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We consider the formation of extreme mass-ratio inspirals (EMRIs) sourced from a stellar cusp centred on a primary supermassive black hole (SMBH) and perturbed by an inspiraling less massive secondary SMBH. The problem is approached numerically, assuming the stars are non-interacting over these short timescales and performing an ensemble of restricted three-body integrations. From these simulations we see that not only can EMRIs be produced during this process, but the dynamics are also quite rich. In particular, most of the EMRIs are produced through a process akin to the Kozai-Lidov mechanism, but with strong effects due to the non-Keplerian stellar potential, general relativity, and non-secular oscillations in the angular momentum on the orbital timescale of the binary SMBH system., Comment: 18 pages, 8 figures, submitted to MNRAS

Self similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find self-similar hydrodynamic solutions that are two- or three-dimensional. Since the deviation from a one-dimensional solution is small, we call these slightly two-dimensional and slightly three-dimensional self-similar solutions, respectively. As an example, we treat strong spherical explosions of the second type. A strong explosion propagates into an ideal gas with negligible temperature and density profile of the form rho(r,theta,phi)=r^{-omega}[1+sigma*F(theta,phi)], where omega>3 and sigma << 1. Analytical solutions are obtained by expanding the arbitrary function F(theta,phi) in spherical harmonics. We compare our results with two dimensional numerical simulations, and find good agreement., Comment: Submitted to Physics of Fluids

We find that the majority of systems hosting multiple tidal disruptions are likely to contain hard binary SMBH systems, and also show that the rates of these repeated events are high enough to be detected by LSST over its lifetime. Therefore, these multiple tidal disruption events provide a novel method to identify super-massive black hole (SMBH) binary systems with parsec to sub-parsec separations. The rates of tidal disruptions are investigated using simulations of non-interacting stars initially orbiting a primary SMBH and the potential of the model stellar cusp. The stars are then evolved forward in time and perturbed by a secondary SMBH inspiraling from the edge of the cusp to its stalling radius. We find with conservative magnitude estimates that the next generation transient survey LSST should detect multiple tidal disruptions in approximately 3 galaxies over 5 years of observation, though less conservative estimates could increase this rate by an order of magnitude., Comment: 5 pages, 3 figures