Efficiency of Magnetized Thin Accretion Disks in the Kerr Metric

The efficiency of thin disk accretion onto black holes depends on the inner boundary condition, specifically the torque applied to the disk at the last stable orbit. This is usually assumed to vanish. I estimate the torque on a magnetized disk using a steady magnetohydrodynamic inflow model originally developed by Takahashi et al., 1990. I find that the efficiency epsilon can depart significantly from the classical thin disk value. In some cases epsilon > 1, i.e. energy is extracted from the black hole.Comment: 11 pages, 3 figures, aastex, submitted to ApJ Letter

Dissipation in Compressible MHD Turbulence

We report results of a three dimensional, high resolution (up to 512^3) numerical investigation of supersonic compressible magnetohydrodynamic turbulence. We consider both forced and decaying turbulence. The model parameters are appropriate to conditions found in Galactic molecular clouds. We find that the dissipation time of turbulence is of order the flow crossing time or smaller, even in the presence of strong magnetic fields. About half the dissipation occurs in shocks. Weak magnetic fields are amplified and tangled by the turbulence, while strong fields remain well ordered.Comment: 5 pages, 3 Postscript figures, LaTeX, accepted by Ap.J.Let

Formal Design of Asynchronous Fault Detection and Identification Components using Temporal Epistemic Logic

Autonomous critical systems, such as satellites and space rovers, must be able to detect the occurrence of faults in order to ensure correct operation. This task is carried out by Fault Detection and Identification (FDI) components, that are embedded in those systems and are in charge of detecting faults in an automated and timely manner by reading data from sensors and triggering predefined alarms. The design of effective FDI components is an extremely hard problem, also due to the lack of a complete theoretical foundation, and of precise specification and validation techniques. In this paper, we present the first formal approach to the design of FDI components for discrete event systems, both in a synchronous and asynchronous setting. We propose a logical language for the specification of FDI requirements that accounts for a wide class of practical cases, and includes novel aspects such as maximality and trace-diagnosability. The language is equipped with a clear semantics based on temporal epistemic logic, and is proved to enjoy suitable properties. We discuss how to validate the requirements and how to verify that a given FDI component satisfies them. We propose an algorithm for the synthesis of correct-by-construction FDI components, and report on the applicability of the design approach on an industrial case-study coming from aerospace.Comment: 33 pages, 20 figure

HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, and van Leer scheme. A variant of constrained transport, proposed earlier by T\'oth, is used to maintain a divergence free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.Comment: 38 pages, 18 figures, submitted to Ap