João Teixeira Pinto

Bifurcation analysis of the twist-Freedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions

Motivated by a recent investigation of Millar and McKay [Mol. Cryst. Liq. Cryst., 435, 277/[937]-286/[946] (2005)], we study the magnetic field twist-Fr´eedericksz transition for a nematic liquid crystal of positive diamagnetic anisotropy with strong anchoring and pre- twist boundary conditions. Despite the pre-twist, the system still possesses Z2 symmetry and a symmetry-breaking pitchfork bifurcation, which occurs at a critical magnetic-field strength that, as we prove, is above the threshold for the classical twist-Fr´eedericksz tran- sition (which has no pre-twist). It was observed numerically by Millar and McKay that this instability occurs precisely at the point at which the ground-state solution loses its monotonicity (with respect to the position coordinate across the cell gap). We explain this surprising observation using a rigorous phase-space analysis.

Bifurcations analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions: the asymmetric case

In the paper, Bifurcation analysis of the twist-Freedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions (2009 Eur. J. Appl. Math. 20 , 269–287) by da Costa et al. the twist-Freedericksz transition in a nematic liquid-crystal one-dimensional cell of lenght L was studied, imposing an antisymmetric net twist Dirichlet condition at the cell boundaries. In the present paper, we extend that study to the more general case of net twist Dirichlet conditions without any kind of symmetry restrictions. We use phase-plane analysis tools and appropriately defined time maps to obtain the bifurcation diagrams of the model when L is the bifurcation parameter, and related these diagrams with the one in the antisymmetric situation. The stability of the bifurcating solutions is investigated by applying the method of Maginu (1978 J. Math. Anal. Appl. 63 , 224–243).

Decoupling of the Ericksen–Leslie equations

We examine the hydrodynamic behaviour of a nematic liquid crystal confined between two parallel electrodes and subject to a non-uniform electric field across the layer. By decoupling the Ericksen–Leslie equations for the nematic, we are able to derive a dynamic equation for the director orientation which is not explicitly dependent on the fluid velocity, rather a non-local term contains the effects of flow. The flow velocity and electric potential are determined subsequently from the calculated director profile. Our numerical scheme enables us to predict an effective rotational viscosity which takes account of fluid shear viscosities and allows us to establish the behaviour in special symmetry cases. Significantly, our calculations also demonstrate how kickback can be avoided, and the switch-off time optimised, by restricting the applied voltage to an appropriate range.

Scaling behaviour in a coagulation?annihilation model and Lotka?Volterra competition systems

FPC, JTP e RS foram parcialmente financiados pelo CAMGSD-LARSyS atraves do financiamento plurianual atribuido pela Fundacao para a Ciencia e Tecnologia (Portugal)

Kickback in nematic liquid crystals

We describe a nonlocal linear partial differential equation arising in the analysis of dynamics of a nematic liquid crystal. We confirm that it accounts for the kickback phenomenon by decoupling the director dynamics from the flow. We also analyse some of the mathematical properties of the decoupled director equation.

On the convergence to critical scaling profiles in submonolayer deposition models

In this work we study the rate of convergence to similarity profiles in a mean field model for the deposition of a submonolayer of atoms in a crystal facet, when there is a critical minimal size

Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition

n\geq 2

Self-similar Behaviour in an Addition Model with Input of Monomers

for the stability of the formed clusters. The work complements recently published related results by the same authors in which the rate of convergence was studied outside of a critical direction

A MATHEMATICAL STUDY OF A BISTABLE NEMATIC LIQUID CRYSTAL DEVICE

x=\tau

Uniqueness in the Freedericksz transition with weak anchoring

in the cluster size