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Abstract

The problem of finding the equilibrium shapes of a drop of nematic liquid crystal in contact with an isotropic fluid is fascinating, but hard to solve. I attempt here to crack this problem.

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References

  • Ambrosio L. (1988 a), A compactness theorem for a special class of functions of bounded variation, Publication no. 13, Scuola Normale Superiore, Pisa, to appear in Boll. Un. Mat. Ital.

    Google Scholar 

  • Ambrosio L. (1988 b), Existence theory for a new class of variational problems, Publication no. 17, Scuola Normale Superiore, Pisa.

    Google Scholar 

  • Ambrosio L., S. Mortola & V. M. Tortorelli (1988), Functional with linear growth defined on vector-valued BV functions, Publication no. 14, Scuola Normale Superiore, Pisa.

    Google Scholar 

  • Bernal J. D. & I. Fankuchen (1941), X-ray and crystallografic studies of plant virus preparations, J. Gen. Physiol., 25, 111–165.

    Article  Google Scholar 

  • Chandrasekhar S. (1966), Surface tension of liquid crystals in Liquid crystals, Brown, Dines & LabesEds., Gordon & Breach, New York, 331–340.

    Google Scholar 

  • De Giorgi E. & L. Ambrosio (1987), Un nuovo tipo di funzionale del calcolo delle variazioni, to appear in Atti Acc. Lincei Rend. fis.

    Google Scholar 

  • Dinghas, A. (1944), Über einen geometrischen Satz von Wulff für die Gleichgewichtsform von Kristallen, Z. Kristallographie, 105, 304–314.

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Ericksen J. L. (1976), Equilibrium theory of liquid crystals in Advances in liquid crystals, vol. II, Glenn & BrownEds., Academic Press, New York, 233–298.

    Google Scholar 

  • Ericksen J. L. (1988), Static theory of point defects in nematic liquid crystals, forthcoming.

    Google Scholar 

  • Fosdick R. L. & E. G. Virga (1989), A variational proof of the stress theorem of Cauchy, Arch. Rational Mech. Anal., 105, 95–103.

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Friedel G. (1922), Les états mésomorphes de la matière, Ann. Phys. (Paris), 18, 273–474.

    Google Scholar 

  • Gurtin M. E. & A. I. Murdoch (1974), A continuum theory of elastic material surfaces, Arch. Rational Mech. Anal., 57, 291–323.

    MathSciNet  ADS  Google Scholar 

  • Haller I. (1972), Elastic constants of nematic crystalline phase of MBBA, J. Chem. Phys., 57, 1400–1405.

    Article  ADS  Google Scholar 

  • Herring C. (1951), Some theorems on the free energy of crystals surface, Phys. Rev., 82, 87–93.

    Article  ADS  MATH  Google Scholar 

  • Kléman M. (1983), Points, lines and walls, J. Wiley & Sons, Chichester etc.

    Google Scholar 

  • Langevin D. (1972), Analyse spectrale de la lumière diffusée par la surface libre d’un crystal liquide nématique. Mesure de la tension superficielle et des coefficients de viscosité, J. Phys. (Paris), 33, 249–256.

    Article  Google Scholar 

  • Noll W. & E. G. Virga (1989), On edge interactions and surface tension, Arch. Rational Mech. Anal., in press.

    Google Scholar 

  • Oseen C. W. (1931), Probleme für die Theorie der anisotropen Flüssigkeiten, Z. Kristallographie, 79, 173–185.

    Google Scholar 

  • Oseen C. W. (1933), The theory of liquid crystals, Trans. Faraday Soc, 29, 883–899.

    Article  Google Scholar 

  • Roccato D. & E. G. Virga (1989), Drops of nematic liquid crystals floating on a fluid, forthcoming.

    Google Scholar 

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

    Article  ADS  Google Scholar 

  • Taylor J. E. (1974), Existence and structure of solutions to a class of nonelliptic variational problems, Symposia Mathematica, 14, 499–508.

    Google Scholar 

  • Taylor J. E. (1978), Crystalline variational problems, Bull. Amer. Math. Soc, 84, 568–588.

    Article  MathSciNet  MATH  Google Scholar 

  • Virga E. G. (1987), Forme di equilibrio di piccole gocce di cristallo liquido, Publication no. 562, Istituto Analisi Numerica, Pavia.

    Google Scholar 

  • Virga E. G. (1988), Metastable equilibrium configurations of fluids with surface tension, Quart. Appl. Math., 46, 217–228.

    MathSciNet  MATH  Google Scholar 

  • Wulff G. (1901), Zur Frage der Geschwindigkeit des Wachsthums und der Auflösung der Kristallflächen, Z. Kristallographie und Mineralogie, 34, 449–530.

    Google Scholar 

  • Zöcher H. (1925), Über freiwillige Strukturbildung in Solen, Z. Anorg. Chem., 147, 91–110.

    Article  Google Scholar 

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Dedicated to Bernard D. Coleman on the occasion of his sixtieth birthday

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© 1991 Springer-Verlag Berlin Heidelberg

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Virga, E.G. (1991). Drops of Nematic Liquid Crystals. In: Markovitz, H., Mizel, V.J., Owen, D.R. (eds) Mechanics and Thermodynamics of Continua. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75975-8_11

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  • DOI: https://doi.org/10.1007/978-3-642-75975-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52999-6

  • Online ISBN: 978-3-642-75975-8

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