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SUMMARY:Liquid Crystal Director Models with Coupled Electric Fields - Gart
 land Jr.\, EC (Kent State University)
DTSTART:20130319T090000Z
DTEND:20130319T095000Z
UID:TALK44000@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Historically\, many liquid-crystal devices and experiments hav
 e involved low-molecular-weight nematic liquid crystals\, in supra-micron-
 size confinements\, with coupled electric fields. In such settings\, equil
 ibrium orientational properties can be modeled most effectively using the 
 Oseen-Frank elastic theory coupled with the equations of electrostatics. I
 n this (mostly) expository talk\, we will discuss some of the issues that 
 arise in the mathematical and numerical treatment of such classical models
 . These issues include the intrinsic minimax nature of such models\, which
  arises from the negative-definite way in which the electrostatic potentia
 l enters the free energy functional and which can also arise when Lagrange
  multipliers are used to enforce the pointwise unit-vector constraints on 
 the liquid-crystal director field\, as well as the complications this inde
 finiteness adds to the assessment of local stability of equilibria. We wil
 l also discuss the anomalous behavior that can be exhibited at the thresho
 lds of certain electric-field-induced instabilities because of the nature 
 of the coupling between the director field and the electric field. In addi
 tion\, we will contrast the macroscopic Oseen-Frank model with the mesosco
 pic Landau-de Gennes model in such contexts.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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