Complex networks created by aggregation

We study aggregation as a mechanism for the creation of complex networks. In this evolution process vertices merge together, which increases the number of highly connected hubs. We study a range of complex network architectures produced by the aggregation. Fat-tailed (in particular, scale-free) distributions of connections are obtained both for networks with a finite number of vertices and growing networks. We observe a strong variation of a network structure with growing density of connections and find the phase transition of the condensation of edges. Finally, we demonstrate the importance of structural correlations in these networks.Comment: 12 pages, 13 figure

A multiple scales approach to crack front waves

Perturbation of a propagating crack with a straight edge is solved using the method of matched asymptotic expansions (MAE). This provides a simplified analysis in which the inner and outer solutions are governed by distinct mechanics. The inner solution contains the explicit perturbation and is governed by a quasi-static equation. The outer solution determines the radiation of energy away from the tip, and requires solving dynamic equations in the unperturbed configuration. The outer and inner expansions are matched via the small parameter L/l defined by the disparate length scales: the crack perturbation length L and the outer length scale l associated with the loading. The method is first illustrated for a scalar crack model and then applied to the elastodynamic mode I problem. The dispersion relation for crack front waves is found by requiring that the energy release rate is unaltered under perturbation. The wave speed is calculated as a function of the nondimensional parameter kl where k is the crack front wavenumber, and dispersive properties of the crack front wave speed are described for the first time. The example problems considered here demonstrate that the potential of using MAE for moving boundary value problems with multiple scales.Comment: 25 pages, 5 figure

Structural characteristics of positionally-disordered lattices: relation to the first sharp diffraction peak in glasses

Positional disorder has been introduced into the atomic structure of certain crystalline lattices, and the orientationally-averaged structure factor S(k) and pair-correlation function g(r) of these disordered lattices have been studied. Analytical expressions for S(k) and g(r) for Gaussian positional disorder in 2D and 3D are confirmed with precise numerical simulations. These analytic results also have a bearing on the unsolved Gauss circle problem in mathematics. As the positional disorder increases, high-k peaks in S(k) are destroyed first, eventually leaving a single peak, that with the lowest-k value. The pair-correlation function for lattices with such high levels of positional disorder exhibits damped oscillations, with a period equal to the separation between the furthest-separated (lowest-k) lattice planes. The last surviving peak in S(k) is, for example for silicon and silica, at a wavevector nearly identical to that of the experimentally-observed first sharp diffraction peak (FSDP) in the amorphous phases of those materials. Thus, for these amorphous materials at least, the FSDP can be regarded as arising from scattering from atomic configurations equivalent to the single family of positionally-disordered local Bragg planes having the furthest separation.Comment: v2: changes in response to referees' comments: Figure 2 made more readable, improved discussion of height of peaks in S(k), other minor changes 4 pages, 3 figures, submitted to Physical Review

Thioxoethenylidene (CCS) as a bridging ligand

The reaction of [Mo(≡CBr)(CO)2(Tp*)] (Tp* = hydrotris(3,5-dimethylpyrazol-1-yl)borate) with [Fe2(μ-SLi)2(CO)6] affords, inter alia, the unsymmetrical binuclear thioxoethenylidene complex [Mo2(μ,σ(C):η2(C′S)-CCS)(CO)4(Tp*)2], which may be more directly obtained from [Mo(≡CBr)(CO)2(Tp*)] and Li2S. The reaction presumably proceeds via the intermediacy of the bis(alkylidynyl)thioether complex S{C≡Mo(CO)2(Tp*)}2, which was, however, not directly observed but explored computationally and found to lie 78.6 kJ mol–1 higher in energy than the final thioxoethenylidene product. Computational interrogation of the molecules [M2(μ-C2S)(CO)2(Tp*)2] (M = Mo, W, Re, Os) reveals three plausible coordination modes for a thioxoethenylidene bridge which involve a progressive strengthening of the C–C bond and weakening of the M–C and M–S bonds, as might be expected from simple effective atomic number considerations.This work was supported by the Australian Research Council (DP130102598 and DP110101611)

