Physical Mesomechanics

, Volume 20, Issue 3, pp 305–310 | Cite as

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

  • A. A. SokolovEmail author
  • A. M. Krivtsov
  • W. H. Müller


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.


heat conduction harmonic crystals one dimensional crystals localized excitations anomalous heat conduction 


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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • A. A. Sokolov
    • 1
    Email author
  • A. M. Krivtsov
    • 1
    • 2
  • W. H. Müller
    • 3
  1. 1.Peter the Great Saint-Petersburg Polytechnic UniversitySt.-PetersburgRussia
  2. 2.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSt.-PetersburgRussia
  3. 3.Institute of Mechanics, Chair of Continuum Mechanics and Constitutive TheoryTechnische Universität BerlinBerlinGermany

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