Saturn's rings are among the most beautiful and puzzling objects in the Solar System, if not all of Space. Their complex striated structure, much like the grooves carved in a vinyl record, inspires equal measures of aesthetic pleasure and theoretical agitation. The rings are composed of trillions of icy boulders ranging in size from a milimetres to metres. These particles undergo, on average, several very gentle collisions per orbit; in fact, their average impact velocity is barely 2 mm/s! But these seemingly innocuous interactions, when allied with their orbital motion, have considerable collective effects. On the other hand, the surface area of the rings is monstrous, and so they `sweep up' an enormous number of small meteoroids (some 10 kg per second). This continual hail of small projectiles significantly shapes the rings' structure and long term evolution.

My PhD was on the dense-gas kinetic theory of the rings, their unusual rheological properties, and the instabilities that might afflict them, and my main aim was to explain the smallest scale structure observed (axisymmetric wavetrains on 100 m scales). Since then I have returned to the topic, on and off, employing different techniques, such as dynamical systems theory, hydrodynamical simulations, and N-body simulations. I have also delved into the role of ballistic transport in explaining structures on large scales: e.g. undulations on 100 km and the morphology of the inner B-ring edge. There are plenty more topics I have my eye on: planetary rings present so many wonderful physics problems, one could spend a good part of one's career happily mucking around!

The planetary ring community is small and so I would not normally recommend a potential student to do a PhD in this area. It would be difficult to secure a postdoc job. However, if I am pushed, I could offer the following topics:
*Hysteresis and phase transitions in Saturn's middle B-ring
*Size distribution dynamics in Saturn's and Chariklo's rings
*The maintenance of sharp edges (the B-ring's outer edge) and narrow ringlets (e.g. Uranus's epsilon ring, Saturn's Maxwell ring, Huygens ring, etc)
*The competition between viscous overstability and self-gravity wakes in Saturn's A-ring

Selected Papers

*The ballistic transport instability in Saturn's rings I: formalism and linear theory (link)
*The ballistic transport instability in Saturn's rings II: nonlinear wave dynamics (link)
*The ballistic transport instability in Saturn's rings III: numerical simulations (link)
*Large-scale N-body simulations of the viscous overstability in Saturn's rings (link)
*Hydrodynamical simulations of viscous overstability in Saturn's rings (link)
*The viscous overstability, nonlinear wavetrains, and finescale structure in dense planetary rings (link)
*Dense planetary rings and the viscous overstability (link)
*Tidal disruption of satellites and formation of narrow rings (link)
*The gravitational instability of a stream of co-orbital particles (link)