The Standing Accretion Shock Instability in the Disk around the Kerr Black Hole

This paper is a sequel to our previous work for accretion onto a Schwarzschild black hole and the so-called standing accretion shock instability (SASI), in this paper we investigate non-axisymmetric perturbations for a Kerr black hole. The linear and non-linear phases for the shock evolution are analyzed in detail by both 2D general relativistic hydrodynamical simulations and linear analysis. Since the structure of steady axisymmetric accretion flows with a standing shock wave is very sensitive to the inner transonic flow, their properties such as Mach numbers, which are important for the stability, depend on the Kerr parameter very much. Although the essential features of the instability do not differ from the previous results for the Schwarzschild black hole, the frame dragging effects specific to the Kerr black hole is also evident. Interestingly, the oscillation periods of the fundamental unstable modes are dependent only on the shock radius irrespective of the injection parameters.Comment: 27 pages, 12 figures, accepted in Ap

Topic-based Delivery of Event Messages in Peer-to-Peer Publish/Subscribe Systems

An event-driven publish/subscribe (PS) model of a distributed system is used in various applications.In this paper, we discuss a peer-to-peer (P2P) model of a topic-based PS system (P2PPS model) where each peer process (peer) can both subscribe interesting topics and publish event messages with topics. In our previous studies, we propose the TBC (topic-based-causally delivery) protocol a homogeneous networkswhere maximum delay time between every pair of peers is same. Here, a pair of event messages are checked if the event messages are related in the topic vector and are causally delivered by takingadvantage of physical time and linear time. In this paper, we consider a system where peers are interconnectedin heterogeneous networks. Here, maximum delay time between every pair of peers is not same.We propose a heterogeneous TBC (HTBC) protocol where event messages are TBC-causally delivered to target peers in heterogeneous network. We evaluate the HTBC protocol and show the number of pair of event messages unnecessarily ordered is reduced in the HTBC protocol.Key Words : Publish/subscribe (PS) systems, Peer-to-peer (P2P) model, Topic-based causal dependency, Topic vectors, Heterogeneous TBC (HTBC) protocol, Linear clock, Physical clock, Heterogeneous networks

Every non-Euclidean oriented matroid admits a biquadratic final polynomial

Richter-Gebert proved that every non-Euclidean uniform oriented matroid admits a biquadratic final polynomial. We extend this result to the non-uniform cas

教科学習の自立・協働型学習における非認知能力向上のための試論 ー理科教育実践に焦点を当てて一

教科学習において生徒たちの非認知能力の向上を目的とした実践を行い、その形成過程の実証を試みた。本稿では理科教育実践に焦点を当てて、授業動画や選択式レベル別演習プリントによる個人の学習選択を基軸とした自立型学習に加えて子どもたちが教師役となることで他者との協働型学習も導入した学習形態で取り組んでいる。この学習形態は、生徒たちの非認知能力を向上させていくために必要となるメタ認知の促進が意図されている。そのため、毎時の授業では非認知能力の行動指標を基に、学びの行動レベルを自らで設定し学習を進めていくこととした。その際、学習時における動機づけ、向上させたい非認知能力に対する意識づけを行い、学習後のリフレクションを継続的に行った。この自立・協働型学習及び継続的なリフレクションによって生徒たちの非認知能力の向上が見られた

General Relativistic Hydrodynamic Simulations and Linear Analysis of the Standing Accretion Shock Instability around a Black Hole

We study the stability of standing shock waves in advection-dominated accretion flows into a Schwarzschild black hole by 2D general relativistic hydrodynamic simulations as well as linear analysis in the equatorial plane. We demonstrate that the accretion shock is stable against axisymmetric perturbations but becomes unstable to non-axisymmetric perturbations. The results of dynamical simulations show good agreement with linear analysis on the stability, oscillation and growing time scales. The comparison of different wave-travel times with the growth time scales of the instability suggests that the instability is likely to be of the Papaloizou-Pringle type, induced by the repeated propagations of acoustic waves. However, the wavelengths of perturbations are too long to clearly define the reflection point. By analyzing the non-linear phase in the dynamical simulations, it is shown that quadratic mode couplings precede the non-linear saturation. It is also found that not only short-term random fluctuations by turbulent motions but also quasi periodic oscillations take place on longer time scales in the non-linear phase. We give some possible implications of the instability for quasi periodic oscillations (QPOs) and the central engine for gamma ray bursts (GRBs).Comment: 34 pages, 11 figures, accepted in Ap