Tailored nematic and magnetization profiles on two-dimensional polygons

Elastic anisotropy in the reduced Landau-de Gennes model

We study the effects of elastic anisotropy on Landau–de Gennes critical points, for nematic liquid crystals, on a square domain. The elastic anisotropy is captured by a parameter, L2, and the critical points are described by 3 d.f. We analytically construct a symmetric critical point for all admissible values of L2, which is necessarily globally stable for small domains, i.e. when the square edge length, λ, is small enough. We perform asymptotic analyses and numerical studies to discover at least five classes of these symmetric critical points—the WORS, Ring±, Constant and pWORS solutions, of which the WORS, Ring+ and Constant solutions can be stable. Furthermore, we demonstrate that the novel Constant solution is energetically preferable for large λ and large L2, and prove associated stability results that corroborate the stabilizing effects of L2 for reduced Landau–de Gennes critical points. We complement our analysis with numerically computed bifurcation diagrams for different values of L2, which illustrate the interplay of elastic anisotropy and geometry for nematic solution landscapes, at low temperatures.

Clustering in ferronematics-The effect of magnetic collective ordering

Clustering of magnetic nanoparticles can dramatically change their collective magnetic properties, and it consequently may influence their performance in biomedical and technological applications. Owing to tailored surface modification of magnetic particles such composites represent stable systems. Here, we report ferronematic mixtures that contain anisotropic clusters of mesogen-hybridized cobalt ferrite nanoparticles dispersed in liquid crystal host studied by different experimental methods-magnetization measurements, small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS), and capacitance measurements. These measurements reveal non-monotonic dependencies of magnetization curves and the Fréedericksz transition on the magnetic nanoparticles concentration. This can be explained by the formation of clusters, whose structures were determined by SAXS measurements. Complementary to the magnetization measurements, SANS measurements of the samples were performed for different magnetic field strengths to obtain information on the orientation of the liquid crystal molecules. We demonstrated that such hybrid materials offer new avenues for tunable materials.

Solution landscapes of the simplified Ericksen–Leslie model and its comparisonwith the reduced Landau–deGennes model

We investigate the solution landscapes of a simplified Ericksen–Leslie (sEL) vector model for nematic liquid crystals, confined in a two-dimensional square domain with tangent boundary conditions. An efficient numerical algorithm is developed to construct the solution landscapes by utilizing the symmetry properties of the model and the domain. Since the sEL model and the reduced Landau–de Gennes (rLdG) models can be viewed as Ginzburg–Landau functionals, we systematically compute the solution landscapes of the sEL model, for different domain sizes, and compare them with the solution landscapes of the corresponding rLdG model. There are many similarities, including the stable diagonal and rotated states, bifurcation behaviours and sub-solution landscapes with low-index saddle solutions. Significant disparities also exist between the two models. The sEL vector model exhibits the stable solution C ± with interior defects, high-index ‘fake defect’ solutions, novel tessellating solutions and certain types of distinctive dynamical pathways. The solution landscape approach provides a comprehensive and efficient way for model comparison and is applicable to a wide range of mathematical models in physics.