Related papers: Instability of point defects in a two-dimensional …
We employ the nonperturbative functional Renormalization Group to study models with an O(N_1)+O(N_2) symmetry. Here, different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the…
We present an analysis and numerical study of an optimal control problem for the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs), which is a crucial component in modern technology. They exhibit long range orientational order…
A stability criterion is derived for self-similar solutions with perfect fluids which obey the equation of state $P=k\rho$ in general relativity. A wide class of self-similar solutions turn out to be unstable against the so-called kink…
The physics of nematic liquid crystals has been subject of intensive research since the late 19th century. However, because of the limitations of chemistry the focus has been centered around uni- and biaxial nematics associated with…
The motion of topological defects is an important feature of the dynamics of all liquid crystals, and is especially conspicuous in active liquid crystals. Understanding defect motion is a challenging theoretical problem, because the…
We study a class of one-dimensional models consisting of a frustrated (N+1)-leg spin ladder, its asymmetric doped version as a special example of a Luttinger liquid in an active environment, and the N-channel Kondo-Heisenberg model away…
Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains (Poulin et al., Science 275, 1770 (1997)). The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all…
The Landau-de Gennes model of liquid crystals is a functional acting on wave functions (order parameters) and vector fields (director fields). In a specific asymptotic limit of the physical parameters, we construct critical points such that…
Motivated by recent experimental observations [U. Delabre et al, Langmuir 24, 3998, 2008] we reconsider an instability of ultrathin nematic films, spread on liquid substrates. Within a continuum elastic theory of liquid crystals, in the…
Liquid crystals are phases of matter intermediate between crystals and liquids. Whereas classical liquid crystals have been known for a long time and are used in electro-optical displays, much less is known about their quantum counterparts.…
Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. We show that the uniaxial symmetry constraint is very restrictive and can in general not be satisfied,…
We consider a system of second order non-linear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin finite element…
We prove the existence of a weak solution to a non-isothermal compressible model for nematic liquid crystals. An initial-boundary value problem is studied in a bounded domain with large data. The existence of a global weak solution is…
We present a comprehensive analytical linear stability analysis of the Toner-Tu model for polar active fluids in the ordered phase. Our results provide exact instability criteria and demonstrate that all generic hydrodynamic instabilities…
We present large scale computer simulations of the nonlinear bulk rheology of lamellar phases (smectic liquid crystals) at moderate to large values of the shear rate (Peclet numbers 10-100), in both two and three dimensions. In two…
Electro-hydrodynamic phenomena in liquid crystals constitute an old but still very active research area. The reason is that these phenomena play the key role in various applications of liquid crystals and due to the general interest of…
We demonstrate that a first order isotropic-to-nematic phase transition in liquid crystals can be succesfully modeled within the generalized Landau-de Gennes theory by selecting an appropriate combination of elastic constants. The numerical…
Present work is a theoretical study on the stability of the thermotropic biaxial nematic liquid crystal phase in model systems. Its main aim is to present the phase diagrams of spatially uniform liquid mesophases and to identify the…
We present a novel framework for the study of disclinations in two-dimensional active nematic liquid crystals, and topological defects in general. The order tensor formalism is used to calculate exact multi-particle solutions of the…
Liquid crystals are assemblies of rod-like molecules which self-organize to form mesophases, in-between ordinary liquids and anisotropic crystals. At each point, the molecules collectively orient themselves along a privileged direction,…