The two-dimensional Smoluchowski equation is employed to study the effect of elongational perturbations on nematic liquid crystal polymers under a weak shear. We use the multiscale asymptotic analysis to show that 1 when the elongational perturbation is small relative to the weak shear, the orientational probability density function pdf tumbles periodically only in an intermediate range of poly...

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the GinzburgLandau approximation, we construct an approximate system with the dissipated energy based on a new formulation of th...

Numerical approximation of the flow of liquid crystals governed by the Ericksen–Leslie equations is considered. Care is taken to develop numerical schemes which inherit the Hamiltonian structure of these equations and associated stability properties. For a large class of material parameters compactness of the discrete solutions is established which guarantees convergence.

The paper shows the successive steps of approximation of Picard unification for the solution of the non-isothermal fluid flow in thin layer including inertia forces and apparent viscosities described by the non-linear dependences. In this paper is presented a unified semi analytical method of solution of the asymmetrical, laminar, steady and unsteady, non-Newtonian lubrication problem flow betw...

Abstract The Ericksen–Leslie system is a fundamental hydrodynamic model that describes the evolution of incompressible liquid crystal flows nematic type. In this paper, we prove uniqueness global weak solutions to general with Ginzburg–Landau type approximation in two dimensional periodic domain. proof based on some delicate energy estimates for difference within suitable functional framework l...

We demonstrate theory and computations for finite-energy line defect solutions in an improvement of Ericksen-Leslie liquid crystal theory. Planar director fields are considered in two and three space dimensions, and we demonstrate straight as well as loop disclination solutions. The possibility of static balance of forces in the presence of a disclination and in the absence of flow and body for...

The virtual colony count (VCC) microbiological assay has been utilized for over a decade to measure the antimicrobial activity of peptides such as defensins and LL-37 against biosafety level (BSL)-1 and BSL-2 bacteria including , , , and Escherichia coli Staphylococcus aureus Bacillus cereus Enterobacter . In addition, a modified pipetting technique was presented in a 2011 aerogenes study of de...

The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen-Leslie equations is considered. Convergence of finite element approximations is established under appropriate regularity hypotheses, and numerical experiments exhibiting the interaction of singularities and the coupling of the director and momentum equations are presented.