Related papers: Transportation cost inequalities for diffusions un…
Transport processes underpin a multitude of phenomena, ranging from the propagation of atoms on lattices, to the mobility patterns of microorganisms and earthquakes, to name a few. The dynamics of these processes is very rich and key to…
Energy-transport equations for the transport of fermions in optical lattices are formally derived from a Boltzmann transport equation with a periodic lattice potential in the diffusive limit. The limit model possesses a formal gradient-flow…
We study in this article the existence and uniqueness of solutions to a class of stochastic transport equations with irregular coefficients and unbounded divergence. In the first result we assume the drift is $L^{2}([0,T] \times \R^{d})\cap…
The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions…
Diffusion, a ubiquitous phenomenon in nature, is a consequence of particle number conservation and locality, in systems with sufficient damping. In this paper we consider diffusive processes in the bulk of Weyl semimetals, which are exotic…
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or…
In this paper, we develop a general methodology to prove weak uniqueness for stochastic differential equations with coefficients depending on some path-functionals of the process. As an extension of the technique developed by Bass \&…
Diffusion coefficients are obtained from linear response functions and from the quantal fluctuation dissipation theorem. They are compared with the results of both the theory of hydrodynamic fluctuations by Landau and Lifschitz as well as…
We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The enhancement of the diffusive transport depends on the system size L and grows…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
A class of functional differential equations are investigated. Using the Girsanov-transformation argument we establish the quadratic transportation cost inequalities for a class of finite-dimensional neutral functional stochastic…
We prove Strichartz estimates for the kinetic transport equation. Our results extend considerably the known in the literature range of the Strichartz estimates for that equation.
In the classical transport theory, the coefficients such as the diffusion, thermal conductivity and viscosity of fluid are usually expressed in a form proportional to the mean free path of molecules. We point out that this may cause a great…
Thermal motion in complex fluids is a complicated stochastic process but ubiquitously exhibits initial ballistic, intermediate sub-diffusive, and long-time non-Gaussian diffusive motion, unless interrupted. Despite its relevance to numerous…
It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in…
We derive third order transport coefficients of skewness for a phase-space kinetic model that considers the processes of scattering collisions, trapping, detrapping and recombination losses. The resulting expression for the skewness tensor…
In this work assuming valid the equipartition theorem and using the normalized q-expectation value, we obtain, until first order approximation, the hydrodynamics equation for the generalized statistics. This equations are different from…
In this work, we consider a one-dimensional It{\^o} diffusion process X t with possibly nonlinear drift and diffusion coefficients. We show that, when the diffusion coefficient is known, the drift coefficient is uniquely determined by an…