Taylor’s swimming sheet is a classical model of microscale propulsion and pumping. Many biological fluids and substances are fibrous, having a preferred direction in their microstructure; for example, cervical mucus is formed of polymer molecules which create an oriented fibrous network. Moreover, suspensions of elongated motile cells produce a form of active oriented matter. To understand how ...

Liquid crystal droplets are of great interest from physics and applications. Rigorous mathematical analysis is challenging as the problem involves harmonic maps (or Oseen-Frank energy minimizers in general), free interfaces, topological defects which could be either inside droplet or on its surface along with some intriguing boundary anchoring conditions for orientation configurations. In this ...

The paper is concerned with a simplified hydrodynamic equation, proposed by Ericksen and Leslie, modeling the flow of nematic liquid crystals. In dimension two, we establish both interior and boundary regularity theorem for such a flow under smallness conditions. As a consequence, we establish the existence of global weak solutions that are smooth away from at most finitely many singular times ...

An experimental and theoretical study of lyotropic chromonic liquid crystals (LCLCs) confined in cylinders with degenerate planar boundary conditions elucidates LCLC director configurations. When the Frank saddle-splay modulus is more than twice the twist modulus, the ground state adopts an inhomogeneous escaped-twisted configuration. Analysis of the configuration yields a large saddle-splay mo...

In this paper, we prove the unique existence of global strong solutions and decay estimates for simplified Ericksen–Leslie system describing compressible nematic liquid crystal flows in RN, 3≤N≤7. Firstly, rewrite Lagrange coordinates, secondly, well-posedness transformed system, which is main task paper. The proof based on maximal Lp-Lq regularity to linearized problem.

Abstract Sometimes, even a cursory remark at the end of lecture, if growing out deep intelligence and directed to sensitive mind, can have momentous consequences. This was case in episode recounted here, which linked Ericksen de Gennes, albeit indirectly.

This paper addresses the non-uniqueness pointed out by Ericksen in his classical analysis of the equilibrium of a one-dimensional elastic bar with non-convex energy [1]. Following some previous work in this area, we suitably regularize the problem in order to investigate this degenerancy. Our approach gives an explicit framework for the the study of the rich variety of finite-scale equilibrium ...