相关论文: Identification of nonlinear heat conduction laws

Thermal conduction is an important energy transfer and damping mechanism in astrophysical flows. Fourier's law - the heat flux is proportional to the negative temperature gradient, leading to temperature diffusion - is a well-known…

We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and…

The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs and how we treated it. It is demonstrated that the Guyer-Krumhansl equation…

Thermal boundary conductance (TBC) is critical in many thermal and energy applications. A decades-old puzzle has been that many of the measured TBCs, such as those well characterized across Al/Si and ZnO/GaN interfaces, significantly exceed…

Compared to other formulations of the second law of thermodynamics, the Clausius statement that heat does not spontaneously flow from cold to hot concerns a system in non-equilibrium states, and in that respect is more ambitious but also…

We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…

In our former study (J. Phys. A: Math. Theor. 43, (2010) 325210 or arXiv:1002.0999v1 [math-ph]) we introduced a modified Fourier-Cattaneo law and derived a non-autonomous telegraph-type heat conduction equation which has desirable…

We consider unsteady ballistic heat transport in a semi-infinite Hooke chain with free end and arbitrary initial temperature profile. An analytical description of the evolution of the kinetic temperature is proposed in both discrete (exact)…

We are concerned with the Calder\'on problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the…

We review all the calculations necessary for the construction of a Lyapunov like functional for nonlinear stability analysis of steady states in thermodynamically isolated/open systems composed of compressible heat conducting fluids.

We study anomalous heat conduction and anomalous diffusion in low dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat…

We present a rigorous approach that leads, from a many-particle description, to a nonlinear, stochastic constitutive relation for the modeling of transient heat conduction processes at nanoscale. By enforcing statistical consistency, in…

We discuss the problem of heat conduction in classical and quantum low dimensional systems from a microscopic point of view. At the classical level we provide convincing numerical evidence for the validity of Fourier law of heat conduction…

The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction…

We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum…

We study invariant random fields of nonlinear multiplicative stochastic heat equations in the weak disorder regime. Under a natural second-moment condition, we show that positive invariant fields are in one-to-one correspondence with…

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer.…

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 derive rigorous quantum mechanical bounds for the heat current through a nanojunction connecting two thermal baths at different temperatures. Based on exact sum rules, these bounds compliment the well-known quantum of thermal conductance…

We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of…