MAGIC092: Introduction to superfluids and turbulence

Course details

A specialist MAGIC course

Semester

Spring 2025
Monday, January 27th to Friday, April 4th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
40

Timetable

Wednesdays
13:05 - 13:55 (UK)

Course forum

Visit the https://v2.maths-magic.ac.uk/forums/magic092-introduction-to-superfluids-and-turbulence

Description

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. 

Prerequisites

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 


Lecturer

  • DP

    Dr Davide Proment

    University
    University of East Anglia

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.

Assessment

The assessment for this course will be released on Tuesday 22nd April 2025 at 00:00 and is due in before Monday 5th May 2025 at 11:00.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.

Files

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Lectures

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