Dynamical Friction Models for Black-Hole Binary Formation in AGN Disks

Stellar-mass black holes (sBH) embedded in gaseous disks of active galactic nuclei (AGN) can be important sources of detectable gravitational radiation for LIGO/Virgo when they form binaries and coalesce due to orbital decay. In this paper, we study the effect of gas dynamical friction (DF) on the formation of BH binaries in AGN disks using $N$-body simulations. We employ two simplified models of DF, with the force on the BH depending on $\Delta {\bf v}$, the velocity of the sBH relative to the background Keplerian gas. We integrate the motion of two sBH initially on circular orbits around the central supermassive black hole (SMBH), and evaluate the probability of binary formation under various conditions. We find that both models of DF (with different dependence of the frictional coefficient on $|\Delta{\bf v}|$) can foster the formation of binaries when the effective friction timescale $\tau$ satisfies $\Omega_{\rm K}\tau\lesssim 20-30$ (where $\Omega_{\rm K}$ is the Keplerian frequency around the SMBH): prograde binaries are formed when the DF is stronger (smaller $\tau$), while retrograde binaries dominate when the DF is weaker (larger $\tau$). We determine the distribution of both prograde and retrograde binaries as a function of initial orbital separation and the DF strength. Using our models of DF, we show that for a given sBH number density in the AGN disk, the formation rate of sBH binaries increases with decreasing $\tau$ and can reach a moderate value with a sufficiently strong DF.Comment: 17 pages, 13 figures, submitted to Ap

Application of pushover analysis in estimating seismic demands for large-span spatial structure

p. 1987-1994Pushover analysis has been widely adopted in the seismic analysis of low- and medium-rise structures. It needs to be studied whether it is accurate for large-span spatial structure. In this paper, pushover analysis of a large-span spatial structure, Beijing A380 hangar structure at Capital International Airport is introduced. The modal load pattern is adopted to perform pushover analysis for the hangar structure. The pushover analysis results are compared with nonlinear response history analysis results. It is concluded that pushover analysis is accurate enough for large-span spatial structure, provided the modal participating mass ratio is larger than about 0.65.Zhang, W.; Qian, J. (2010). Application of pushover analysis in estimating seismic demands for large-span spatial structure. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/718

Roof Isolation System - A Vibration Absorber for Buildings

A roof isolation system is proposed to reduce the dynamic response of buildings to earthquake excitations. In the system, frictional materials are inserted between the roof slab and the beams that support the slab. The roof slab and the beams are connected by springs. The optimum stiffness of the system is determined to minimize the seismic response of the buildings. A comparative study of the responses of an eight-story frame structure with and without the proposed system to ground motions was carried out to assess the system effectiveness. The study showed that the system energy dissipation capacity is nonlinear. The effectiveness of the system is related to the frequency and the acceleration of the ground motion. The system reduces the maximum lateral displacement response and the maximum inter-story drift response of the building by as much as 45% except for the roof

Roof Isolation System - A Vibration Absorber for Buildings

A roof isolation system is proposed to reduce the dynamic response of buildings to earthquake excitations. In the system, frictional materials are inserted between the roof slab and the beams that support the slab. The roof slab and the beams are connected by springs. The optimum stiffness of the system is determined to minimize the seismic response of the buildings. A comparative study of the responses of an eight-story frame structure with and without the proposed system to ground motions was carried out to assess the system effectiveness. The study showed that the system energy dissipation capacity is nonlinear. The effectiveness of the system is related to the frequency and the acceleration of the ground motion. The system reduces the maximum lateral displacement response and the maximum inter-story drift response of the building by as much as 45% except for the roof