Lectures on the functional renormalization group method

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained in a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scalar theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.Comment: 47 pages, 11 figures, final versio

Oxygen abundance of γ Vel from [O III] 88 μm Herschel/PACS spectroscopy

We present Herschel PACS spectroscopy of the [O III] 88.4 μm fine-structure line in the nearby WC8+O binary system γ Vel to determine its oxygen abundance. The critical density of this line corresponds to several 105R∗ such that it is spatially extended in PACS observations at the 336 pc distance to γ Vel. Two approaches are used, the first involving a detailed stellar atmosphere analysis of γ Vel using CMFGEN, extending to Ne ∼ 100 cm−3 in order to fully sample the line formation region of [O III] 88.4 μm. The second approach involves the analytical model introduced by Barlow et al. and revised by Dessart et al., additionally exploiting ISO LWS spectroscopy of [O III] 51.8 μm. We obtain higher luminositiesfor the WR and O components of γ Vel with respect to De Marco et al., log L/L⊙ = 5.31 and 5.56, respectively, primarily due to the revised (higher) interferometric distance. We obtain an oxygen mass fraction of XO = 1.0 ± 0.3 per cent for an outer wind volume filling factor of f = 0.5 ± 0.25, favouring either standard or slightly reduced Kunz et al. rates for the 12C(α, γ ) 16O reaction from comparison with BPASS binary population synthesis models. We also revisit neon and sulphur abundances in the outer wind of γ Vel from ISO SWS spectroscopy of [S IV] 10.5 μm, [Ne II] 12.8 μm, and [Ne III] 15.5 μm. The inferred neon abundance XNe = 2.0+0.4 −0.6 per cent is in excellent agreement with BPASS predictions, while the sulphur abundance of XS = 0.04 ± 0.01 per cent agrees with the solar abundance, as expected for unprocessed elements

Exact renormalization group flow equations for non-relativistic fermions: scaling towards the Fermi surface

We construct exact functional renormalization group (RG) flow equations for non-relativistic fermions in arbitrary dimensions, taking into account not only mode elimination but also the rescaling of the momenta, frequencies and the fermionic fields. The complete RG flow of all relevant, marginal and irrelevant couplings can be described by a system of coupled flow equations for the irreducible n-point vertices. Introducing suitable dimensionless variables, we obtain flow equations for generalized scaling functions which are continuous functions of the flow parameter, even if we consider quantities which are dominated by momenta close to the Fermi surface, such as the density-density correlation function at long wavelengths. We also show how the problem of constructing the renormalized Fermi surface can be reduced to the problem of finding the RG fixed point of the irreducible two-point vertex at vanishing momentum and frequency. We argue that only if the degrees of freedom are properly rescaled it is possible to reach scale-invariant non-Fermi liquid fixed points within a truncation of the exact RG flow equations.Comment: 20 Revtex pages, with 4 figures; final version to appear in Phys. Rev. B; references and some explanations adde

Putting context to numbers : a geotechnical risk trajectory to cost overrun extremism

The study investigates the cause of the unusually high cost overruns experienced in highway project delivery in the tropical wetland setting of the Niger Delta region of Nigeria. This is in view of the extensive literature supporting the link between geology, the lack of geotechnical best practices and cost overruns. An empirical profiling of cost overrun research further reveals the predominance of mono-method studies based on survey methods, correlative analysis and archival data modelling techniques, all of which are underlain by positivism. The study argues that such positivist philosophies, although methodologically valid, cannot adequately explain and provide in-depth understanding of the contextual cost overrun drivers in highway organisations., Using a robust and thoughtfully designed mix of methods, the paper examines the contribution of geotechnical risks to cost overruns experienced in highway project, and demonstrates the relevance of context in cost overrun research. Cost overrun data from documentary sources for 61 completed highway projects in the Niger Delta are gathered and analysed, revealing an average value of 216%, with extreme cases, ranging up to 1925% of budgeted cost. To uncover the intrinsic contextual drivers, 16 interviews were conducted with participants from the three highway agencies in the region, responsible for the execution of the sampled highway projects. Adopting a geotechnical narrative, the data is thematically analysed, deductively and inductively. The results of the analysis identified that poor project governance, management and procurement practices, have inhibited the competent management of geotechnical risk, creating a propensity for extreme cost overruns on the highway projects. The study submits the phenomenon of cost overruns in public infrastructure projects is underlain by a complexity of contextual social constructs, which would have been overlooked in positivists studies. Cost overrun research therefore, needs to be contextually and numerically anchored. Keywords: Context, Cost overruns, Highway projects, Mixed methods, Social Construct

Photometric variability of massive young stellar objects

The Vista Variables in the Via Lactea (VVV) survey has allowed for an unprecedented number of multi-epoch observations of the southern Galactic plane. In a recent paper, 13 massive young stellar objects (MYSOs) have already been identified within the highly variable (?Ks > 1 mag) YSO sample of another published work. This study aims to understand the general nature of variability in MYSOs. Here we present the first systematic study of variability in a large sample of candidate MYSOs. We examined the data for variability of the putative driving sources of all known Spitzer extended green objects (EGOs; 270) and bright 24 ?m sources coinciding with the peak of 870 ?m detected ATLASGAL clumps (448), a total of 718 targets. Of these, 190 point sources (139 EGOs and 51 non-EGOs) displayed variability (IQR > 0.05, ?Ks > 0.15 mag). 111 and 79 light-curves were classified as periodic and aperiodic respectively. Light-curves have been sub-classified into eruptive, dipper, fader, short-term-variable and long-period-variable-YSO categories. Lomb-Scargle periodogram analysis of periodic light-curves was carried out. 1–870 ?m spectral energy distributions of all the variable sources were fitted with YSO models to obtain the representative properties of the variable sources. 41% of the variable sources are represented by > 4 M? objects, and only 6% were modelled as > 8 M? objects. The highest-mass objects are mostly non-EGOs, and deeply embedded, as indicated by nearly twice the extinction when compared with EGO sources. By placing them on the HR diagram we show that most of the lower mass, EGO type objects are concentrated on the putative birth-line position, while the luminous non-EGO type objects group around the zero-age-main-sequence track. Some of the most luminous far infrared (FIR) sources in the massive clumps and infrared quiet driving sources of EGOs have been missed out by this study owing to an uniform sample selection method. A high rate of detectable variability in EGO targets (139 out of 153 searched) implies that near-infrared variability in MYSOs is closely linked to the accretion phenomenon and outflow activity

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types

The PHENIX Experiment at RHIC

The physics emphases of the PHENIX collaboration and the design and current status of the PHENIX detector are discussed. The plan of the collaboration for making the most effective use of the available luminosity in the first years of RHIC operation is also presented.Comment: 5 pages, 1 figure. Further details of the PHENIX physics program available at http://www.rhic.bnl.gov/phenix