Fernando Pestana da Costa

Asymptotic behaviour of low density solutions to the generalized Becker-Döring equations

Abstract. The asymptotic behaviour of solutions to the generalized Becker-Döring equations is studied. It is proved that solutions converge strongly to a unique equilibrium if the initial density is sufficiently small.

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).

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

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n\geq 2

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

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

Kinetics and Thermodynamics of Poly(9,9-dioctylfluorene) β-Phase Formation in Dilute Solution

x=\tau

The 9-Anthroate chromophore as a fluorescent probe for water

in the cluster size

Uniqueness in the Freedericksz transition with weak anchoring

x

CONVERGENCE TO SELF-SIMILARITY IN AN ADDITION MODEL WITH POWER-LIKE TIME-DEPENDENT INPUT OF MONOMERS

vs. time