Localized heat perturbation in harmonic 1D crystals: Solutions for the equation of anomalous heat conduction |
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| Authors: | A. A. Sokolov A. M. Krivtsov W. H. Müller |
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| Affiliation: | 1.Peter the Great Saint-Petersburg Polytechnic University,St.-Petersburg,Russia;2.Institute of Problems of Mechanical Engineering,Russian Academy of Sciences,St.-Petersburg,Russia;3.Institute of Mechanics, Chair of Continuum Mechanics and Constitutive Theory,Technische Universit?t Berlin,Berlin,Germany |
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| Abstract: | ![]()
In this paper exact analytical solutions for the equation that describes anomalous heat propagation in a harmonic 1D lattices are obtained. Rectangular, triangular and sawtooth initial perturbations of the temperature field are considered. The solution for an initially rectangular temperature profile is investigated in detail. It is shown that the decay of the solution near the wavefront is proportional to (1/sqrt t ). In the center of the perturbation zone the decay is proportional to 1/t. Thus, the solution decays slower near the wavefront, leaving clearly visible peaks that can be detected experimentally. |
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