Exact Solution for the Critical State in Thin Superconductor Strips with Field Dependent or Anisotropic Pinning

An exact analytical solution is given for the critical state problem in long thin superconductor strips in a perpendicular magnetic field, when the critical current density j_c(B) depends on the local induction B according to a simple three-parameter model. This model describes both isotropic superconductors with this j_c(B) dependence, but also superconductors with anisotropic pinning described by a dependence j_c(theta) where theta is the tilt angle of the flux lines away from the normal to the specimen plane

Quasi-Monte Carlo rules for numerical integration over the unit sphere S2\mathbb{S}^2

We study numerical integration on the unit sphere $\mathbb{S}^2 \subset \mathbb{R}^3$ using equal weight quadrature rules, where the weights are such that constant functions are integrated exactly. The quadrature points are constructed by lifting a $(0,m,2)$-net given in the unit square $[0,1]^2$ to the sphere $\mathbb{S}^2$ by means of an area preserving map. A similar approach has previously been suggested by Cui and Freeden [SIAM J. Sci. Comput. 18 (1997), no. 2]. We prove three results. The first one is that the construction is (almost) optimal with respect to discrepancies based on spherical rectangles. Further we prove that the point set is asymptotically uniformly distributed on $\mathbb{S}^2$. And finally, we prove an upper bound on the spherical cap $L_2$-discrepancy of order $N^{-1/2} (\log N)^{1/2}$ (where $N$ denotes the number of points). This slightly improves upon the bound on the spherical cap $L_2$-discrepancy of the construction by Lubotzky, Phillips and Sarnak [Comm. Pure Appl. Math. 39 (1986), 149--186]. Numerical results suggest that the $(0,m,2)$-nets lifted to the sphere $\mathbb{S}^2$ have spherical cap $L_2$-discrepancy converging with the optimal order of $N^{-3/4}$

A Biased Random Key Genetic Algorithm Approach for Unit Commitment Problem

A Biased Random Key Genetic Algorithm (BRKGA) is proposed to find solutions for the unit commitment problem. In this problem, one wishes to schedule energy production on a given set of thermal generation units in order to meet energy demands at minimum cost, while satisfying a set of technological and spinning reserve constraints. In the BRKGA, solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0, 1]. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as in the crossover strategy. Tests have been performed on benchmark large-scale power systems of up to 100 units for a 24 hours period. The results obtained have shown the proposed methodology to be an effective and efficient tool for finding solutions to large-scale unit commitment problems. Furthermore, from the comparisons made it can be concluded that the results produced improve upon some of the best known solutions

Studies of the Cabbibo-Suppressed Decays D+→π0ℓ+νD^+ \to \pi^0 \ell^+ \nu and D+→ηe+νeD^+ \to \eta e^+ \nu_e

Using 4.8 fb$^{-1}$ of data taken with the CLEO II detector, the branching fraction for the Cabibbo-suppressed decay $D^+\to\pi^0\ell^+\nu$ measured relative to the Cabibbo favored decay $D^+\to\bar{K^0}\ell^+\nu$ is found to be $0.046\pm 0.014\pm 0.017$. Using $V_{cs}$ and $V_{cd}$ from unitarity constraints, we determine $| f_+^{\pi}(0)/f_+^K(0)|^2=0.9\pm 0.3\pm 0.3$ We also present a 90% confidence level upper limit for the branching ratio of the decay $D^+ \to \eta e^+\nu_e$ relative to that for $D^+ \to \pi^0 e^+\nu_e$ of 1.5.Comment: 10 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Genome-wide association and Mendelian randomisation analysis provide insights into the pathogenesis of heart failure

Heart failure (HF) is a leading cause of morbidity and mortality worldwide. A small proportion of HF cases are attributable to monogenic cardiomyopathies and existing genome-wide association studies (GWAS) have yielded only limited insights, leaving the observed heritability of HF largely unexplained. We report results from a GWAS meta-analysis of HF comprising 47,309 cases and 930,014 controls. Twelve independent variants at 11 genomic loci are associated with HF, all of which demonstrate one or more associations with coronary artery disease (CAD), atrial fibrillation, or reduced left ventricular function, suggesting shared genetic aetiology. Functional analysis of non-CAD-associated loci implicate genes involved in cardiac development (MYOZ1, SYNPO2L), protein homoeostasis (BAG3), and cellular senescence (CDKN1A). Mendelian randomisation analysis supports causal roles for several HF risk factors, and demonstrates CAD-independent effects for atrial fibrillation, body mass index, and hypertension. These findings extend our knowledge of the pathways underlying HF and may inform new therapeutic strategies