Related papers: Anisotropic tempered diffusion equations
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these…
The temporal Fokker-Planck equation is analytically integrated in an arbitrary number of spatial dimensions but with the 2D and 3D results highlighted. It is shown that a temporal power-law ansatz for the anisotropic diffusion coefficients…
The quark-gluon plasma created in a relativistic heavy-ion collisions possesses a sizable pressure anisotropy in the local rest frame at very early times after the initial nuclear impact and this anisotropy only slowly relaxes as the system…
In this paper, we study all transport coefficients of second-order dissipative fluid dynamics derived by V. E. Ambrus et al. [Phys. Rev. D 106, 076005 (2022)] from the relativistic Boltzmann equation in the relaxation-time approximation for…
We consider the free boundary problems of degenerate elliptic equations that describe the level set formulation of the interface motion evolved by anisotropic forced mean curvature flows. The type of free boundary problems in this paper was…
We formulate a stochastic equation to model the erosion of a surface with fixed inclination. Because the inclination imposes a preferred direction for material transport, the problem is intrinsically anisotropic. At zeroth order, the…
Slender rods in concentrated suspensions constitute strongly interacting systems with rich dynamics: transport slows down drastically and the anisotropy of the motion becomes arbitrarily large. We develop a mesoscopic description of the…
We use an orthonormal frame approach to provide a general framework for the first order hyperbolic reduction of the Einstein equations coupled to a fairly generic class of matter models. Our analysis covers the special cases of dust and…
We apply the second-order Israel-Stewart theory of relativistic fluid- and thermodynamics to a physically realistic model of a radiative fluid in a simple anisotropic cosmological background. We investigate the asymptotic future of the…
The P-wave slowness and group-velocity surfaces in elliptically anisotropic media are ellipsoids. Elliptical anisotropy is convenient to use as the reference medium in perturbation methods designed to solve P-wave wave-propagation problems…
In this letter, we propose a reduced-order model to bridge the particle transport mechanics and the macroscopic fluid dynamics in the highly scattered regime. A rigorous mathematical derivation and a concise physical interpretation are…
In this paper, we consider functionals based on moments and non-linear entropies which have a linear growth in time in case of source-type so-lutions to the fast diffusion or porous medium equations, that are also known as Barenblatt…
We prove a hydrodynamic limit for the totally asymmetric simple exclusion process with spatially inhomogeneous jump rates given by a speed function that may admit discontinuities. The limiting density profiles are described with a…
A complete theoretical presentation of the Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor (CAFFE model) is given. The CAFFE model is an application of the theory of mixtures with continuous…
We develop a recursive approach for deriving closed-form solutions to both conditional and unconditional moments of affine jump diffusions with state-independent jump intensities. Using these moment solutions, we construct closed-form…
Consider a balance law where the flux depends explicitly on the space variable. At jump discontinuities, modeling considerations may impose the defect in the conservation of some quantities, thus leading to non conservative products. Below,…
We put forward a complete theory on moment explosion for fairly general state-spaces. This includes a characterization of the validity of the affine transform formula in terms of minimal solutions of a system of generalized Riccati…
A thermodynamic framework that predicts the thermal conductivity $\lambda$ of simple fluids beyond the dilute-gas limit is introduced. By generalizing the transition-rate approach of particles on a lattice to conserved quantities in…
A simple expression for the non-equilibrium distribution function in ultra-fast transient processes is proposed. Postulating its dependence on temporal derivatives of the equilibrium integrals of motion, non-equilibrium analogues of the…
We derive a functional for the entropy contributed by any microscopic degrees of freedom as arising from their measurable pair correlations. Applicable both in and out of equilibrium, this functional yields the maximum entropy which a…