Richard Norton

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In this paper we consider the problem of computing the spectrum of a Schrödinger operator with discontinuous, periodic potential in two dimensions using Fourier (or planewave expansion) methods. Problems of this kind are currently of great interest in the design of new optical devices to determine band gaps and to compute localised modes in photonic crystal(More)
The effect of the two antibiotics ceftazidime and meropenem on a collection of 46 Burkholderia pseudomallei isolates representing clinical and environmental sources across northern Australia was investigated by using a series of in vitro test methods. The susceptibility testing methods used included Kirby-Bauer disk diffusion, Etest MIC, broth microdilution(More)
In this paper we consider the discretization error in space and time of an H 1 gradient flow for an energy integral where the energy density is given by the sum of a double-well potential term and a bending energy term. We show that the problem is equivalent to a nonlinear heat equation with nonlocal nonlinearity and adapt the standard error analysis theory(More)
In this paper we study two-dimensional models for the motion of a viscoelastic material with a non-monotone stress-strain relationship. We prove existence of infinitely many stationary solutions to two model problems. This is achieved by constructing sequences of increasingly oscillatory functions, whose limit is a stationary solution. These equilibria may(More)
Photonic crystal fibres are novel optical devices that can be designed to guide light of a particular frequency. This requires two phenomena to occur. First, the frequency of light must be in a gap of the spectrum of the fibre's cladding (usually a periodic arrangement of air holes), so that the cladding acts as a barrier to that frequency of light. Second,(More)
In this paper we consider the numerical computation of band gaps in photonic crystal fibres. We approximate the solution to a variational eigenvalue problem using the planewave expansion method (spectral Galerkin method). As well as presenting implementation and error analysis results we consider solving a modified problem where the piecewise constant(More)
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