Monopole clusters in Abelian projected gauge theories

We show that the monopole currents which one obtains in the maximally Abelian gauge of SU(2) fall into two quite distinct classes (when the volume is large enough). In each field configuration there is precisely one cluster that permeates the whole lattice volume. It has a current density and a magnetic screening mass that scale and it produces the whole of the string tension. The remaining clusters have a number density that follows an approximate power law proportional to the inverse cube of l where l is the length of the monopole world line in lattice units. These clusters are localised in space-time with radii which vary as the square root of l. In terms of the radius r these `lumps' have a scale-invariant distribution proportional to (dr/r . 1/{r^4}). Moreover they appear not to contribute at all to the string tension. The fact that they are scale-invariant at small distances would seem to rule out an instanton origin.Comment: LaTeX, 31 pages, 11 PostScript figures. Typo in Table 2 correcte

The monopole mass in the three-dimensional Georgi-Glashow model

We study the three-dimensional Georgi-Glashow model to demonstrate how magnetic monopoles can be studied fully non-perturbatively in lattice Monte Carlo simulations, without any assumptions about the smoothness of the field configurations. We examine the apparent contradiction between the conjectured analytic connection of the `broken' and `symmetric' phases, and the interpretation of the mass (i.e., the free energy) of the fully quantised 't Hooft-Polyakov monopole as an order parameter to distinguish the phases. We use Monte Carlo simulations to measure the monopole free energy and its first derivative with respect to the scalar mass. On small volumes we compare this to semi-classical predictions for the monopole. On large volumes we show that the free energy is screened to zero, signalling the formation of a confining monopole condensate. This screening does not allow the monopole mass to be interpreted as an order parameter, resolving the paradox.Comment: 12 pages, 7 figures, uses revtex. Minor changes made to the text to match with the published version at http://link.aps.org/abstract/PRD/v65/e12500

On the Shapley-like Payoff Mechanisms in Peer-Assisted Services with Multiple Content Providers

This paper studies an incentive structure for cooperation and its stability in peer-assisted services when there exist multiple content providers, using a coalition game theoretic approach. We first consider a generalized coalition structure consisting of multiple providers with many assisting peers, where peers assist providers to reduce the operational cost in content distribution. To distribute the profit from cost reduction to players (i.e., providers and peers), we then establish a generalized formula for individual payoffs when a "Shapley-like" payoff mechanism is adopted. We show that the grand coalition is unstable, even when the operational cost functions are concave, which is in sharp contrast to the recently studied case of a single provider where the grand coalition is stable. We also show that irrespective of stability of the grand coalition, there always exist coalition structures which are not convergent to the grand coalition. Our results give us an important insight that a provider does not tend to cooperate with other providers in peer-assisted services, and be separated from them. To further study the case of the separated providers, three examples are presented; (i) underpaid peers, (ii) service monopoly, and (iii) oscillatory coalition structure. Our study opens many new questions such as realistic and efficient incentive structures and the tradeoffs between fairness and individual providers' competition in peer-assisted services.Comment: 13 pages, 4 figures, an extended version of the paper to be presented in ICST GameNets 2011, Shanghai, China, April 201

Monopole clusters, Z(2) vortices and confinement in SU(2)

We extend our previous study of magnetic monopole currents in the maximally Abelian gauge [hep-lat/9712003] to larger lattices at small lattice spacings (20^4 at beta = 2.5 and 32^4 at beta = 2.5115). We confirm that at these weak couplings there continues to be one monopole cluster that is very much longer than the rest and that the string tension, K, is entirely due to it. The remaining clusters are compact objects whose population as a function of radius follows a power law that deviates from the scale invariant form, but much too weakly to suggest a link with the analytically calculable size distribution of small instantons. We also search for traces of Z(2) vortices in the Abelian projected fields; either as closed loops of `magnetic' flux or through appropriate correlations amongst the monopoles. We find, by direct calculation, that there is no confining condensate of such flux loops. We also find, through the calculation of doubly charged Wilson loops within the monopole fields, that there is no suppression of the q=2 effective string tension out to at distances of at least r ~ 1.6/sqrt{K}, suggesting that if there are any vortices they are not encoded in the monopole fields.Comment: 26 pages of LaTeX and PostScript figure

Decay estimates for variable coefficient wave equations in exterior domains

In this article we consider variable coefficient, time dependent wave equations in exterior domains. We prove localized energy estimates if the domain is star-shaped and global in time Strichartz estimates if the domain is strictly convex.Comment: 15 pages. In the new version, some typos are fixed and a minor correction was made to the proof of Lemma 1

