Related papers: Lagrangian based heat conduction
Direct numerical simulations of the time dependent parallel heat transport equation modeling heat pulses driven by power modulation in 3-dimensional chaotic magnetic fields are presented. The numerical method is based on the Fourier…
Let $L_t:=\Delta_t+Z_t$ for a $C^{1,1}$-vector field $Z$ on a differential manifold $M$ with boundary $\partial M$, where $\Delta_t$ is the Laplacian induced by a time dependent metric $g_t$ differentiable in $t\in [0,T_c)$. We first…
We study temperature distribution in a heat conducting problem, for a system of p-Laplace equation, giving rise to a free boundary.
We propose a unified framework to study the turbulent transport problem from the perspective of nonequilibrium statistical mechanics. By combining Krarichnan's turbulence thermalization assumption and Ruelle's recent work on nonequilibrium…
Phonon heat transport in mesoscopic systems is investigated using methods analogous to the Landauer description of electrical conductance. A "universal heat conductance" expression that depends on the properties of the conducting pathway…
We present a detailed derivation of Fourier's law in a class of stochastic energy exchange systems that naturally characterize two-dimensional mechanical systems of locally confined particles in interaction. The stochastic systems consist…
Given a connected compact Riemannian manifold $(M,g)$ without boundary, $\dim M\ge 2$, we consider a space--time fractional diffusion equation with an interior source that is supported on an open subset $V$ of the manifold. The…
In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if $\phi$ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition…
We provide the details of an implementation of Fourier techniques for solving second-order linear partial differential equations (with constant coefficients) using a computer algebra system. The general Sturm-Liouville problem for the heat,…
Exact assessment of thermal spreading resistance is of great importance to the thermal management of electronic devices, especially when completely considering the heat conduction process from the nanoscale heat source to the macroscopic…
We study by means of numerical simulations the model of dissipative particle dynamics with energy conservation for the simple case of thermal conduction. It is shown that the model displays correct equilibrium fluctuations and reproduces…
Basic derivative formulas are presented for hypoelliptic heat semigroups and harmonic functions extending earlier work in the elliptic case. Emphasis is placed on developing integration by parts formulas at the level of local martingales.…
The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size $L$ is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, $T_{h}$ and…
We develop a theory for heat transport via electromagnetic waves inside media, and use it to derive a spatially nonlocal thermal conductivity tensor, in terms of the electromagnetic Green's function and potential, for any given system.…
Applying simultaneously the methodology of Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC), we demonstrate that, in…
The propagators (fundamental solutions) of the heat and Schr\"odinger's equations on the half-line with a combined harmonic oscillator and inverse-square potential calculated in the recent paper [{\em J. Math. Phys.} {\bf 59}, 051507…
Extended irreversible thermodynamics is a theory that expands the classical framework of nonequilibrium thermodynamics by going beyond the local-equilibrium assumption. A notable example of this is the Maxwell-Cattaneo heat flux model,…
In this paper we introduce a stochastic integral with respect to the solution X of the fractional heat equation on [0,1], interpreted as a divergence operator. This allows to use the techniques of the Malliavin calculus in order to…
We show that the heat transport between two bodies, mediated by electromagnetic fluctuations, can be controlled with an intermediate quantum circuit - leading to the device concept Mesoscopic Photon Heat Transistor (MPHT). Our theoretical…
Let $\Omega$ be a two-dimensional heat conduction body. We consider the problem of determining the heat source $F(x,t)=\varphi(t)f(x,y)$ with $\varphi$ be given inexactly and $f$ be unknown. The problem is nonlinear and ill-posed. By a…