Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property

Freshwater gobies 30 million years ago: New insights into character evolution and phylogenetic relationships of dagger Pirskeniidae (Gobioidei, Teleostei)

The modern Gobioidei (Teleostei) comprise eight families, but the extinct dagger Pirskeniidae from the lower Oligocene of the Czech Republic indicate that further families may have existed in the past. However, the validity of the dagger Pirskeniidae has been questioned and its single genus dagger Pirskeniushas been assigned to the extant family Eleotridae in previous works. The objective of this study is to clarify the status of the dagger Pirskeniidae. Whether or not the dagger Pirskeniidae should be synonymised with the Eleotridae is also interesting from a biogeographical point of view as Eleotridae is not present in Europe or the Mediterranean Sea today. We present new specimens and re-examine the material on which the two known species of dagger Pirskeniusare based (dagger P.diatomaceusObrhelova, 1961;dagger P.radoniPrikryl, 2014). To provide a context for phylogenetically informative characters related to the palatine and the branchiostegal rays, three early-branching gobioids (Rhyacichthys,Protogobius,Perccottus), an eleotrid (Eleotris) and a gobiid (Gobius) were subjected to micro-CT analysis. The new data justify revalidation of the family dagger Pirskeniidae, and a revised diagnosis is presented for both dagger Pirskeniusand dagger Pirskeniidae. Moreover, we provide for the first time an attempt to relate a fossil gobioid to extant taxa based on phylogenetic analysis. The results indicate a sister-group relationship of dagger Pirskeniidae to the Thalasseleotrididae + Gobiidae + Oxudercidae clade. Considering the fossil record, the arrival of gobioids in freshwater habitats in the early Oligocene apparently had generated new lineages that finally were not successful and became extinct shortly after they had diverged. There is currently no evidence that the Eleotridae was present in the European ichthyofauna in the past

First Measurement of Antikaon Phase-Space Distributions in Nucleus-Nucleus Collisions at Subthreshold Beam Energies

Differential production cross sections of K$^-$ and K$^+$ mesons have been measured as function of the polar emission angle in Ni+Ni collisions at a beam energy of 1.93 AGeV. In near-central collisions, the spectral shapes and the widths of the rapidity distributions of K$^-$ and K$^+$ mesons are in agreement with the assumption of isotropic emission. In non-central collisions, the K$^-$ and K$^+$ rapidity distributions are broader than expected for a single thermal source. In this case, the polar angle distributions are strongly forward-backward peaked and the nonisotropic contribution to the total yield is about one third both for K$^+$ and K$^-$ mesons. The K$^-$/K$^+$ ratio is found to be about 0.03 independent of the centrality of the reaction. This value is significantly larger than predicted by microscopic transport calculations if in-medium modifications of K mesons are neglected.Comment: 16 pages, 3 figures, accepted for publication in Physics Letters

Measurement of the Total Cross Section for the Reaction p + p → p + p + pio

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

A Precision Measurement of pp Elastic Scattering Cross Sections at Intermediate Energies

We have measured differential cross sections for \pp elastic scattering with internal fiber targets in the recirculating beam of the proton synchrotron COSY. Measurements were made continuously during acceleration for projectile kinetic energies between 0.23 and 2.59 GeV in the angular range $30 \leq \theta_{c.m.} \leq 90$ deg. Details of the apparatus and the data analysis are given and the resulting excitation functions and angular distributions presented. The precision of each data point is typically better than 4%, and a relative normalization uncertainty of only 2.5% within an excitation function has been reached. The impact on phase shift analysis as well as upper bounds on possible resonant contributions in lower partial waves are discussed.Comment: 23 pages 29 figure

A versatile method for simulating pp -> ppe+e- and dp -> pne+e-p_spec reactions

We have developed a versatile software package for the simulation of di-electron production in $pp$ and $dp$ collisions at SIS energies. Particular attention has been paid to incorporate different descriptions of the Dalitz decay $\Delta \to N e^+e^-$ via a common interface. In addition, suitable parameterizations for the virtual bremsstrahlung process $NN \to NN e^+e^-$ based on one-boson exchange models have been implemented. Such simulation tools with high flexibility of the framework are important for the interpretation of the di-electron data taken with the HADES spectrometer and the design of forthcoming experiments