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

Updated opacities from the opacity project

Using the code autostructure, extensive calculations of inner-shell atomic data have been made for the chemical elements He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Cr, Mn, Fe and Ni. The results are used to obtain updated opacities from the Opacity Project (OP). A number of other improvements on earlier work have also been included. Rosseland-mean opacities from the OP are compared with those from OPAL. Differences of 5-10 per cent occur. The OP gives the 'Z-bump', at log(T) 5.2, to be shifted to slightly higher temperatures. The opacities from the OP, as functions of temperature and density, are smoother than those from OPAL. The accuracy of the integrations used to obtain mean opacities can depend on the frequency mesh used. Tests involving variation of the numbers of frequency points show that for typical chemical mixtures the OP integrations are numerically correct to within 0.1 per cent. The accuracy of the interpolations used to obtain mean opacities for any required values of temperature and density depends on the temperature-density meshes used. Extensive tests show that, for all cases of practical interest, the OP interpolations give results correct to better than 1 per cent. Prior to a number of recent investigations which have indicated a need for downward revisions in the solar abundances of oxygen and other elements, there was good agreement between properties of the Sun deduced from helioseismology and from stellar evolution models calculated using OPAL opacities. The revisions destroy that agreement. In a recent paper, Bahcall et al. argue that the agreement would be restored if opacities for the regions of the Sun with 2 × 106T 5 × 106 K (0.7-0.4 R) were larger than those given by OPAL by about 10 per cent. In the region concerned, the present results from the OP do not differ from those of OPAL by more than 2.5 per cent

Note on Tests of the Factorization Hypothesis and the Determination of Meson Decay Constants

We discuss various tests of the factorization hypothesis making use of the close relationship between semi-leptonic and factorized nonleptonic decay amplitudes. It is pointed out that factorization leads to truely model-independent predictions for the ratio of nonleptonic to semi-leptonic decay rates, if in the nonleptonic decay a spin one meson of arbitrary mass or a pion take the place of the lepton pair. Where the decay constants of those mesons are known, these predictions represent ideal tests of the factorization hypothesis. In other cases they may be used to extract the decay constants. Currently available data on the decays $\bar B^0 \to D^+\pi^-,\, D^{*+}\pi^-,\, D^+\varrho^-,\, D^{*+}\varrho^-$ are shown to be in excellent agreement with the factorization results. A weighted average of the four independent values for the QCD coefficient $a_1$ extracted from the data gives $a_1=1.15\pm 0.06$ suggesting that it may be equal to the Wilson coefficient $c_1(\mu)$ evaluated at the scale $\mu = m_b$.Comment: (9 pages, ReVTeX, no figures), HD-THEP-92-3

Water temperature studies on the R. North Tyne after impoundment by Kielder dam. 3. Preliminary examination of water temperature data

The report describes the results of preliminary analyses of data obtained from a series of water temperature loggers sited at various distances (0.8 to 21.8 km) downstream of Kielder dam on the River North Tyne and in two natural tributaries. The report deals with three aspects of the water temperature records: An analysis of an operational aspect of the data sets for selected stations, a simple examination of the effects of impoundment upon water temperature at or close to the point of release, relative to natural river temperatures, and an examination of rate of change of monthly means of daily mean, maximum, minimum and range (maximum - minimum) with distance downstream of the point of release during 1983

Patchiness and Demographic Noise in Three Ecological Examples

Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only -at most- local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy

An integrated modelling approach for assessing the effect of multiscale complexity on groundwater source yields

A new multi-scale groundwater modelling methodology is presented to simulate pumped water levels in abstraction boreholes within regional groundwater models, providing a robust tool for assessing the sustainable yield of supply boreholes and improving our understanding of groundwater availability during drought. A 3D borehole-scale model, which solves the Darcy-Forchheimer equation in cylindrical co-ordinates to simulate both linear and non-linear radial flow to a borehole in a heterogeneous aquifer, is embedded within a Cartesian grid, using a hybrid radial-Cartesian finite difference method. The local-scale model is coupled to a regional groundwater model, ZOOMQ3D, using the OpenMI model linkage software, providing a flexible and efficient tool for assessing the behaviour of a groundwater source within its regional hydrogeological context during historic droughts and under climate change. The advantages of the new method are demonstrated through application to a Chalk supply borehole in the UK

Performing heritage: the use of live 'actors' in heritage presentations

This paper investigates the phenomenon of 'living history' presentations of heritage, using live 'actors' to portray historical characters. Its aim is to discuss these presentations in the context of what may be understood as 'heritage', and of the nature of 'performance'. Four case studies of heritage sites, each important as a tourist attraction, have been selected for detailed study, together with a number of other examples of heritage performance. It is clear from the empirical work that different performance strategies are employed within the heritage industry and by individual 'actors'. Most of the performers take part as a leisure activity, and many do not consider themselves to be 'performing' at all. The greatest concern of participants lies in the degree of authenticity of the performance. Through 'living history', the 'actors' are drawn into an experience of heritage which has real meaning for them, and which may contribute both to a sense of identity and to an enhanced understanding of society, past and present. The popularity of such presentations with visitors also indicates that similar benefits are perceived by the 'audience'

Pressure-induced phase transitions of halogen-bridged binuclear metal complexes R_4[Pt_2(P_2O_5H_2)_4X]nH_2O

Recent contrasting observations for halogen (X)-bridged binuclear platinum complexes R_4[Pt_2(P_2O_5H_2)_4X]nH_2O, that is, pressure-induced Peierls and reverse Peierls instabilities, are explained by finite-temperature Hartree-Fock calculations. It is demonstrated that increasing pressure transforms the initial charge-polarization state into a charge-density-wave state at high temperatures, whereas the charge-density-wave state oppositely declines with increasing pressure at low temperatures. We further predict that higher-pressure experiments should reveal successive phase transitions around room temperature.Comment: 5 pages, 4 figures embedded, to be published in Phys. Rev. B 64, September 1 (2001) Rapid Commu

Electromagnetic Decays of Heavy Baryons

The electromagnetic decays of the ground state baryon multiplets with one heavy quark are calculated using Heavy Hadron Chiral Perturbation Theory. The M1 and E2 amplitudes for S^{*}--> S gamma, S^{*} --> T gamma and S --> T gamma are separately computed. All M1 transitions are calculated up to O(1/Lambda_chi^2). The E2 amplitudes contribute at the same order for S^{*}--> S gamma, while for S^{*} --> T gamma they first appear at O(1/(m_Q \Lambda_\chi^2)) and for S --> T gamma are completely negligible. The renormalization of the chiral loops is discussed and relations among different decay amplitudes are derived. We find that chiral loops involving electromagnetic interactions of the light pseudoscalar mesons provide a sizable enhancement of these decay widths. Furthermore, we obtain an absolute prediction for the widths of Xi^{0'(*)}_c--> Xi^{0}_c gamma and Xi^{-'(*)}_b--> Xi^{-}_b gamma. Our results are compared to other estimates existing in the literature.Comment: 17 pages, 3 figures, submitted to Phys. Rev.