Integral circulant graphs of prime power order with maximal energy

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count n and a set D of divisors of n in such a way that they have vertex set Zn and edge set {{a, b} : a, b in Zn; gcd(a - b, n) in D}. Using tools from convex optimization, we study the maximal energy among all integral circulant graphs of prime power order ps and varying divisor sets D. Our main result states that this maximal energy approximately lies between s(p - 1)p^(s-1) and twice this value. We construct suitable divisor sets for which the energy lies in this interval. We also characterize hyperenergetic integral circulant graphs of prime power order and exhibit an interesting topological property of their divisor sets.Comment: 25 page

A New Recursion Relation for the 6j-Symbol

The 6j-symbol is a fundamental object from the re-coupling theory of SU(2) representations. In the limit of large angular momenta, its asymptotics is known to be described by the geometry of a tetrahedron with quantized lengths. This article presents a new recursion formula for the square of the 6j-symbol. In the asymptotic regime, the new recursion is shown to characterize the closure of the relevant tetrahedron. Since the 6j-symbol is the basic building block of the Ponzano-Regge model for pure three-dimensional quantum gravity, we also discuss how to generalize the method to derive more general recursion relations on the full amplitudes.Comment: 10 pages, v2: title and introduction changed, paper re-structured; Annales Henri Poincare (2011

Fingerprinting fluid source in calcite veins: combining LA-ICP-MS U-Pb calcite dating with trace elements and clumped isotope palaeothermometry

Application of geochemical proxies to vein minerals - particularly calcite - can fingerprint the source of fluids controlling various important geological processes from seismicity to geothermal systems. Determining fluid source, e.g. meteoric, marine, magmatic or metamorphic waters, can be challenging when using only trace elements and stable isotopes as different fluids can have overlapping geochemical characteristics, such as δ18O. In this contribution we show that by combining the recently developed LA-ICP-MS U-Pb calcite geochronometer with stable isotopes (including clumped isotope palaeothermometry) and trace element analysis, the fluid source of veins can be more readily determined. Calcite veins hosted in the Devonian Montrose Volcanic Formation at Lunan Bay in the Midland Valley Terrane of Central Scotland were used as a case study. δD values of fluid inclusions in the calcite, and parent fluid δ18O values reconstructed from clumped isotope palaeothermometry, gave values which could represent a range of fluid sources: metamorphic or magmatic fluids, or surface waters which had undergone much fluid-rock interaction. Trace elements showed no distinctive patterns and shed no further light on fluid source. LA-ICP-MS U-Pb dating determined the vein calcite precipitation age – 318±30 Ma – which rule out metamorphic or magmatic fluid sources as no metamorphic or magmatic activity was occurring in the area at this time. The vein fluid source was therefore a surface water (meteoric based on paleogeographic reconstruction) which had undergone significant water-rock interaction. This study highlights the importance of combining the recently developed LA-ICP-MS U-Pb calcite geochronometer with stable isotopes and trace elements to help determine fluid sources of veins, and indeed any geological feature where calcite precipitated from a fluid that may have resided in the crust for a period of time (e.g. fault precipitates or cements)

CsI(Tl) for WIMP dark matter searches

We report a study of CsI(Tl) scintillator to assess its applicability in experiments to search for dark matter particles. Measurements of the mean scintillation pulse shapes due to nuclear and electron recoils have been performed. We find that, as with NaI(Tl), pulse shape analysis can be used to discriminate between electron and nuclear recoils down to 4 keV. However, the discrimination factor is typically (10-15)% better than in NaI(Tl) above 4 keV. The quenching factor for caesium and iodine recoils was measured and found to increase from 11% to ~17% with decreasing recoil energy from 60 to 12 keV. Based on these results, the potential sensitivity of CsI(Tl) to dark matter particles in the form of neutralinos was calculated. We find an improvement over NaI(Tl) for the spin independent WIMP-nucleon interactions up to a factor of 5 assuming comparable electron background levels in the two scintillators.Comment: 16 pages, 8 figures, to be published in Nucl. Instrum. and Meth. in Phys. Res.

