A mathematical analogy between paraxial optics with two circular polarizations of light in a defocusing Kerr medium positive dispersion, binary Bose-Einstein condensates cold atoms the phase separation regime, and hydrodynamics immiscible compressible liquids can help theoretical search for unknown three-dimensional coherent optical structures. In this work, transversely trapped (by smooth prof...

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...