I am an Applied Mathematician who works in the fields of nonlinear waves, nonlinear optics, solitary waves, modulation theory and combustion theory. I am based at the University of Wollongong in Australia, where I am Dean of Research.
nonlinear optics
Reorientational versus Kerr dark and gray solitary waves using modulation theory, PHYSICAL REVIEW E (2011)
We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution...
Modulation analysis of boundary induced motion of optical solitary waves in a nematic liquid crystal, Physical Review A (Atomic, Molecular and Optical Physics) (2009)
We consider the motion of a solitary wave, a nematicon, in a finite cell filled...
Collisionless shock resolution in nematic liquid crystals, Physical Review A (Atomic, Molecular and Optical Physics), (2008)
The diffractive resolution on a collisionless shock formed along the spatial profile of a beam...
Dipole soliton formation in a nematic liquid crystal in the non-local limit, Physica D-Nonlinear Phenomena (2008)
The interaction of two symmetric solitary waves, termed nematicons, in a liquid crystal is considered...
Mathematical modelling of nematicons and their interactions, IEEE/LEOS Winter Topical Meeting (2008)
The mathematical modelling of guided wave (nematicon) propagation in liquid crystals is considered. Model equations...
solitons and modulation theory
The analytical evolution of NLS solitons due to the numerical discretization error, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2011)
Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves,...
Evolution of solitary waves for a perturbed nonlinear Schrodinger equation, Applied Mathematics and Computation (2010)
Soliton perturbation theory is used to determine the evolution of a solitary wave described by...
Soliton perturbation theory for a higher-order Hirota equation, Mathematics and Computers in Simulation (2009)
Solitary wave evolution for a higher order Hirota equation is examined. For the higher order...
Evolution of higher-order gray Hirota solitary waves, Studies in Applied Mathematics (2008)
The defocusing Hirota equation has dark and gray soliton solutions which are stable on a...
Undular bores and the initial-boundary value problem for the modified Korteweg-de Vries equation, Wave Motion (2008)
Two types of analytical undular bore solutions, of the initial value problem for the modified...
combustion theory
Semi-analytical solutions for a Gray-Scott reaction-diffusion cell with an applied electric field, Chemical Engineering Science (2008)
An ionic version of the Gray–Scott chemical reaction scheme is considered in a reaction–diffusion cell,...
Self-heating in compost piles due to biological effects, Chemical Engineering Science (2007)
The increase in temperature in compost piles/landfill sites due to micro-organisms undergoing exothermic reactions is...
Cubic autocatalysis with Michaelis - Menten Kinetics: semi-analytical solutions for the reaction - diffusion cell, Chemical Engineering Science (2004)
Cubic-autocatalysis with Michaelis–Menten decay is considered in a one-dimensional reaction–diffusion cell. The boundaries of the...
Semi-analytical solutions for one - and two-dimensional pellet problems., Proceedings of the Royal Society of London. Mathematical, Physical and Engineering Sciences (2004)
The problem of heat and mass transfer within a porous catalytic pellet in which an...
Cubic autocatalytic reaction-diffusion equations: semi-analytical solutions, PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2002)
The Gray-Scott model of cubic-autocatalysis with linear decay is coupled with diffusion and considered in...
mathematical modelling
A perturbation DRBEM model for weakly nonlinear wave run-ups around islands, Engineering Analysis with Boundary Elements (2009)
In this paper, the dual reciprocity boundary element method (DRBEM) based on the perturbation method...
Numerical simulation of contaminant flow in a wool scour bowl., Mathematical and Computer Modelling, (2007)
Wool scouring is the process of washing dirty wool after shearing. Our model numerically simulates...
Modelling a wool scour bowl, ANZIAM Journal (2006)
Wool scouring is the process of washing dirty wool after shearing. Our model simulates, using...
microwave heating
Microwave thawing of cylinders., Applied Mathematical Modelling (2004)
Microwave thawing of a cylinder is examined. The electromagnetic field is governed by Maxwell's equations,...
A comparison of semi-analytical and numerical solutions for the microwave heating of a lossy material in a three-dimensional waveguide (2003)
The microwave heating of a three-dimensional block in an infinitely long rectangular waveguide propagating the...
The microwave heating of three-dimensional blocks: semi-analytical solutions, IMA JOURNAL OF APPLIED MATHEMATICS (2002)
The microwave heating of three-dimensional blocks, by the transverse magnetic waveguide mode TM11, is considered...
The occurrence of limit-cycles during feedback control of microwave heating, MATHEMATICAL AND COMPUTER MODELLING (2002)
The microwave heating of one- and two-dimensional slabs, subject to linear feedback control, is examined....