On the Time-Dependent Ginzburg-Landau Equations of Nematics

Abstract

In this study we shall examine the relationship between tensorial and vector approaches for elastodynamics in the framework of continuum theory of nematics. It will be elucidated that the Lagrange multipliers have to be involved in the tensorial framework as well as the vector one to assure the equnvalence between them. A contraction for the tensorial indices in the time-dependent Ginzburg-Landau equation will be found to eventually result in the vector form concerned with the Ericksen-Leslie equation without flow dynamics.