Solid mechanics
Department of Mathematics, Room 414
University of Glasgow
University Gardens
Glasgow, G12 8QW
United Kingdom
T: +44 (0)141 330 6535
F: +44 (0)131 330 4111
I am currently employed as an RCUK Fellow in the Department of Mathematics 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
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. My research in this area has been to examine the simplest case of straight nanowire growth, and to obtain a quantitative model that relates the growth rate and diameter of a silicon whisker to the silane flux of the surrounding atmosphere. The next step is to determine the stability of the solution, where the emphasis is not only on learning the critical conditions and wavelength of any instability, but understanding the mechanism.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.Publications
Roper, S.M. & Davis, S.H. & Voorhees, P.W. 2007
Convection in a mushy layer with a deformable permeable interface.
J. Fluid Mech. ()
Roper, S.M. & Davis, S.H. & Voorhees, P.W. & Golovin,
A. A. & Weiss, M. 2007
Steady growth of silicon nanowires via the VLS mechanism.
J. App. Phys. 102
Roper, S.M. & Davis, S.H. & Voorhees, P.W. 2007
Forced convection in a mushy zone with sidewall heat-losses.
Materials and Metallurgical Transactions A 35, 1069—1079
Roper, S.M. & Lister, J.R. 2007
Buoyancy-driven crack propagation: the limit of large fracture toughness.
J. Fluid Mech. 580, 359—380.
Roper, S.M. & Lister, J.R. 2005
Buoyancy-driven crack propagation from an over-pressured source.
J. Fluid Mech. 536, 79—98.
Rebecca Hoyle, Daniel Jefferson, Robert Leese, Steve Noble & Steven
Roper
Network design for urban light transport.
European Study Group in Industry 2003, University of Bristol
Mathematical and Computational links
- ESAM.
- The Department of Applied Maths and Theoretical Physics, DAMTP, University of Cambridge, UK.
- The Journal of Fluid Mechanics.
- The American Physical Society.
- A useful FORTRAN 77 page.
- The Numerical Recipes homepage.
- The GNU page.
- Only as powerful as its user, VIM.
- The LaTeX project site and the TeX users group.
- Assorted programming reference sites, Perl, Bash and Awk.
Funding links
- The Web of Science.
- The EPSRC, the NERC and the Royal Society.
Visualisation
Teaching
Autumn 2007 I have no formal teaching duties this term.
Winter/Spring 2008 I have no formal teaching duties this term.
Autumn 2008, Winter/Spring 2010 Numerical Analysis.
Winter/Spring 2010 Writing and Presenting Mathematics.
I am happy to discuss the possibility of Level 4/5 projects with any interested students. Examples of the types of project on offer are Solidification, Geometric Integration and something I hope to learn about myself and might be offered in the future Computational Chemistry.