Guidelines for Statistical Testing

This document provides an introduction to statistical testing. Statistical testing of software is here defined as testing in which the test cases are produced by a random process meant to produce different test cases with the same probabilities with which they would arise in actual use of the software. Statistical testing of software has these main advantages: for the purpose of reliability assessment and product acceptance, it supports directly estimates of reliability, and thus decisions on whether the software is ready for delivery or for use in a specific system. This feature is unique to statistical testing; for the purpose of improving the software, it tends to discover defects which would cause failures with the higher frequencies before those that would cause less frequent failures, thus focusing correction efforts in the most cost-effective way and delivering better software for a given debugging effort. Statistical testing has been reported to achieve dramatic improvements; from the point of view of costs, it facilitates the automation of the test process, thus allowing more testing at acceptable cost than manual testing would allow. This document explains the basic theory underlying statistical testing and provides guidance for its application. The material is organised to facilitate use both as an introduction for software engineers who are new to this approach to testing, and as a reference source during application. Statistical testing is applicable to practically all kinds of software, so this document is not markedly specialised for space applications, though the examples are mostly space-related and the discussion of the software lifecycle is meant to apply to common practice among ESA suppliers

Accurate light-time correction due to a gravitating mass

This work arose as an aftermath of Cassini's 2002 experiment \cite{bblipt03}, in which the PPN parameter $\gamma$ was measured with an accuracy $\sigma_\gamma = 2.3\times 10^{-5}$ and found consistent with the prediction $\gamma =1$ of general relativity. The Orbit Determination Program (ODP) of NASA's Jet Propulsion Laboratory, which was used in the data analysis, is based on an expression for the gravitational delay which differs from the standard formula; this difference is of second order in powers of $m$ -- the sun's gravitational radius -- but in Cassini's case it was much larger than the expected order of magnitude $m^2/b$, where $b$ is the ray's closest approach distance. Since the ODP does not account for any other second-order terms, it is necessary, also in view of future more accurate experiments, to systematically evaluate higher order corrections and to determine which terms are significant. Light propagation in a static spacetime is equivalent to a problem in ordinary geometrical optics; Fermat's action functional at its minimum is just the light-time between the two end points A and B. A new and powerful formulation is thus obtained. Asymptotic power series are necessary to provide a safe and automatic way of selecting which terms to keep at each order. Higher order approximations to the delay and the deflection are obtained. We also show that in a close superior conjunction, when $b$ is much smaller than the distances of A and B from the Sun, of order $R$, say, the second-order correction has an \emph{enhanced} part of order $m^2R/b^2$, which corresponds just to the second-order terms introduced in the ODP. Gravitational deflection of the image of a far away source, observed from a finite distance from the mass, is obtained to $O(m^2)$.Comment: 4 figure

Irreversible and reversible modes of operation of deterministic ratchets

We discuss a problem of optimization of the energetic efficiency of a simple rocked ratchet. We concentrate on a low-temperature case in which the particle's motion in a ratchet potential is deterministic. We show that the energetic efficiency of a ratchet working adiabatically is bounded from above by a value depending on the form of ratchet potential. The ratchets with strongly asymmetric potentials can achieve ideal efficiency of unity without approaching reversibility. On the other hand we show that for any form of the ratchet potential a set of time-protocols of the outer force exist under which the operation is reversible and the ideal value of efficiency is also achieved. The mode of operation of the ratchet is still quasistatic but not adiabatic. The high values of efficiency can be preserved even under elevated temperatures

High H2 Sorption Energetics in Zeolitic Imidazolate Frameworks

A combined experimental and theoretical study of H2 sorption was carried out on two isostructural zeolitic imidazolate frameworks ZIFs , namely ZIF 68 and ZIF 69. The former consists of Zn2 ions that are coordinated to two 2 nitroimidazolate and two benzimidazolate linkers in a tetrahedral fashion, while 5 chlorobenzimidazolate is used in place of benzimidazolate in the latter compound. H2 sorption measurements showed that the two ZIFs display similar isotherms and isosteric heats of adsorption Qst . The experimental initial H2 Qst value for both ZIFs was determined to be 8.1 kJ mol 1, which is quite high for materials that do not contain exposed metal centers. Molecular simulations of H2 sorption in ZIF 68 and ZIF 69 confirmed the similar H2 sorption properties between the two ZIFs, but also suggest that H2 sorption is slightly favored in ZIF 68 with regards to uptake at 77 K 1.0 atm. This work also presents inelastic neutron scattering INS spectra for H2 sorbed in ZIFs for the first time. The spectra for ZIF 68 and ZIF 69 show a broad range of intensities starting from about 4 meV. The most favorable H2 sorption site in both ZIFs corresponds to a confined region between two adjacent 2 nitroimidazolate linkers. Two dimensional quantum rotation calculations for H2 sorbed at this site in ZIF 68 and ZIF 69 produced rotational transitions that are in accord with the lowest energy peak observed in the INS spectrum for the respective ZIFs. We found that the primary binding site for H2 in the two ZIFs generates high barriers to rotation for the adsorbed H2, which are greater than those in several metal organic frameworks MOFs which possess open metal sites. H2 sorption was also observed for both ZIFs in the vicinity of the nitro groups of the 2 nitroimidazolate linkers. This study highlights the constructive interplay of experiment and theory to elucidate critical details of the H2 sorption mechanism in these two isostructural ZIF

