Shawn Walker : A Numerical Scheme for the Generalized Ericksen Model of Liquid Crystals With Applications to Virus DNA Packing

Posted by Mimi Dai , part of the Analysis and Applied Mathematics Seminar.

At

Feb. 11, 2019, 4 p.m.

In

636 SEO

Abstract

We consider the generalized Ericksen model of liquid crystals, which is an energy with 8 independent ``elastic'' constants that depends on two order parameters n (director) and s (variable degree of orientation). In addition, we present a new finite element discretization for this energy, that can handle the degenerate elliptic part without regularization, is stable and it Gamma-converges to the continuous energy. Moreover, it does not require the mesh to be weakly acute (which was an important assumption in our previous work). A minimization scheme for computing discrete minimizers will also be discussed. Furthermore, we include other effects such as weak anchoring (normal and tangential), as well as fully coupled electro-statics with flexo-electric and order-electric effects. We also present several simulations (in 2-D and 3-D) illustrating the effects of the different elastic constants and electric field parameters. At the end of the talk, we discuss a problem on the packing of DNA inside viral capsids. We show how the generalized Ericksen model can be used to simulate the packing of DNA inside viral capsids, and to estimate packing pressures inside the capsid. This part is joint with Carme Calderer (UMN), Dmitry Golovaty (U. Akron), Javier Arsuaga (U.C. Davis).