Related papers: A shape optimization problem for nematic and chole…
In this paper we examine the modelling and minimisation of cholesteric liquid crystals systems within the Oseen-Frank theory. We focus on a cuboid domain with the frustrated boundary conditions ${\bf n}(0,x,y)=(1,0,0)$ and ${\bf…
Toroidal nematics are nematic liquid crystals confined within a circular torus and subject to planar degenerate anchoring on the boundary of the torus. They may be droplets floating in an isotropic environment or cavities carved out of a…
We investigate a shape optimization problem for a heat-conducting fluid governed by a Boussinesq system. The main goal is to determine an optimal domain shape that yields a temperature distribution as uniform as possible. Initially, we…
We are interested in the optimization of convex domains under a PDE constraint. Due to the difficulties of approximating convex domains in $\mathbb{R}^3$, the restriction to rotationally symmetric domains is used to reduce shape…
In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…
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 the optimization of the positive principal eigenvalue of an indefinite weighted problem, associated with the Neumann Laplacian in a box $\Omega\subset\mathbb{R}^N$, which arises in the investigation of the survival threshold in…
Mathematical crystal chemistry views crystal structures as the optimal solutions of mathematical optimization problem formalizing inorganic structural chemistry. This paper introduces the minimum and maximum atomic radii depending on the…
The purpose of the paper is to give a complete characterization of the continuity of lower envelopes in the infinite dimensional spaces in terms of the notion of c-regularity. As an application we introduce a variational unconstrained…
We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field $\mathbf{n}$ and its degree of orientation $s$,…
This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem.…
In this study, a shape optimization problem for the two-dimensional stationary Navier--Stokes equations with an artificial boundary condition is considered. The fluid is assumed to be flowing through a rectangular channel, and the…
Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal…
We consider planar liquid crystal elastomers: two dimensional objects made of anisotropic responsive materials, that upon activation remain flat however change their planar shape. We derive a closed form, analytical solution based on the…
We analyse a recent generalised free-energy for liquid crystals posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i. e., uniform…
We investigate a PDE-constrained optimization problem, with an intuitive interpretation in terms of the design of robust membranes made out of an arbitrary number of different materials. We prove existence and uniqueness of solutions for…
In [J. Cantarella, D. DeTurck, H. Gluck and M. Teytel, J. Math. Phys. 41:5615 (2000)] the helicity isoperimetric problem which asks to find a smooth domain of fixed volume which maximises Biot-Savart helicity among all other smooth domains…
The stability of shapes formed by three viscoelastic droplets during their arrested coalescence has been investigated using micromanipulation experiments. Addition of a third droplet to arrested droplet doublets is shown to be controlled by…
An eigenvalue problem arising in optimal insulation related to the minimization of the heat decay rate of an insulated body is adapted to enforce a positive lower bound imposed on the distribution of insulating material. We prove the…
Understanding and controlling the director field configuration, shape, and orientation in nematic and cholesteric liquid crystals is of fundamental importance in several branches of science. Liquid crystalline droplets, also known as…