Projects in Applied Mathematics (MATH3422/4422)

Dynamics of accretion discs:

This project is about the dynamics of the material surrounding massive astrophysical bodies such as forming stars or compact objects. Owing to the conservation of its angular momentum, the cosmic material falling in a gravitational well tends to form a disc which, in the presence of dissipative processes, allows for accretion (i.e. the absorption of the material by the central core). Such accretion discs are found in a variety of environments: around young stars where they are the sites of planetary formation, around super-massive black holes in the centre of active galaxies and around the compact stars that disrupt their companions in interacting binary systems.
Understanding the extremely rich and complex dynamics of accretion discs is central to modern astrophysics and calls for in-depth understanding of the physics and mathematics of rotating and conducting fluids. This project could involve, for instance, finding equilibrium states of dissipative fluids in differential rotation and studying their hydrodynamic or magnetohydrodynamic stability.
Some knowledge of fluid dynamics (e.g. MATH2620) would be an advantage to undertake this project and some knowledge of vector calculus is necessary. Furthermore, this project has scope for analytical and numerical work. In the latter case, knowledge of numerical analysis would be helpful (e.g. MATH2600, MATH3474).

References:
Accretion power in astrophysics by J. Frank, A. King & D. Raine (Cambridge University Press, 2002)
Accretion discs in astrophysics by J.E. Pringle (Ann. Rev. Astron. Astrophys. 1981, 19, 137-162)

Interested candidates should contact Evy Kersalé.
(email: kersale@maths.leeds.ac.uk - phone: 0113 343 5180)