Ericksen Leslie equation describes the time evolution of a spin vector and velocity in liquid crystals. This equation has following property: (i) the length preserving of a spin vector, (ii) the energy conservation or the dissipation property, (iii) the incompressibility of a velocity vector. In physics papers, the fourth order Runge-Kutta’s method is used for numerical analysis of some types o...

We present a model and discretization that couples the Ericksen model of liquid crystals with variable degree of orientation to the Allen-Cahn equations with a mass constraint. The coupled system models liquid crystal droplets with anisotropic surface tension effects due to the liquid crystal molecular alignment. The total energy consists of the Ericksen energy, phase-field (Allen-Cahn) energy,...

We present a rigorous derivation of the Ericksen-Leslie equation starting from the Doi-Onsager equation. As in the fluid dynamic limit of the Boltzmann equation, we first make the Hilbert expansion for the solution of the Doi-Onsager equation. The existence of the Hilbert expansion is connected to an open question whether the energy of the EricksenLeslie equation is dissipated. We show that the...

There are two competing descriptions of nematic liquid crystal dynamics: the Ericksen-Leslie director theory and the Eringen micropolar approach. Up to this day, these two descriptions have remained distinct in spite of several attempts to show that the micropolar theory includes the director theory. In this paper we show that this is the case by using symmetry reduction techniques and introduc...

We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation methods, the structure of bifurcations from double zero eigenvalues. Our results provide evidence in support of Müller’s conjecture [18] concerning the symmetr...

The nematic fluid pumping mechanism responsible for the heat driven flow in microfluidic channels and capillaries is described a number of applications. This can be generated either by laser beam focused inside microvolume at channel boundary, or inhomogeneous heating capillary boundaries. As an example, scenario vortex excitation microsized volume, under influence temperature gradient caused f...

We study a fully developed creeping flow of nematic liquid crystals in curved pipe with circular cross-section. A special limit zero Deborah number and an infinite Ericksen is considered, so the orientation director are described by transversely isotropic fluid (TIF) model. Analytical solutions obtained expanding governing equation small curvature ?, defined as ratio radius to bend. show that p...

I present an explicit framework for weak phase transformations in complex crystals which is alternative to the one given by Ericksen (2001) and myself (2002b). This approach seems better suited to treat complex lattices with many atoms in the unit cell. As an example, we analyze the model of quartz in Pitteri (2002b) from the present point of view.