We investigate the structure of nematic liquid crystal thin films described by the Landau-de Gennes tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the elasticity constant goes to zero a limiting uniaxial texture forms with disclination lines corresponding to a finite number of defects, all of degree 1 2 or all of degree − 1 2 . We also state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.

The astrophysical phenomenon of mimetic helical magnetic field (h B)-assisted self-assembly is herein introduced to build helical superstructures that display chiroptical properties. As a building block, magnetoplasmonic (MagPlas) Ag@Fe3O4 core–shell nanoparticles are used to guide plasmonic Ag nanoparticles onto a helical magnetic flux. The chirality of the assembled helical structures and tailored circular dichroism are successfully tuned in real time, and the handedness of the assembled structures is dynamically switched by the h B at the millisecond level, which is at least 6000-fold faster than other template-assisted methods. The peak position of circular dichroism can be reconfigured by altering the plasmonic resonance or coupling by controlling the size of the Ag core and magnetic flux density. The h B-induced chirality modulation represents a method to control the polarization state of light at the nexus of plasmonics, magnetic self-assembly, colloidal science, liquid crystals, and chirality. It presents active and dynamic chiral assemblies of magnetoplasmonic nanomaterials, enabling further practical applications in optical devices.

The purpose of this article is to generalize the theory of stability of functional equations to the case of n‐Banach spaces. In this article, we prove the generalized Hyers–Ulam stabilities of the Cauchy functional equations, Jensen functional equations and quadratic functional equations on n‐Banach spaces.

We present modeling and analysis of smectic C phases of liquid crystals capable of sustaining spontaneous polarization. The layered liquid crystals are also assumed to be chiral. We study minimization of the total energy subject to electrostatic constraints. In order to determine mathematically and physically relevant boundary conditions, we appeal to the analogy between the current problem and the vorticity in fluids. We place a special emphasis on the nonlocal and selfenergy effects arising from spontaneous polarization. We discuss examples pertaining to the electric field created by the liquid crystal in dielectric medium, and also to the possible role of a domain shape as an energy reduction mechanism.

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