The investigator studies the stability and instability of equilibria in fluids and plasmas, focusing on the two-dimensional Euler equation in fluids and on Vlasov systems in plasma physics and stellar dynamics. He aims to develop general methods of finding linearly growing modes (especially for asymmetric modes and boundary modes), to investigate nonlinear stability under sharp linear stability criteria and for non-monotonic equilibria that cannot be handled by the usual energy-Casimir method, and to establish nonlinear instability from linear instability when the particle trajectory is non-integrable.
A plasma is a gas composed of particles, each carrying a positive or negative electrical charge, with approximately equal concentrations of each charge. Most of the universe is plasma; examples include the solar wind, the ionosphere, galactic nebulae, and comet tails. Plasmas also arise in physics and engineering, for instance in nuclear fusion. The investigator studies the stability and instability of equilibria in fluids and plasmas. Mathematical advances here enhance our understanding of the physical mechanisms that govern stability and instability, and so can lead to better numerical methods for simulations of these complex phenomena. Fluid stability is important in understanding the mechanisms of ocean waves and the movements of the atmosphere as well as in engineering applications. Questions of plasma stability arise in areas as diverse as sunspots, fundamental plasma physics, the design of fusion machines, and plasma display devices.
