Matched pair analysis of the Vlasov plasma
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Dosyalar
Tarih
2021-06
Yazarlar
Dergi Başlığı
Dergi ISSN
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Yayıncı
American Institute of Mathematical Sciences-AIMS
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
We present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these (Lie-Poisson) systems as couplings of mutually interacting (Lie-Poisson) subdynamics. The mutual interaction is beyond the well-known semi-direct product theory. Accordingly, as the geometric framework of the present discussion, we address the matched pair Lie-Poisson formulation allowing mutual interactions. Moreover, both for the kinetic moments and the Vlasov plasma cases, we observe that one of the constitutive subdynamics is the compressible isentropic fluid flow, and the other is the dynamics of the kinetic moments of order >= 2. In this regard, the algebraic/geometric (matched pair) decomposition that we offer, is in perfect harmony with the physical intuition. To complete the discussion, we present a momentum formulation of the Vlasov plasma, along with its matched pair decomposition.
Açıklama
The first named author would like to thank Hasan Gumral for the enlightening discussions on the Vlasov plasma, especially on the momentumVlasov dynamics. OE would also like to express his gratitute to Miroslav Grmela, Michal Pavelka, and Petr Vagner for the illuminating discussions on the (ir)reversible plasma dynamics. Both authors present their hearthy thanks to Mansur Ismailov for the clarifying discussions on the functional analytical details. The authors acknowledge the support by TUBITAK (the Scientific and Technological Research Council of Turkey) under the project "Matched pairs of Lagrangian and Hamiltonian Systems" with the project number 117F426.
Anahtar Kelimeler
Brackets, Dynamics, Equations, Geometry, Hopf-Algebras, Lifts, Lie-poisson equation, Matched pairs of Lie Algebras, Matched pairs of Lie groups, Moments, Poisson-Lie-groups, Products, Tulczyjews triplet, Vlasov plasma
Kaynak
Journal Of Geometric Mechanics
WoS Q Değeri
Q4
Scopus Q Değeri
Cilt
13
Sayı
2
Künye
Esen, O. & Sütlü, S. (2021). Matched pair analysis of the Vlasov plasma. Journal Of Geometric Mechanics, 13(2), 209-246. doi:10.3934/jgm.2021011