Shocked Molecular Hydrogen in the 3C 326 Radio Galaxy System

The Spitzer spectrum of the giant FR II radio galaxy 3C 326 is dominated by very strong molecular hydrogen emission lines on a faint IR continuum. The H2 emission originates in the northern component of a double-galaxy system associated with 3C 326. The integrated luminosity in H2 pure-rotational lines is 8.0E41 erg/s, which corresponds to 17% of the 8-70 micron luminosity of the galaxy. A wide range of temperatures (125-1000 K) is measured from the H2 0-0 S(0)-S(7) transitions, leading to a warm H2 mass of 1.1E9 Msun. Low-excitation ionic forbidden emission lines are consistent with an optical LINER classification for the active nucleus, which is not luminous enough to power the observed H2 emission. The H2 could be shock-heated by the radio jets, but there is no direct indication of this. More likely, the H2 is shock-heated in a tidal accretion flow induced by interaction with the southern companion galaxy. The latter scenario is supported by an irregular morphology, tidal bridge, and possible tidal tail imaged with IRAC at 3-9 micron. Unlike ULIRGs, which in some cases exhibit H2 line luminosities of comparable strength, 3C 326 shows little star-formation activity (~0.1 Msun/yr). This may represent an important stage in galaxy evolution. Starburst activity and efficient accretion onto the central supermassive black hole may be delayed until the shock-heated H2 can kinematically settle and coolComment: 27 pages, 7 figures, accepted for publication in the Astrophysical Journa

Electron spin relaxation in organic semiconductors probed through muSR

Muon spin spectroscopy and in particular the avoided level crossing technique is introduced, with the aim of showing it as a very sensitive local probe for electron spin relaxation in organic semiconductors. Avoided level crossing data on TMS-pentacene at different temperatures are presented, and they are analysed to extract the electron spin relaxation rate, that is shown to increase on increasing the temperature from 0.02 MHz to 0.33 MHz at 3 K and 300 K respectively.Comment: International Conference TSN2010 "Trends in spintronics and nanomagnetism

A Yule-Simon process with memory

The Yule-Simon model has been used as a tool to describe the growth of diverse systems, acquiring a paradigmatic character in many fields of research. Here we study a modified Yule-Simon model that takes into account the full history of the system by means of an hyperbolic memory kernel. We show how the memory kernel changes the properties of preferential attachment and provide an approximate analytical solution for the frequency distribution density as well as for the frequency-rank distribution.Comment: 7 pages, 5 figures; accepted for publication in Europhysics Letter

The OLS-lens survey: The discovery of five new galaxy-galaxy strong lenses from the SDSS

Bright galaxy-galaxy strong lenses are much more powerful than lensed quasars for measuring the mass profiles of galaxies, but until this year only a handful have been known. Here we present five new examples, identified via the optimal line-of-sight gravitational lens search strategy applied to luminous red galaxies in the Sloan Digital Sky Survey (SDSS). Our survey largely complements a similar survey by Bolton et al., who recently presented several new lenses. The lensed background galaxies are selected from the SDSS spectra via the presence of narrow emission line signatures, including the [OII] 3726,3729, Hb and [OIII] 4960,5008 lines, superposed on the spectra of the bright, intervening, deflector galaxies. Our five confirmed new systems include deflector galaxies with redshifts z=0.17-0.28 and lensed galaxies with redshifts z=0.47-1.18. Simulations of moderately deep (few orbits) HST-ACS imaging of systems such as these, where the lensed source is brighter than r~23, are presented. These demonstrate the feasibility of measuring accurately the inner slope of the dark matter halo to within an uncertainty sigma(gamma)~0.1, the dark matter fraction within the Einstein radius, and the mass-to-light ratio of the stars alone, independently of dynamical measurements. The high success rate of our search so far, >60%, and the relatively modest observational resources necessary to confirm the gravitational lens nature of the candidates, demonstrate that compilation of a sample of ~100 galaxy-galaxy lenses from the SDSS is readily achievable, opening up a rich new field in dark matter studies.Comment: To appear in MNRAS. Three figs provided as low-res jpegs. Full-resolution PS of paper at http://astro.ic.ac.uk/~sjw4/MF1373rv.ps.g