Related papers: A note on an invariant for one-dimensional heat co…
The purpose of this work is to produce a family of equations describing the evolution of the temperature in a rigid heat conductor. This is obtained by means of successive approximations of the Fourier law, via memory relaxations and…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
In this reply we answer the comment by A. Dhar (cond-mat/0203077) on our Letter "Simple one dimensional model of heat conduction which obeys Fourier's law" (Phys. Rev. Lett. 86, 5486 (2001), cond-mat/0104453)
This brief note aims at condensing some results on the 32-point approximate DFT and discussing its arithmetic complexity.
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
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…
We derive Fourier's law for a completely coherent quasi one--dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show…
Heat conduction of one-dimensional chain of equivalent rigid particles in the field of external on-site potential is considered. Zero diameters of the particles correspond to exactly integrable case with divergent heat conduction…
We study numerically the thermal conductivity in several different one dimensional chains. We show that the phonon-lattice interaction is the main ingredient of the Fourier heat law. Our argument provides a rather satisfactory explanation…
We propose an extension to the original result derived by Simoncelli et al. (https://doi.org/10.1038/s41567-019-0520-x) to encompass the effects of a space and time dependent heat source. Via a Fourier Transfrom, we obtain closed form…
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…
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…
These brief lecture notes are intended mainly for undergraduate students in engineering or physics or mathematics who have met or will soon be meeting the Dirac delta function and some other objects related to it. These students might have…
We introduce a new method for computing the heat invariants of a 2-dimensional Riemannian manifold based on a result by S.Agmon and Y.Kannai. Two explicit expressions for the heat invariants are presented. The first one depends on the…
When the variations of surface temperature are measured both spatially and temporally, analytical expressions that correctly account for multi-dimensional transient conduction can be applied. To enhance the accessibility of these accurate…
The aim of this note is to provide a natural extension of Gelfond's constant $e^\pi$ using a hypergeometric function approach. An extension is also found for the square root of this constant. A few interesting special cases are presented.
The note contains the proof of the uniqueness theorem for the inverse problem in the case of $n$-th order differential equation.
Heat conduction experiments are performed in order to identify effects beyond Fourier. Two experimental setups are discussed. First, a simple experiment by a heterogeneous material is investigated from the point of view of generalized heat…
We study the dynamical correlation functions and heat conduction for the simplest model of quasi one-dimensional (1d) dielectric crystal i.e. a chain of classical particles coupled by quadratic and cubic intersite potential. Even in the…
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…