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This article is cited in 2 scientific papers (total in 2 papers)
Universality of the relaxation structure of equations for the dynamics of continuous media and dissipative Poisson brackets
M. Yu. Kovalevskyab, V. T. Matskevichb, A. Ya. Razumnyic a Belgorod State University
b National Science Centre Kharkov Institute of Physics and Technology
c V. N. Karazin Kharkiv National University
Abstract:
We generalize the Hamilton equations for dynamical processes with relaxation. We introduce a dissipative Poisson bracket in terms of the dissipation function. We obtain the universal structure of the relaxation terms in the equations for the dynamics of condensed media and verify this result for structureless liquids, elastic solids, and quantum liquids. In the examples of the condensed media under consideration, we obtain expressions for the dissipative Poisson brackets for the complete set of dynamical parameters.
Keywords:
Hamiltonian approach, entropy, dissipative Poisson bracket, kinetic coefficient, solid, quantum liquid, dissipation function.
Received: 10.01.2008 Revised: 10.04.2008
Citation:
M. Yu. Kovalevsky, V. T. Matskevich, A. Ya. Razumnyi, “Universality of the relaxation structure of equations for the dynamics of continuous media and dissipative Poisson brackets”, TMF, 158:2 (2009), 277–291; Theoret. and Math. Phys., 158:2 (2009), 233–245
Linking options:
https://www.mathnet.ru/eng/tmf6314https://doi.org/10.4213/tmf6314 https://www.mathnet.ru/eng/tmf/v158/i2/p277
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Abstract page: | 625 | Full-text PDF : | 232 | References: | 94 | First page: | 11 |
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