The Effective Potential, the Renormalisation Group and Vacuum Stability

We review the calculation of the the effective potential with particular emphasis on cases when the tree potential or the renormalisation-group-improved, radiatively corrected potential exhibits non-convex behaviour. We illustrate this in a simple Yukawa model which exhibits a novel kind of dimensional transmutation. We also review briefly earlier work on the Standard Model. We conclude that, despite some recent claims to the contrary, it can be possible to infer reliably that the tree vacuum does not represent the true ground state of the theory.Comment: 23 pages; 5 figures; v2 includes minor changes in text and additional reference

Interstitials, Vacancies and Dislocations in Flux-Line Lattices: A Theory of Vortex Crystals, Supersolids and Liquids

We study a three dimensional Abrikosov vortex lattice in the presence of an equilibrium concentration of vacancy, interstitial and dislocation loops. Vacancies and interstitials renormalize the long-wavelength bulk and tilt elastic moduli. Dislocation loops lead to the vanishing of the long-wavelength shear modulus. The coupling to vacancies and interstitials - which are always present in the liquid state - allows dislocations to relax stresses by climbing out of their glide plane. Surprisingly, this mechanism does not yield any further independent renormalization of the tilt and compressional moduli at long wavelengths. The long wavelength properties of the resulting state are formally identical to that of the ``flux-line hexatic'' that is a candidate ``normal'' hexatically ordered vortex liquid state.Comment: 21 RevTeX pgs, 7 eps figures uuencoded; corrected typos, published versio

Topological Defects on Fluctuating Surfaces: General Properties and the Kosterlitz-Thouless Transition

We investigate the Kosterlitz-Thouless transition for hexatic order on a free fluctuating membrane and derive both a Coulomb gas and a sine-Gordon Hamiltonian to describe it. The Coulomb-gas Hamiltonian includes charge densities arising from disclinations and from Gaussian curvature. There is an interaction coupling the difference between these two densities, whose strength is determined by the hexatic rigidity, and an interaction coupling Gaussian curvature densities arising from the Liouville Hamiltonian resulting from the imposition of a covariant cutoff. In the sine-Gordon Hamiltonian, there is a linear coupling between a scalar field and the Gaussian curvature. We discuss gauge-invariant correlation function for hexatic order and the dielectric constant of the Coulomb gas. We also derive renormalization group recursion relations that predict a transition with decreasing bending rigidity $\kappa$.Comment: REVTEX, 45 pages with 11 postscript figures compressed using uufiles. Accepted for publication in Phys. Rev.

Impact of droughts on the carbon cycle in European vegetation : a probabilistic risk analysis using six vegetation models

Peer reviewedPublisher PD

Turbulent superfluid profiles in a counterflow channel

We have developed a two-dimensional model of quantised vortices in helium II moving under the influence of applied normal fluid and superfluid in a counterflow channel. We predict superfluid and vortex-line density profiles which could be experimentally tested using recently developed visualization techniques.Comment: 3 double figures, 9 page

Quality of Life in a Mixed Ethnic Population after Myocardial Infarction

Background: Although South Asian people are a significant ethnic group at increased risk of coronary heart disease and high mortality rates and experience greater delays with respect to diagnosis, referral and treatment, comparatively little is known about their quality of life during recovery from a myocardial infarction.Objectives: We sought to determine and compare the impact of ethnicity on quality of life after myocardial infarction (MI) in a mixed ethnic population (South Asian and white people) in the UK.Methods: A 2x2 mixed-group design with repeated measures on the second factor. The independent variables were ethnic group (white/South Asian) and time since MI (2 weeks/3 months). The dependent variables were the subscale scores on the Short-Form 36-item health survey (SF-36) and the Hospital Anxiety and Depression Scale (HADS).Results: At 2 weeks, significant differences were observed between groups on 5 of the 8 SF-36 subscale domain scores, with the white group reporting higher quality of life. Significant improvement in reported quality of life occurred in both groups over time on all domains of the SF-36, except bodily pain. There was a significantly greater improvement in favour of the white group for the role-physical domain. There was no significant difference between groups in terms of anxiety or depression at 2 weeks. Both groups showed a significant reduction in anxiety and depression by 3 months, but the degree of reduction was not significantly different between them. At 3 months, there was no significant difference between groups in terms of anxiety scores, but the South Asian group scored significantly higher on the depression scale.Conclusions: South Asian people have significantly poorer quality of life than white people after MI. While both groups showed improvement over time, South Asian people reported significantly less improvement in physical role function and were more depressed at 3 months. Identifying the factors accounting for such differences is important to develop models of care for delivering the most effective and culturally-sensitive interventions to this group

