A geometric perspective to open irreversible thermodynamic systems: GENERIC, Matrix and port-contact systems
Authors
Audrey Favache, Denis Dochain, Bernhard Maschke
Abstract
Not available
Citation
- Journal: Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference
- Year: 2009
- Volume:
- Issue:
- Pages: 8387–8392
- Publisher: IEEE
- DOI: 10.1109/cdc.2009.5399977
BibTeX
@inproceedings{Favache_2009,
title={{A geometric perspective to open irreversible thermodynamic systems: GENERIC, Matrix and port-contact systems}},
DOI={10.1109/cdc.2009.5399977},
booktitle={{Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference}},
publisher={IEEE},
author={Favache, Audrey and Dochain, Denis and Maschke, Bernhard},
year={2009},
pages={8387--8392}
}References
- Edwards BJ, Öttinger HC, Jongschaap RJJ (1997) On The Relationships Between Thermodynamic Formalisms For Complex Fluids. Journal of Non-Equilibrium Thermodynamics 22(4). https://doi.org/10.1515/jnet.1997.22.4.35 – 10.1515/jnet.1997.22.4.356
- Jongschaap RJJ, de Haas KH, Damen CAJ (1994) A generic matrix representation of configuration tensor rheological models. Journal of Rheology 38(4):769–796. https://doi.org/10.1122/1.55059 – 10.1122/1.550592
- eberard, On the interconnection structures of open physical systems. Proc 3rd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (2006)
- Cortés J, van der Schaft A, Crouch PE (2005) Characterization of Gradient Control Systems. SIAM J Control Optim 44(4):1192–1214. https://doi.org/10.1137/s036301290342556 – 10.1137/s0363012903425568
- Jongschaap RJJ (2001) The matrix model, a driven state variables approach to non-equilibrium thermodynamics. Journal of Non-Newtonian Fluid Mechanics 96(1–2):63–76. https://doi.org/10.1016/s0377-0257(00)00136- – 10.1016/s0377-0257(00)00136-1
- callen, Thermodynamics (1960)
- gibbs, Graphical methods in the Thermodynamics of fluids. Trans Academy of Arts and Sciences (0)
- herman, Geometry Physics and Systems (1973)
- Arnold VI (1989) Mathematical Methods of Classical Mechanics. Springer New Yor – 10.1007/978-1-4757-2063-1
- {“status”:”error” – 10.1016/0034-4877(78)90010-1
- Chen M (1999) On the geometric structure of thermodynamics. Journal of Mathematical Physics 40(2):830–837. https://doi.org/10.1063/1.53268 – 10.1063/1.532688
- eberard, Extensions des systèmes hamiltoniens à ports aux systèmes irréversibles: une approche par la géométrie de contact. (2006)
- Mrugała R (1985) Submanifolds in the thermodynamic phase space. Reports on Mathematical Physics 21(2):197–203. https://doi.org/10.1016/0034-4877(85)90059- – 10.1016/0034-4877(85)90059-x
- Libermann P, Marle C-M (1987) Symplectic Geometry and Analytical Mechanics. Springer Netherland – 10.1007/978-94-009-3807-6
- Brogliato B, Maschke B, Lozano R, Egeland O (2007) Dissipative Systems Analysis and Control. Springer Londo – 10.1007/978-1-84628-517-2
- Mrugaa̵ R (2000) On a special family of thermodynamic processes and their invariants. Reports on Mathematical Physics 46(3):461–468. https://doi.org/10.1016/s0034-4877(00)90012- – 10.1016/s0034-4877(00)90012-0
- van derschaft, The Hamiltonian formulation of energy conserving physical systems with external ports. Arch Elektron Ubertragungstechn (1995)
- gibbs, Method of geometrical representation of the thermodynamic properties of substances by means of surfaces. Trans Academy of Arts and Sciences (1873)
- Eberard D, Maschke BM, van der Schaft AJ (2007) An extension of Hamiltonian systems to the thermodynamic phase space: Towards a geometry of nonreversible processes. Reports on Mathematical Physics 60(2):175–198. https://doi.org/10.1016/s0034-4877(07)00024- – 10.1016/s0034-4877(07)00024-9
- van der Schaft A (2000) L2 - Gain and Passivity Techniques in Nonlinear Control. Springer Londo – 10.1007/978-1-4471-0507-7
- Grmela M, Öttinger HC (1997) Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys Rev E 56(6):6620–6632. https://doi.org/10.1103/physreve.56.662 – 10.1103/physreve.56.6620
- Öttinger HC, Grmela M (1997) Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism. Phys Rev E 56(6):6633–6655. https://doi.org/10.1103/physreve.56.663 – 10.1103/physreve.56.6633
- Grmela M (2002) Reciprocity relations in thermodynamics. Physica A: Statistical Mechanics and its Applications 309(3–4):304–328. https://doi.org/10.1016/s0378-4371(02)00564- – 10.1016/s0378-4371(02)00564-2
- Mrugala R, Nulton JD, Christian Schön J, Salamon P (1991) Contact structure in thermodynamic theory. Reports on Mathematical Physics 29(1):109–121. https://doi.org/10.1016/0034-4877(91)90017- – 10.1016/0034-4877(91)90017-h
- Jongschaap R, Öttinger HC (2004) The mathematical representation of driven thermodynamic systems. Journal of Non-Newtonian Fluid Mechanics 120(1–3):3–9. https://doi.org/10.1016/j.jnnfm.2003.11.00 – 10.1016/j.jnnfm.2003.11.008
- Carathéodory C (1909) Untersuchungen über die Grundlagen der Thermodynamik. Math Ann 67(3):355–386. https://doi.org/10.1007/bf0145040 – 10.1007/bf01450409
- favache, Thermodynamics and process control. (2009)
- Muschik W, Gümbel S, Kröger M, Öttinger HC (2000) A simple example for comparing GENERIC with rational non-equilibrium thermodynamics. Physica A: Statistical Mechanics and its Applications 285(3–4):448–466. https://doi.org/10.1016/s0378-4371(00)00252- – 10.1016/s0378-4371(00)00252-1
- Öttinger HC (1999) Nonequilibrium Thermodynamics – A Tool for Applied Rheologists. Applied Rheology 9(1):17–26. https://doi.org/10.1515/arh-2009-000 – 10.1515/arh-2009-0002
- Grmela M (2002) Lagrange hydrodynamics as extended Euler hydrodynamics: Hamiltonian and GENERIC structures. Physics Letters A 296(2–3):97–104. https://doi.org/10.1016/s0375-9601(02)00190- – 10.1016/s0375-9601(02)00190-1
- abraham, Foundations of Mechanics (1994)
- Ortega J-P, Planas-Bielsa V (2004) Dynamics on Leibniz manifolds. Journal of Geometry and Physics 52(1):1–27. https://doi.org/10.1016/j.geomphys.2004.01.00 – 10.1016/j.geomphys.2004.01.002
- de groot, Non-equilibrium thermodynamics (1962)