Effects of surface plasma treatment on threshold voltage hysteresis and instability in metal-insulator-semiconductor (MIS) AlGaN/GaN heterostructure HEMTs

In a bid to understand the commonly observed hysteresis in the threshold voltage (VTH) in AlGaN/GaN metal-insulator-semiconductor high electron mobility transistors during forward gate bias stress, we have analyzed a series of measurements on devices with no surface treatment and with two different plasma treatments before the in-situ Al2O3 deposition. The observed changes between samples were quasi-equilibrium VTH, forward bias related VTH hysteresis, and electrical response to reverse bias stress. To explain these effects, a disorder induced gap state model, combined with a discrete level donor, at the dielectric/semiconductor interface was employed. Technology Computer-Aided Design modeling demonstrated the possible differences in the interface state distributions that could give a consistent explanation for the observations

Distinguishing Among Strong Decay Models

Two competing models for strong hadronic decays, the $^3P_0$ and $^3S_1$ models, are currently in use. Attempts to rule out one or the other have been hindered by a poor understanding of final state interactions and by ambiguities in the treatment of relativistic effects. In this article we study meson decays in both models, focussing on certain amplitude ratios for which the relativistic uncertainties largely cancel out (notably the $S/D$ ratios in $b_1\rightarrow\pi\omega$ and $a_1\rightarrow\pi\rho$), and using a Quark Born Formalism to estimate the final state interactions. We find that the $^3P_0$ model is strongly favoured. In addition, we predict a $P/F$ amplitude ratio of $1.6\pm .2$ for the decay $\pi_2\rightarrow\pi\rho$. We also study the parameter-dependence of some individual amplitudes (as opposed to amplitude ratios), in an attempt to identify a ``best'' version of the $^3P_0$ model.Comment: 20 pages, uuencoded postscript file with 7 figures, MIT-CTP-2295; CMU-HEP94-1

Spin Foam Perturbation Theory for Three-Dimensional Quantum Gravity

We formulate the spin foam perturbation theory for three-dimensional Euclidean Quantum Gravity with a cosmological constant. We analyse the perturbative expansion of the partition function in the dilute-gas limit and we argue that the Baez conjecture stating that the number of possible distinct topological classes of perturbative configurations is finite for the set of all triangulations of a manifold, is not true. However, the conjecture is true for a special class of triangulations which are based on subdivisions of certain 3-manifold cubulations. In this case we calculate the partition function and show that the dilute-gas correction vanishes for the simplest choice of the volume operator. By slightly modifying the dilute-gas limit, we obtain a nonvanishing correction which is related to the second order perturbative correction. By assuming that the dilute-gas limit coupling constant is a function of the cosmological constant, we obtain a value for the partition function which is independent of the choice of the volume operator.Comment: Revised version. We prove that the first-order volume expectation value vanishes and therefore we consider a dilute gas limit based on the second-order perturbative correction. 32 pages, 16 Figure

A Measurement of Time-Averaged Aerosol Optical Depth using Air-Showers Observed in Stereo by HiRes

Air fluorescence measurements of cosmic ray energy must be corrected for attenuation of the atmosphere. In this paper we show that the air-showers themselves can yield a measurement of the aerosol attenuation in terms of optical depth, time-averaged over extended periods. Although the technique lacks statistical power to make the critical hourly measurements that only specialized active instruments can achieve, we note the technique does not depend on absolute calibration of the detector hardware, and requires no additional equipment beyond the fluorescence detectors that observe the air showers. This paper describes the technique, and presents results based on analysis of 1258 air-showers observed in stereo by the High Resolution Fly's Eye over a four year span.Comment: 7 pages, 3 figures, accepted for publication by Astroparticle Physics Journa

Cosmological Models with Fractional Derivatives and Fractional Action Functional

Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional cosmological models in both cases is given.Comment: 14 page