Analysis of Nematic Liquid Crystals with Disclination Lines

We investigate the structure of nematic liquid crystal thin films described by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the elasticity constant goes to zero a limiting uniaxial texture forms with disclination lines corresponding to a finite number of defects, all of degree 1/2 or all of degree -1/2. We also state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.Comment: 40 pages, 1 figur

Dynamics for Ginzburg-Landau vortices under a mixed flow

Abstract. We consider a complex Ginzburg-Landau equation that contains a Schrödinger term and a damping term that is proportional to the time derivative. Given well-prepared initial conditions that correspond to quantized vortices, we establish the vortex motion law until collision time. 1. introduction We study the asymptotic behavior of the complex Ginzburg-Landau equation (αε + i)∂tuε = ∆uε + 1 ε2 uε(1 − |uε | 2 (1.1) uε(·, 0) = u 0 (1.2) ε(·) as ε → 0, where uε(t) : Ω → C, Ω ⊂ R 2 a bounded and simply connected C 1 domain, with either Dirichlet boundary conditions (1.3) uε = g on ∂Ω, where g ∈ C 1 (∂Ω, S 1), or Neumann boundary conditions

Simulating Southern Hemisphere extra-tropical climate variability with an idealised coupled atmosphere-ocean model

A quasi-geostrophic model of Southern Hemisphere’s wintertime atmospheric circulation with horizontal resolution T21 has been coupled to a global ocean circulation model with a resolution of 2� ×2� and simplified physics. This simplified coupled model reproduces qualitatively some features of the first and the second EOF of atmospheric 833 hPa geopotential height in accordance with NCEP data. The variability patterns of the simplified coupled model have been compared with variability patterns simulated by four complex state-of-the-art coupled CMIP5 models. The first EOF of the simplified model is too zonal and does not reproduce the right position of the centre of action over the Pacific Ocean and its extension to the tropics. The agreement in the second EOF between the simplified and the CMIP5 models is better. The total variance of the simplified model is weaker than the observational variance and those of the CMIP5 models. The transport properties of the Southern Ocean circulation are in qualitative accord with observations. The simplified model exhibits skill in reproducing essential features of decadal and multi-decadal climate variability in the extratropical Southern Hemisphere. Notably, 800 yr long coupled model simulations reveal sea surface temperature fluctuations on the timescale of several decades in the Antarctic Circumpolar Current region