Astrophysics Colloquium by Tom Abel (KIPAC)

N-body simulations have become an indispensable tool to study the gravitational dynamics of the putative collisionless dark matter making up the majority of mass in the Universe. These are the same techniques used in the study of terrestrial and space plasmas. In this somewhat technical talk I will describe some of the most common algorithms and the relevant approximations they employ. Interpreting the N bodies being advected by the method as tracers of the incompressible fluid in phase space I illustrate how one can extract a large amount of information from existing simulations which hitherto had been thought of as inaccessible. This approach which traces the dark matter sheet through phase space, also leads straightforwardly to new visualization techniques and somewhat more difficult but also more accurate simulation techniques. The new algorithms overcome some well known shortcomings of traditional approaches but come with their own complexities. The most challenging issues in describing the full behavior of the dark matter fluid in phase space have their origin in the fantastically fast evolution and complexity on the Hamiltonian dynamics in systems with three spatial dimensions. We have also started to explore these ideas for new techniques for use in plasma physics and have found very encouraging results in one dimensional plasmas. Studying the two stream instability, Landau damping and simple waves all show much reduced errors for given computational resources avoiding the numerical noise of previous approaches.