The hierarchical galaxy formation picture suggests that super massive black holes (MBHs) observed in galactic nuclei today have grown from coalescence of massive black hole binaries (MBHB) after galaxy merging. Once the components of a MBHB become gr
avitationally bound, strong three-body encounters between the MBHB and stars dominate its evolution in a dry gas free environment, and change the MBHBs energy and angular momentum (semi-major axis, eccentricity and orientation). Here we present high accuracy direct N-body simulations of spherical and axisymmetric (rotating) galactic nuclei with order a million stars and two massive black holes that are initially unbound. We analyze the properties of the ejected stars due to slingshot effects from three-body encounters with the MBHB in detail. Previous studies have investigated the eccentricity and energy changes of MBHs using approximate models or Monte-Carlo three body scatterings. We find general agreement with the average results of previous semi-analytic models for spherical galactic nuclei, but our results show a large statistical variation. Our new results show many more phase space details of how the process works, and also show the influence of stellar system rotation on the process. We detect that the angle between the orbital plane of the MBHBs and that of the stellar system (when it rotates) influences the phase-space properties of the ejected stars. We also find that massive MBHB tend to switch stars with counter-rotating orbits into co-rotating orbits during their interactions.
A two-dimensional Frenkel-Kontorova model is set up. Its application to the tribology is considered. The materials and the commensurability between two layers strongly affect the static friction force. It is found that the static friction force is la
rger between two layer of same materials than that for different materials. For two-dimensional case the averaged static friction force is larger for the uncommensurate case than that for the commensurate case, which is completely different from one-dimensional case. The directions of the propagation of the center of mass and the external driving force are usually different except at some special symmetric directions. The possibility to obtain superlubricity is suggested.
