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Lifts of symmetric tensors: Fluids, plasma, and grad hierarchy

Oğul Esen, Miroslav Grmela, Hasan Gümral and Michal Pavelka

Article (2019)

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Cite this document: Esen, O., Grmela, M., Gümral, H. & Pavelka, M. (2019). Lifts of symmetric tensors: Fluids, plasma, and grad hierarchy. Entropy, 21(9). doi:10.3390/e21090907
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Abstract

Geometrical and algebraic aspects of the Hamiltonian realizations of the Euler's fluid and the Vlasov's plasma are investigated. A purely geometric pathway (involving complete lifts and vertical representatives) is proposed, which establishes a link from particle motion to evolution of the field variables. This pathway is free from Poisson brackets and Hamiltonian functionals. Momentum realizations (sections on tau*tau*Q) of (both compressible and incompressible) Euler's fluid and Vlasov's plasma are derived. Poisson mappings relating the momentum realizations with the usual field equations are constructed as duals of injective Lie algebra homomorphisms. The geometric pathway is then used to construct the evolution equations for 10-moments kinetic theory. This way the entire Grad hierarchy (including entropic fields) can be constructed in a purely geometric way. This geometric way is an alternative to the usual Hamiltonian approach to mechanics based on Poisson brackets.

Uncontrolled Keywords

diffeomorphisms group; cotangent lift; vertical representative; fluids; kinetic theory; entropy; continuum-mechanics; poisson brackets; complex fluids; thermodynamics; equations; dynamics; formulation; geometry; moments; systems

Open Access document in PolyPublie
Subjects: 1800 Génie chimique > 1800 Génie chimique
Department: Département de génie chimique
Research Center: Non applicable
Funders: CRSNG/NSERC, Czech Science Foundation, Charles University Research Program
Grant number: 3100319, 3100735, 17-15498Y, UNCE/SCI/023
Date Deposited: 16 Aug 2021 14:26
Last Modified: 17 Aug 2021 01:20
PolyPublie URL: https://publications.polymtl.ca/4857/
Document issued by the official publisher
Journal Title: Entropy (vol. 21, no. 9)
Publisher: MDPI
Official URL: https://doi.org/10.3390/e21090907

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