Uniform and optimal schemes for stiff initial-value problems

AbstractWe formulate a class of difference schemes for stiff initial-value problems, with a small parameter ϵ multiplying the first derivative. We derive necessary conditions for uniform convergence with respect to the small parameter ϵ, that is the solution of the difference scheme uih satisfies |uih−u(xi)| ⪕ Ch, where C is independent of h and ϵ. We also derive sufficient conditions for uniform convergence and show that a subclass of schemes is also optimal in the sense that |uih−u(xi)| ⪕ C min (h, ϵ). Finally, we show that this class contains higher-order schemes

A comparative study of high-field diamagnetic fluctuations in deoxygenated YBa2Cu3O(7-x) and polycrystalline (Bi-Pb)2Sr2Ca3O(10)

We studied three single crystals of YBa2Cu3O{7-x} with Tc= 62.5, 52, and 41 K, and a textured specimen of (Bi-Pb)2Sr2Ca2Cu3O10 with Tc=108 K, for H//c axis. The reversible data were interpreted in terms of 2D lowest-Landau-level fluctuation theory. The data were fit well by the 2D LLL expression for magnetization obtained by Tesanovic etal., producing reasonable values of kappa but larger values of dHc2/dT. Universality was studied by obtaining a simultaneous scaling of Y123 data and Bi2223. An expression for the 2D x-axis LLL scaling factor used to obtain the simultaneous scaling was extracted from theory, and compared with the experimental values. The comparison between the values of the x-axis produced a deviation of 40% which suggests that the hypothesis of universality of the 2D-LLL fluctuations is not supported by the studied samples. We finaly observe that Y123 magnetization data for temperatures above $T_c$ obbey a universal scaling obtained for the diamagnetic fluctuation magnetization from a theory considering non-local field effects. The same scaling was not obbeyed by the corresponding magnetization calculated from the two-dimensional lowest-Landau-level theory.Comment: 7 pages 5 figures, accept in Journ. Low Temp. Phy

Weak Localization Effect in Superconductors by Radiation Damage

Large reductions of the superconducting transition temperature $T_{c}$ and the accompanying loss of the thermal electrical resistivity (electron-phonon interaction) due to radiation damage have been observed for several A15 compounds, Chevrel phase and Ternary superconductors, and $\rm{NbSe_{2}}$ in the high fluence regime. We examine these behaviors based on the recent theory of weak localization effect in superconductors. We find a good fitting to the experimental data. In particular, weak localization correction to the phonon-mediated interaction is derived from the density correlation function. It is shown that weak localization has a strong influence on both the phonon-mediated interaction and the electron-phonon interaction, which leads to the universal correlation of $T_{c}$ and resistance ratio.Comment: 16 pages plus 3 figures, revtex, 76 references, For more information, Plesse see http://www.fen.bilkent.edu.tr/~yjki

Grids of stellar models with rotation VII : models from 0.8 to 300 M⊙ at supersolar metallicity (Z = 0.020)

We present a grid of stellar models at supersolar metallicity (Z = 0.020) extending the previous grids of Geneva models at solar and sub-solar metallicities. A metallicity of Z = 0.020 was chosen to match that of the inner Galactic disc. A modest increase of 43 per cent (= 0.02/0.014) in metallicity compared to solar models means that the models evolve similarly to solar models but with slightly larger mass-loss. Mass-loss limits the final total masses of the supersolar models to 35 M⊙ even for stars with initial masses much larger than 100 M⊙. Mass-loss is strong enough in stars above 20 M⊙ for rotating stars (25 M⊙ for non-rotating stars) to remove the entire hydrogen-rich envelope. Our models thus predict SNII below 20 M⊙ for rotating stars (25 M⊙ for non-rotating stars) and SNIb (possibly SNIc) above that. We computed both isochrones and synthetic clusters to compare our supersolar models to the Westerlund 1 (Wd1) massive young cluster. A synthetic cluster combining rotating and non-rotating models with an age spread between log10(age/yr) = 6.7 and 7.0 is able to reproduce qualitatively the observed populations of WR, RSG, and YSG stars in Wd1, in particular their simultaneous presence at log10(L/L⊙) = 5–5.5. The quantitative agreement is imperfect and we discuss the likely causes: synthetic cluster parameters, binary interactions, mass-loss and their related uncertainties. In particular, mass-loss in the cool part of the HRD plays a key role

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results