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Hamiltonian coupling of electromagnetic field and matter

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Abstract

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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Notes

  1. Using that \(F_u\) is a vector field, that acts on scalars as \(F_{u_i}\partial _i H_\rho \).

  2. Hand-written notes are available upon personal request to the corresponding author. The calculation were checked using the automated Poisson bracket manipulation program [60].

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Acknowledgements

M. P. is grateful to professor František Maršík for his generous support and for revealing the world of thermodynamics. O.E. is grateful to professor Hasan Gümral for the enlightening discussions on the Lie–Poisson dynamics and to professor Serkan Sütlü for the invaluable comments on the applications of the matched pair dynamics in case of the field theories. This project was supported by Natural Sciences and Engineering Research Council of Canada (NSERC). The work was partially developed within the POLYMEM project, Reg. no CZ.1.07/2.3.00/20.0107, that is co-funded from the European Social Fund (ESF) in the Czech Republic: “Education for Competitiveness Operational Programme”, from the CENTEM project, Reg. no. CZ.1.05/2.1.00/03.0088, co-funded by the ERDF as part of the Ministry of Education, Youth and Sports OP RDI programme and, in the follow-up sustainability stage, supported through CENTEM PLUS (LO1402) by financial means from the Ministry of Education, Youth and Sports under the “National Sustainability Programme I”. Further, this work was also supported by Charles University in Prague, project GA UK No 70515, and by Czech Science Foundation, project no. 17-15498Y.

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Authors and Affiliations

  1. Department of Mathematics, Gebze Technical University, 41400, Gebze, Kocaeli, Turkey

    Oğul Esen

  2. New Technologies - Research Centre, University of West Bohemia, Univerzitní 8, 306 14, Pilsen, Czech Republic

    Michal Pavelka

  3. Mathematical Institute, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 186 75, Prague, Czech Republic

    Michal Pavelka

  4. École Polytechnique de Montréal, C.P.6079 Suc. Centre-ville, Montréal, QC, H3C 3A7, Canada

    Michal Pavelka & Miroslav Grmela

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  1. Oğul Esen
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Correspondence to Michal Pavelka.

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Esen, O., Pavelka, M. & Grmela, M. Hamiltonian coupling of electromagnetic field and matter. Int J Adv Eng Sci Appl Math 9, 3–20 (2017). https://doi.org/10.1007/s12572-017-0179-4

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