In a previous Letter Borsanyi et al., Phys. Rev. Lett. 111, 252001 (2013) we determined the isospin mass splittings of the baryon octet from a lattice calculation based on N_{f}=2+1 QCD simulations ...to which QED effects have been added in a partially quenched setup. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. Our ensembles include 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. For the parameter which quantifies violations to Dashen's theorem, we obtain ϵ=0.73(2)(5)(17), where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, m_{u}=2.27(6)(5)(4) and m_{d}=4.67(6)(5)(4) MeV in the modified minimal subtraction scheme at 2 GeV and the isospin breaking ratios m_{u}/m_{d}=0.485(11)(8)(14), R=38.2(1.1)(0.8)(1.4), and Q=23.4(0.4)(0.3)(0.4). Our results exclude the m_{u}=0 solution to the strong CP problem by more than 24 standard deviations.
While electromagnetic and up-down quark mass difference effects on octet baryon masses are very small, they have important consequences. The stability of the hydrogen atom against beta decay is a ...prominent example. Here, we include these effects by adding them to valence quarks in a lattice QCD calculation based on Nf=2+1 simulations with five lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. This allows us to gain control over all systematic errors, except for the one associated with neglecting electromagnetism in the sea. We compute the octet baryon isomultiplet mass splittings, as well as the individual contributions from electromagnetism and the up-down quark mass difference. Our results for the total splittings are in good agreement with experiment.
The numerical and computational aspects of the overlap formalism in lattice quantum chromodynamics are extremely demanding due to a matrix–vector product that involves the sign function of the ...Hermitian Wilson matrix. In this paper we investigate several methods to compute the product of the matrix sign-function with a vector, in particular Lanczos based methods and partial fraction expansion methods. Our goal is two-fold: we give realistic comparisons between known methods together with novel approaches and we present error bounds which allow to guarantee a given accuracy when terminating the Lanczos method and the multishift-CG solver, applied within the partial fraction expansion methods.
Recent developments in European supercomputing are reviewed covering both the latest hardware trends and the increasing difficulties faced by scientists in utilising these machines to perform ...large-scale numerical simulations. These challenges are reflected in the large number of international initiatives which have come into being over the last few years, founded in anticipation of exascale hardware which is foreseen within the next decade. The role of a key institution in supercomputing within these programmes is described using the example of the Jülich Supercomputing Centre (JSC), and progress in setting up its own community-oriented support units for scientific computing – Simulation Laboratories – is reported on. Finally, an assessment is made of some common grand challenges and their suitability for scaling to exaflop-scale computation.
Structuring of glassy carbon (GC) can be performed by various methods such as sawing, laser ablation, and reactive ion etching (RIE). Laser machining with a tripled Nd:YAG laser at an irradiation ...wavelength of 355 nm allows the fabrication of V-shaped channels with depths >600 μm and aspect ratios >5. This method is very flexible for rapid prototyping, but is comparatively slow due to the sequential machining. A complete flowfield consisting of 100 parallel channels with a depth of 250 μm and a top width of 50 μm was prepared by direct laser ablation and tested in a micro fuel cell. As an alternative, a novel process combining laser structuring of a metal mask with subsequent reactive ion etching was developed. The quality of the metal layer and the ablation behavior are strongly influenced by the metal adhesion, which depends on the GC pretreatment and the deposition technique. Reactive ion etching of glassy carbon can be performed with etch rates of ≈40 μm h−1, but the high pressure conditions of 100 mTorr (0.13 mbar) limit the aspect ratio to <1.5 due to pronounced underetching. The fabrication of structures with aspect ratios >4 and etch rates of ≈10 μm h−1 is possible with the use of alternative etching devices with different design or plasma sources.
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