Formal Analysis of Linear Control Systems using Theorem Proving

Control systems are an integral part of almost every engineering and physical system and thus their accurate analysis is of utmost importance. Traditionally, control systems are analyzed using paper-and-pencil proof and computer simulation methods, however, both of these methods cannot provide accurate analysis due to their inherent limitations. Model checking has been widely used to analyze control systems but the continuous nature of their environment and physical components cannot be truly captured by a state-transition system in this technique. To overcome these limitations, we propose to use higher-order-logic theorem proving for analyzing linear control systems based on a formalized theory of the Laplace transform method. For this purpose, we have formalized the foundations of linear control system analysis in higher-order logic so that a linear control system can be readily modeled and analyzed. The paper presents a new formalization of the Laplace transform and the formal verification of its properties that are frequently used in the transfer function based analysis to judge the frequency response, gain margin and phase margin, and stability of a linear control system. We also formalize the active realizations of various controllers, like Proportional-Integral-Derivative (PID), Proportional-Integral (PI), Proportional-Derivative (PD), and various active and passive compensators, like lead, lag and lag-lead. For illustration, we present a formal analysis of an unmanned free-swimming submersible vehicle using the HOL Light theorem prover.Comment: International Conference on Formal Engineering Method

Searching for highly obscured AGN in the XMM-Newton serendipitous source catalog

The majority of active galactic nuclei (AGN) are obscured by large amounts of absorbing material that makes them invisible at many wavelengths. X-rays, given their penetrating power, provide the most secure way for finding these AGN. The XMM-Newton serendipitous source catalog is the largest catalog of X-ray sources ever produced; it contains about half a million detections. These sources are mostly AGN. We have derived X-ray spectral fits for very many 3XMM-DR4 sources ($\gtrsim$ 114 000 observations, corresponding to $\sim$ 77 000 unique sources), which contain more than 50 source photons per detector. Here, we use a subsample of $\simeq$ 1000 AGN in the footprint of the SDSS area (covering 120 deg$^2$) with available spectroscopic redshifts. We searched for highly obscured AGN by applying an automated selection technique based on X-ray spectral analysis that is capable of efficiently selecting AGN. The selection is based on the presence of either a) flat rest-frame spectra; b) flat observed spectra; c) an absorption turnover, indicative of a high rest-frame column density; or d) an Fe K$\alpha$ line with an equivalent width > 500 eV. We found 81 highly obscured candidate sources. Subsequent detailed manual spectral fits revealed that 28 of them are heavily absorbed by column densities higher than 10$^{23}$ cm$^{-2}$. Of these 28 AGN, 15 are candidate Compton-thick AGN on the basis of either a high column density, consistent within the 90% confidence level with N$_{\rm H}$ $>$10$^{24}$ cm$^{-2}$, or a large equivalent width (>500 eV) of the Fe K$\alpha$ line. Another six are associated with near-Compton-thick AGN with column densities of $\sim$ 5$\times$10$^{23}$ cm$^{-2}$. A combination of selection criteria a) and c) for low-quality spectra, and a) and d) for medium- to high-quality spectra, pinpoint highly absorbed AGN with an efficiency of 80%.Comment: 18 pages, 10 figures, accepted for publication in A&

BAT X-ray Survey - III: X-ray Spectra and Statistical Properties

In this concluding part of the series of three papers dedicated to the Swift/BAT hard X-ray survey (BXS), we focus on the X-ray spectral analysis and statistical properties of the source sample. Using a dedicated method to extract time-averaged spectra of BAT sources we show that Galactic sources have, generally, softer spectra than extragalactic objects and that Seyfert 2 galaxies are harder than Seyfert 1s. The averaged spectrum of all Seyfert galaxies is consistent with a power-law with photon index of 2.00 (+/-0.07). The cumulative flux-number relation for the extragalactic sources in the 14-170 keV band is best described by a power-law with a slope alpha=1.55 (+/-0.20) and a normalization of 9.6$\pm1.9 \times 10^{-3}$ AGN deg$^{-2}$ (or 396(+/-80) AGN all-sky) above a flux level of 2$\times 10^{-11}$erg cm$^{-2}$ s$^{-1}$ (~0.85 mCrab). The integration of the cumulative flux per unit area indicates that BAT resolves 1-2% of the X-ray background emission in the 14-170 keV band. A sub-sample of 24 extragalactic sources above the 4.5 sigma detection limit is used to study the statistical properties of AGN. This sample comprises local Seyfert galaxies (z=0.026, median value) and ~10% blazars. We find that 55% of the Seyfert galaxies are absorbed by column densities of Log(N_H)>22, but that none is a bona fide Compton-thick. This study shows the capabilities of BAT to probe the hard X-ray sky to the mCrab level.Comment: Accepted for publication in The Astrophysical Journal; 42 pages, 4 tables, 51 figure

