5,758 research outputs found
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
Non-disturbing quantum measurements
We consider pairs of quantum observables (POVMs) and analyze the relation
between the notions of non-disturbance, joint measurability and commutativity.
We specify conditions under which these properties coincide or
differ---depending for instance on the interplay between the number of outcomes
and the Hilbert space dimension or on algebraic properties of the effect
operators. We also show that (non-)disturbance is in general not a symmetric
relation and that it can be decided and quantified by means of a semidefinite
program.Comment: Minor corrections in v
Stereoisomerism in pentaerythritol-bridged cyclotriphosphazene tri-spiranes: spiro and ansa 1,3-propanediyldioxy disubstituted derivatives
Four isomeric products were isolated and purified from the reaction of 1,3-propanediol with the tetra-spirane cyclophosphazene-organophosphate compound (1): viz. the di-monospiro (2a), di-monoansa (2b) and two monospiro-monoansa derivatives (2c) and (2d). It is shown by 31P NMR spectroscopy on addition of a chiral solvating agent (CSA) that both the di-monospiro (2a) and di-monoansa (2b) derivatives are racemates, as expected, whereas no splitting of NMR signals occurred on addition of CSA to solutions of (2c) and (2d). It is found by X-ray crystallography that the two monospiro-monoansa spirane derivatives, (2c) and (2d), are meso diastereoisomers, which represent a new case of the stereochemistry of bis di-substituted cyclophosphazene derivatives of (1). It is also observed from the 31P NMR spectrum of the reaction mixture, supported by the yields of pure compounds, that formation of a spiro group is about 4.5 times more likely than that of an ansa moiety under the conditions of the reaction
Structural investigations of phosphorus-nitrogen compounds. 7. Relationships between physical properties, electron densities, reaction mechanisms and hydrogen-bonding motifs of N3P3Cl(6-n)(NHBut)(n) derivatives
A series of compounds of the N3P3Cl(6-n)(NHBut)n family (where n = 0, 1, 2, 4 and 6) are presented and their molecular parameters are related to trends in physical properties, which provides insight into a potential reaction mechanism for nucleophilic substitution. The crystal structures of N3P3Cl5(NHBut) and N3P3Cl2(NHBut)4 have been determined at 120K and those of N3P3Cl6 and N3P3Cl4(NHBut)2 have been re-determined at 120K. These are compared with the known structure of N3P3(NHBut)6 studied at 150K. Trends in molecular parameters (phosphazene ring, P-Cl & P-N(HBut) distances, PCl2 angles and endo- and exo-cyclic phosphazene ring parameters) across the series are observed. Hydrogen-bonding motifs are identified, characterised and compared. Both the molecular and hydrogen bonding parameters are related to the electron distribution in bonds and the derived basicities of the cyclophosphazene series of compounds. These findings provide evidence for a proposed mechanism for nucleophilic substitution at a phosphorus site bearing a PCl(NHBut) moiety
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