Mock Catalogs for UHECR Studies

We provide realistic mock-catalogs of cosmic rays above 40 EeV, for a pure proton composition, assuming their sources are a random subset of ordinary galaxies in a simulated, volume-limited survey, for various choices of source density: 10^-3.5 Mpc^-3, 10^-4.0 Mpc^-3 and 10^-4.5 Mpc^-3. The spectrum at the source is taken to be E^-2.3 and the effects of cosmological redshifting as well as photo-pion and e^+ e^- energy losses are included.Comment: 7 pages, 4 figure

Eigenfunctions for singular fully non linear equations in unbounded domains

In this paper we prove some Harnack inequality for fully non linear degenerate elliptic equations, in the two dimensional case, extending the results of Davila Felmer and Quaas in the singular case but in all dimensions. We then apply this result for the existence of an eigenfunction in smooth bounded domain.Comment: 30 pages 2 figure

Cost-utility of transcatheter aortic valve implantation for inoperable patients with severe aortic stenosis treated by medical management: a UK cost-utility analysis based on patient-level data from the ADVANCE study.

OBJECTIVE: To use patient-level data from the ADVANCE study to evaluate the cost-effectiveness of transcatheter aortic valve implantation (TAVI) compared to medical management (MM) in patients with severe aortic stenosis from the perspective of the UK NHS. METHODS: A published decision-analytic model was adapted to include information on TAVI from the ADVANCE study. Patient-level data informed the choice as well as the form of mathematical functions that were used to model all-cause mortality, health-related quality of life and hospitalisations. TAVI-related resource use protocols were based on the ADVANCE study. MM was modelled on publicly available information from the PARTNER-B study. The outcome measures were incremental cost-effectiveness ratios (ICERs) estimated at a range of time horizons with benefits expressed as quality-adjusted life-years (QALY). Extensive sensitivity/subgroup analyses were undertaken to explore the impact of uncertainty in key clinical areas. RESULTS: Using a 5-year time horizon, the ICER for the comparison of all ADVANCE to all PARTNER-B patients was £13 943 per QALY gained. For the subset of ADVANCE patients classified as high risk (Logistic EuroSCORE >20%) the ICER was £17 718 per QALY gained). The ICER was below £30 000 per QALY gained in all sensitivity analyses relating to choice of MM data source and alternative modelling approaches for key parameters. When the time horizon was extended to 10 years, all ICERs generated in all analyses were below £20 000 per QALY gained. CONCLUSION: TAVI is highly likely to be a cost-effective treatment for patients with severe aortic stenosis

Probing the Circumgalactic Medium at High-Redshift Using Composite BOSS Spectra of Strong Lyman-alpha Forest Absorbers

We present composite spectra constructed from a sample of 242,150 Lyman-alpha (Lya) forest absorbers at redshifts 2.4<z<3.1 identified in quasar spectra from the Baryon Oscillation Spectroscopic Survey (BOSS) as part of Data Release 9 of the Sloan Digital Sky Survey III. We select forest absorbers by their flux in bins 138 km/s wide (approximately the size of the BOSS resolution element). We split these absorbers into five samples spanning the range of flux -0.05 < F<0.45. Tests on a smaller sample of high-resolution spectra show that our three strongest absorption bins would probe circumgalactic regions (projected separation < 300 proper kpc and |Delta v| < 300km/s) in about 60% of cases for very high signal-to-noise ratio. Within this subset, weakening Lya absorption is associated with decreasing purity of circumgalactic selection once BOSS noise is included. Our weaker two Lya absorption samples are dominated by the intergalactic medium. We present composite spectra of these samples and a catalogue of measured absorption features from HI and 13 metal ionization species, all of which we make available to the community. We compare measurements of seven Lyman series transitions in our composite spectra to single line models and obtain further constraints from their associated excess Lyman limit opacity. This analysis provides results consistent with column densities over the range 14.4 <~ Log (N_HI) <~ 16.45. We compare our measurements of metal absorption to a variety of simple single-line, single-phase models for a preliminary interpretation. Our results imply clumping on scales down to ~30 pc and near-solar metallicities in the circumgalactic samples, while high-ionization metal absorption consistent with typical IGM densities and metallicities is visible in all samples.Comment: 23 pages, 15 figures, 5 tables, link to downloadable data included. Accepted by MNRAS 2014 March 20. New sections 3.4 and 6.1 limiting the occurrence and impact of Lyman limit system

