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The morphology and stability of material phases

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References

  1. 1.

    Gibbs, J. W., On the equilibrium of heterogeneous substances. (Trans. Conn. Acad. 1875–1878). The Scientific Papers, Vol. I, pp. 55–353. New Haven: Yale University Press 1907.

  2. 2.

    Truesdell, C., & R. A. Toupin, The Classical Field Theories. Flügge's Handbuch der Physik, III/1. Berlin-Heidelberg-New York: Springer 1960.

  3. 3.

    Coleman, B. D., & J. M. Greenberg, Thermodynamics and the stability of fluid motion. Arch. Rational Mech. Anal. 25, 321–341 (1967).

  4. 4.

    Coleman, B. D., On the stability of equilibrium states of general fluids. Arch. Rational Mech. Anal. 36, 1–32 (1970).

  5. 5.

    Dunn, J. E., & R. L. Fosdick, Lemmas in thermodynamic stability: a priori constitutive inequalities and induced global bounds on thermodynamic states. Arch. Rational Mech. Anal. 67, 183–224 (1978).

  6. 6.

    Ericksen, J. L., A thermo-kinetic view of elastic stability theory. Int. J. Solids Structures 2, 573–580 (1966).

  7. 7.

    Ericksen, J. L., Thermoelastic stability. Proc. 5th U.S. National Congr. Appl. Mech., 187–193 (1966).

  8. 8.

    Koiter, W. T., Thermodynamics of elastic stability. Proc. 3rd Canadian Congr. of Appl. Mech., Calgary, 29–37 (1971).

  9. 9.

    Gurtin, M. E., Thermodynamics and the energy criterion for stability. Arch. Rational Mech. Anal. 52, 93–103 (1973).

  10. 10.

    Gurtin, M. E., Thermodynamics and stability. Arch. Rational Mech. Anal. 59, 63–96 (1975).

  11. 11.

    Gurtin, M. E., Modern continuum thermodynamics. Mechanics Today. New York: Pergamon 1973.

  12. 12.

    Truesdell, C., & W. Noll, The Non-Linear Field Theories of Mechanics. Flügge's Handbuch der Physik, III/3. Berlin-Heidelberg-New York: Springer 1965.

  13. 13.

    Keenan, J. H., Thermodynamics. New York: Wiley, 6th printing 1947.

  14. 14.

    Denbigh, K., The Principles of Chemical Equilibrium. Cambridge: University Press, 2nd edition 1966.

  15. 15.

    Callen, H. B., Thermodynamics. New York-London: Wiley, 4th printing 1963.

  16. 16.

    Buchdahl, H. A., The Concepts of Classical Thermodynamics. Cambridge: University Press 1966.

  17. 17.

    Van't Hoff, J.H., Études de dynamique chimique. Amsterdam: 1884.

  18. 18.

    Van't Hoff, J. H., Studies In Chemical Dynamics, translated by Thomas Ewan, Amsterdam: Frederik Muller and Co., London: Williams and Norgate 1896.

  19. 19.

    Le Chatelier, H., Comptes Rendus 99, 786 (1884).

  20. 20.

    Coleman, B. D., & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Anal. 13, 167–178 (1963).

  21. 21.

    Coleman, B. D., & V. J. Mizel, Existence of caloric equations of state in thermodynamics. J. Chem. Physics 40, 1116–1125 (1964).

  22. 22.

    Coleman, B. D., Thermodynamics of materials with memory. Arch. Rational Mech. Anal. 17, 1–46 (1964).

  23. 23.

    Gurtin, M. E., On the thermodynamics of materials with memory. Arch. Rational Mech. Anal. 28, 40–50 (1968).

  24. 24.

    Dunn, J. E., & R. L. Fosdick, Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade. Arch. Rational Mech. Anal. 56, 191–252 (1974).

  25. 25.

    Rockafellar, R. T., Convex Analysis. Princeton: University Press 1970.

  26. 26.

    Roberts, A. W., & D. E. Varberg, Convex Functions. New York-London: Academic Press 1973.

  27. 27.

    Stoer, J., & C. Witzgall, Convexity and Optimization in Finite Dimensions I. Berlin-Heidelberg-New York: Springer 1970.

  28. 28.

    Halmos, P. R., The range of a vector measure. Bull. Amer. Math. Soc. 54, 416–421 (1948).

  29. 29.

    Noll, W., On certain convex sets of measures and on phases of reacting mixtures. Arch. Rational Mech. Anal. 38, 1–12 (1970).

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Communicated by M. E. Gurtin

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Dunn, J.E., Fosdick, R.L. The morphology and stability of material phases. Arch. Rational Mech. Anal. 74, 1–99 (1980). https://doi.org/10.1007/BF00250831

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Keywords

  • Neural Network
  • Complex System
  • Nonlinear Dynamics
  • Electromagnetism
  • Material Phasis