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

Nonlinear Outcome of Gravitational Instability in Disks with Realistic Cooling

We consider the nonlinear outcome of gravitational instability in optically thick disks with a realistic cooling function. We use a numerical model that is local, razor-thin, and unmagnetized. External illumination is ignored. Cooling is calculated from a one-zone model using analytic fits to low temperature Rosseland mean opacities. The model has two parameters: the initial surface density Sigma_0 and the rotation frequency Omega. We survey the parameter space and find: (1) The disk fragments when t_c,eff Omega = 1, where t_c,eff is an effective cooling time defined as the average internal energy of the model divided by the average cooling rate. This is consistent with earlier results that used a simplified cooling function. (2) The initial cooling time t_c0 or a uniform disk with Q = 1 can differ by orders of magnitude from t_c,eff in the nonlinear outcome. The difference is caused by sharp variations in the opacity with temperature. The condition t_c0 Omega = 1 therefore does not necessarily indicate where fragmentation will occur. (3) The largest difference between t_c,eff and t_c0 is near the opacity gap, where dust is absent and hydrogen is largely molecular. (4) In the limit of strong illumination the disk is isothermal; we find that an isothermal version of our model fragments for Q < 1.4. Finally, we discuss some physical processes not included in our model, and find that most are likely to make disks more susceptible to fragmentation. We conclude that disks with t_c,eff Omega < 1 do not exist.Comment: 30 pages, 12 figure

Impact of dimensionless numbers on the efficiency of MRI-induced turbulent transport

The magneto-rotational instability is presently the most promising source of turbulent transport in accretion disks. However, some important issues still need to be addressed to quantify the role of MRI in disks; in particular no systematic investigation of the role of the physical dimensionless parameters of the problem on the dimensionless transport has been undertaken yet. First, we complete existing investigations on the field strength dependence by showing that the transport in high magnetic pressure disks close to marginal stability is highly time-dependent and surprisingly efficient. Second, we bring to light a significant dependence of the global transport on the magnetic Prandtl number, with $\alpha\propto Pm^\delta$ for the explored range: $0.12<Pm<8$ and $200<Re<6400$ ($\delta$ being in the range 0.25 to 0.5). We show that the dimensionless transport is not correlated to the dimensionless linear growth rate, contrarily to a largely held expectation. More generally, these results stress the need to control dissipation processes in astrophysical simulations.Comment: 11 pages, 11 figures, accepted to MNRA

Imaging an Event Horizon: Mitigation of Source Variability of Sagittarius A*

The black hole in the center of the Galaxy, associated with the compact source Sagittarius A* (Sgr A*), is predicted to cast a shadow upon the emission of the surrounding plasma flow, which encodes the influence of general relativity in the strong-field regime. The Event Horizon Telescope (EHT) is a Very Long Baseline Interferometry (VLBI) network with a goal of imaging nearby supermassive black holes (in particular Sgr A* and M87) with angular resolution sufficient to observe strong gravity effects near the event horizon. General relativistic magnetohydrodynamic (GRMHD) simulations show that radio emission from Sgr A* exhibits vari- ability on timescales of minutes, much shorter than the duration of a typical VLBI imaging experiment, which usually takes several hours. A changing source structure during the observations, however, violates one of the basic assumptions needed for aperture synthesis in radio interferometry imaging to work. By simulating realistic EHT observations of a model movie of Sgr A*, we demonstrate that an image of the average quiescent emission, featuring the characteristic black hole shadow and photon ring predicted by general relativity, can nonetheless be obtained by observing over multiple days and subsequent processing of the visibilities (scaling, averaging, and smoothing) before imaging. Moreover, it is shown that this procedure can be combined with an existing method to mitigate the effects of interstellar scattering. Taken together, these techniques allow the black hole shadow in the Galactic center to be recovered on the reconstructed image.Comment: 10 pages, 12figures, accepted for publication in Ap

Analysis of Clumps in Molecular Cloud Models: Mass Spectrum, Shapes, Alignment and Rotation

Observations reveal concentrations of molecular line emission on the sky, called ``clumps,'' in dense, star-forming molecular clouds. These clumps are believed to be the eventual sites of star formation. We study the three-dimensional analogs of clumps using a set of self-consistent, time-dependent numerical models of molecular clouds. The models follow the decay of initially supersonic turbulence in an isothermal, self-gravitating, magnetized fluid. We find the following. (1) Clumps are intrinsically triaxial. This explains the observed deficit of clumps with a projected axis ratio near unity, and the apparent prolateness of clumps. (2) Simulated clump axes are not strongly aligned with the mean magnetic field within clumps, nor with the large-scale mean fields. This is in agreement with observations. (3) The clump mass spectrum has a high-mass slope that is consistent with the Salpeter value. There is a low-mass break in the slope at \sim 0.5 \msun, although this may depend on model parameters including numerical resolution. (4) The typical specific spin angular momentum of clumps is $4 \times 10^{22} {\rm cm^2 s^{-1}}$. This is larger than the median specific angular momentum of binary stars. Scaling arguments suggest that higher resolution simulations may soon be able to resolve the scales at which the angular momentum of binary stars is determined.Comment: 14 pages, 13 figures, to appear in 2003 July 20 Ap

The thermal-viscous disk instability model in the AGN context

Accretion disks in AGN should be subject to the same type of instability as in cataclysmic variables (CVs) or in low-mass X-ray binaries (LMXBs), which leads to dwarf nova and soft X-ray transient outbursts. It has been suggested that this thermal/viscous instability can account for the long term variability of AGNs. We test this assertion by presenting a systematic study of the application of the disk instability model (DIM) to AGNs. We are using the adaptative grid numerical code we have developed in the context of CVs, enabling us to fully resolve the radial structure of the disk. We show that, because in AGN disks the Mach numbers are very large, the heating and cooling fronts are so narrow that they cannot be resolved by the numerical codes that have been used until now. In addition, these fronts propagate on time scales much shorter than the viscous time. As a result, a sequence of heating and cooling fronts propagate back and forth in the disk, leading only to small variations of the accretion rate onto the black hole, with short quiescent states occurring for very low mass transfer rates only. Truncation of the inner part of the disk by e.g. an ADAF does not alter this result, but enables longer quiescent states. Finally we discuss the effects of irradiation by the central X-ray source, and show that, even for extremely high irradiation efficiencies, outbursts are not a natural outcome of the model.Comment: Astronomy & Astrophysics - in pres

Vortices in Thin, Compressible, Unmagnetized Disks

We consider the formation and evolution of vortices in a hydrodynamic shearing-sheet model. The evolution is done numerically using a version of the ZEUS code. Consistent with earlier results, an injected vorticity field evolves into a set of long-lived vortices, each of which has a radial extent comparable to the local scale height. But we also find that the resulting velocity field has a positive shear stress, . This effect appears only at high resolution. The transport, which decays with time as t^-1/2, arises primarily because the vortices drive compressive motions. This result suggests a possible mechanism for angular momentum transport in low-ionization disks, with two important caveats: a mechanism must be found to inject vorticity into the disk, and the vortices must not decay rapidly due to three-dimensional instabilities.Comment: 8 pages, 10 figures (high resolution figures available in ApJ electronic edition