigh-Benard instability in a horizontal fluid layer is investigated by assuming the fluid as a binary mixture and the concentration buoyancy as the driving force. The focus of this study is on the anomalous diffusion…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…
We describe how to solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to…
Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is…
In a very long Gaussian polymer on time scales shorter that the maximal relaxation time, the mean squared distance travelled by a tagged monomer grows as ~t^{1/2}. We analyze such sub-diffusive behavior in the presence of one or two…
There is no agreement in the literature on the rate of diffusion of a particle in a cooling granular gas. Predictions and model assumptions range from the conventional to very exotic dependence of the mean square distance (MSD) on time.…
The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered.…
We present a stochastic model for amplifying, diffusive media like, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field with contains a…