Geometry of plasma dynamics II: Lie algebra of Hamiltonian vector fields

Esen, Oğul; Gümral, Hasan

doi:10.3934/jgm.2012.4.239

Cited by 18 publications

(24 citation statements)

References 41 publications

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“…Contact geometry seems to be the so far most general geometric formulation of non-equilibrium thermodynamics. It started with works of Hermann [11] in equilibrium thermodynamics and continued to non-equilibrium thermodynamics, e.g., [12,15,[39][40][41] and many others. Here, we adopt a recent version of contact-geometric formulation of GENERIC from [14].…”

Section: Contact Geometrymentioning

confidence: 99%

Dynamic Maximum Entropy Reduction

Klika

Pavelka

Vágner

et al. 2019

Entropy

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Any physical system can be regarded on different levels of description varying by how detailed the description is. We propose a method called Dynamic MaxEnt (DynMaxEnt) that provides a passage from the more detailed evolution equations to equations for the less detailed state variables. The method is based on explicit recognition of the state and conjugate variables, which can relax towards the respective quasi-equilibria in different ways. Detailed state variables are reduced using the usual principle of maximum entropy (MaxEnt), whereas relaxation of conjugate variables guarantees that the reduced equations are closed. Moreover, an infinite chain of consecutive DynMaxEnt approximations can be constructed. The method is demonstrated on a particle with friction, complex fluids (equipped with conformation and Reynolds stress tensors), hyperbolic heat conduction and magnetohydrodynamics.

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Section: Contact Geometrymentioning

confidence: 99%

Dynamic Maximum Entropy Reduction

Klika

Pavelka

Vágner

et al. 2019

Entropy

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“…We remark that, we do understood that the potential φ is externally given. Otherwise, there exists a non-standard fraction 1/2 in front of the potential φ if the Poisson equation, which is the gauge invariance of the canonical symplectic formulation on T * Q, is coupled to the Vlasov equation [27,18]. In this case, the coupled system is called Poisson-Vlasov equations.…”

Section: Boltzmann Equationmentioning

confidence: 99%

Hamiltonian coupling of electromagnetic field and matter

Esen

Pavelka

Grmela

2017

Int J Adv Eng Sci Appl Math

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Reversible part of evolution equations of physical systems is often generated by a Poisson bracket. We discuss geometric means of construction of Poisson brackets and their mutual coupling (direct, semidirect and matched pair products) as well as projections of Poisson brackets to less detailed Poisson brackets. This way the Hamiltonian coupling of transport of mixtures with electrodynamics is elucidated.

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“…In the presence of a symmetry by the (left) action of G, we arrive at a reduced Lagrangian function(al) L which is free from the group variable. In this case, the first term in the right hand side of (1.1) drops, and the dynamics is governed by the Euler-Poincaré equations (1.2) d dt δL δξ = −ad * ξ δL δξ , on the Lie algebra g. The Euler-Poincaré equation has been written for a wide spectrum of Lie groups; from matrix Lie groups to diffeomorphism groups, see for instance [26,37,15,16,23,4,24] and the references therein. It is also possible to find various different forms of the Euler-Poincaré equations in the literature.…”

Section: Introductionmentioning

confidence: 99%

Lagrangian dynamics on matched pairs

Esen

Sütlü

2017

Journal of Geometry and Physics

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Abstract. Given a matched pair of Lie groups, we show that the tangent bundle of the matched pair group is isomorphic to the matched pair of the tangent groups. We thus obtain the EulerLagrange equations on the trivialized matched pair of tangent groups, as well as the EulerPoincaré equations on the matched pair of Lie algebras. We show explicitly how these equations cover those of the semi-direct product theory. In particular, we study the trivialized, and the reduced Lagrangian dynamics on the group SL(2, C).

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Geometry of plasma dynamics II: Lie algebra of Hamiltonian vector fields

Cited by 18 publications

References 41 publications

Dynamic Maximum Entropy Reduction

Dynamic Maximum Entropy Reduction

Hamiltonian coupling of electromagnetic field and matter

Lagrangian dynamics on matched pairs

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