Nonlinear Eigenvalues and Bifurcation Problems for Pucci's Operator

In this paper we extend existing results concerning generalized eigenvalues of Pucci's extremal operators. In the radial case, we also give a complete description of their spectrum, together with an equivalent of Rabinowitz's Global Bifurcation Theorem. This allows us to solve equations involving Pucci's operators

A new critical curve for the Lane-Emden system

We study stable positive radially symmetric solutions for the Lane-Emden system $-\Delta u=v^p$ in $\R^N$, $-\Delta v=u^q$ in $\R^N$, where $p,q\geq 1$. We obtain a new critical curve that optimally describes the existence of such solutions.Comment: 13 pages, 1 figur

Development and characterisation of pressed packaging solutions for high-temperature high-reliability SiC power modules

SiC is a wide bandgap semiconductor with better electrothermal properties than silicon, including higher temperature of operation, higher breakdown voltage, lower losses and the ability to switch at higher frequencies. However, the power cycling performance of SiC devices in traditional silicon packaging systems is in need of further investigation since initial studies have shown reduced reliability. These traditional packaging systems have been developed for silicon, a semiconductor with different electrothermal and thermomechanical properties from SiC, hence the stresses on the different components of the package will change. Pressure packages, a packaging alternative where the weak elements of the traditional systems like wirebonds are removed, have demonstrated enhanced reliability for silicon devices however, there has not been much investigation on the performance of SiC devices in press-pack assemblies. This will be important for high power applications where reliability is critical. In this paper, SiC Schottky diodes in pressure packages have been evaluated, including the electrothermal characterisation for different clamping forces and contact materials, the thermal impedance evaluation and initial thermal cycling studies, focusing on the use of aluminium graphite as contact material

Baryon Acoustic Oscillations in the Ly{\alpha} forest of BOSS DR11 quasars

We report a detection of the baryon acoustic oscillation (BAO) feature in the flux-correlation function of the Ly{\alpha} forest of high-redshift quasars with a statistical significance of five standard deviations. The study uses 137,562 quasars in the redshift range $2.1\le z \le 3.5$ from the Data Release 11 (DR11) of the Baryon Oscillation Spectroscopic Survey (BOSS) of SDSS-III. This sample contains three times the number of quasars used in previous studies. The measured position of the BAO peak determines the angular distance, $D_A(z=2.34)$ and expansion rate, $H(z=2.34)$, both on a scale set by the sound horizon at the drag epoch, $r_d$. We find $D_A/r_d=11.28\pm0.65(1\sigma)^{+2.8}_{-1.2}(2\sigma)$ and $D_H/r_d=9.18\pm0.28(1\sigma)\pm0.6(2\sigma)$ where $D_H=c/H$. The optimal combination, $\sim D_H^{0.7}D_A^{0.3}/r_d$ is determined with a precision of $\sim2\%$. For the value $r_d=147.4~{\rm Mpc}$, consistent with the CMB power spectrum measured by Planck, we find $D_A(z=2.34)=1662\pm96(1\sigma)~{\rm Mpc}$ and $H(z=2.34)=222\pm7(1\sigma)~{\rm km\,s^{-1}Mpc^{-1}}$. Tests with mock catalogs and variations of our analysis procedure have revealed no systematic uncertainties comparable to our statistical errors. Our results agree with the previously reported BAO measurement at the same redshift using the quasar-Ly{\alpha} forest cross-correlation. The auto-correlation and cross-correlation approaches are complementary because of the quite different impact of redshift-space distortion on the two measurements. The combined constraints from the two correlation functions imply values of $D_A/r_d$ and $D_H/r_d$ that are, respectively, 7% low and 7% high compared to the predictions of a flat $\Lambda$CDM cosmological model with the best-fit Planck parameters. With our estimated statistical errors, the significance of this discrepancy is $\approx 2.5\sigma$.Comment: Accepted for publication in A&A. 17 pages, 18 figure

Homogenization of weakly coupled systems of Hamilton--Jacobi equations with fast switching rates

We consider homogenization for weakly coupled systems of Hamilton--Jacobi equations with fast switching rates. The fast switching rate terms force the solutions converge to the same limit, which is a solution of the effective equation. We discover the appearance of the initial layers, which appear naturally when we consider the systems with different initial data and analyze them rigorously. In particular, we obtain matched asymptotic solutions of the systems and rate of convergence. We also investigate properties of the effective Hamiltonian of weakly coupled systems and show some examples which do not appear in the context of single equations.Comment: final version, to appear in Arch. Ration. Mech. Ana