Function Spaces for Liquid Crystals

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Partial Sobolev spaces and anisotropic smectic liquid crystals

The partial Sobolev spaces with respect to a vector field are introduced, and are used to studyminimization problems of the functionals which are degenerate in the sense that they do not have control on either the tangential part or the perpendicular part of the magnetic gradients. Based on these results we obtain the asymptotic behavior of the minimizers of the anisotropic Landau-de Gennes fun...

Photoalignment of liquid crystals by liquid crystals

We observed light-induced alignment of the nematic liquid crystal, 4, 4(')-n-pentylcyanobiphenyl (5CB), on a fused quartz. Irradiation of the adsorbed layer with polarized ultraviolet light produced homogeneous alignment in a 5CB-filled liquid crystal cell with the easy orientation axis perpendicular to the polarization direction. The measured anchoring energy increases with illumination up to ...

The concentration function problem for $G$-spaces

‎In this note‎, ‎we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$‎. ‎We prove a necessary and sufficient condition for the concentration functions of a‎ ‎spread-out irreducible probability measure $mu$ on $G$ to converge to zero.

Molecular Crystals and Liquid Crystals