BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Asymptotics of Landau-de Gennes theory - Jonathan Robbins (Univers
 ity of Bristol)
DTSTART:20190114T110000Z
DTEND:20190114T114500Z
UID:TALK116860@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We consider the Landau-de Gennes model for nematic liquid crys
 tals in a two-dimensional domain subject to integer-degree boundary condit
 ions\, consistent with the absence of defects\, in the physically relevant
  regime of weak elasticity. At leading order\, the minimum-energy configur
 ation is described by the simpler Oseen-Frank theory. We obtain the next-o
 rder corrections using a Gamma-convergence approach. These turn out to be 
 determined by an algebraic rather than a differential equation. The most i
 mportant qualitative feature is the appearance of biaxiality\, with streng
 th and orientation determined by the gradient of the Frank director. The r
 esults are applied to the variational problem in which only the degree of 
 the boundary conditions is fixed. In contrast to an analogous and well-kno
 wn problem in the Ginzburg-Landau model of vortices\, it is found that the
  energy is only partially degenerate at leading order\, with a family of c
 onformal boundary conditions\, parameterised by the positions of escape po
 ints (the analogues of vortices)\, achieving the minimum possible energy. 
 This partial degeneracy is lifted at the next order.<br> <br> This is join
 t work with G di Fratta\, V Slastikov and A Zarnescu.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR