The mathematical representation of driven thermodynamic systems

Journal of Non-Newtonian Fluid Mechanics

Volumn 120, Issue 1-3, 2004, Pages 3-9

  Jongschaap, Robert ^a   Öttinger, Hans Christian ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Dirac structures; Driven systems; GENERIC; Matrix model; Nonequilibrium thermodynamics

Indexed keywords

ELECTRIC POWER UTILIZATION; EQUATIONS OF MOTION; NON NEWTONIAN LIQUIDS; PISTONS; THERMODYNAMICS;

DYNAMICAL EQUATIONS; NONEQUILIBRIUM THERMODYNAMICS;

FLUID MECHANICS;

MATHEMATICAL ANALYSIS;

EID: 3242777610     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2003.11.008     Document Type: Article

References (20)

1. Jongschaap R.J.J.Öttinger H.C.Nonequilibrium thermodynamics and complex fluids J. Non-Newton. Fluid Mech. 96 1-2 2001 1-3
2. Maschke B.M.J.van der Schaft A.Breedveld P.C.An intrinsic Hamiltonian-formulation of network dynamics-nonstandard Poisson structures and gyrators J. Frankl. Inst.-Eng. Appl. Math. 329 5 1992 923-966
3. van der Schaft A.Maschke B.The Hamiltonian-formulation of energy conserving physical systems with external ports Aeu.-Arch. Elektron. Ubertrag. Tech.-Int. J. Electron. Commun. 49 5-6 1995 362-371
4. M. Dalsmo, A.J. van der Schaft, On representations and integrability of mathematical structures in energy-conserving physical systems, Siam J. Control Optim. 37 54-91.
5. van der Schaft A.J.Maschke B.M.Hamiltonian formulation of distributed-parameter systems with boundary energy flow J. Geom. Phys. 42 1-2 2002 166-194
6. Cervera J.van der Schaft A.J.Banos A.On composition of Dirac structures and its implications for control by interconnection Springer Lect. Notes Control Inform. Sci. 281 2003 55-63
7. Dirac P.Generalized Hamiltonian dynamics Can. J. Math. 2 1950 129-148
8. T. Courant, A. Weinstein, Beyond Poisson Structures, Hermann, Paris, 1988.
9. Courant T.Dirac manifolds Trans. Am. Math. Soc. 319 1990 631-661
10. I. Dorfman, Dirac Structures and Integrability of Nonlinear Evolution Equations, Wiley, Chichester, 1993.
11. Grmela M.Öttinger H.C.Dynamics and thermodynamics of complex fluids. I. Development of a general formalism Phys. Rev. E 56 6 1997 6620-6632
12. Öttinger H.C.Grmela M.Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism Phys. Rev. E 56 6 1997 6633-6655
13. Jongschaap R.J.J.Microscopic modeling of the flow properties of polymers Rep. Prog. Phys. 53 1 1990 1-55
14. Jongschaap R.Towards a unified formulation of microrheological models Springer Lect. Notes Phys. 381 1991 215-247
15. Jongschaap R.J.J.Dehaas K.H.Damen C.A.J.A generic matrix representation of configuration tensor rheological models J. Rheol. 38 4 1994 769-796
16. Edwards B.J.Öttinger H.C.Jongschaap R.J.J.On the relationships between thermodynamic formalisms for complex fluids J. Non-Equilib. Thermodyn. 22 4 1997 356-373
17. Jongschaap R.J.J.A generalized thermodynamic approach to microrheological modeling Appl. Sci. Res. 48 2 1991 117-128
18. Schaft A.v.d.Maschke B.The Hamiltonian formulation of energy conserving physical systems with external ports Arch. Elektronik Übertragungstechnik 49 1995 362-371
19. Muschik W.Gümbel S.KrÖger M.Öttinger H.A simple example for comparing GENERIC with rational non-equilibrium thermodynamics Physica A 285 2000 448-466
20. S. Groot, P. Mazur, Non-Equilibrium Thermodynamics, North-Holland, Amsterdam, 1969.