Related papers: Order Reconstruction for Nematics on Squares with …
We construct an order reconstruction (OR)-type Landau-de Gennes critical point on a square domain of edge length $\lambda$, motivated by the well order reconstruction solution numerically reported by Kralj and Majumdar. The OR critical…
We study nematic equilibria on three-dimensional square wells, with emphasis on Well Order Reconstruction Solutions (WORS) as a function of the well size, characterized by $\lambda$, and the well height denoted by $\epsilon$. The WORS are…
We study the effects of elastic anisotropy on the Landau-de Gennes critical points for nematic liquid crystals, in a square domain. The elastic anisotropy is captured by a parameter, $L_2$, and the critical points are described by three…
Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader…
We study order reconstruction (OR) solutions in the Beris-Edwards framework for nematodynamics, for both passive and active nematic flows in a microfluidic channel. OR solutions exhibit polydomains and domain walls, and as such, are of…
The detailed analysis of the global structure of the renormalization-group (RG) flow diagram for a model with isotropic and cubic interactions is carried out in the framework of the massive field theory directly in three dimensions (3D)…
We investigate critical points of a Landau-de Gennes (LdG) free energy in three-dimensional (3D) cuboids, that model nematic equilibria. We develop a hybrid saddle dynamics-based algorithm to efficiently compute solution landscapes of these…
We consider a variational two-dimensional Landau-de Gennes model in the theory of nematic liquid crystals in a disk of radius $R$. We prove that under a symmetric boundary condition carrying a topological defect of degree $\frac{k}{2}$ for…
A systematic analysis of defect textures in facetted nanoparticles with polygonal configurations embedded in a nematic matrix is performed using the Landau-de Gennes model, homeotropic strong anchoring in a square domain with uniform…
We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general $k$-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent with the…
As we found previously, when critical points occur within grid intervals, the accuracy relations of smoothness indicators of WENO-JS would differ from that assuming critical points occurring on grid nodes, and accordingly the global…
We use nematic Multi-particle Collision Dynamics (N-MPCD) simulations to study confined nematic liquid crystals in square domains, with three distinct mean-field potentials: the classical Maier-Saupe and Marrucci-Greco models, and a more…
We study the critical behavior of the $O(n)$ model under steady shear flow using a dynamical renormalization group (RG) method. Incorporating the strong anisotropy in scaling ansatz, which has been neglected in earlier RG analyses, we…
We study reduced nematic equilibria on regular two-dimensional polygons with Dirichlet tangent boundary conditions, in a reduced two-dimensional Landau-de Gennes framework, discussing their relevance in the full three-dimensional framework…
The emergence of nematic order on deformable closed surfaces plays a pivotal role in the morphogenesis of active biological matter, such as the regeneration of Hydra. In this work, we present a continuum model that couples the…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
We study the behaviour of global minimizers of a continuum Landau-de Gennes energy functional for nematic liquid crystals, in three-dimensional axially symmetric domains domains diffeomorphic to a ball (a nematic droplet) and in a…
We study equilibrium configurations of nematic liquid crystals confined to two-dimensional isosceles triangles, subject to tangent boundary conditions. This toy problem is motivated by the effects of geometrical asymmetry on equilibria in…
We construct a phenomenological Landau-de Gennes theory for hard colloidal rods by performing an order parameter expansion of the chemical-potential dependent grand potential. By fitting the coefficients to known results of Onsager theory,…
Finite difference schemes are the method of choice for solving nonlinear, degenerate elliptic PDEs, because the Barles-Sougandis convergence framework [Barles and Sougandidis, Asymptotic Analysis, 4(3):271-283, 1991] provides sufficient…