Orientability and Energy Minimization in Liquid Crystal Models
By J. Ball, Arghir Zarnescu. 2010
188 citations recorded by the source corpus.
Uniaxial nematic liquid crystals are modelled in the Oseen–Frank theory through a unit vector field n. This theory has the apparent drawback that it does not respect the head-to-tail symmetry in which n should be equivalent to −n. This symmetry is preserved in the constrained Landau–de Gennes theory that works with the tensor $${Q=s \left(n\otimes n-\frac{1}{3} Id\right)}$$. We study the differences and the overlaps between the two theories. These depend on the regularity class used as well as on the topology of the underlying domain. We show that for simply-connected domains and in the natural energy class W1,2 the two theories coincide, but otherwise there can be differences between the two theories, which we identify. In the case of planar domains with holes and various boundary conditions, for the simplest form of the energy functional, we completely characterise the instances in which the predictions of the constrained Landau–de Gennes theory differ from those of the Oseen–Frank theory.
Subfields: Electronic, Optical and Magnetic Materials, Mechanical Engineering, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e01dc0e10303b547efe53522ef0205eaaab588e9
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In Electronic, Optical and Magnetic Materials
In Mechanical Engineering
In Statistical and Nonlinear Physics
Citations in the corpus
- Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System (2010, background): “Physically, it can be interpreted as a suitably normalized second-order moment of the probability distribution function describing the orientation of rod-like liquid crystal molecules (see [1] for more details).”