Supernova enrichment and dynamical histories of solar-type stars in clusters

We use N-body simulations of star cluster evolution to explore the hypothesis that short-lived radioactive isotopes found in meteorites, such as 26-Al, were delivered to the Sun's protoplanetary disc from a supernova at the epoch of Solar System formation. We cover a range of star cluster formation parameter space and model both clusters with primordial substructure, and those with smooth profiles. We also adopt different initial virial ratios - from cool, collapsing clusters to warm, expanding associations. In each cluster we place the same stellar population; the clusters each have 2100 stars, and contain one massive 25M_Sun star which is expected to explode as a supernova at about 6.6Myr. We determine the number of Solar (G)-type stars that are within 0.1 - 0.3pc of the 25M_Sun star at the time of the supernova, which is the distance required to enrich the protoplanetary disc with the 26-Al abundances found in meteorites. We then determine how many of these G-dwarfs are unperturbed `singletons'; stars which are never in close binaries, nor suffer sub-100au encounters, and which also do not suffer strong dynamical perturbations. The evolution of a suite of twenty initially identical clusters is highly stochastic, with the supernova enriching over 10 G-dwarfs in some clusters, and none at all in others. Typically only ~25 per cent of clusters contain enriched, unperturbed singletons, and usually only 1 - 2 per cluster (from a total of 96 G-dwarfs in each cluster). The initial conditions for star formation do not strongly affect the results, although a higher fraction of supervirial (expanding) clusters would contain enriched G-dwarfs if the supernova occurred earlier than 6.6Myr. If we sum together simulations with identical initial conditions, then ~1 per cent of all G-dwarfs in our simulations are enriched, unperturbed singletons.Comment: 14 pages, 5 figures, accepted for publication in MNRA

If you can't be with the one you love, love the one you're with: How individual habituation of agent interactions improves global utility

Simple distributed strategies that modify the behaviour of selfish individuals in a manner that enhances cooperation or global efficiency have proved difficult to identify. We consider a network of selfish agents who each optimise their individual utilities by coordinating (or anti-coordinating) with their neighbours, to maximise the pay-offs from randomly weighted pair-wise games. In general, agents will opt for the behaviour that is the best compromise (for them) of the many conflicting constraints created by their neighbours, but the attractors of the system as a whole will not maximise total utility. We then consider agents that act as 'creatures of habit' by increasing their preference to coordinate (anti-coordinate) with whichever neighbours they are coordinated (anti-coordinated) with at the present moment. These preferences change slowly while the system is repeatedly perturbed such that it settles to many different local attractors. We find that under these conditions, with each perturbation there is a progressively higher chance of the system settling to a configuration with high total utility. Eventually, only one attractor remains, and that attractor is very likely to maximise (or almost maximise) global utility. This counterintutitve result can be understood using theory from computational neuroscience; we show that this simple form of habituation is equivalent to Hebbian learning, and the improved optimisation of global utility that is observed results from wellknown generalisation capabilities of associative memory acting at the network scale. This causes the system of selfish agents, each acting individually but habitually, to collectively identify configurations that maximise total utility

An Error-Components Three-Stage Least-Squares Model of Investment Allocation by Farm Households

This paper is an assessment of patterns of investment by farm households via an econometric model adapted from a land allocation approach of Holt (1999). This analysis will shed light on the importance of different classes of assets to farm household well-being, and show the reaction of farm households to a variety of market, international and government effects.Farm Management,

Exploratory Modelling of Financial Reporting and Analysis Practices in Small Growth Enterprises

This paper reports an exploratory study of statistical modelling of historical financial reporting and analysis in a sample of small growth enterprises. The study sought to identify those factors that determine whether particular financial reporting and analysis practices are undertaken, and to represent these explanatory factors in expressions that reflect their relative and combined influence. Dichotomous logistic regression is employed to model financial analysis and polytomous logistic regression is used to model financial reporting. The models developed seem moderately encouraging in terms of the statistical significance and predictive ability. The overall classification success for financial analysis is a modest 65 percent; but identifying users of financial ratio analysis is achieved with just below 90 percent accuracy. The overall classification success for a trichotomous financial reporting scale exceeds 70 percent; with anticipation of financial reporting at the highest level being as accurate as 90 percent. External validation of the models remains an important priority

The origin of very wide binary systems

The majority of stars in the Galactic field and halo are part of binary or multiple systems. A significant fraction of these systems have orbital separations in excess of thousands of astronomical units, and systems wider than a parsec have been identified in the Galactic halo. These binary systems cannot have formed through the 'normal' star-formation process, nor by capture processes in the Galactic field. We propose that these wide systems were formed during the dissolution phase of young star clusters. We test this hypothesis using N-body simulations of evolving star clusters and find wide binary fractions of 1-30%, depending on initial conditions. Moreover, given that most stars form as part of a binary system, our theory predicts that a large fraction of the known wide 'binaries' are, in fact, multiple systems.Comment: 4 pages, 1 figure, to appear in the proceedings of IAU Symposium 266, eds. R. de Grijs & J.R.D. Lepin

Commensurate lattice distortion in the layered titanium oxypnictides Na2_{2}Ti2Pn2_{2}Pn_{2}O (Pn=Pn = As, Sb) determined by X-ray diffraction

We report single crystal X-ray diffraction measurements on Na$_2$Ti$_{2}Pn_{2}$O ($Pn$ = As, Sb) which reveal a charge superstructure that appears below the density wave transitions previously observed in bulk data. From symmetry-constrained structure refinements we establish that the associated distortion mode can be described by two propagation vectors, ${\bf q}_{1} = (1/2, 0, l)$ and ${\bf q}_{2} = (0, 1/2, l)$, with $l=0$ (Sb) or $l = 1/2$ (As), and primarily involves in-plane displacements of the Ti atoms perpendicular to the Ti--O bonds. The results provide direct evidence for phonon-assisted charge density wave order in Na$_2$Ti$_{2}Pn_{2}$O and identify a proximate ordered phase that could compete with superconductivity in doped BaTi$_{2}$Sb$_{2}$O

Probing the Rotational Velocity of Galactic WO Stars with Spectropolarimetry

Oxygen sequence Wolf-Rayet stars (WO) are thought to be the final evolution phase of some high-mass stars, as such they may be the progenitors of Type Ic SNe as well as potential progenitors of broad-lined Ic and long gamma-ray bursts. We present the first spectropolarimetric observations of the Galactic WO stars WR93b and WR102 obtained with FORS1 on the Very Large Telescope. We find no sign of a line effect, which could be expected if these stars were rapid rotators. We also place constraints on the amplitude of a potentially undetected line effect. This allows us to derive upper limits on the possible intrinsic continuum polarization and find Pcont \u3c 0.077 per cent and Pcont \u3c 0.057 per cent for WR93b and WR102, respectively. Furthermore, we derive upper limits on the rotation of our WO stars by considering our results in the context of the wind compression effect. We estimate that for an edge-on case the rotational velocity of WR93b is vrot \u3c 324 km s−1 while for WR102 vrot \u3c 234 km s−1. These correspond to values of vrot/vcrit \u3c 19 per cent and j) \u3c 18.0 cm2 s−1 for WR93b and 2 s−1 for WR102. The upper limits found on vrot/vcrit and log(j) for our WO stars are therefore similar to the estimates calculated for Galactic Wolf-Rayet (WR) stars that do show a line effect. Therefore, although the presence of a line effect in a single WR star is indicative of fast rotation, the absence of a line effect does not rule out significant rotation, even when considering the edge-on scenario