Related papers: Lagrangian based heat conduction
The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier-Stokes-Duhem equations together with the continuity and thermal…
We use the integral form of the Boltzmann equation which allows us to take into account the memory effects using the initial condition that selects the solutions going to the local equilibrium Maxwell distribution in the $t \to -\infty$…
In this paper, we consider the Fourier spectral method for numerically solving the 2D convective Cahn-Hilliard equation. The semi-discrete and fully discrete schemes are established. Moreover, the existence, uniqueness and the optimal error…
We introduce a simple prescription for calculating the spectra of thermal fluctuations of temperature-dependent quantities of the form $\hat{\delta T}(t)=\int d^3\vec{r} \delta T(\vec{r},t) q(\vec{r})$. Here $T(\vec{r}, t)$ is the local…
The general isotropic constitutive equations of heat conduction with second sound and ballistic propagation in isotropic materials is given using Non-Equilibrium Thermodynamics with Internal Variables (NET-IV). The consequences of Onsager…
In this paper, we present a Hamiltonian and thermodynamic theory of heat transport on various levels of description. Transport of heat is formulated within kinetic theory of polarized phonons, kinetic theory of unpolarized phonons,…
This work investigates the two-dimensional thermal behavior of a bilayer medium subject to both internal and external heat sources. The model incorporates diffusion, advection, and temperature-dependent volumetric heat generation or…
We demonstrate that non-diffusive, fluid-like heat transport, such as heat backflowing from cooler to warmer regions, can be induced, controlled, and amplified in extreme thermal conductors such as graphite and hexagonal boron nitride. We…
The thermal conductivity, $\kappa$, of a homogeneous chain of generically-ranged interacting planar rotors, more precisely the inertial $\alpha-XY$ model, is numerically studied with the coupling constant decaying as $r^{-\alpha}$. The…
The paper introduces a multi-scale processing method for quantitative study and visualization of convective heat transfer using diffractive optical element based background-oriented schlieren technique. The method relies on robust…
I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional systems of arbitrary sizes whose ends are in contact with thermal baths at different…
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…
We consider heat conduction across an ordered oscillator chain with harmonic interparticle interactions and also onsite harmonic potentials. The onsite spring constant is the same for all sites excepting the boundary sites. The chain is…
We analyze some exact and approximate solutions to nonlinear equations for heat transfer models. We prove that recent results derived from a method based on Lie algebras are either trivial or wrong. We test a simple analytical expression…
Using the Onsager-Machlup functional integral approach, we obtain the work distribution function and the distribution of the dissipated heat of a Brownian particle subjected to a confining harmonic potential and an oscillatory driving…
We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its…
The heat equation, based on Fourier's law, is commonly used for description of heat conduction. However, Fourier's law is valid under the assumption of local thermodynamic equilibrium, which is violated in very small dimensions and short…
We investigate the stationary nonequilibrium states of a quasi one-dimensional system of heavy particles whose interaction is mediated by purely elastic collisions with light particles, in contact at the boundary with two heat baths with…
This paper presents an operational framework for the computation of the discretized solutions for relativistic equations of Klein-Gordon and Dirac type. The proposed method relies on the construction of an evolution-type operador from the…
This paper describes a method for efficiently computing parallel transport of tangent vectors on curved surfaces, or more generally, any vector-valued data on a curved manifold. More precisely, it extends a vector field defined over any…