Center Domains and their Phenomenological Consequences

We argue that the domain structure of deconfined QCD matter, which can be inferred from the properties of the Polyakov loop, can simultaneously explain the two most prominent experimentally verified features of the quark-gluon plasma, namely its large opacity as well as its near ideal fluid properties

Properties of canonical determinants and a test of fugacity expansion for finite density lattice QCD with Wilson fermions

We analyze canonical determinants, i.e., grand canonical determinants projected to a fixed net quark number. The canonical determinants are the coefficients in a fugacity expansion of the grand canonical determinant and we evaluate them as the Fourier moments of the grand canonical determinant with respect to imaginary chemical potential, using a dimensional reduction technique. The analysis is done for two mass-degenerate flavors of Wilson fermions at several temperatures below and above the confinement/deconfinement crossover. We discuss various properties of the canonical determinants and analyse the convergence of the fugacity series for different temperatures.Comment: Typo removed, paragraph added in the discussion. Version to appear in Phys. Rev.

Total reward in the UK in the public and private sectors

Recent controversy has surrounded the relative value of public and private sector remuneration. We define a comprehensive measure of Total Reward (TR) which includes not just pay, but pensions and other 'benefits in kind', evaluate it as the present value of the sum of all these payments over the lifetime and compare it in the UK public and private sectors. Our results suggest that TR is equalized over the lifecycle for men while women have a clear TR advantage in the public sector by the end of their career. We suggest that the current controversy over public-private sector pension differentials and the perennial issues of public/private sector pay gaps requires a life time perspective and that the concept of TR is appropriate

Helly-Type Theorems in Property Testing

Helly's theorem is a fundamental result in discrete geometry, describing the ways in which convex sets intersect with each other. If $S$ is a set of $n$ points in $R^d$, we say that $S$ is $(k,G)$-clusterable if it can be partitioned into $k$ clusters (subsets) such that each cluster can be contained in a translated copy of a geometric object $G$. In this paper, as an application of Helly's theorem, by taking a constant size sample from $S$, we present a testing algorithm for $(k,G)$-clustering, i.e., to distinguish between two cases: when $S$ is $(k,G)$-clusterable, and when it is $\epsilon$-far from being $(k,G)$-clusterable. A set $S$ is $\epsilon$-far $(0<\epsilon\leq1)$ from being $(k,G)$-clusterable if at least $\epsilon n$ points need to be removed from $S$ to make it $(k,G)$-clusterable. We solve this problem for $k=1$ and when $G$ is a symmetric convex object. For $k>1$, we solve a weaker version of this problem. Finally, as an application of our testing result, in clustering with outliers, we show that one can find the approximate clusters by querying a constant size sample, with high probability

Coherent center domains from local Polyakov loops

We analyze properties of local Polyakov loops using quenched as well as dynamical SU(3) gauge configurations for a wide range of temperatures. It is demonstrated that for both, the confined and the deconfined regime, the local Polyakov loop prefers phase values near the center elements 1, exp(i 2 pi/3), exp(-i 2 pi/3). We divide the lattice sites into three sectors according to these phases and show that the sectors give rise to the formation of clusters. For a suitable definition of these clusters we find that in the quenched case deconfinement manifests itself as the onset of percolation of the clusters. A possible continuum limit of the center clusters is discussed

Trapped by the Entrapment.

Popliteal entrapment syndrome results from extrinsic compression of the popliteal artery by the surrounding musculotendinous structures and is a rare cause of limb ischaemia. The purpose of this report is to highlight potential mistakes in the management of popliteal entrapment. In 2000, a 23 year old man underwent a popliteal to popliteal artery bypass surgery for what was initially diagnosed as a traumatic popliteal artery thrombosis. After being initially lost to follow up for 13 years, this "unspecified traumatic" thrombosis led to several inappropriate endovascular and open procedures misinterpreted as being caused by late graft failure. These included thrombectomy, aneurysmorrhaphy, polytetrafluoroethylene covered stent graft, a redo femoropopliteal bypass, and bypass thrombolysis. The diagnosis was reached 19 years after the initial surgery, when the patient underwent a redo bypass using a retrogeniculate approach. An abnormal lateral insertion of the gastrocnemius muscle medial head, and its accessory slip, constricted the artery, and also involved the popliteal vein (Type V), thus explaining previous revascularisation failures. Surgery consisted of resecting the accessory slip and the aneurysmal bypass. The artery was reconstructed with the cephalic vein. The patient was discharged on clopidogrel 75 mg, with no further complication, and a patent bypass at six months. Based on post-operative imaging (duplex ultrasound and magnetic resonance imaging), with forced plantarflexion and dorsiflexion, asymptomatic popliteal entrapment was also present on the contralateral side. The finding of an isolated popliteal artery lesion in a young individual should be considered to be caused by popliteal artery entrapment, unless proven otherwise. Definitive surgical release of the popliteal artery should be favoured over other strategies

SCD Patterns Have Singular Diffraction

Among the many families of nonperiodic tilings known so far, SCD tilings are still a bit mysterious. Here, we determine the diffraction spectra of point sets derived from SCD tilings and show that they have no absolutely continuous part, that they have a uniformly discrete pure point part on the z-axis, and that they are otherwise supported on a set of concentric cylinder surfaces around this axis. For SCD tilings with additional properties, more detailed results are given.Comment: 11 pages, 2 figures; Accepted for Journal of Mathematical Physic

Liquid‐Liquid Equilibrium and Interfacial Properties of the System Water + Hexylacetate + 1‐Hexanol

Experimental and theoretical investigations of the phase diagram and the interfacial tension are presented. The theoretical framework was able to predict the phase behavior and the interfacial tension with a high accuracy, where only binary experimental data enter the model parameter. The theory permits the calculation of the concentration profiles across the interface. The profiles show that 1-hexanol will be enriched, which was expected. In same circumstances a competition between hexylacetate and 1-hexanol was figured out leading to slight minima in the profile of 1-hexanol

The consequences of SU(3) colorsingletness, Polyakov Loop and Z(3) symmetry on a quark-gluon gas

Based on quantum statistical mechanics we show that the $SU(3)$ color singlet ensemble of a quark-gluon gas exhibits a $Z(3)$ symmetry through the normaized character in fundamental representation and also becomes equivalent, within a stationary point approximation, to the ensemble given by Polyakov Loop. Also Polyakov Loop gauge potential is obtained by considering spatial gluons along with the invariant Haar measure at each space point. The probability of the normalized character in $SU(3)$ vis-a-vis Polyakov Loop is found to be maximum at a particular value exhibiting a strong color correlation. This clearly indicates a transition from a color correlated to uncorrelated phase or vise-versa. When quarks are included to the gauge fields, a metastable state appears in the temperature range $145\le T({\rm{MeV}}) \le 170$ due to the explicit $Z(3)$ symmetry breaking in the quark-gluon system. Beyond $T\ge 170$ MeV the metastable state disappears and stable domains appear. At low temperature a dynamical recombination of ionized $Z(3)$ color charges to a color singlet $Z(3)$ confined phase is evident along with a confining background that originates due to circulation of two virtual spatial gluons but with conjugate $Z(3)$ phases in a closed loop. We also discuss other possible consequences of the center domains in the color deconfined phase at high temperature.Comment: Version published in J. Phys.