Non-perturbative studies of gauge theories: their renormalisation and hierarchies of scales

Two aspects of gauge theories are studied in the non-perturbative regime; firstly, using a set of pre-determined, approximate renormalised Feynman rules, the divergent parts of the O(α(_8)) virtual graphs of the process e(^+)e" → qq are determined to explicitly test whether multiplicative renormalisation is preserved by these rules. The calculation is performed using dimensional regularisation in 2(2 - ɛ) dimensional Euclidean space, where the divergences appear as 1/ɛ(^n) poles as ɛ → 0 Though the corrections to both the fermion-photon vertex and to the final state self energy are shown to have 1/ɛ singularities, the coefficients of these are quite different. This mis-match in singular behaviour signals the breakdown of multiplicative renormalisation, which, in turn, implies that the physical process is not guaranteed to be finite and the rules used are in admissable as a set of consistent Feynman rules. The second investigation is to solve numerically the Schwinger-Dyson equation for the fermion propagator in QED in three (Euclidean) dimensions. The aim being to study the scale of dynamical mass generation. To control infrared divergences the 1/N (flavour) expansion is used and to close the equation vertex and gauge propagator are approximated by their lowest order forms in 1/N. Numerical solutions for the fermion self energy and wavefunction renormalisation are determined. The latter is found not to be suppressed by O(1/N), contrary to the expectation of Appelquist et al, and the coupled equation for these functions has to be solved. It is then found that a mass scale is dynamically generated and that a scale hierarchy between it and the dimensionful coupling, α, of many orders of magnitude exists (typically m/a ~ 10(^-7) for N(_F)=5). Thus showing, albeit in a simplified 'toy' model, how large scale hierarchies can 'naturally' occur in gauge theories with spontaneously broken symmetries

Spatial field correlation, the building block of mesoscopic fluctuations

The absence of self averaging in mesoscopic systems is a consequence of long-range intensity correlation. Microwave measurements suggest and diagrammatic calculations confirm that the correlation function of the normalized intensity with displacement of the source and detector, $\Delta R$ and $\Delta r$, respectively, can be expressed as the sum of three terms, with distinctive spatial dependences. Each term involves only the sum or the product of the square of the field correlation function, $F \equiv F_{E}^2$. The leading-order term is the product, the next term is proportional to the sum. The third term is proportional to $[F(\Delta R)F(\Delta r) + [F(\Delta R)+F(\Delta r)] + 1]$.Comment: Submitted to PR

Small scale energy release driven by supergranular flows on the quiet Sun

In this article we present data and modelling for the quiet Sun that strongly suggest a ubiquitous small-scale atmospheric heating mechanism that is driven solely by converging supergranular flows. A possible energy source for such events is the power transfer to the plasma via the work done on the magnetic field by photospheric convective flows, which exert drag of the footpoints of magnetic structures. In this paper we present evidence of small scale energy release events driven directly by the hydrodynamic forces that act on the magnetic elements in the photosphere, as a result of supergranular scale flows. We show strong spatial and temporal correlation between quiet Sun soft X-ray emission (from <i>Yohkoh</i> and <i>SOHO</i> MDI-derived flux removal events driven by deduced photospheric flows. We also present a simple model of heating generated by flux submergence, based on particle acceleration by converging magnetic mirrors. In the near future, high resolution soft X-ray images from XRT on the <i>Hinode</i> satellite will allow definitive, quantitative verification of our results

Mitochondrial differentiation, introgression and phylogeny of species in the Tegenaria atrica group (Araneae, Agelenidae)

The relationships between the three members of the Tegenaria atrica group (T. atrica, T. saeva and T. gigantea) were examined with DNA sequence data from mitochondrial CO1, 16S rRNA, tRNAleu(CUN) and ND1 genes. Members of this group of large house spiders have overlapping distributions in western Europe and hybridize with each other to a variable degree. The close relatedness of all three species was supported by all analyses. T. saeva and T. gigantea are more closely affiliated than either is to T. atrica. Haplotypes clearly assignable to T. gigantea were also present in many specimens of T. saeva suggesting asymmetrical introgression of mtDNA from T. gigantea into T. saeva. Molecular clock calibrations (CO1) suggest that deeper divisions within the genus Tegenaria may be in excess of 10 million years old, and that the evolutionary history of the T. atrica group has been moulded by Quaternary glacial-interglacial cycles

The Canada-UK Deep Submillimetre Survey: The Survey of the 14-hour field

We have used SCUBA to survey an area of 50 square arcmin, detecting 19 sources down to a 3sigma sensitivity limit of 3.5 mJy at 850 microns. We have used Monte-Carlo simulations to assess the effect of source confusion and noise on the SCUBA fluxes and positions, finding that the fluxes of sources in the SCUBA surveys are significantly biased upwards and that the fraction of the 850 micron background that has been resolved by SCUBA has been overestimated. The radio/submillmetre flux ratios imply that the dust in these galaxies is being heated by young stars rather than AGN. We have used simple evolution models based on our parallel SCUBA survey of the local universe to address the major questions about the SCUBA sources: (1) what fraction of the star formation at high redshift is hidden by dust? (2) Does the submillimetre luminosity density reach a maximum at some redshift? (3) If the SCUBA sources are proto-ellipticals, when exactly did ellipticals form? However, we show that the observations are not yet good enough for definitive answers to these questions. There are, for example, acceptable models in which 10 times as much high-redshift star formation is hidden by dust as is seen at optical wavelengths, but also acceptable ones in which the amount of hidden star formation is less than that seen optically. There are acceptable models in which very little star formation occurred before a redshift of three (as might be expected in models of hierarchical galaxy formation), but also ones in which 30% of the stars have formed by this redshift. The key to answering these questions are measurements of the dust temperatures and redshifts of the SCUBA sources.Comment: 41 pages (latex), 17 postscript figures, to appear in the November issue of the Astronomical Journa

The state of peer-to-peer network simulators

Networking research often relies on simulation in order to test and evaluate new ideas. An important requirement of this process is that results must be reproducible so that other researchers can replicate, validate and extend existing work. We look at the landscape of simulators for research in peer-to-peer (P2P) networks by conducting a survey of a combined total of over 280 papers from before and after 2007 (the year of the last survey in this area), and comment on the large quantity of research using bespoke, closed-source simulators. We propose a set of criteria that P2P simulators should meet, and poll the P2P research community for their agreement. We aim to drive the community towards performing their experiments on simulators that allow for others to validate their results