Formalization of Transform Methods using HOL Light

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover. In particular, we present the motivation of the formalization, which is followed by the related work. Next, we present the task completed so far while highlighting some of the challenges faced during the formalization. Finally, we present a roadmap to achieve our objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201

The Madison plasma dynamo experiment: a facility for studying laboratory plasma astrophysics

The Madison plasma dynamo experiment (MPDX) is a novel, versatile, basic plasma research device designed to investigate flow driven magnetohydrodynamic (MHD) instabilities and other high-$\beta$ phenomena with astrophysically relevant parameters. A 3 m diameter vacuum vessel is lined with 36 rings of alternately oriented 4000 G samarium cobalt magnets which create an axisymmetric multicusp that contains $\sim$14 m$^{3}$ of nearly magnetic field free plasma that is well confined and highly ionized $(>50\%)$. At present, 8 lanthanum hexaboride (LaB$_6$) cathodes and 10 molybdenum anodes are inserted into the vessel and biased up to 500 V, drawing 40 A each cathode, ionizing a low pressure Ar or He fill gas and heating it. Up to 100 kW of electron cyclotron heating (ECH) power is planned for additional electron heating. The LaB$_6$ cathodes are positioned in the magnetized edge to drive toroidal rotation through ${\bf J}\times{\bf B}$ torques that propagate into the unmagnetized core plasma. Dynamo studies on MPDX require a high magnetic Reynolds number $Rm > 1000$, and an adjustable fluid Reynolds number $10< Re <1000$, in the regime where the kinetic energy of the flow exceeds the magnetic energy ($M_A^2=($v$/$v$_A)^2 > 1$). Initial results from MPDX are presented along with a 0-dimensional power and particle balance model to predict the viscosity and resistivity to achieve dynamo action.Comment: 14 pages, 13 figure

Unveiling the hard X-ray spectrum from the "burst-only" source SAX J1753.5-2349 in outburst

Discovered in 1996 by BeppoSAX during a single type-I burst event, SAX J1753.5-2349 was classified as "burst-only" source. Its persistent emission, either in outburst or in quiescence, had never been observed before October 2008, when SAX J1753.5-2349 was observed for the first time in outburst. Based on INTEGRAL observations,we present here the first high-energy emission study (above 10 keV) of a so-called "burst-only". During the outburst the SAX J1753.5-2349 flux decreased from 10 to 4 mCrab in 18-40 keV, while it was found being in a constant low/hard spectral state. The broad-band (0.3-100 keV) averaged spectrum obtained by combining INTEGRAL/IBIS and Swift/XRT data has been fitted with a thermal Comptonisation model and an electron temperature >24 keV inferred. However, the observed high column density does not allow the detection of the emission from the neutron star surface. Based on the whole set of observations of SAX J1753.5-2349, we are able to provide a rough estimate of the duty cycle of the system and the time-averaged mass-accretion rate. We conclude that the low to very low luminosity of SAX J1753.5-2349 during outburst may make it a good candidate to harbor a very compact binary system.Comment: 5 pages, 3 figures, 2 tables; accepted for publication in MNRAS Letter

Broadband Suzaku observations of IGR J16207-5129

An analysis of IGR J16207-5129 is presented based on observations taken with Suzaku. The data set represents ~80 ks of effective exposure time in a broad energy range between 0.5 and 60 keV, including unprecedented spectral sensitivity above 15 keV. The average source spectrum is well described by an absorbed power law in which we measured a large intrinsic absorption of nH = 16.2(-1.1/+0.9)x10^22 /cm2. This confirms that IGR J16207-5129 belongs to the class of absorbed HMXBs. We were able to constrain the cutoff energy at 19(-4/+8) keV which argues in favor of a neutron star as the primary. Our observation includes an epoch in which the source count rate is compatible with no flux suggesting a possible eclipse. We discuss the nature of this source in light of these and of other recent results.Comment: 12 pages, 6 figures, accepted for publication in Ap