English
Related papers

Related papers: Series Solutions for Orthotropic Diffusion in a Cu…

200 papers

Using a so-called hemispherical model we derive a general transport equation for cosmic ray and thermal particles scattered in pitch angle by magnetic inhomogeneities in a moving collisionless plasma. The weak scattering through 90 degrees…

Astrophysics · Physics 2009-11-11 V. N. Zirakashvili

We study the diffusive dynamics of a Brownian particle in proximity of a flat surface under non-equilibrium conditions, which are created by an anisotropic thermal environment with different temperatures being active along distinct spatial…

Statistical Mechanics · Physics 2017-09-13 Stefano Bo , Ralf Eichhorn

We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 J. Vidal , R. Mosseri , J. Bellissard

We discuss the molecular diffusion transport in infinitely dilute liquid solutions under non-isothermal conditions. This discussion is motivated by an occurring misinterpretation of thermodynamic transport equations written in terms of…

Statistical Mechanics · Physics 2018-04-18 Denis S. Goldobin

We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…

Analysis of PDEs · Mathematics 2017-08-04 Peter D. Miller , David A. Smith

It has been observed in many numerical simulations, experiments and from various theoretical treatments that heat transport in one-dimensional systems of interacting particles cannot be described by the phenomenological Fourier's law. The…

Statistical Mechanics · Physics 2019-11-12 Abhishek Dhar , Anupam Kundu , Aritra Kundu

We analyze numerically a forward-backward diffusion equation with a cubic-like diffusion function, -emerging in the framework of phase transitions modeling- and its "entropy" formulation determined by considering it as the singular limit of…

Analysis of PDEs · Mathematics 2010-08-31 Pauline Lafitte , Corrado Mascia

The spatial diffusion of cosmic rays in turbulent magnetic fields can, in the most general case, be fully anisotropic, i.e. one has to distinguish three diffusion axes in a local, field-aligned frame. We reexamine the transformation for the…

We derive an explicit representation of the fundamental solution to the heat equation in a half-space of ${\mathbb R}^N$ with a diffusive dynamical boundary condition, and establish sharp pointwise upper and lower bounds. We also…

Analysis of PDEs · Mathematics 2026-04-02 Kazuhiro Ishige , Sho Katayama , Tatsuki Kawakami

Context: Thermal conductivity provides important contributions to the energy evolution of the upper solar atmosphere, behaving as a non-linear concentration-dependent diffusion equation. Recently, different methods have been offered as…

Solar and Stellar Astrophysics · Physics 2024-12-11 George Cherry , Boris Gudiksen , Mikolaj Szydlarski

We consider the Navier--Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A…

Analysis of PDEs · Mathematics 2020-09-24 Ling Wan , Tao Wang

The wave-like nature of electrons leads to the existence of upper bounds on the thermoelectric response of nanostructured devices [R. S. Whitney, Phys. Rev. Lett. 112, 130601 (2014); Phys. Rev. B 91, 115425 (2015)]. This fundamental result,…

Mesoscale and Nanoscale Physics · Physics 2022-08-24 Giuseppe Bevilacqua , Alessandro Cresti , Giuseppe Grosso , Guido Menichetti , Giuseppe Pastori Parravicini

We investigate the dynamics of plasma-based acceleration processes with collisionless particle dynamics and non negligible thermal effects. We aim at assessing the applicability of fluid-like models, obtained by suitable closure assumptions…

We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds c {\in}]c*,…

Analysis of PDEs · Mathematics 2014-12-19 Léonard Monsaingeon , Alexeï Novikov , Jean-Michel Roquejoffre

In the present paper we propose a reduced temperature non-equilibrium model for simulating multicomponent flows with inter-phase heat transfer, diffusion processes (including the viscosity and the heat conduction) and external energy…

Numerical Analysis · Mathematics 2021-08-19 Chao Zhang , Lifeng Wang , Zhijun Shen , Zhiyuan Li , Igor Menshov

We present a robust and accurate numerical method for the anisotropic diffusion equation in curvilinear coordinates. This study extends the recent work [Muir et al., Computer Physics Communications, 2025] for solving the anisotropic…

Numerical Analysis · Mathematics 2026-04-23 Dean Muir , Kenneth Duru , Stuart Hudson , Matthew Hole

We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following [Du Toit et al., Comp. Phys.…

Computational Physics · Physics 2024-09-11 L. Chacon , Jason Hamilton , Natalia Krasheninnikova

We establish existence of global-in-time weak solutions to the one dimensional, compressible Navier-Stokes system for a viscous and heat conducting ideal polytropic gas (pressure $p=K\theta/\tau$, internal energy $e=c_v \theta$), when the…

Analysis of PDEs · Mathematics 2009-06-26 Helge Kristian Jenssen , Trygve Karper

We expand previous work on an inverse approach to Einstein Field Equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of…

General Relativity and Quantum Cosmology · Physics 2011-02-01 James Richardson , Mustapha Ishak

We present a novel implementation of an extremum preserving anisotropic diffusion solver for thermal conduction on the unstructured moving Voronoi mesh of the AREPO code. The method relies on splitting the one-sided facet fluxes into normal…

Cosmology and Nongalactic Astrophysics · Physics 2016-02-17 Rahul Kannan , Volker Springel , Rüdiger Pakmor , Federico Marinacci , Mark Vogelsberger