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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2026 / Cilt: 21 Sayı: 2

On Matched Pair of Dissipation Systems

Sönümlemeli Sistemlerin Eşlenmesi Üzerine

Oğul Esen(GEBZE TEKNİK ÜNİVERSİTESİ)0000-0002-6766-0287
Gökhan Özcan(GEBZE TEKNİK ÜNİVERSİTESİ)0000-0001-6260-4641
Serkan Sütlü(IŞIK ÜNİVERSİTESİ)0000-0003-0925-8668
Pages
273–282
Publication Date
2021-04-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We shall then illustrate our results on 3 and 4 dimensional examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work we propose a method to analyse the collective motion of two mutually interacting dissipative systems.
📊
Key Findings & Data:It is obvious that; the differential equations controlling the matched motion will include extra terms generated by the mutual interactions, apart from writing the equations of the two systems together.
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Conclusion & Impact:We shall then illustrate our results on 3 and 4 dimensional examples.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:eşlenmiş Lie cebirleri · Metriplektik sistemler · Rayleigh sönümlemesi

Abstract

In this work we propose a method to analyse the collective motion of two mutually interacting dissipative systems. It is obvious that; the differential equations controlling the matched motion will include extra terms generated by the mutual interactions, apart from writing the equations of the two systems together. These additional terms will be produced in this work by the mutual actions of Lie algebras, and in this way a pure geometric / algebraic construction will be realized. We shall then illustrate our results on 3 and 4 dimensional examples.

Özet

Bu makalede karşılıklı etki tepki içindeki iki sönümlemeli sistemin beraber (kollektif- eşlenmiş) hareketinin analizi üzerine bir yöntem öneriyoruz. Aşikardır ki; eşlenmiş hareketi kontrol eden diferansiyel denklemler iki sistemin denklemlerini bir arada yazmak dışında karşılıklı etki tepkinin doğurduğu fazladan terimler içerecektir. Karşılıklı etkiyi belirleyen ilave terimler, Lie cebirlerinin karşılıklı etkisi ile üretilecektir ve bu şekilde pür geometrik/cebirsel bir inşa gerçekleştirilecektir. Sonrasında elde ettiğimiz sonuçları 3 ve 4 boyutlu örneklerde göstereceğiz.

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Cite This Article

Esen, O., Özcan, G., Sütlü, S. (2021). On Matched Pair of Dissipation Systems. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 21 Sayı: 2, 273–282. https://doi.org/10.35414/akufemubid.803443

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References (22)

  1. Bloch, A., Krishnaprasad, P. S., Marsden, J. E. and Ratiu, T. S., 1996. The Euler-Poincaré equations and double bracket dissipation. Communications in Mathematical Physics., 175, 1, 1-42.
  2. Esen, O. and Sütlü, S. 2016. Hamiltonian dynamics on matched pairs. International Journal of Geometric Methods in Modern Physics, 13, 10, 1650128.
  3. Esen, O. and Sütlü, S. 2017. Lagrangian dynamics on matched pairs. Journal of Geometry and Physics, 111, 142-157.
  4. Esen, O., Kudeyt, M. and Sütlü, S. 2021. Second order Lagrangian dynamics on double cross product groups. Journal of Geometry and Physics, 159, 103934.
  5. Esen, O. and Sütlü, S. 2021. Discrete dynamical systems over double cross-product Lie groupoids. International Journal of Geometric Methods in Modern Physics.
  6. Grmela, M., 1984a. Bracket formulation of dissipative fluid mechanics equations. Physics Letters A, 102, 8, 355–358.
  7. Grmela, M., 1984b. Particle and bracket formulations of kinetic equations. Contemp. Math, 28, 125-132.
  8. Grmela, M. and Öttinger, H. C., 1997. Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Physical Review E, 56, 6, 6620.
  9. Holm, D. D. 2011. Geometric Mechanics Part I: Dynamics and Symmetry. World Scientific Publishing Company.
  10. Kaufman, A. N. 1984. Dissipative Hamiltonian systems: a unifying principle. Physics Letters A, 100, 8, 419-422.
  11. de León, M. and Rodrigues, P. R., 2011. Methods of differential geometry in analytical mechanics. Elsevier.
  12. Majid, S., 1990. Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations. Pacific Journal of Mathematics, 141, 2, 311-332.
  13. Majid, S., 2000. Foundations of Quantum Group Theory. Cambridge University Press.
  14. Marsden, J. E. and Ratiu, T. S., 2013. Introduction to mechanics and symmetry: a basic exposition of classical mechanical systems. Springer Science & Business Media, 17.
  15. Mielke, A., 2011. Formulation of thermoelastic dissipative material behavior using GENERIC. Continuum Mechanics and Thermodynamics, 23, 3, 233-256.
  16. Morrison, P. J., 1984. Bracket formulation for irreversible classical fields. Physics Letters A, 100, 8, 423-427.
  17. Morrison, P. J., 1986. A paradigm for joined Hamiltonian and dissipative systems. Physica D: Nonlinear Phenomena, 18, 1-3, 410-419.
  18. Morrison, P. J., 2009. Thoughts on brackets and dissipation: old and new. Journal of Physics: Conference Series IOP Publishing, 169, 1.
  19. Pavelka, M., Klika, V. and Grmela, M., 2018. Multiscale thermo-dynamics: introduction to GENERIC. Walter de Gruyter.
  20. Shannon, C. E., 1948. A mathematical theory of communication. 27, J. L. Doob, The Bell System Technical Journal, 379-423.
  21. Şuhubi, E. S. 2008. Dış Form Analizi. Türkiye Bilimler Akademisi.
  22. Shannon, C. E., 1948. A mathematical theory of communication. 27, J. L. Doob, The Bell System Technical Journal, 379-423.