Microlensing of Sub-parsec Massive Binary Black Holes in Lensed QSOs: Light Curves and Size-Wavelength Relation

Sub-parsec binary massive black holes (BBHs) are long anticipated to exist in many QSOs but remain observationally elusive. In this paper, we propose a novel method to probe sub-parsec BBHs through microlensing of lensed QSOs. If a QSO hosts a sub-parsec BBH in its center, it is expected that the BBH is surrounded by a circum-binary disk, each component of the BBH is surrounded by a small accretion disk, and a gap is opened by the secondary component in between the circum-binary disk and the two small disks. Assuming such a BBH structure, we generate mock microlensing light curves for some QSO systems that host BBHs with typical physical parameters. We show that microlensing light curves of a BBH QSO system at the infrared-optical-UV bands can be significantly different from those of corresponding QSO system with a single massive black hole (MBH), mainly because of the existence of the gap and the rotation of the BBH (and its associated small disks) around the center of mass. We estimate the half-light radii of the emission region at different wavelengths from mock light curves and find that the obtained half-light radius vs. wavelength relations of BBH QSO systems can be much flatter than those of single MBH QSO systems at a wavelength range determined by the BBH parameters, such as the total mass, mass ratio, separation, accretion rates, etc. The difference is primarily due to the existence of the gap. Such unique features on the light curves and half-light radius-wavelength relations of BBH QSO systems can be used to select and probe sub-parsec BBHs in a large number of lensed QSOs to be discovered by current and future surveys, including the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS), the Large Synoptic Survey telescope (LSST) and Euclid.Comment: 18 pages, 17 figures, accepted for publication in the Astrophysical Journa

Use multiple modeling approaches to study sustained online communities

In recent years, extensive studies of many interesting aspects of online community dynamics promoted a better understanding of this area. One of the most challenging problems facing builders of online communities is the design of incentive mechanisms that can ensure user participation. However, running online community experiments in the real world is expensive, and requires a great deal of motivation from users. In this thesis two major approaches are explored: system dynamics modeling and agent-based modeling, to simulate the overall behaviours of participants in online communities. Although these models are developed by using two different methodologies, both of them can provide insights into the user motivation process, incentive mechanism evaluation and community development. The target online community for my study is called Comtella, which is used in several senior Computer Science classes in the Department of Computer Science, University of Saskatchewan. Simulation models for the Comtella online community have been developed and the simulation results are useful to provide future directions for incentive mechanism improvement

Adaptive and Robust Fault-Tolerant Tracking Control of Contact force of Pantograph-Catenary for High-Speed Trains

Abstract This paper presents a modified multi-body dynamic model and a linear time-invariant model with actuator faults (loss of effectiveness faults, bias faults) and matched and unmatched uncertainties. Based on the fault model, a class of adaptive and robust tracking controllers are proposed which are adjusted online to tolerate the time-varying loss of effectiveness faults and bias faults, and compensate matched disturbances without the knowledge of bounds. For unmatched uncertainties, optimal control theory is added to the controller design processes. Simulations on a pantograph are shown to verify the efficiency of the proposed fault-tolerant design approach