相关论文: Some Insights in Superdiffusive Transport

We introduce a class of interacting fermionic quantum models in $d$ dimensions with nodal interactions that exhibit superdiffusive transport. We establish non-perturbatively that the nodal structure of the interactions gives rise to…

The problem of anomalous diffusion in momentum (velocity) space is considered based on the master equation and the appropriate probability transition function (PTF). The approach recently developed by the author for coordinate space, is…

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…

This paper provides numerical results that demonstrate the validity of the nonclassical diffusion approximation to the nonclassical transport equation in certain 1-D diffusive systems. This result provides a more solid foundation in which…

Reaction dynamics involving subdiffusive species is an interesting topic with only few known results, especially when the motion of different species is characterized by different anomalous diffusion exponents. Here we study the reaction…

A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…

This paper proposes a simple model of anomalous diffusion, in which a particle moves with the velocity field induced by a single "dipole" (a doublet or a pair of source and sink), whose moment is modulated randomly at each time step. A…

The theory of first order Fermi acceleration at shocks assumes that particles diffuse due to scattering off slow-moving magnetic irregularities. However, cosmic rays are closely tied to magnetic field lines, and the transport process,…

We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…

Diffusion processes are important in several physical, chemical, biological and human phenomena. Examples include molecular encounters in reactions, cellular signalling, the foraging of animals, the spread of diseases, as well as trends in…

This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for the exponential convergence to a unique quasi-stationary distribution in total variation,…

The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained…

Based on the superconvergent approximation at some point (depending on the fractional order $\alpha$, but not belonging to the mesh points) for Gr\"{u}nwald discretization to fractional derivative, we develop a series of high order…

We consider a one-dimensional fermionic lattice system with long-ranged power-law decaying hopping with exponent $\alpha$. The system is further subjected to dephasing noise in the bulk. We investigate two variants of the problem: (i) an…

Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…

Using molecular dynamics simulations we investigate the translational dynamics of particles with dipolar interactions in homogenous external fields. For a broad range of concentrations, we find that the anisotropic, yet normal diffusive…

In mathematical modeling of the non-squared frequency-dependent diffusions, also known as the anomalous diffusions, it is desirable to have a positive real Fourier transform for the time derivative of arbitrary fractional or odd integer…

We present a novel mechanism of phase-dependent electric transport in diffusive normal metal-superconductor structures. We provide a detailed theoretical and numerical analysis of recent unexplained experiments essentially explaining them.

We study anomalous transport arising in disordered one-dimensional spin chains, specifically focusing on the subdiffusive transport typically found in a phase preceding the many-body localization transition. Different types of transport can…

Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the Advection Diffusion Equation supplemented by a time derivative of non-integer order. We are describing an inverse method…