69,717 research outputs found
A systematic approach to atomicity decomposition in Event-B
Event-B is a state-based formal method that supports a refinement process in which an abstract model is elaborated towards an implementation in a step-wise manner. One weakness of Event-B is that control flow between events is typically modelled implicitly via variables and event guards. While this fits well with Event-B refinement, it can make models involving sequencing of events more difficult to specify and understand than if control flow was explicitly specified. New events may be introduced in Event-B refinement and these are often used to decompose the atomicity of an abstract event into a series of steps. A second weakness of Event-B is that there is no explicit link between such new events that represent a step in the decomposition of atomicity and the abstract event to which they contribute. To address these weaknesses, atomicity decomposition diagrams support the explicit modelling of control flow and refinement relationships for new events. In previous work,the atomicity decomposition approach has been evaluated manually in the development of two large case studies, a multi media protocol and a spacecraft sub-system. The evaluation results helped us to develop a systematic definition of the atomicity decomposition approach, and to develop a tool supporting the approach. In this paper we outline this systematic definition of the approach, the tool that supports it and evaluate the contribution that the tool makes
On aberration in gravitational lensing
It is known that a relative translational motion between the deflector and
the observer affects gravitational lensing. In this paper, a lens equation is
obtained to describe such effects on actual lensing observables. Results can be
easily interpreted in terms of aberration of light-rays. Both radial and
transverse motions with relativistic velocities are considered. The lens
equation is derived by first considering geodesic motion of photons in the
rest-frame Schwarzschild spacetime of the lens, and, then, light-ray detection
in the moving observer's frame. Due to the transverse motion images are
displaced and distorted in the observer's celestial sphere, whereas the radial
velocity along the line of sight causes an effective re-scaling of the lens
mass. The Einstein ring is distorted to an ellipse whereas the caustics in the
source plane are still point-like. Either for null transverse motion or up to
linear order in velocities, the critical curve is still a circle with its
radius corrected by a factor (1+z_d) with respect to the static case, z_d being
the relativistic Doppler shift of the deflector. From the observational point
of view, the orbital motion of the Earth can cause potentially observable
corrections of the order of the microarcsec in lensing towards the
super-massive black hole at the Galactic center. On a cosmological scale,
tangential peculiar velocities of cluster of galaxies bring about a typical
flexion in images of background galaxies in the weak lensing regime but future
measurements seem to be too much challenging.Comment: 8 pages, 2 figures, in press on PR
The metal and dust yields of the first massive stars
We quantify the role of Population (Pop) III core-collapse supernovae (SNe)
as the first cosmic dust polluters. Starting from a homogeneous set of stellar
progenitors with masses in the range [13 - 80] Msun, we find that the mass and
composition of newly formed dust depend on the mixing efficiency of the ejecta
and the degree of fallback experienced during the explosion. For standard Pop
III SNe, whose explosions are calibrated to reproduce the average elemental
abundances of Galactic halo stars with [Fe/H] < -2.5, between 0.18 and 3.1 Msun
(0.39 - 1.76 Msun) of dust can form in uniformly mixed (unmixed) ejecta, and
the dominant grain species are silicates. We also investigate dust formation in
the ejecta of faint Pop III SN, where the ejecta experience a strong fallback.
By examining a set of models, tailored to minimize the scatter with the
abundances of carbon-enhanced Galactic halo stars with [Fe/H ] < -4, we find
that amorphous carbon is the only grain species that forms, with masses in the
range 2.7 10^{-3} - 0.27 Msun (7.5 10^{-4} - 0.11 Msun) for uniformly mixed
(unmixed) ejecta models. Finally, for all the models we estimate the amount and
composition of dust that survives the passage of the reverse shock, and find
that, depending on circumstellar medium densities, between 3 and 50% (10 - 80%)
of dust produced by standard (faint) Pop III SNe can contribute to early dust
enrichment.Comment: Accepted by MNRAS, 22 pages, 12 figures, 12 table
Study of leakage currents in pCVD diamonds as function of the magnetic field
pCVD diamond sensors are regularly used as beam loss monitors in accelerators
by measuring the ionization of the lost particles. In the past these beam loss
monitors showed sudden increases in the dark leakage current without beam
losses and these erratic leakage currents were found to decrease, if magnetic
fields were present. Here we report on a systematic study of leakage currents
inside a magnetic field. The decrease of erratic currents in a magnetic field
was confirmed. On the contrary, diamonds without erratic currents showed an
increase of the leakage current in a magnetic field perpendicular to the
electric field for fields up to 0.6T, for higher fields it decreases. A
preliminary model is introduced to explain the observations.Comment: 6 pages, 16 figures, poster at Hasselt Diamond Workshop, Mar 2009,
accepted version for publicatio
Implications of the isotope effects on the magnetization, magnetic torque and susceptibility
We analyze the magnetization, magnetic torque and susceptibility data of
La2-xSrxCu(16,18)O4 and YBa2(63,65)CuO7-x near Tc in terms of the universal
3D-XY scaling relations. It is shown that the isotope effect on Tc mirrors that
on the anisotropy. Invoking the generic behavior of the anisotropy the doping
dependence of the isotope effects on the critical properties, including Tc,
correlation lengths and magnetic penetration depths are traced back to a change
of the mobile carrier concentration.Comment: 5 pages, 3 figure
Superluminal Caustics of Close, Rapidly-Rotating Binary Microlenses
The two outer triangular caustics (regions of infinite magnification) of a
close binary microlens move much faster than the components of the binary
themselves, and can even exceed the speed of light. When , where
is the caustic speed, the usual formalism for calculating the lens
magnification breaks down. We develop a new formalism that makes use of the
gravitational analog of the Li\'enard-Wiechert potential. We find that as the
binary speeds up, the caustics undergo several related changes: First, their
position in space drifts. Second, they rotate about their own axes so that they
no longer have a cusp facing the binary center of mass. Third, they grow larger
and dramatically so for . Fourth, they grow weaker roughly in
proportion to their increasing size. Superluminal caustic-crossing events are
probably not uncommon, but they are difficult to observe.Comment: 12 pages, 7 ps figures, submitted to Ap
The Molecular Gas Distribution and Schmidt Law in M33
The relationship between the star formation rate and surface density of
neutral gas within the disk of M33 is examined with new imaging observations of
CO J=1-0 emission gathered with the FCRAO 14m telescope and IRAS HiRes images
of the 60 micron and 100 micron emission. The Schmidt law, Sigma_SFR ~
Sigma_gas^n, is constructed using radial profiles of the HI 21cm, CO, and far
infrared emission. A strong correlation is identified between the star
formation rate and molecular gas surface density. This suggests that the
condensation of giant molecular clouds is the limiting step to star formation
within the M33 disk. The corresponding molecular Schmidt index, n_{mol}, is
1.36 +/- 0.08. The star formation rate has a steep dependence on total mass gas
surface density, (Sigma_{HI}+Sigma_{H_2}), owing to the shallow radial profile
of the atomic gas which dominates the total gas surface density for most radii.
The disk pressure of the gas is shown to play a prominent role in regulating
the molecular gas fraction in M33.Comment: 19 pages + 5 figures. Accepted for publication in Ap
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