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I am currently employed as a lecturer in the School of Mathematics and Statistics at the University of Glasgow. I am a member of the Solid Mechanics group.

I was a PhD student in the Institute of Theoretical Geophysics within DAMTP at the University of Cambridge, where I worked with John Lister on some problems in fluid driven fracture. I spent time as a post-doc in ESAM at Northwestern University in Evanston, Illinois, working with Professors Stephen Davis and Peter Voorhees on directional solidification of alloys and mushy layers and the growth of nanowires.

Research

Solidification

When a multicomponent alloy is cooled compositional and thermal effects can alter the form of the solidified material, producing microsegregation. With the addition of gravity there is also the possibility of large scale (compared to the micro scales) convective fluid motion, which can redistribute heat and solute and lead to interesting forms of macrosegregation. In particular the formation of mushy layers during the solidification of binary alloys can lead to chimney formation and the presence of freckles in the sample. Interesting interactions between fluid flow, thermal and solutal diffusion and surface energetics occur.

Fluid Driven Fracture

When a fluid fills a crack, the elastic-fluid interaction can lead to an extension of the crack. This phenomenon is called fluid-driven fracture. A geophysical example is the motion of lava through a vertical crack, called a dyke. The dyke may solidify and the surrounding country rock eroded to reveal the dyke's structure, or the dyke may reach the surface and give rise to curtains of fire, as seen in effusive eruptions in Hawaii. Fluid driven fracture is also a concern of the oil industry, where fractures are propagated in order to access reservoirs of oil. Laboratory experiments to model geophysical fluid fracture use gelatin and and, typically, water. In all situations the governing equations combine elasticity, fracture mechanics and fluid dynamics and can the situation can be further complicated by solidification of the fluid, including the effects of porosity on the solid, allowing for a variety of rheologies for the fluid and exsolution of vapour.

Nanowire growth

Nanowires are rods of semi-conductor (such as silicon or germanium) which are 10-100 nm in diameter and can micrometres in length. They have desirable properties for the construction of nanoscale structures and in electronic applications. They can be grown via a technique known as Vapour-Liquid-Solid deposition, in which a catalyst particle (usually gold) is melted on a substrate, forming an alloy. The atmosphere surrounding the droplet contains the desired semi-conductor in a molecular compound (silicon, for example as silane SiH4), the decomposition of which is enhanced by the catalyst droplet. The droplet absorbs the semi-conductor until a certain super-saturation is achieved and the nanowire column precipitates at the base of the droplet. A variety of morphologies exist depending the precise nature of the component elements and the growth conditions. Straight wires, branched wires and exotic helical wires have all been observed.

Teaching

Details of all mathematics courses offered at the University of Glasgow can be found at this Moodle.

Lecture notes for the level-4 course Numerical Analysis can be found here. Comments and corrections are welcomed.

I am happy to discuss the possibility of Level 4/5 projects with any interested students. Some of the projects I have offered in the past are on Solidification, Geometric Integration, Similarity solutions, Minimisation/optimisation problems, the Wulff construction and the Hartree-Fock method.

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