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We present a spectroscopic component analysis of 18 candidate young, wide, non-magnetic, double-degenerate binaries identified from a search of the Sloan Digital Sky Survey Data Release 7 (DR7). All but two pairings are likely to be physical systems. We show SDSS J084952.47+471247.7 + SDSS J084952.87+471249.4 to be a wide DA+DB binary, only the second identified to date. Combining our measurements for the components of 16 new binaries with results for three similar, previously known systems within the DR7, we have constructed a mass distribution for the largest sample to date (38) of white dwarfs in young, wide, non-magnetic, double-degenerate pairings. This is broadly similar in form to that of the isolated field population with a substantial peak around M~0.6 Msun. We identify an excess of ultra-massive white dwarfs and attribute this to the primordial separation distribution of their progenitor systems peaking at relatively larger values and the greater expansion of their binary orbits during the final stages of stellar evolution. We exploit this mass distribution to probe the origins of unusual types of degenerates, confirming a mild preference for the progenitor systems of high-field-magnetic white dwarfs, at least within these binaries, to be associated with early-type stars. Additionally, we consider the 19 systems in the context of the stellar initial mass-final mass relation. None appear to be strongly discordant with current understanding of this relationship., Comment: 20 pages, 5 Tables, 7 figures. accepted for publication in MNRAS

It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the K3ST model, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this paper we rectify this shortcoming by showing how to extend the general Markov model on trees to to include arbitrary splits; and even further to more general network models. This is achieved by exploring the algebra of the generators of the continuous-time Markov chain together with the "splitting" operator that generates the branching process on phylogenetic trees. For simplicity we proceed by discussing the two state case and note that our results are easily extended to more states with little complication. Intriguingly, upon restriction of the two state general Markov model to the parameter space of the binary symmetric model, our extension is indistinguishable from the previous approach only on trees; as soon as any incompatible splits are introduced the two approaches give rise to differing probability distributions with disparate structure. Through exploration of a simple example, we give a tentative argument that our approach to extending to more general networks has desirable properties that the previous approaches do not share. In particular, our construction allows for the possibility of convergent evolution of previously divergent lineages; a property that is of significant interest for biological applications., Comment: 17 pages, 5 figures

Graphene is at the centre of nanotechnology research. In order to fully exploit its outstanding properties, a mass production method is necessary. Two main routes are possible: large-scale growth or large-scale exfoliation. Here, we demonstrate graphene dispersions with concentrations up to ~0.01 mg/ml by dispersion and exfoliation of graphite in organic solvents such as N-methyl-pyrrolidone. This occurs because the energy required to exfoliate graphene is balanced by the solvent-graphene interaction for solvents whose surface energy matches that of graphene. We confirm the presence of individual graphene sheets with yields of up to 12% by mass, using absorption spectroscopy, transmission electron microscopy and electron diffraction. The absence of defects or oxides is confirmed by X-ray photoelectron, infra-red and Raman spectroscopies. We can produce conductive, semi-transparent films and conductive composites. Solution processing of graphene opens up a whole range of potential large-scale applications from device or sensor fabrication to liquid phase chemistry.