Significant effects of weak gravitational lensing on determinations of the cosmology from Type Ia Supernov\ae

Significant adjustments to the values of the cosmological parameters estimated from high-redshift Type Ia Supernov\ae data are reported, almost an order of magnitude greater than previously found. They arise from the effects of weak gravitational lensing on observations of high-redshift sources. The lensing statistics used have been obtained from computations of the three-dimensional shear in a range of cosmological N-body simulations, from which it is estimated that cosmologies with an underlying deceleration parameter q_0 = -0.51 +0.03/-0.24 may be interpreted as having q_0 = -0.55 (appropriate to the currently popular cosmology with density parameter $\Omega_M = 0.3$ and vacuum energy density parameter $\Omega_{\Lambda} = 0.7$). In addition, the standard deviation expected from weak lensing for the peak magnitudes of Type Ia Supernov\ae at redshifts of 1 is expected to be approximately 0.078 magnitudes, and 0.185 magnitudes at redshift 2. This latter value is greater than the accepted intrinsic dispersion of 0.17 magnitudes. Consequently, the effects of weak lensing in observations of high-redshift sources must be taken properly into account.Comment: 9 pages, LaTeX, 4 figure

Fracture Mechanics implications for apparent static friction coefficient in contact problems involving slip-weakening laws

We consider the effect of differing coefficients of static and dynamic friction coefficients on the behaviour of contacts involving microslip. The classic solutions of Cattaneo and Mindlin are unchanged if the transition in coefficients is abrupt, but if it occurs over some small slip distance, the solution has some mathematical similarities with those governing the normal tractions in adhesive contact problems. In particular, if the transition to dynamic slip occurs over a sufficiently small area, we can identify a `JKR' approximation, where the transition region is condensed to a line. A local singularity in shear traction is then predicted, with a stress-intensity factor that is proportional to the the square root of the local contact pressure and to a certain integral of the friction coefficient-slip distance relation. We can also define an equivalent of the `small-scale yielding' criterion, which enables us to assess when the singular solution provides a good approximation. One consequence of the results is that the static coefficient of friction determined from force measurements in experiments is significantly smaller than the value that holds at the microscale.Comment: 6 figure

Detecting hierarchical and overlapping network communities using locally optimal modularity changes

Agglomerative clustering is a well established strategy for identifying communities in networks. Communities are successively merged into larger communities, coarsening a network of actors into a more manageable network of communities. The order in which merges should occur is not in general clear, necessitating heuristics for selecting pairs of communities to merge. We describe a hierarchical clustering algorithm based on a local optimality property. For each edge in the network, we associate the modularity change for merging the communities it links. For each community vertex, we call the preferred edge that edge for which the modularity change is maximal. When an edge is preferred by both vertices that it links, it appears to be the optimal choice from the local viewpoint. We use the locally optimal edges to define the algorithm: simultaneously merge all pairs of communities that are connected by locally optimal edges that would increase the modularity, redetermining the locally optimal edges after each step and continuing so long as the modularity can be further increased. We apply the algorithm to model and empirical networks, demonstrating that it can efficiently produce high-quality community solutions. We relate the performance and implementation details to the structure of the resulting community hierarchies. We additionally consider a complementary local clustering algorithm, describing how to identify overlapping communities based on the local optimality condition.Comment: 10 pages; 4 tables, 3 figure

The structure of R&D collaboration networks in the European Framework Programmes

Using a large and novel data source, we study the structure of R&D collaboration net-works in the first five EU Framework Programmes (FPs). The networks display proper-ties typical for complex networks, including scale-free degree distributions and the small-world property. Structural features are common across FPs, indicating similar network formation mechanisms despite changes in governance rules. Several findings point towards the existence of a stable core of interlinked actors since the early FPs with integration increasing over time. This core consists mainly of universities and research organisations. We observe assortative mixing by degree of projects, but not by degree of organisations. Unexpectedly, we find only weak association between central projects and project size, suggesting that different types of projects attract different groups of actors. In particular, large projects appear to have included few of the pivotal actors in the networks studied. Central projects only partially mirror funding priorities, indicating field-specific differences in network structures. The paper concludes with an agenda for future research.R&D collaboration, EU Framework Programmes, Complex Networks, Small World Effect, Centrality Measures, European Research Area

Use of the BT2 water line list to determine the rotational temperature and H2O column density of the circumstellar envelope on five dates

BT2 is the most accurate and complete synthetic water line list in existence; it includes over 505 million transitions. BT2 spectra generated at various temperatures and column densities were fitted to observed H band spectra of V838 Mon recorded on 5 dates between 20 Nov. 2002 and 25 Dec. 2004. Five absorption features in the observed spectra were identified as being due to water. With one exception, where there was a single strong water line, all of the featues were blends of water lines. 17 individual water lines were assigned and the rotational temperatures and H2O column densities of the circumstellar ejected envelope were determined for each of the five dates