PhD/ Quantized Vortex Dynamics in Superfluids
School of Mathematics, University of East Anglia, Norwich, UK
The aim of the project is to develop improved models for superfluids. These low temperature systems (<2.2K for Helium) exhibit some remarkable properties such as the ability to flow without any dissipation. They also give rise to the phenomena of second sound attributed to the wave-like propagation of temperature fluctuations in contrast to the diffusion of temperature in normal fluids. Such unique properties of superfluid Helium has led to its use as a coolant for superconducting magnets. However, many problems remain in modelling the dynamics of these systems. At extremely low temperatures, the system can be visualized as comprising a tangle of vortices. Vortices in superfluids are distinct from their classical counterparts in two ways. Firstly, the circulation around each vortex is quantized in terms of Planck’s constant. Secondly, vortices in superfluids are topological defects inducing irrotational motion throughout the flow. Consequently, the superfluid density is depleted towards the centre of each vortex, giving rise to an intrinsically compressible entity. Quantized vortices, therefore, radiate sound (phonons) as they move throughout the flow. However, existing models that describe the motion of superfluid turbulence, in superfluid Helium for example, do not account for the radiated sound field. These models are based on the phenomenological two-fluid model of Landau that predated the prediction of quantized vortices. An alternative model derived from microscopic arguments in the form of the Gross-Pitaevskii equation that incorporates all the essential physics will be used to develop a detailed understanding of the radiated sound field and the ensuing wave-vortex interactions. The student will have the opportunity to work in an emerging field at the interface of applied mathematics and low temperature physics. Methods that the student will be expected to apply and develop as part of this project will include a combination of asymptotic methods and numerical analysis/ simulation. The expected start date is 1st, January 2010. UK/EU APPLICANTS ONLY ARE ELIGIBLE FOR THIS FUNDING (this is because of the eligibility rules of the funding body) For informal enquiries about this position, please contact Dr. Hayder Salman at H.Salman@damtp.cam.ac.uk. How to apply: An application can be downloaded from our website at http://www1.uea.ac.uk/cm/home/services/units/mac/aao/courses/PG. Completed application forms should be submitted to the Admissions Office, Faculty of Science, University of East Anglia, Norwich, NR4 7TJ. THE DEADLINE FOR RECEIPT OF COMPLETED APPLICATIONS IS WEDNESDAY 30th SEPTEMBER 2009.