Related papers: A Model Problem for Nematic-Isotropic Transitions …
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…
Computer simulations are presented of the isotropic-to-nematic transition in a liquid crystal confined between two parallel plates a distance H apart. The plates are neutral and do not impose any anchoring on the particles. Depending on the…
We introduce a rigorous approach to the study of the symmetry breaking and pattern formation phenomenon for isotropic functionals with local/nonlocal interactions in competition. We consider a general class of nonlocal variational problems…
We compute the $\Gamma$-limit of energy functionals describing mechanical systems composed of a thin nematic liquid crystal elastomer sustaining a homogeneous and isotropic elastic membrane. We work in the regime of infinitesimal…
Liquid crystals in two dimensions undergo a first-order isotropic-to-quasi-nematic transition, provided the particle interactions are sufficiently ``sharp and narrow''. This implies phase coexistence between isotropic and quasi-nematic…
We report numerical results for the hydrodynamics of inhomogeneous lyotropic and extensile active nematic gels. By simulating the coupled Cahn-Hilliard, Navier-Stokes, and Beris-Edwards equation for the evolution of the composition, flow…
We present in this paper a detailed analysis of the flexoelectric instability of a planar nematic layer in the presence of an alternating electric field (frequency $\omega$), which leads to stripe patterns (flexodomains) in the plane of the…
We provide a series of rigidity results for a nonlocal phase transition equation. The prototype equation that we consider is of the form $$ (-\Delta)^{s/2} u=u-u^3,$$ with~$s\in(0,1)$. More generally, we can take into account equations like…
We present the general theory of Ising transitions in isotropic elastic media with vanishing thermal expansion. By constructing a minimal model with appropriate spin-lattice couplings, we show that in two dimensions near a continuous…
Motivated by recent experiments, the isotropic-nematic phase transition in chromonic liquid crystals is studied. As temperature decreases, nematic nuclei nucleate, grow, and coalesce, giving rise to tactoid microstructures in an isotropic…
A Self Consistent Field Theory description of equilibrium, but non uniform, configurations adopted by semi flexible liquid crystal molecules is presented. Two cases are considered, isotropic-nematic phase boundaries, and topological defects…
The effect of rough walls on the phase behaviour of a confined liquid crystal (LC) fluid is studied using constant pressure Monte Carlo simulations. The LC is modelled as a fluid of soft ellipsoidal molecules and the rough walls are…
In this article we consider systems of parallel hard {\it superellipsoids}, which can be viewed as a possible interpolation between ellipsoids of revolution and cylinders. Superellipsoids are characterized by an aspect ratio and an exponent…
Topological defects resulted from boundary constraints in confined liquid crystals have attracted extensive research interests. In this paper, we use numerical simulation to study the phase transition dynamics in the context of stochastic…
By analyzing elastic theory for nematic liquid crystals, we distinguish three regimes of elastic constants. In one regime, the Ericksen inequalities are satisfied, and the ground state of the director field is uniform. In a second regime,…
We present a model to describe complex phases observed at mesoscopic scales in ultrathin magnetic films. The model is based on the interaction between dipolar as well as quadrupolar magnetic moments. In the special case of strong…
We consider a phenomenological continuum model for an active nematic fluid and show a universal, model independent, instability which renders the homogeneous nematic state unstable to order fluctuations. Using numerical and analytic tools…
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…
We explore reshaping of nematoelastic films upon imbibing an isotropic solvent under conditions when isotropic and nematic phases coexist. The structure of the interphase boundary is computed taken into account the optimal nematic…
We consider the weakly first order phase transition between the isotropic and ordered phases of nematics in terms of the behavior of topological line defects. Analytical and Monte Carlo results are presented for a new coarse-grained lattice…