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Using slow manifolds to model liquid crystals in Q-tensor theories

Presented by: 
G D'Alessandro University of Southampton
Date: 
Wednesday 17th April 2013 - 12:00 to 13:00
Venue: 
INI Seminar Room 1
Abstract: 
The $Q$-tensor description of the nematic director field is very powerful as it can cope with defects and complicated geometries. On the other hand, it is also computationally very expensive because the equations for the tensor components are stiff: the contain time scales that differ by six to eight orders of magnitude.

In this talk I will discuss how we can use the stiffness of the director equations to our advantage: we can separate the two time scales, eliminate the fast one and reduce the dynamics of interest to a slow manifold, where the equations are no longer stiff. The ensuing approximate model is both accurate and fast.

Of course, there is a price to be paid: the approximation is valid only away from defects. I will conclude the talk discussing how we are attempting to overcome this restriction.

Co-author Keith Daly (University of Southampton)

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons