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Role of thermodynamics in extensions of mesoscopic dynamical theories Cover

Role of thermodynamics in extensions of mesoscopic dynamical theories

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Open Access
|May 2016

References

  1. 1. L. Euler, Principes généraux du mouvement des fluides,, vol. 11, 1755 (English translation available in Physica D 237, 1825-1839, 2008).
  2. 2. C. Truesdell,. New York, NY, USA: Springer, 2nd ed., 1984.
  3. 3. R. B. Bird, O. Hassager, R. C. Armstrong, and C. F. Curtiss,, vol. 1. New York, NY, USA: Wiley, 1987.
  4. 4. R. B. Bird, O. Hassager, R. C. Armstrong, and C. F. Curtiss,, vol. 2. New York, NY, USA: Wiley, 1987.
  5. 5. C. Cattaneo, Sulla conduzione del calore,, vol. 3, pp. 83–101, 1948.
  6. 6. R. Peierls, Zur kinetischen Theorie der Wärmeleitung in Kristallen,, vol. 395, pp. 1055–1101, 1929.
  7. 7. J. W. Gibbs,. New York, NY, USA: Longmans Green and Co., 1984.
  8. 8. E. T. Jaynes, Foundations of probability theory and statistical mechanics, in, New York, NY, USA: Springer, 1967.
  9. 9. R. Hermann,. New York, NY, USA: Marcel Dekker, 1984.
  10. 10. V. I. Arnold,. New York, NY, USA: Springer, 1989.
  11. 11. V. I. Arnold, Sur la géometrie différentielle des groupes de lie de dimension infini et ses applications dans l’hydrodynamique des fluides parfaits, ann,, vol. 16, p. 319, 1966.
  12. 12. M. Grmela, Thermodynamical lift of the nonlinear onsager-casimir vector field, in(J. E. Harnad, J. Marsden, ed.), pp. 199–207, CRM, Univ. de Montreal, 1990.
  13. 13. M. Grmela, Multiscale equilibrium and nonequilibrium thermodynamics in chemical engineering,, vol. 39, pp. 76–128, 2010.
  14. 14. M. Grmela, Contact geometry of mesoscopic thermodynamics and dynamics,, vol. 16, pp. 1652–1686, 2014.
  15. 15. I. E. Dzyaloshinskii and G. E. Volovick, Poisson brackets in condense matter physics,, vol. 125, pp. 67–97, 1980.
  16. 16. M. Grmela, Particle and bracket formulations of kinetic equations,, vol. 28, pp. 125–132, 1984.
  17. 17. A. N. Kaufman, Dissipative hamiltonian systems: A unifying principle,, vol. 100, p. 419, 1984.
  18. 18. P. J. Morrison, Bracket formulation for irreversible classical fields,, vol. 100, p. 423, 1984.
  19. 19. M. M. Grmela and H. Öttinger, Dynamics and thermodynamics of complex fluids: General formulation,, vol. 56, pp. 6620–6633, 1997.
  20. 20. H. C. Öttinger and M. Grmela, Dynamics and thermodynamics of complex fluids: Illustration of the general formalism,, vol. 56, pp. 6633–6650, 1997.
  21. 21. M. Grmela, Fluctuations in extended mass-action-law dynamics,, vol. 241, pp. 976–986, 2012.
  22. 22. A. Clebsch, Über die integration der hydrodynamische gleichungen,, vol. 56, pp. 1–10, 1895.
  23. 23. M. Grmela, Role of thermodynamics in multiscale physics,, vol. 65, pp. 1457–1470, 2013.
  24. 24. D. Jou, J. Casas-Vàzquez, and G. Lebon,. Berlin: Springer, 4th ed., 2010.
  25. 25. M. Grmela, A. Ammar, and F. C. G. Maîtrejean, A mesoscopic rheological model of moderately concentrated colloids,, vol. 212, pp. 1–12, 2014.
  26. 26. R. J. DiPerna and P. L. Lions, Global solutions of Boltzmann’s equation and the entropy inequality,, vol. 114, pp. 47–55, 1991.
