Validation of Ultrahigh Dependability for Software-Based Systems

Modern society depends on computers for a number of critical tasks in which failure can have very high costs. As a consequence, high levels of dependability (reliability, safety, etc.) are required from such computers, including their software. Whenever a quantitative approach to risk is adopted, these requirements must be stated in quantitative terms, and a rigorous demonstration of their being attained is necessary. For software used in the most critical roles, such demonstrations are not usually supplied. The fact is that the dependability requirements often lie near the limit of the current state of the art, or beyond, in terms not only of the ability to satisfy them, but also, and more often, of the ability to demonstrate that they are satisfied in the individual operational products (validation). We discuss reasons why such demonstrations cannot usually be provided with the means available: reliability growth models, testing with stable reliability, structural dependability modelling, as well as more informal arguments based on good engineering practice. We state some rigorous arguments about the limits of what can be validated with each of such means. Combining evidence from these different sources would seem to raise the levels that can be validated; yet this improvement is not such as to solve the problem. It appears that engineering practice must take into account the fact that no solution exists, at present, for the validation of ultra-high dependability in systems relying on complex software

On The Low Frequency Quasi Periodic Oscillations of X-ray Sources

Based on the interpretation of the twin kilohertz Quasi Periodic Oscillations (kHz QPOs) of X-ray spectra of Low Mass X-Ray Binaries (LMXBs) to the Keplerian and the periastron precession frequencies at the magnetosphere-disk of X-ray neutron star (NS) respectively, we ascribe the low frequency Quasi Periodic Oscillations (LFQPO) and HBO (15-60 Hz QPO for Z sources or Atoll sources) to the periastron precession at some outer disk radius. The obtained conclusions include: all QPO frequencies increase with increasing the accretion rate. The obtained theoretical relations between HBO (LFQPO) frequency and the kHz QPO frequency are similar to the measured empirical formula. Further, the possible dynamical mechanism for QPO production is discussed.Comment: 6 pages, 2 figures, accepted by APSS, 200

A Statistical Mechanical Problem in Schwarzschild Spacetime

We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.Comment: Corrected an equation misprint, added four references, and brief comments on the system's center of mass and the thermodynamic limi

Are the magnetic fields of millisecond pulsars ~ 10^8 G?

It is generally assumed that the magnetic fields of millisecond pulsars (MSPs) are $\sim 10^{8}$G. We argue that this may not be true and the fields may be appreciably greater. We present six evidences for this: (1) The $\sim 10^{8}$ G field estimate is based on magnetic dipole emission losses which is shown to be questionable; (2) The MSPs in low mass X-ray binaries (LMXBs) are claimed to have $< 10^{11}$ G on the basis of a Rayleygh-Taylor instability accretion argument. We show that the accretion argument is questionable and the upper limit $10^{11}$ G may be much higher; (3) Low magnetic field neutron stars have difficulty being produced in LMXBs; (4) MSPs may still be accreting indicating a much higher magnetic field; (5) The data that predict $\sim 10^{8}$ G for MSPs also predict ages on the order of, and greater than, ten billion years, which is much greater than normal pulsars. If the predicted ages are wrong, most likely the predicted $\sim 10^{8}$ G fields of MSPs are wrong; (6) When magnetic fields are measured directly with cyclotron lines in X-ray binaries, fields $\gg 10^{8}$ G are indicated. Other scenarios should be investigated. One such scenario is the following. Over 85% of MSPs are confirmed members of a binary. It is possible that all MSPs are in large separation binaries having magnetic fields $> 10^{8}$ G with their magnetic dipole emission being balanced by low level accretion from their companions.Comment: 16 pages, accept for publication in Astrophysics and Space Scienc

Forced oscillations in a hydrodynamical accretion disk and QPOs

This is the second of a series of papers aimed to look for an explanation on the generation of high frequency quasi-periodic oscillations (QPOs) in accretion disks around neutron star, black hole, and white dwarf binaries. The model is inspired by the general idea of a resonance mechanism in the accretion disk oscillations as was already pointed out by Abramowicz & Klu{\'z}niak (\cite{Abramowicz2001}). In a first paper (P\'etri \cite{Petri2005a}, paper I), we showed that a rotating misaligned magnetic field of a neutron star gives rise to some resonances close to the inner edge of the accretion disk. In this second paper, we suggest that this process does also exist for an asymmetry in the gravitational potential of the compact object. We prove that the same physics applies, at least in the linear stage of the response to the disturbance in the system. This kind of asymmetry is well suited for neutron stars or white dwarfs possessing an inhomogeneous interior allowing for a deviation from a perfectly spherically symmetric gravitational field. We show by a linear analysis that the disk initially in a cylindrically symmetric stationary state is subject to three kinds of resonances: a corotation resonance, a Lindblad resonance due to a driven force and a parametric sonance. The highest kHz QPOs are then interpreted as the orbital frequency of the disk at locations where the response to the resonances are maximal. It is also found that strong gravity is not required to excite the resonances.Comment: Accepte

Fast variability from black-hole binaries

Currently available information on fast variability of the X-ray emission from accreting collapsed objects constitutes a complex phenomenology which is difficult to interpret. We review the current observational standpoint for black-hole binaries and survey models that have been proposed to interpret it. Despite the complex structure of the accretion flow, key observational diagnostics have been identified which can provide direct access to the dynamics of matter motions in the close vicinity of black holes and thus to the some of fundamental properties of curved spacetimes, where strong-field general relativistic effects can be observed.Comment: 20 pages, 11 figures. Accepted for publication in Space Science Reviews. Also to appear in hard cover in the Space Sciences Series of ISSI "The Physics of Accretion onto Black Holes" (Springer Publisher

Menus for Feeding Black Holes

Black holes are the ultimate prisons of the Universe, regions of spacetime where the enormous gravity prohibits matter or even light to escape to infinity. Yet, matter falling toward the black holes may shine spectacularly, generating the strongest source of radiation. These sources provide us with astrophysical laboratories of extreme physical conditions that cannot be realized on Earth. This chapter offers a review of the basic menus for feeding matter onto black holes and discusses their observational implications.Comment: 27 pages. Accepted for publication in Space Science Reviews. Also to appear in hard cover in the Space Sciences Series of ISSI "The Physics of Accretion onto Black Holes" (Springer Publisher

Accretion, Outflows, and Winds of Magnetized Stars

Many types of stars have strong magnetic fields that can dynamically influence the flow of circumstellar matter. In stars with accretion disks, the stellar magnetic field can truncate the inner disk and determine the paths that matter can take to flow onto the star. These paths are different in stars with different magnetospheres and periods of rotation. External field lines of the magnetosphere may inflate and produce favorable conditions for outflows from the disk-magnetosphere boundary. Outflows can be particularly strong in the propeller regime, wherein a star rotates more rapidly than the inner disk. Outflows may also form at the disk-magnetosphere boundary of slowly rotating stars, if the magnetosphere is compressed by the accreting matter. In isolated, strongly magnetized stars, the magnetic field can influence formation and/or propagation of stellar wind outflows. Winds from low-mass, solar-type stars may be either thermally or magnetically driven, while winds from massive, luminous O and B type stars are radiatively driven. In all of these cases, the magnetic field influences matter flow from the stars and determines many observational properties. In this chapter we review recent studies of accretion, outflows, and winds of magnetized stars with a focus on three main topics: (1) accretion onto magnetized stars; (2) outflows from the disk-magnetosphere boundary; and (3) winds from isolated massive magnetized stars. We show results obtained from global magnetohydrodynamic simulations and, in a number of cases compare global simulations with observations.Comment: 60 pages, 44 figure