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 supermassive 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 indepth 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, 137162)
Interested candidates should contact Evy Kersalé.
(email: kersale@maths.leeds.ac.uk  phone:
0113 343 5180)

