Abstract
We discuss a dynamical theory for nematic liquid crystals describing the stage of evolution in which the hydrodynamic fluid motion has already equilibrated and the subsequent evolution proceeds via diffusive motion of the orientational degrees of freedom. This diffusion induces a slow motion of singularities of the order parameter field. Using asymptotic methods for gradient flows, we establish a relation between the Doi-Smoluchowski kinetic equation and vortex dynamics in two-dimensional systems. We also discuss moment closures for the kinetic equation and Landau-de Gennes-type free energy dissipation.
Highlights
Dynamics of liquid crystalline systems is traditionally described in a framework of theories combining fluid dynamics equations, constitutive relations between the hydrodynamic stress tensor and liquid crystalline order parameters, and evolution equations for the latter [3], [6], [9], [12]
In the absence of hydrodynamic motion, the relaxation of the orientational degrees of freedom is induced by the free energy dissipation
To accomplish this task we use asymptotic methods for gradient flows to the way it is used in the Ginzburg-Landau theory [4], [7], [13], [14], [16]
Summary
Dynamics of liquid crystalline systems is traditionally described in a framework of theories combining fluid dynamics equations, constitutive relations between the hydrodynamic stress tensor and liquid crystalline order parameters, and evolution equations for the latter [3], [6], [9], [12]. The elastic free energy density is a quadratic functional of the order-parameter field equivalent to that of the Landau-de Gennes theory: Fe( ) = We define the reduced free energy E(n) as a functional of the order parameter n alone, E(n) =
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