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The strengths and short-comings of the point-dipole model for polar fluids of spherical molecules are illustrated by considering the physically more relevant case of extended dipoles formed by two opposite charges $\pm q$ separated by a…
The method employed by Einstein to derive his famous relation between the diffusion coefficient and the friction coefficient of a Brownian particle is used to derive a generalized Einstein relation for the mutual diffusion coefficient of a…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is…
In this paper we study a nonlocal reaction-diffusion equation in which the diffusion depends on the gradient of the solution. We prove first the existence and uniqueness of regular and strong solutions. Second, we obtain the existence of…
We study the transport properties of an impurity in a sheared granular gas, in the framework of the Boltzmann equation for inelastic Maxwell models. We investigate here the impact of a nonequilibrium phase transition found in such systems,…
A comparative study of high and zero temperature plasma for the case of damping rate, drag and diffusion coefficients have been presented. In each of these quantities, it is revealed how the magnetic interaction dominates over the electric…
One of the Darken equations gives a relationship between the intrinsic and the tracer diffusion coefficients, $D_A$ and $D_A^*$, of species $A$ in a solid binary mixture. In its original version, the equation reads $D_A = D_A^* \Gamma$,…
In this paper we investigate the variable coefficient two-sided fractional diffusion, advection, reaction equations on a bounded interval. It is known that the fractional diffusion operator may lose coercivity due to the variable…
We analyze diffusion of particles on a two dimensional square lattice. Each lattice site contains an arbitrary number of particles. Interactions affect particles only in the same site, and are macroscopically represented by the excess…
A non-equilibrium thermodynamics model able to analyze the combined effect of diffusion and adsorption in porous materials is proposed. The model considers the coupled dynamics of the diffusive phase, described by a diffusion type equation,…
Experimental studies of systems containing active proteins that undergo conformational changes driven by catalytic chemical reactions have shown that the diffusion coefficients of passive tracer particles and active molecules are larger…
We present a microscopic open quantum systems theory of thermally-damped vortex motion in oblate atomic superfluids that includes previously neglected energy-damping interactions between superfluid and thermal atoms. This mechanism couples…
Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide rigorous mathematical proofs of two types of nonequilibrium FDTs for…
We continue to investigate the diffusive compressible Euler (dcE) model for viscous and heat conducting compressible fluid flow, which has been proposed by M. Sv\"ard as an alternative to the Navier-Stokes-Fourier (NSF) equations. The…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
One considers the motion of a test particle in an homogeneous fluid in equilibrium at temperature $T$, undergoing dissipative collisions with the fluid particles. It is shown that the corresponding linear Boltzmann equation still posseses a…
We calculate the basic parameters of the Fermi Liquid: the scattering vertex, the Landau interaction function, the effective mass, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short ranged interaction at…
The diffusion transport coefficients of a binary granular suspension where one of the components is present in tracer concentration are determined from the (inelastic) Enskog kinetic equation. The effect of the interstitial gas on the solid…
We present a discussion of the linear thermoelectric response of an interacting electron gas in a quantizing magnetic field. Boundary currents can carry a significant fraction of the net current passing through the system. We derive general…