Statistical Foundations of Liquid-Crystal Theory. I: Discrete Systems of Rod-Like Molecules

Archive for Rational Mechanics and Analysis

Volumn 206, Issue 3, 2012, Pages 1039-1072

  Seguin, Brian ^a   Fried, Eliot ^b  

^a MCGILL UNIVERSITY   (Canada)

^b Department of Mechanical Engineering ^*  (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84868120318     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-012-0550-3     Document Type: Article

References (33)

1. Oseen C. W.: The theory of liquid crystals. Trans. Faraday Soc. 29, 883-899 (1933).
2. Ericksen J. L.: Conservation laws for liquid crystals. Trans. Soc. Rheol. 5, 23-34 (1961).
3. Leslie F.: Some constitutive equations for anisotropic fluids. Q. J. Mech. Appl. Math. 19, 357-370 (1966).
4. de Gennes P., Prost J.: The Physics of Liquid Crystals. Oxford University Press, New York (1995).
5. Chandrasekhar S.: Liquid Crystals. Cambridge University Press, New York (1992).
6. Virga E. G.: Variational Theories of Liquid Crystals. Chapman & Hall, London (1994).
7. Stephen M. J., Straley J. P.: Physics of liquid crystals. Rev. Mod. Phys. 46, 617-704 (1974).
8. Ericksen J. L.: Equilibrium theory of liquid crystals. Adv. Liq. Cryst. 2, 233-298 (1976).
9. Jenkins J. T.: Flows of nematic liquid crystals. Annu. Rev. Fluid Mech. 10, 197-219 (1978).
10. Leslie E. M.: Theory of flow phenomena in liquid crystals. Adv. Liq. Cryst. 4, 1-81 (1979).
11. de Gennes P. G.: Phenomenology of short-range-order effects in the isotropic phase of nematic materials. Phys. Lett. A 30, 454-455 (1969).
12. Landau, L. D. Theory of phase transformations. I. Physikalische Zeitschrift der Sowjetunion11, 26-47 (1937).
13. Landau, L. D.: Theory of phase transformations. II. Physikalische Zeitschrift der Sowjetunion11, 545-555 (1937).
14. Ericksen J. L.: Anisotropic fluids. Arch. Rational Mech. Anal. 4, 231-237 (1959).
15. MacMillan E. A Theory of Anisotropic Fluids. Dissertation, The University of Minnesota, Minneapolis, (1987).
16. Ericksen J. L.: Liquid crystals with variable degree of orientation. Arch. Rational Mech. Anal. 113, 97-120 (1991).
17. Sonnet A. M., Maffettone P. L., Virga E. G.: Continuum theory for nematic liquid crystals with tensorial order. J. Non-Newtonian Fluid Mech. 119, 51-59 (2004).
18. Irving J. H., Kirkwood J. G.: The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J. Chem. Phys. 18, 817-829 (1950).
19. Noll, W.: Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der statistischen Mechanik. J. Rational Mech. Anal. 4, 627-646 (1955). Translated into English by Lehoucq, R. B., Lilienfeld-Toal, A.: J. Elast. 100, 5-24 (2010).
20. Lubensky T. C.: Molecular description of nematic liquid crystals. Phys. Rev. A 6, 2497-2514 (1970).
21. Müller I.: Thermodynamics. Pitman, London (1985).
22. Capriz C., Podio Guidugli P.: Discrete and continuous bodies with affine structure. Ann. Mat. Pur. Appl. 4, 195-211 (1976).
23. Fried E.: New insights into the classical mechanics of particle systems. Discrete Contin. Dyn. Syst. 28, 1469-1504 (2010).
24. Noll, W.: La Mécanique Classique, Basée sur un Axiome d'Objectivité. "La Méthode Axiomatique dans les Mécaniques Classiques et Nouvelles" (Colloque International, Paris, 1959). Gauthier-Vallars, 47-56, 1963.
25. Beatty M. F.: On the foundation principles of general classical mechanics. Arch. Rational Mech. Anal. 24, 246-273 (1967).
26. Green A. E., Rivlin R. S.: On Cauchy's equations of motion. Z. Angew. Math. Phys. 15, 290-292 (1964).
27. Reed, M., Simon, B.: Methods of Modern Mathematical Physics I: Functional Analysis. Academic Press, San Diago, 1980.
28. Gurtin M. E., Williams W. O.: On the first law of thermodynamics. Arch. Rational Mech. Anal. 42, 77-92 (1971).
29. Rao A. V.: Dynamics of Particles and Rigid Bodies. Cambridge University Press, Cambridge (2006).
30. Landau, L., Lifchitz, E.: Mecanique. Editions Mir, Moscow, 1969.
31. Noll, W.: Five contributions to natural philosophy. Published as B1 on the website www. math. cmu. edu/~wn0g/noll (2004).
32. Maier W., Saupe A.: Eine einfache molekulare Theorie des nematischen Kristallinflüssigen Zustands. Z. Naturforsch. 13a, 564-566 (1958).
33. Coleman B. D., Noll W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Anal. 13, 167-178 (1963).