Continuous Melting of a "Partially Pinned" Two-Dimensional Vortex Lattice in a Square Array of Pinning Centers

The structure and equilibrium properties of a two-dimensional system of superconducting vortices in a periodic pinning potential with square symmetry are studied numerically. For a range of the strength of the pinning potential, the low-temperature crystalline state exhibits only one of the two basic periodicities (in the $x$- and $y$-directions) of the pinning potential. This ``partially pinned'' solid undergoes a continuous melting transition to a weakly modulated liquid as the temperature is increased. A spin model, constructed using symmetry arguments, is shown to reproduce the critical behavior at this transition.Comment: 5 pages, 4 figure

Hydrodynamics of Spatially Ordered Superfluids

We derive the hydrodynamic equations for the supersolid and superhexatic phases of a neutral two-dimensional Bose fluid. We find, assuming that the normal part of the fluid is clamped to an underlying substrate, that both phases can sustain third-sound modes and that in the supersolid phase there are additional modes due to the superfluid motion of point defects (vacancies and interstitials).Comment: 24 pages of ReVTeX and 7 uuencoded figures. Submitted for publication in Phys. Rev.

Periodic harmonic functions on lattices and points count in positive characteristic

This survey addresses pluri-periodic harmonic functions on lattices with values in a positive characteristic field. We mention, as a motivation, the game "Lights Out" following the work of Sutner, Goldwasser-Klostermeyer-Ware, Barua-Ramakrishnan-Sarkar, Hunzikel-Machiavello-Park e.a.; see also 2 previous author's preprints for a more detailed account. Our approach explores harmonic analysis and algebraic geometry over a positive characteristic field. The Fourier transform allows us to interpret pluri-periods of harmonic functions on lattices as torsion multi-orders of points on the corresponding affine algebraic variety.Comment: These are notes on 13p. based on a talk presented during the meeting "Analysis on Graphs and Fractals", the Cardiff University, 29 May-2 June 2007 (a sattelite meeting of the programme "Analysis on Graphs and its Applications" at the Isaac Newton Institute from 8 January to 29 June 2007

Erbium environment in glass-ceramics investigated by atom probe tomography

Glass-ceramics (considered here as a glassy host containing crystalline or amorphous nanoparticles) are of interest for luminescent properties as they can combine the sturdiness and low cost of a matrix host with particular spectroscopic behavior that would not appear in this host [1]. Ideally, nanoparticles would fully encapsulate luminescent ions to produce engineered spectroscopic properties. This approach is particularly promising for optical fibers. Indeed, silica is the most common glass used to prepare such waveguides. However, it is necessary to overcome some of its characteristics (high phonon energy, low luminesent ions solubility, ...) which may be detrimental to luminescent properties. As silicate systems have a large phase immiscibility domain when they contain divalent metal oxides (such as Mg), one can take advantage of thermal treatments inherent to the MCVD (Modified Chemical Vapor Deposition) process to obtain nanoparticles through phase separation [2]. By modifying Mg concentration, we have observed modifications of luminescent properties of Er3+ ions [3]. However the question arises of the partition of rare-earth ions in nanoparticles. Qualitative partition of erbium ions in nanoparticles was reported thanks to Secondary Ion Mass Spectrometry analyses [4]. However, the spatial resolution is about the particle size. To go further, we take advantages of recent developments in Atom Probe Tomography (APT) which allowed the extension of such studies to glass-ceramics [5]. Partition of erbium ions is clearly observed in nanoparticles smaller than 10 nm (Figure 1). During this presentation, we will discuss this partition and the most probable nearest neighbors and correlate these results with luminescent properties