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Symmetric conservative form of low-temperature phonon gas hydrodynamics

I.-Kinetic aspect of the theory

  • Published:
Il Nuovo Cimento D

Summary

The low-temperature phonon gas hydrodynamics, proposed by Nielsen and Skhlovsky, is reconsidered as the next example of the physical system which admits the symmetric conservative form of the governing equations. By means of this example, the unique correspondence between the hydrodynamics equations admitting symmetric conservative form and the description of the state of a gas by the distribution function, which maximizes the entropy and the entropy flux under the respective set of constraints, is demonstrated. It is shown that such a distribution function implies concavity of the entropy, hyperbolicity of the system of governing equations and the finite speeds of propagation of disturbances in the neighbourhood of the local thermodynamic equilibrium. It is also indicated that the theory considerably simplifies when the domain of phonon wave vectors is approximated by the whole three-dimensional vector space.

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Authors and Affiliations

  1. Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Swiętokrzyska 21, 00-049, Warsaw, Poland

    W. Larecki & S. Piekarski

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  1. W. Larecki
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  2. S. Piekarski
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The authors of this paper have agreed to not receive the proofs for correction.

This work was supported in 50% by C.P.B.P.02.01 and in 50% by C.P.B.P.02.03. The reported research was performed with the framework of joint research program of the Department of the Theory of Continuous Media at the Institute of Fundamental Technological Research Polish Academy of Sciences and the Faculty of Physic at the University of Padeborn, FRG.

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Larecki, W., Piekarski, S. Symmetric conservative form of low-temperature phonon gas hydrodynamics. Il Nuovo Cimento D 13, 31–53 (1991). https://doi.org/10.1007/BF02451273

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  • DOI: https://doi.org/10.1007/BF02451273

PACS 63.20

PACS 66.70

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