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Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
A system of degenerate drift-diffusion equations for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a three-dimensional bounded domain with mixed…
Ion diffusion is a central part of materials physics of fabrication, deformation, phase transformation, structure stability and electrochemical devices. Conventional theory focuses on the defects that mediate diffusion and explains how…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
Spin transport in magnetic tunnel junctions in the presence of spin diffusion is considered theoretically. Combining ballistic tunneling across the barrier and diffusive transport in the electrodes, we solve the spin dynamics equation in…
The distribution of voltage in sub-micron cellular domains remains poorly understood. In neurons, the voltage results from the difference in ionic concentrations which are continuously maintained by pumps and exchangers. However, it not…
The problem of eliminating fast-relaxing variables to obtain an effective drift-diffusion process in position is solved in a uniform and straightforward way for models with velocity a function jointly of position and fast variables. A more…
Though electrical noise and conduction current are assigned to corpuscle-like electrons drifting in solid matter, this model hardly fits in the Fluctuation-Dissipation framework. However, fluctuations of energy due to displacements of…
Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…
The stochastic advection of low energy deuterium ions is studied in a three dimensional realistic turbulence model in conditions relevant for current tokamak fusion experiments. The diffusion coefficients are calculated starting from the…
The pn junction is a fundamental electrical component in modern electronics and optoelectronics. Currently, there is a great deal of interest in the two-dimensional (2D) pn junction. Although many experiments have demonstrated the working…
Non-stationarity of an underlying data generating process that leads to distributional changes over time is a key characteristic of Data Streams. This phenomenon, commonly referred to as Concept Drift, has been intensively studied, and…
Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…
The spin and charge transport in materials with spin-dependent conductivity has been studied. It was shown that there is a charge accumulation along spin diffusion in a ferromagnetic metal, which causes a shortening of the spin diffusion…
We study the noise induced transport of an overdamped Brownian particle in frictional ratchet systems in the presence of external Gaussian white noise fluctuations. The analytical expressions for current and diffusion coefficient are…
We study the phenomena of noise induced transport in frictional ratchet systems. For this we consider a Brownian particle moving in a space dependent frictional medium in the presence of external white noise fluctuations. To get the…
We study supervised multiclass classification for diffusion processes, where each class is characterized by a distinct drift function and trajectories are observed at discrete times. We first derive a multidimensional Bayes rule and then…
We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence…
An exact analytical theory is developed for calculating the diffusion coefficient of charge carriers in strongly anisotropic disordered solids with one-dimensional hopping transport mode for any dependence of the hopping rates on space and…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…