Thermophysical Phenomena in Metal Additive Manufacturing by Selective Laser Melting: Fundamentals, Modeling, Simulation and Experimentation

Among the many additive manufacturing (AM) processes for metallic materials, selective laser melting (SLM) is arguably the most versatile in terms of its potential to realize complex geometries along with tailored microstructure. However, the complexity of the SLM process, and the need for predictive relation of powder and process parameters to the part properties, demands further development of computational and experimental methods. This review addresses the fundamental physical phenomena of SLM, with a special emphasis on the associated thermal behavior. Simulation and experimental methods are discussed according to three primary categories. First, macroscopic approaches aim to answer questions at the component level and consider for example the determination of residual stresses or dimensional distortion effects prevalent in SLM. Second, mesoscopic approaches focus on the detection of defects such as excessive surface roughness, residual porosity or inclusions that occur at the mesoscopic length scale of individual powder particles. Third, microscopic approaches investigate the metallurgical microstructure evolution resulting from the high temperature gradients and extreme heating and cooling rates induced by the SLM process. Consideration of physical phenomena on all of these three length scales is mandatory to establish the understanding needed to realize high part quality in many applications, and to fully exploit the potential of SLM and related metal AM processes

The Two Phases of Galaxy Formation

Cosmological simulations of galaxy formation appear to show a two-phase character with a rapid early phase at z>2 during which in-situ stars are formed within the galaxy from infalling cold gas followed by an extended phase since z<3 during which ex-situ stars are primarily accreted. In the latter phase massive systems grow considerably in mass and radius by accretion of smaller satellite stellar systems formed at quite early times (z>3) outside of the virial radius of the forming central galaxy. These tentative conclusions are obtained from high resolution re-simulations of 39 individual galaxies in a full cosmological context with present-day virial halo masses ranging from 7e11 M_sun h^-1 < M_vir < 2.7e13 M_sun h^-1 and central galaxy masses between 4.5e10 M_sun h^-1 < M_* < 3.6e11 M_sun h^-1. The simulations include the effects of a uniform UV background, radiative cooling, star formation and energetic feedback from SNII. The importance of stellar accretion increases with galaxy mass and towards lower redshift. In our simulations lower mass galaxies ($M_* < 9e10 M_sun h^-1) accrete about 60 per cent of their present-day stellar mass. High mass galaxy ($M_* > 1.7e11 M_sun h^-1) assembly is dominated by accretion and merging with about 80 per cent of the stars added by the present-day. In general the simulated galaxies approximately double their mass since z=1. For massive systems this mass growth is not accompanied by significant star formation. The majority of the in-situ created stars is formed at z>2, primarily out of cold gas flows. We recover the observational result of archaeological downsizing, where the most massive galaxies harbor the oldest stars. We find that this is not in contradiction with hierarchical structure formation. Most stars in the massive galaxies are formed early on in smaller structures, the galaxies themselves are assembled late.Comment: 13 pages, 13 figures, accepted for publication in Ap

Impact of a theoretically based sex education programme (SHARE) delivered by teachers on NHS registered conceptions and terminations: final results of cluster randomised trial

&lt;b&gt;Objective&lt;/b&gt;: To assess the impact of a theoretically based sex education programme (SHARE) delivered by teachers compared with conventional education in terms of conceptions and terminations registered by the NHS. Design Follow-up of cluster randomised trial 4.5 years after intervention. &lt;b&gt;Setting&lt;/b&gt;: NHS records of women who had attended 25 secondary schools in east Scotland. &lt;b&gt;Participants&lt;/b&gt;: 4196 women (99.5% of those eligible). &lt;b&gt;Intervention&lt;/b&gt;: SHARE programme (intervention group) v existing sex education (control group). &lt;b&gt;Main outcome measure&lt;/b&gt;: NHS recorded conceptions and terminations for the achieved sample linked at age 20. &lt;b&gt;Results&lt;/b&gt;: In an "intention to treat" analysis there were no significant differences between the groups in registered conceptions per 1000 pupils (300 SHARE v 274 control; difference 26, 95% confidence interval –33 to 86) and terminations per 1000 pupils (127 v 112; difference 15, –13 to 42) between ages 16 and 20. &lt;b&gt;Conclusions&lt;/b&gt;: This specially designed sex education programme did not reduce conceptions or terminations by age 20 compared with conventional provision. The lack of effect was not due to quality of delivery. Enhancing teacher led school sex education beyond conventional provision in eastern Scotland is unlikely to reduce terminations in teenagers