Potential Projects

If you are interested in studying for a Ph.D. in applied mathematics at Newcastle you should apply through the official channels. The following projects reflect my research interests and address important open questions:

Counterflow turbulence

The two-fluid model of superfluid helium was invented by Tisza & Landau in the late 1930s to account for the remarkable flow properties of liquid helium at very low temperatures. These properties include the fluid’s ability to perfectly conduct heat and to flow without friction, superfluidity. Counterflow is a mechanism of heat conduction in these special fluids, in which the counterflow of two fluids prevents the formation of any localised "hot spots" ( hence bubbles don’t form in boiling liquid helium below 2.17 Kelvin). This (apparently) ideal heat transfer makes liquid helium very useful to engineers: lacking any other usable fluid (below 4 K, all other materials freeze), liquid helium can cool many important devices, from infrared detectors on board orbiting satellites, to the powerful superconducting magnets that accelerate elementary particles or that form the heart of medical imaging equipment. However above a certain critical velocity the smooth laminar flow of the superfluid component transitions into into a disordered tangle of quantized vortex filaments, which dissipate kinetic energy. A number of important open questions are outstanding in this turbulent regime and we would aim to address some of these questions with detailed numerical simulations.

Agent-based modelling of the spread of the Neolithic

The transition from hunter-gathering to early farming — signifying the start of the Neolithic era in traditional archaeological terminology — was one of the most important steps made by humanity in developing the complex modern societies that exist today. The mechanism of the spread throughout Europe of Neolithic farming techniques, which developed in the Near East. We shall pioneer the use of agent-based models to study the spread of Neolithic farming from the Fertile Crescent into Western Europe. Agent-based modelling is a computational technique where the actions and interactions of autonomous “agents” are simulated . Such techniques have previously been applied in a wide range of fields from the spread of epidemics and biowarfare to modelling financial markets. There is the potential to visit active dig sites in Ukraine and present results at leading mathematical and archaeological conferences.

Leapfrogging vortices at absolute zero

The theory of vortex motion is one of the great successes of classical fluid mechanics, and finds application in such diverse areas as meteorology, aerodynamics and superfluid physics. One of the most elementary problems involves a so-called vortex pair, where two vortices of equal strength but opposite sign are placed close to one another. Each vortex is then swept along at the local flow velocity due to the other, and, as a consequence, the two vortices travel along together, with uniform speed. The closer the vortices, i.e. the smaller the breadth of the pair, the faster the speed of travel. What happens, however, if one such vortex pair chases another? In fact, as a result of the mutual interaction, the pair in front becomes wider and slows down, while the one behind becomes more narrow and speeds up. In this way it can happen that the two vortex pairs exchange places, over and over again, by repeatedly passing through one another, ‘leapfrogging’.
This was first investigated theoretically by A. E. H. Love in 1894. He found that the nature of the vortex motion depends on the ratio of the breadths, and suggested a single parameter controlled wether leapfrogging was possible, or not. At the time Love's investigation was purely a theoretical play thing, in real fluids vortex motion is much more complicated due to the effect of viscosity. This was until the work of Wiemann, Cornell and Keterlee, who confirmed Bose and Einstein's theoretical prediction of a new state of matter in 1995, for which they were awarded the Nobel prize. This new state of matter is called a Bose-Einstein condensate (BEC), a fluid whose properties are strongly constrained by quantum mechanics. A BEC truly allows us to study the toy model of Love in a real, experimentally realisable system.

Two-fluid turbulence at low temperatures

Nearly every fluid in the universe is affected by turbulence, from the flow of blood in your body, clouds in the atmosphere, and the interstellar medium in the galaxy. Although our understanding of the nature of turbulence is improving, we are a long way from a full understanding of the random, chaotic motion of these liquids and gases. Part of the problem is that although we commonly think of turbulence as being a collection of vortices or eddies, in a classical fluid such as water or air these vortices are not well defined elements. However at very low the weirdness of quantum mechanics changes the game. The fluid loses its friction and rotational motion in the fluid is constrained to thin well defined quantised vortices, mini tornadoes, which thread through the fluid. This project would investigate the coupling between the normal and superfluid components of liquid helium, when both fluids are driven into a turbulent state. We would aim to model experiments taking place in Grenoble and Prague, and disseminate our work at leading international conferences.

Past/Present Students

Nicola Hewett - Newcastle summer studentship 2015 - TBC
Alexander Hindle - Newcastle summer studentship 2015 - TBC
Kieren Charles - Newcastle MMath 2015-present - Prehistoric population dynamics
Scott Richardson - Glasgow PhD 2013-present - Bioconvection
Roxanne Barry - Glasgow MSci 2014/15 - Mathematical models of animal stampedes
Simon Fong- Glasgow 4H project 2014/15 - The morphology of bird flocks
Russell Davidson - Glasgow MSci 2013/14 - The ABC dynamo
Gemma Caldwell - Glasgow 4H project 2013/14 - Bird flocking and mosh pits
David Russell - Glasgow 4H project 2013/14 - The Galloway-Proctor dynamo
Andrew Mooney - Glasgow 4H project 2013/14 - Formation of rain droplets in chaotic flows
Elena Ardito - Glasgow MSc 2013 - 2D Turbulence in Bose-Einstein condensates
Michaela Howard - Glasgow 4H project 2012/13 - The collapse of the bronze age Minoan empire
Adam Sayers - Glasgow 4H project 2012/13 - Magnetic fields in spiral galaxies
Owen Morris - Glasgow 4H project 2012/13 - Clustering of intertial particles in chaotic flows
Lucy Sherwin - Newcastle PhD 2011-present - Quantum turbulence

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License