This page lists potential PhD projects in fluids and solids, offered by faculty members of the School of Mathematics. For further details of the School's research in this area, please see the Mathematical Physics Research Group page. For further information about an individual project, please contact the listed supervisor. For information about submitting an application, please see our Research Degrees page.

Superfluids far from Equilibrium Superfluids far from Equilibrium

Supervisor: Dr Hayder Salman

The study of superfluidity is currently one of the most fascinating fields of research in fluid dynamics involving some of the most unusual phenomena seen in fluids. These include the ability of the fluid to flow without any dissipation, the propagation of heat as a wave rather than by diffusion, and the quantisation of circulation of superfluid vortices as determined by quantum mechanical constraints.

Originally discovered in liquid Helium, nowadays superfluids are being studied in a broad range of systems including atomic and molecular Bose-Einstein condensates (BECs), exciton-polariton condensates (consisting of light and matter waves), and spin-wave systems to name a few. The discovery of superfluidity in these new systems is currently driving theoretical research towards a better understanding of non-equilibrium phenomena. Such non-equilibrium effects have relevance to the study of turbulence in quantum fluids, finite temperature effects in  BECs, non-equilibrium condensates, as well as describing non-equilibrium phase transitions. Despite its importance and broad relevance to these problems, the underlying theory for non-equilibrium phenomena is not well developed and is currently a very active area of investigation.

This PhD project aims to improve our understanding of how to model non-equilibrium phenomena in superfluids, which in turn will lead to improved models for the different systems described above. You will join a growing an active research group working on the modelling of superfluid phenomena. The primary tools to tackle the project are a combination of theory and numerical models of different complexity. There will also be an opportunity to collaborate with international groups based in Germany, New Zealand and Australia. This project will place you at the frontier of a fast moving new subject, which promises many exciting new possibilities.

References:

For further information, please contact Dr Hayder Salman.

Topological Defects in Superfluids Topological Defects in Superfluids

Supervisor: Dr Davide Proment

This interdisciplinary project at the border of applied mathematics and physics focus on the study of superfluids. Superfluids are special fluids having no viscosity and inherently related to Bose–Einstein condensates, which may be qualitatively thought as particle lasers. This exotic states of matter are nowadays realised in confined Alkali gas or in liquid helium at very low temperatures — near the absolute zero — and represent promising systems for studying many-body particle physics and developing new technological applications like quantum computers.

In the specific, the aim of the project is to fully understand the properties and the dynamics of the topological defects that may arise in superfluids. These are usually called quantum vortices and have a complicate motion which strongly differs considering a two-dimensional or a three-dimensional system. Main unsolved questions in this framework will be addressed using analytical calculations and numerical simulations.

By selecting this project, the PhD student would be able to learn new concepts of condensed matter physics and strengthen his/her skills in mathematical modelling and numerical simulations. The possibility to collaborate outside University of East Anglia with experimental physicists will also be envisaged.

References:

  • R.J. Donnelly (1991). Quantized Vortices in Helium II, Vol. 2, Cambridge University Press.
  • L.P. Pitaevskii & S. Stringari (2003). Bose–Einstein Condensation, No. 116, Oxford University Press.
  • G.E. Volovik (2009). The Universe in a Helium Droplet, Oxford University Press.

For further information, please contact Dr Davide Proment.