相关论文: Heat equation on a network using the Fokas method

We consider the heat equation for monolayer two-dimensional materials in the presence of heat flow into a substrate and Joule heating due to electrical current. We compare devices including a nanowire of constant width and a bow tie (or…

In this work we investigate heat conduction along a ladder-model conformed by two coupled one dimensional lattices with different anharmonicity. We study how the interchain coupling modifies the thermal properties of the isolated systems.…

In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving…

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order…

We address the problem of heat conduction in 1-D nonlinear chains; we show that, acting on the parameter which controls the strength of the on site potential inside a segment of the chain, we induce a transition from conducting to…

The first part of this chapter gives an introduction to heat transfer and cooling techniques at low temperature. We review the fundamental laws of heat transfer (conduction, convection and radiation) and give useful data specific to…

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…

In modern surgery, a multitude of minimally intrusive operational techniques are used which are based on the punctual heating of target zones of human tissue via laser or radio-frequency currents. Traditionally, these processes are modeled…

We investigate heat transport through a one-dimensional open coupled scalar field theory, depicted as a network of harmonic oscillators connected to thermal baths at the boundaries. The non-Hermitian dynamical matrix of the network…

We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as…

We present the computer simulation results of a chain of hard point particles with alternating masses interacting on its extremes with two thermal baths at different temperatures. We found that the system obeys Fourier's law at the…

In this paper, we show that a hybrid method using coupled boundary measurements can determine electrical conductivity, thermal conductivity, and the product of heat capacity and heat density within a bounded domain on the plane uniquely up…

I analyse the transport of particles of arbitrary statistics (Bose, Fermi and fractional exclusion statistics) through one-dimensional (1D) channels. Observing that the particle, energy, entropy and heat fluxes through the 1D channel are…

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

In this paper, we study the heat equation with an irregular spatially dependent thermal conductivity coefficient. We prove that it has a solution in an appropriate very weak sense. Moreover, the uniqueness result and consistency with the…

The paper revisits recent counterintuitive results on divergence of heat conduction coefficient in two-dimensional lattices. It was reported that in certain lattices with on-site potential, for which one-dimensional chain has convergent…

The realization of single-molecule thermal conductance measurements has driven the need for theoretical tools to describe conduction processes that occur over atomistic length scales. In macroscale systems, the principle that is typically…

Common intuition tells us that if one part of a connected system is cooled continuously, the other parts should also cool down. This intuition can be given a microscopic foundation for the case of a generic quantum system coupled to a…

Using previous results and general thermodynamical formalism,an expression is obtained for the specific heat per particle under constant volume of a degenerate non-relativistic electron gas on a 1D lattice.The result is a non-linear…

It is necessary to use more general models than the classical Fourier heat conduction law to describe small-scale thermal conductivity processes. The effects of heat flow memory and heat capacity memory (internal energy) in solids are…