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New Variational Problems in the Statics of Liquid Crystals

  • Epifanio G. Virga
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 54)

Abstract

Liquid crystals are anisotropic fluids that exhibit a preferred direction, possibly different at each place. The preferred direction is the optical axis of the material, that here we describe by a unit vector n. Most liquid crystals present different phases as the temperature varies. We restrict attention to only one of these phases: our development concerns nematic liquid crystals. We assume the region of space occupied by a liquid crystal as given and we denote it by B. Thus n is a field of B into S2 the unit sphere in the translation space of the three-dimensional Euclidean space ε. Formally,
$$n:B \to {S^2},B \subset \varepsilon ,{S^2}: = \left\{ {u \in v\left| u \right| = 1} \right\},{\text{ where v: = }}\varepsilon {\text{ - }}\varepsilon $$

Keywords

Liquid Crystal Prefer Direction Nematic Liquid Crystal Isotropic Phase Cholesteric Liquid Crystal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1993

Authors and Affiliations

  • Epifanio G. Virga
    • 1
  1. 1.Facoltà di IngegneriaUniversità di PisaPisaItaly

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