Conference papers

Modelling Two-Dimensional Photopolymer Patterns Produced With Multiple-Beam Holography

Dana Mackey et al. — Fri, 25 May 2012 10:22:28 PDT

Periodic structures referred to as photonic crystals attract considerable interest due to their potential applications in areas such as nanotechnology, photonics, plasmonics, etc. Among various techniques used for their fabrication, multiple-beam holography is a promising method enabling defect-free structures to be produced in a single step over large areas.

In this paper we use a mathematical model describing photopolymerisation to simulate two-dimensional structures produced by the interference pattern of three noncoplanar beams. The holographic recording of different lattices is studied by variation of certain parameters such as beam wave vectors, time and intensity of illumination.

A Note on Hopfian and Co-Hopfian Abelian Groups

Brendan Goldsmith et al. — Tue, 20 Dec 2011 05:54:23 PST

The notions of Hopfian and co-Hopfian groups have been of interest for some time. In this present work we exploit some unpublished ideas of Corner to answer questions relating to such groups. In particular, we extend an answer given by Corner to a problem of Beaumont and Pierce and show how the properties may be lifted from subgroups to the whole group in certain situations.

On the (Non)-Integrability of the Perturbed KdV Hierarchy with Generic Self-consistent Sources

Vladimir Gerdjikov et al. — Mon, 07 Feb 2011 01:33:53 PST

Generalized Moonshine and Orbifold Constructions

Michael Tuite et al. — Fri, 21 Jan 2011 05:02:07 PST

A brief review is given of some of our recent work on Generalised Monstrous Moonshine using abelian orbifoldings of the Moonshine Module.

Two component integrable systems modelling shallow water waves

Rossen Ivanov — Wed, 19 Jan 2011 08:05:46 PST

Our aim is to describe the derivation of shallow water model equations for the constant vorticity case and to demonstrate how these equations can be related to two integrable systems: a two component integrable generalization of the Camassa-Holm equation and the Kaup - Boussinesq system.

Poisson Structures of Equations associated with groups of diffeomorphisms

Rossen Ivanov — Sat, 15 Jan 2011 03:58:52 PST

A class of equations describing the geodesic flow for a right-invariant metric on the group of diffeomorphisms of Rn is reviewed from the viewpoint of their Lie-Poisson structures. A subclass of these equations is analogous to the Euler equations in hydrodynamics (for n = 3), preserving the volume element of the domain of fluid flow. An example in n = 1 dimension is the Camassa-Holm equation, which is a geodesic flow equation on the group of diffeomorphisms, preserving the H1 metric.

Two soliton interactions of BD.I multicomponent NLS equations and their gauge equivalent

Vladimir Gerdjikov et al. — Thu, 13 Jan 2011 06:47:19 PST

Using the dressing Zakharov-Shabat method we re-derive the effects of the two-soliton interactions for the MNLS equations related to the BD.I-type symmetric spaces. Next we generalize this analysis for the Heisenberg ferromagnet type equations, gauge equivalent to MNLS.

The Camassa-Holm Hierarchy and Soliton Perturbations

Georgi Grahovski et al. — Wed, 12 Jan 2011 09:04:44 PST

The theory of soliton perturbations is considered. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of “squared solutions” of the spectral problem, associated to the soliton equation. The Inverse Scattering Transform for the corresponding hierarchy of soliton equations can be viewed as a GFT where the expansions of the solutions have generalised Fourier coefficients given by the scattering data. The GFT provides a natural setting for the analysis of small perturbations to an integrable equation: starting from a purely soliton solution one can ’modify’ the soliton parameters such as to incorporate the changes caused by the perturbation. As illustrative examples the perturbed equations of the Camassa-Holm hierarchy are presented.

Creating the human resources for technology: the case of Ireland and the specific role of DIT.

Brendan Goldsmith — Fri, 03 Jul 2009 07:08:13 PDT

No abstract available

Creating the human resources for enhancing innovation in regional economies

Brendan Goldsmith — Fri, 03 Jul 2009 07:07:38 PDT

No abstract available