Introduction to superfluids and turbulence (MAGIC092)
Due to technical reasons the first two lectures scheduled on Friday 7 and 14 October are cancelled. To compensate this change, two extra lectures are added in week 7 and 9, on Wednesday 16 Nov 16-17 and Tue 29 Nov 13-14, respectively. As a result the first lecture of the course will be on Friday 21 Oct 9-10.
The aim of the course is to give a mathematical introduction to superfluids and superfluid turbulence. Some of the existing mathematical models used to describe superfluid liquid Helium and Bose-Einstein condensates of dilute gases will be devised. Experimental and numerical experiments will also complement the course as examples. More details on the course topics are given in the Syllabus.
Autumn 2016 (Monday, October 3 to Friday, December 9)
Calculus, partial differential equation, general concepts of mechanics and fluid mechanics. A basic knowledge of quantum mechanics would be preferable.
Syllabus: - brief history of superfluidity, introduction to different types of superfluids; - Landau’s two-fluid model; - the Biot-Savart model and the Euler equation; - the local induction approximation limit; - Hasimoto’s transformations and some of the nonlinear Schroedinger equation solutions; - Bose-Einstein condensates and the Gross-Pitaevskii equation; - Bogoliubov excitations and quantised vortices; - vortex reconnections; - introduction to classical turbulence and Kolmogorov’s -5/3 law; - superfluid turbulence phenomenology.
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The assessment for this course will be via a single take-home paper in January with 2 weeks to complete and submit online. There will be 4 questions and you will need to complete correctly 60
Introduction to superfluids and turbulence assessment
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