In this paper, a new first-order, sphere-constraint-preserving numerical scheme is
constructed for the Ericksen-Leslie equations with variable density. Firstly, by denoting the …

LIQUID CRYSTAL VARIATIONAL, PROBLEMS: MODELING, NUMERICAL ANALYSIS AND
COMPUTATION Lucas Christopher Bouck Doctor of Ph Page 1 ABSTRACT Title of Dissertation …

Liquid crystals are materials that experience an intermediate phase where the material can
flow like a liquid, but the molecules maintain an orientation order. The Frank-Oseen model is …

In this paper, we propose and analyze a series of novel algorithms based on projection-free
accelerated gradient flows to minimize bending energies for nonlinear plates with non …

We present a set of novel accelerated gradient flow methods for solving quadratic energy
minimization problems with nonconvex constraints. Our algorithms are built on novel …

In this paper, we study the numerical approximation for the simplified Ericksen-Leslie system
with variable density. Firstly, by denoting the orientation field vector d in the polar coordinate …

This dissertation focuses on the numerical analysis and scientific computation of two classes
of nonlinear variational problems that originate from materials science: the large deformation …

Liquid crystals (LCs) are materials which exhibit properties intermediate between isotropic
liquids and crystalline solids. The Ericksen model describes nematic LCs in terms of a unit …