Related papers: Preserving Monotonicity in Anisotropic Diffusion
We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. In the case of simplicial meshes, the…
Inspired by non-Hermitian physics, Li et al. (Science 364, 170-173) theoretically predicted and experimentally demonstrated a stationary temperature profile in a diffusive heat transfer system - seemingly indicating that heat "stops"…
Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new…
Temperature is a major source of inaccuracy in high-sensitivity accelerometers and gravimeters. Active thermal control systems require power and may not be ideal in some contexts such as airborne or spaceborne applications. We propose a…
We study the numerical anisotropy existent in compact difference schemes as applied to hyperbolic partial differential equations, and propose an approach to reduce this error and to improve the stability restrictions based on a previous…
We initiate a study of anisotropic plasma at strong coupling using the AdS/CFT correspondence. We construct an exact dual geometry which represents a static uniform but anisotropic system and find, that although it is singular, it allows…
Thermal equilibrium properties of nanoscale systems deviate from standard macroscopic predictions due to a non-negligible coupling to the environment. For anisotropic three-dimensional materials, we derive the mean force corrections to the…
In this work, high order asymptotic preserving schemes are constructed and analysed for kinetic equations under a diffusive scaling. The framework enables to consider different cases: the diffusion equation, the advection-diffusion equation…
We construct numerical schemes to solve kinetic equations with anomalous diffusion scaling. When the equilibrium is heavy-tailed or when the collision frequency degenerates for small velocities, an appropriate scaling should be made and the…
The present paper examines the possibility of asymmetric effect of the adjacent to barrier physically different media, or anisotropic structure of the barrier itself, on probability of the oppositely directed transitions of current carriers…
According to conventional wisdom, a system placed in an environment with a different temperature tends to relax to the temperature of the latter, mediated by the flows of heat and/or matter that are set solely by the temperature difference.…
We study in details the dynamics of the one dimensional symmetric trap model, via a real-space renormalization procedure which becomes exact in the limit of zero temperature. In this limit, the diffusion front in each sample consists in two…
X-ray observations of hot gas in galaxy clusters often show steeper temperature gradients across cold fronts -- contact discontinuities, driven by the differential gas motions. These sharp (a few kpc wide) surface brightness/temperature…
Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems…
We investigate the anharmonic phonon scattering across a weakly interacting interface by developing a quantum mechanics-based theory. We find that the contribution from anharmonic three-phonon scatterings to interfacial thermal conductance…
We present some new nonparametric estimators of entropies and we establish almost sure consistency and central limit Theorems for some of the most important entropies in the discrete case. Our theorical results are validated by simulations.
We study stochastic particle systems that conserve the particle density and exhibit a condensation transition due to particle interactions. We restrict our analysis to spatially homogeneous systems on finite lattices with stationary product…
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and second law are formulated consistently. In the linear response regime,…
We initiate a non-perturbative study of anisotropic, non-conformal and confining gauge theories that are holographically realized in gravity by generic Einstein-Axion-Dilaton systems. In the vacuum our solutions describe RG flows from a…
An intriguing phenomenon in non-equilibrium quantum thermodynamics is the asymmetry of thermal processes. Relaxation to thermal equilibrium is the most important dissipative process, being a key concept for the design of heat engines and…