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We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature) profile from a given initial distribution, by diagonalising the Hamiltonian, i.e., the Laplacian with alternating diffusion constants, and expanding the temperature profile by its eigenstates. We show that there are basically phases with or without edge states. The edge states affect the heat conduction around heat baths. In particular, rapid heat transfer to heat baths would be observed in a short time regime, which is estimated to be $t<10^{-2}$s for $asim 10^{-3}$m system and $t< 1$s for $asim 10^{-2}$m system composed of two kinds of familiar metals such as titanium, zirconium and aluminium, gold, etc. We also discuss the effective lattice model which simplifies the calculation of edge states up to high energy. It is suggested that these high energy edge states also contribute to very rapid heat conduction in a very short time regime.
We study the relativistic heat equation in one space dimension. We prove a local regularity result when the initial datum is locally Lipschitz in its support. We propose a numerical scheme that captures the known features of the solutions and allows
In this paper we give a brief review of the relation between microscopic dynamical properties and the Fourier law of heat conduction as well as the connection between anomalous conduction and anomalous diffusion. We then discuss the possibility to control the heat flow.
We analyze the heat current flowing across interacting quantum dots within the Coulomb blockade regime. Power can be generated by either voltage or temperature biases. In the former case, we find nonlinear contributions to the Peltier effect that are
Heat conduction of a real quasi-one dimensional material, the finite length carbon nanowire (CNW), inserted into the single-walled carbon nanotube (SWNT) has been studied by the molecular dynamical (MD) method, in which both of the longitudinal as we
The world communicates to our senses of vision, hearing and touch in the language of waves, as the light, sound, and even heat essentially consist of microscopic vibrations of different media. The wave nature of light and sound has been extensively i