Localized heat perturbation in harmonic 1D crystals: Solutions for the equation of anomalous heat conduction

被引：21
作者：
Sokolov, A. A. [1 ]
Krivtsov, A. M. [1 ,2 ]
Mueller, W. H. [3 ]
机构：
[1] Peter Great St Petersburg Polytech Univ, St Petersburg 195251, Russia
[2] Russian Acad Sci, Inst Problems Mech Engn, St Petersburg 199178, Russia
[3] Tech Univ Berlin, Chair Continuum Mech & Constitut Theory, Inst Mech, D-10587 Berlin, Germany
来源：
PHYSICAL MESOMECHANICS | 2017年 / 20卷 / 03期
基金：
俄罗斯科学基金会;
关键词：
heat conduction; harmonic crystals; one dimensional crystals; localized excitations; anomalous heat conduction; ENERGY OSCILLATIONS; LA CHALEUR; LEQUATION;
D O I：
10.1134/S1029959917030067
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
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/root 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.
引用
收藏
页码：305 / 310
页数：6
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