Related papers: A Generalized Linear Transport Model for Spatially…
We present a general phase-space kinetic model for charged particle transport through combined localised and delocalised states, capable of describing scattering collisions, trapping, detrapping and losses. The model is described by a…
Stochastic models for spatio-temporal transport face a critical trade-off between physical realism and interpretability. The advection model with a single constant velocity is interpretable but physically limited by its perfect correlation…
The stochastic differential and integral equations describing the system of particles weakly interacting among themselves which are absorbed and scattered by particles of a medium are considered. The time-dependent transport equation with…
Effective medium theory of transport in disordered systems, whose basis is the replacement of spatial disorder by temporal memory, is extended in several practical directions. Restricting attention to a 1-dimensional system with bond…
The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space enables to…
Recently a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other non-linear theories the new approach has the advantage that it provides a full time-dependent description of the…
We derive new diffusion solutions to the monoenergetic generalized linear Boltzmann transport equation (GLBE) for the stationary collision density and scalar flux about an isotropic point source in an infinite $d$-dimensional absorbing…
We present a field theory for the statistics of charge and current fluctuations in diffusive systems. The cumulant generating function is given by the saddle-point solution for the action of this field theory. The action depends on two…
Linear particle transport in stochastic media is key to such relevant applications as neutron diffusion in randomly mixed immiscible materials, light propagation through engineered optical materials, and inertial confinement fusion, only to…
When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…
We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions…
We introduce a non-exponential radiative framework that takes into account the local spatial correlation of scattering particles in a medium. Most previous works in graphics have ignored this, assuming uncorrelated media with a uniform,…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We address the description of solutes flow with trapping processes in porous media. Starting from a small-scale model for tracer particles trajectories, we derive the corresponding governing equations for the concentration of the mobile and…
A general approach for investigating transport phenomena in porous media is presented. This approach has the capacity to represent various kinds of irregularity in porous media without the need for excessive detail or computational effort.…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We propose exact results for the full counting statistics, or the scaled cumulant generating function, pertaining to the transfer of arbitrary conserved quantities across an interface in homogeneous integrable models out of equilibrium. We…
This paper develops a scattering theory for the asymmetric transport observed at interfaces separating two-dimensional topological insulators. Starting from the spectral decomposition of an unperturbed interface Hamiltonian, we present a…
A non-perturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line…
Superdiffusion is an anomalous transport behavior. Recently, a new mechanism, termed the ``nodal mechanism," has been proposed to induce superdiffusion in quantum models. However, existing realizations of the nodal mechanism have so far…