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Some problems of the statistical description of hydrodynamic motion and autowave processes

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  • Klimontovich, Yu.L.

Abstract

The main aim of this report is to expose some ideas, methods and results concerning the statistical description of autowave processes in any active medium and of the hydrodynamic motion in liquids on the basis of the kinetic equations for the joint distribution functions of the internal and space variables of these media. For transition to hydrodynamic equations, “physical Knudsen parameter” is used instead of the Knudsen parameter. The role of self-diffusion is considered. Three examples of active media of small macroscopic elements are presented: a medium of bistable elements, a medium of Van der Pol oscillators and a medium with chemical reactions. In all cases the generalized Fisher-Kolmogorov-Petrovski-Piscunov (FKPP) equations are obtained from the kinetic equations. For the description of kinetic fluctuations, the corresponding Langevin equations are considered.

Suggested Citation

  • Klimontovich, Yu.L., 1991. "Some problems of the statistical description of hydrodynamic motion and autowave processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 179(3), pages 471-495.
    • Handle: RePEc:eee:phsmap:v:179:y:1991:i:3:p:471-495
    DOI: 10.1016/0378-4371(91)90089-U
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