Casimir Effect in Hyperbolic Polygons

We derive a trace formula for the spectra of quantum mechanical systems in hyperbolic polygons which are the fundamental domains of discrete isometry groups acting in the two dimensional hyperboloid. Using this trace formula and the point splitting regularization method we calculate the Casimir energy for a scalar fields in such domains. The dependence of the vacuum energy on the number of vertexes is established.Comment: Latex, 1

Motivation for Air-Launch: Past, Present, and Future

Air-launch is defined as two or more air-vehicles joined and working together, that eventually separate in flight, and that have a combined performance greater than the sum of the individual parts. The use of the air-launch concept has taken many forms across civil, commercial, and military contexts throughout the history of aviation. Air-launch techniques have been applied for entertainment, movement of materiel and personnel, efficient execution of aeronautical research, increasing aircraft range, and enabling flexible and efficient launch of space vehicles. For each air-launch application identified in the paper, the motivation for that application is discussed

Strengthening the Case for Asteroidal Accrection: Evidence for Subtle and Diverse Disks at White Dwarfs

Spitzer Space Telescope IRAC 3-8 micron and AKARI IRC 2-4 micron photometry are reported for ten white dwarfs with photospheric heavy elements; nine relatively cool stars with photospheric calcium, and one hotter star with a peculiar high carbon abundance. A substantial infrared excess is detected at HE 2221-1630, while modest excess emissions are identified at HE 0106-3253 and HE 0307+0746, implying these latter two stars have relatively narrow (Delta r < 0.1 Rsol) rings of circumstellar dust. A likely 7.9 micron excess is found at PG 1225-079 and may represent, together with G166-58, a sub-class of dust ring with a large inner hole. The existence of attenuated disks at white dwarfs substantiates the connection between their photospheric heavy elements and the accretion of disrupted minor planets, indicating many polluted white dwarfs may harbor orbiting dust, even those lacking an obvious infrared excess.Comment: 13 pages, emulateapj, accepted to Ap

The Stability of the Suggested Planet in the nu Octantis System: A Numerical and Statistical Study

We provide a detailed theoretical study aimed at the observational finding about the nu Octantis binary system that indicates the possible existence of a Jupiter-type planet in this system. If a prograde planetary orbit is assumed, it has earlier been argued that the planet, if existing, should be located outside the zone of orbital stability. However, a previous study by Eberle & Cuntz (2010) [ApJ 721, L168] concludes that the planet is most likely stable if assumed to be in a retrograde orbit with respect to the secondary system component. In the present work, we significantly augment this study by taking into account the observationally deduced uncertainty ranges of the orbital parameters for the stellar components and the suggested planet. Furthermore, our study employs additional mathematical methods, which include monitoring the Jacobi constant, the zero velocity function, and the maximum Lyapunov exponent. We again find that the suggested planet is indeed possible if assumed to be in a retrograde orbit, but it is virtually impossible if assumed in a prograde orbit. Its existence is found to be consistent with the deduced system parameters of the binary components and of the suggested planet, including the associated uncertainty bars given by observations.Comment: 11 pages, 10 figures, 3 tables; Monthly Notices of the Royal Astronomical Society (in press

Fourier Acceleration of Langevin Molecular Dynamics

Fourier acceleration has been successfully applied to the simulation of lattice field theories for more than a decade. In this paper, we extend the method to the dynamics of discrete particles moving in continuum. Although our method is based on a mapping of the particles' dynamics to a regular grid so that discrete Fourier transforms may be taken, it should be emphasized that the introduction of the grid is a purely algorithmic device and that no smoothing, coarse-graining or mean-field approximations are made. The method thus can be applied to the equations of motion of molecular dynamics (MD), or its Langevin or Brownian variants. For example, in Langevin MD simulations our acceleration technique permits a straightforward spectral decomposition of forces so that the long-wavelength modes are integrated with a longer time step, thereby reducing the time required to reach equilibrium or to decorrelate the system in equilibrium. Speedup factors of up to 30 are observed relative to pure (unaccelerated) Langevin MD. As with acceleration of critical lattice models, even further gains relative to the unaccelerated method are expected for larger systems. Preliminary results for Fourier-accelerated molecular dynamics are presented in order to illustrate the basic concepts. Possible extensions of the method and further lines of research are discussed.Comment: 11 pages, two illustrations included using graphic