  27. 27. S. K. Godunov, Symmetric form of the magnetohydrodynamic equation,, vol. 3, no. 1, pp. 26–34, 1972.
  28. 28. K. O. Friedrichs, Conservation equations and the laws of motion in classical physics,, vol. 31, pp. 123 – 131, 1978.
  29. 29. B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity,, vol. 13, pp. 167–178, 1963.
  30. 30. H. Grad,, vol. 12. Springer-Verlag: Encyclopedia of Physics, 1958.
  31. 31. R. T. Müller, I.,. New York, NY, USA: Springer, 1998.
  32. 32. T. Ruggeri, The entropy principle: from continuum mechanics to hyperbolic systems of balance laws,, vol. Serie 8, Vol. 8-B, no. 1, pp. 1–20, 2005.
  33. 33. V. A. Cimmelli, D. Jou, T. Ruggeri, and P. Ván, Entropy principle and recent results in non-equilibrium theories,, vol. 16, pp. 1756–1807, 2014.
  34. 34. H. Struchtrup,. Berlin, Germany: Springer, 2005.
  35. 35. G. M. Kremer,. Berlin, Germany: Springer, 2010.
  36. 36. P. Ván, A. Berezovski, and J. Engelbrecht, Internal variables and dynamic degrees of freedom,, vol. 33, pp. 235–254, 2008.
  37. 37. A. Berezovski, J. Engelbrecht, and M. A. Maugin, Generalized thermo-mechanics with dual internal variables,, vol. 81, pp. 229–240, 2011.
  38. 38. J. Casas-Vázquez and D. Jou, Temperature in non-equilibrium states: A review of open problems and current proposals,, vol. 66, pp. 1937–2023, 2003.
  39. 39. M. Grmela, Weakly nonlocal hydrodynamics,, vol. 47, p. 351, 1993.
  40. 40. M. Grmela, Extensions of classical hydrodynamics,, vol. 132, pp. 581–602, 2008.
  41. 41. V. A. Cimmelli, An extension of liu procedure in weakly nonlocal thermodynamics,, vol. 48, p. 113510, 2007.
  42. 42. P. Ván, Weakly nonlocal irreversible thermodynamics,, vol. 12, pp. 142–169, 2003.
  43. 43. E. Johannessen and D. Bedeaux, The nonequilibrium van der waals square gradient model. (ii) local equilibrium of the Gibbs surface,, vol. 330, pp. 354–372, 2003.
  44. 44. J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. interfacial free energy,, vol. 28, p. 258, 1958.
  45. 45. M. Grmela, G. Lebon, and C. Dubois, Multiscale thermodynamics and mechanics of heat,, vol. 83, 2011.
  46. 46. T. Ruggeri, Can constitutive relations be represented by non-local equations?,, vol. 70, pp. 597–611, 2012.
  47. 47. M. Grmela and J. Teichmann, Lagrangian formulation of the Maxwell-Cattaneo hydrodynamics,, vol. 21, pp. 297–313, 1983.
  48. 48. T. Arima, S. Taniguchi, T. Ruggeri, and M. Sugiyama, Extended thermodynamics of dense gases,, vol. 24, pp. 271–292, 2012.
  49. 49. Z. Y. Guo and G. W. Hou, Thermal wawe based on thermomass model,, vol. 132, p. 072403, 2010.
  50. 50. V. A. Cimmelli and W. Kosinski, Nonequilibrium semiempirical temperature in materials with thermal relaxation,, vol. 43, p. 753, 1991.
  51. 51. B. L. Holian and P. M. Mareschal, Heat-flow equation motivated by the ideal-gas shock wave,, vol. 82, p. 026707, 2010.
  52. 52. L. Onsager and S. Machlup, Fluctuations and irreversible processes,, vol. 91, pp. 1505–1512, 1953.
Language: English
Page range: 56 - 80
Submitted on: Dec 12, 2014
Accepted on: May 7, 2015
Published on: May 20, 2016
Published by: Italian Society for Applied and Industrial Mathemathics
In partnership with: Paradigm Publishing Services

© 2016 Miroslav Grmela, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.