Related papers: Fractional diffusion limit for collisional kinetic…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
In this article we derive in the hydrodynamic limit a generalized fractional porous medium equation, in the sense that the regional fractional Laplacian is applied to a function of the density given in terms of a power series, instead of a…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
Using the recently developed ``Maximum Entropy'' (or ``least biased'') distribution function to truncate the moment hierarchy arising from kinetic theory, we formulate a far-from-equilibrium macroscopic theory that provides the possibility…
We study a kinetic model for non-reactive mixtures of monatomic gases with hard-sphere cross-sections under isothermal condition. By considering a diffusive scaling of the kinetic model and using the method of moments, we formally obtain…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
In this paper, we provide a result of exponential stability for several dissipative linear kinetic equations with heavy-tailed equilibria. The approach, inspired by the so-called $L^2$-hypocoercivity method, is robust enough to provide…
We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from averaging the…
Diffusion with multipole-moment conservation gives rise to transport laws that generalize Fick's law and has attracted growing attention following experimental advances in strongly tilted optical lattices. It was recently shown that…
A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum…
This paper is devoted to kinetic equations without confinement. We investigate the large time behaviour induced by collision operators with fat tailed local equilibria. Such operators have an anomalous diffusion limit. In the appropriate…
Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…
In this article we derive the fractional porous medium equation for any power of the fractional Laplacian as the hydrodynamic limit of a microscopic dynamics of random particles with long range interactions, but the jump rate highly depends…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian…
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.…
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…
The problem of diffusion in a time-dependent (and generally inhomogeneous) external field is considered on the basis of a generalized master equation with two times, introduced in [1,2]. We consider the case of the quasi Fokker-Planck…
This paper investigates the diffusion limit of a kinetic BGK-type equation, focusing on its relaxation to a nonlinear aggregation-diffusion equation, where the diffusion exhibits a porous-medium-type nonlinearity. Unlike previous studies by…
Self-diffusion along the longitudinal coordinate in a channel of varying cross section is considered. The starting point is the two-dimensional Enskog-Boltzmann-Lorentz kinetic equation with appropriated boundary conditions. It is…