Skip to main content
SpringerLink
Log in

Liquid crystals with variable degree of orientation

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Chandrasekhar, S., Liquid Crystals, Cambridge U. Press, Cambridge (1977).

    Google Scholar 

  2. Currie, P. K., Parodi's relation as a stability condition for nematics, Mol. Cryst. Liq. Cryst. 28 (1974), pp. 335–338.

    Google Scholar 

  3. Kuzzu, N. & Doi M., Constitutive equation for nematic liquid crystals under a weak velocity gradient derived from a molecular kinetic equation, J. Phys. Soc. Japan 52 (1983), pp. 3486–3494.

    Google Scholar 

  4. De Gennes, P. G., The Physics of Liquid Crystals, Oxford U. Press (Clarendon), London-New York (1974).

    Google Scholar 

  5. Ericksen, J. L., Static theory of point defects in nematic liquid crystals, To appear in an anniversary volume.

  6. Kinderlehrer, D., Recent developments in liquid crystal theory, to appear in Proc. Colloque Lions, Paris (1988), to be published by North-Holland.

  7. Cladis, P., A review of cholesteric blue phases, in Theory and Applications of Liquid crystals (ed. Ericksen, J. L. & Kinderlehrer, D.), IMA Volumes in Mathematics and its Applications, Springer-Verlag, New York-Berlin-Heidelberg-London-Paris-Tokyo 5 (1987), pp. 73–98.

    Google Scholar 

  8. Sethna, J., Theory of the blue phases of chiral nematic liqud crystals, in Theory and Applications of Liquid Crystals (ed. Ericksen, J. L. & Kinderlehrer, D.), IMA Volumes in Mathematics and its Applications, Springer-Verlag, New York-Berlin-Heidelberg-London-Paris-Tokyo 5 (1987), pp. 305–324.

    Google Scholar 

  9. Fan, C., Disclination lines in liquid crystals, Phys. Lett. 34 A (1971), pp. 335–336.

    Google Scholar 

  10. Doi, M., Molecular dynamics and rheological properties of concentrated solutions of rodlike polymers in isotropic and liquid crystalline phases, J. Polymer Sci. 19 (1981), pp. 229–243.

    Google Scholar 

  11. MacMillan, E., A Theory of Anisotropic Fluids, Ph. D. Thesis, U. Minnesota (1987).

  12. Hardt, R. M., Point and line singularities in liquid crystals, To appear in Proc. Conference on Variational Problems, École Normale Supérieure, Paris (1988).

  13. Lin, F. H., Nonlinear theory of defects in nematic liquid crystals — Phase transition and flow phenomena, to appear in Comm. Pure Appl. Math.

  14. Maddocks, J., A model for disclinations in nematic liquid crystals, in Theory and Applications of Liquid Crystals (ed. Ericksen, J. L. & Kinderlehrer, D.), IMA Volumes in Mathematics and its Applications, Springer-Verlag, New York-Berlin-Heidelberg-London-Paris-Tokyo 5 (1987), pp. 255–270.

    Google Scholar 

  15. Wissbrun, K., Rheology of rod-like polymers in the liquid crystalline state, J. Rheol. 25 (1981), pp. 619–662.

    Google Scholar 

  16. Calderer, M. C., Multiphase flows of liquid crystal polymers, to appear in J. Differential Equations.

  17. Calderer, M. C., Stability analysis of liquid crystal polymers exhibiting a banding structure, to appear in J. Rheol.

  18. Calderer, M. C., Analysis of Ericksen's equations for liquid crystal polymers in shear flow regions, pending publication.

  19. Ericksen, J. L., A thermodynamic view of order parameters for liquid crystals, in Lecture Notes in Mathematics, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo 1063 (1984), pp. 27–36.

    Google Scholar 

  20. Leslie, F. M., Some constitutive equations for liquid crystals, Arch. Rational Mech. Anal. 28 (1968), pp. 265–283.

    Google Scholar 

  21. Ericksen, J. L., On generalized momentum, Int. J. Solids Structures 18 (1982), pp. 315–317.

    Google Scholar 

  22. Ericksen, J. L., Conservation laws for liquid crystals, Trans. Soc. Rheol. 5 (1961), pp. 23–34.

    Google Scholar 

  23. Stephen, M. J. & Straley, J. P., Physics of liquid crystals, Rev. Mod. Phys. 46 (1974), pp. 617–704.

    Google Scholar 

  24. Truesdell, C., Rational Thermodynamics, 2nd ed., Springer-Verlag, New York-Berlin-Heidelberg-Tokyo (1984).

    Google Scholar 

  25. Lam, L., Constraints, dissipation functions and cholesteric liquid crystals, Zeits. Phys. B 27 (1977), pp. 349–356.

    Google Scholar 

  26. Currie, P. K., Parodi's relation as a stability condition for nematics, Mol. Cryst. Liq. Cryst. 28 (1974), pp. 335–338.

    Google Scholar 

  27. Landau, L. D. & Lifshitz, E. M., Theory of Elasticity, 3rd ed. (with revisions by Lifshitz, E. M., Kosevitch, A. M. & Pitaevskii, L. P., transl. Sykes, J. B. & Reid, W. H.), Pergamon Press, Oxford-New York-Beijing-Frankfurt-São Paulo-Sydney-Tokyo-Toronto (1986).

    Google Scholar 

  28. Frank, F. C., On the theory of liquid crystals, Discuss. Faraday Soc. 25 (1958), pp. 19–28.

    Google Scholar 

  29. Ericksen, J. L., Inequalities in liquid crystal theory, Phys. Fluids 9 (1966), pp. 1205–1207.

    Google Scholar 

  30. Longa, L., Monselesan, D. & Trebin, H. R., An extension of the Landau-Ginsburgde Gennes theory for liquid crystals, Liquid Cryst. 2 (1987), pp. 769–796.

    Google Scholar 

  31. Nehring, J. & Saupe, A., Calculation of the elastic constants of liquid crystals, J. Chem. Phys. 56 (1972), pp. 5527–5528.

    Google Scholar 

  32. Gramsberger, E. F., Longa, L. & De Jeu, W. H., Landau theory for the nematic-isotropic phase transition, Phys. Reports 135 (1986), pp. 195–257.

    Google Scholar 

  33. Smith, G. F., On isotropic integrity bases, Arch. Rational Mech. Anal. 18 (1965), pp. 282–292.

    Google Scholar 

  34. Wang, C.-C., A new representation theorem for isotropic functions: an answer to Professor G. F. Smith's criticism of my paper on representations for isotropic functions, Part 1. Scalar valued isotropic functions, Arch. Rational Mech. Anal. 36 (1970), pp. 166–197.

    Google Scholar 

  35. Berry, G. C., Rheological properties of nematic solutions of rod-like polymers, submitted to Mol. Cryst. Liq. Cryst.

  36. Jenkins, J. T., Cholesteric energies, J. Fluid Mech. 45 (1971), pp. 465–475.

    Google Scholar 

  37. Leslie, F. M., Some thermal effects in cholesteric liquid crystals, Proc. Roy. Soc. London A 307 (1968), pp. 359–372.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. 05 378 Buckskin Bob Lane, 97439, Florence, Oregon

    J. L. Ericksen

Authors
  1. J. L. Ericksen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by B. Coleman

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ericksen, J.L. Liquid crystals with variable degree of orientation. Arch. Rational Mech. Anal. 113, 97–120 (1991). https://doi.org/10.1007/BF00380413

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00380413

Keywords

Search

Navigation