Related papers: Biaxiality at the Isotropic-Nematic Interface with…
We present numerical and analytic results for uniaxial and biaxial order at the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory. We study the case where an oblique anchoring condition is imposed asymptotically on the…
We study a crack lying along an imperfect interface in an anisotropic bimaterial. A method is devised where known weight functions for the perfect interface problem are used to obtain singular integral equations relating the tractions and…
We analyze the interplay between wetting and anchoring of nematic liquid crystals on disordering, e.g., rough substrates in the framework of the Landau-de Gennes theory, in situations of competing homeotropic and planar easy axes on the…
Recent experiments report that the long looked for thermotropic biaxial nematic phase has been finally detected in some thermotropic liquid crystalline systems. Inspired by these experimental observations we concentrate on some elementary…
We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing…
In this paper, we consider the isotropic-nematic phase transition with anisotropic elasticity governed by the Landau-de Gennes dynamics of liquid crystals. For $-\frac{3}{2}< L<0,$ we rigorously justify the limit from the Landau-de Gennes…
Within the Onsager theory we study free planar isotropic-nematic interfaces in binary mixtures of hard rods. For sufficiently different particle shapes the bulk phase diagrams of these mixtures exhibit a triple point, where an isotropic (I)…
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, within the Oseen-Frank and Landau-de Gennes theories for nematic liquid crystals. We analyse the defect-free state in the Oseen-Frank…
We present the first calculations of the pressure tensor profile in the vicinity of the planar interface between isotropic liquid and nematic liquid crystal, using Onsager's density functional theory and computer simulation. When the liquid…
We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau-de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model…
We study the symmetry and the spatial uniformity of orientational order of the biaxial nematic phase in the light of recent experimental observations of phase biaxiality in thermotropic bent-core and calamitic-tetramer nematics. We present…
We apply a recently developed technique to determine adapted coordinates for the sixth degree Landau-deGennes potential, in which the potential is specially simple, to analyze the possibility of a direct transition between the fully…
We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau--de Gennes framework in terms of two geometry-dependent variables: half short edge length…
Nematic liquid crystals at rough and fluctuating interfaces are analyzed within the Frank elastic theory and the Landau-de Gennes theory. We study specifically interfaces that locally favor planar anchoring. In the first part we reconsider…
In this paper we provide a formal matched asymptotic analysis for large solutions to the Gelfand-Liouville problem in planar, doubly connected domains in the plane. Using these, we rigorously construct a good approximate solution to the…
Disclination configurations of a nematic liquid crystal are studied within a self-consistent molecular field theory. The theory is based on a tensor order parameter, and can accommodate anisotropic elastic energies without the known…
Scaled particle theory for a binary mixture of hard discorectangles and for a binary mixture of hard rectangles is used to predict possible liquid-crystal demixing scenarios in two dimensions. Through a bifurcation analysis from the…
A convergent approximation is proposed for a mean field density-density correlation function in a system with a two-phase interface. It is based on a fourth-order expansion of the Hamiltonian in terms of fluctuations around the equilibrium…
This study undertakes the mathematical modelling and numerical analysis of dislocations within the framework of differential geometry. The fundamental configurations, i.e. reference, intermediate and current configurations, are expressed as…
Addressing the intricate challenges in plane elasticity, especially with non-vanishing traction and complex geometries, requires innovative methods. This paper offers a novel approach, drawing inspiration from the Neumann problem for the…