BDDC and FETI-DP under Minimalist Assumptions

The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary simple abstract form. It is shown that their properties can be obtained from only on a very small set of algebraic assumptions. The presentation is purely algebraic and it does not use any particular definition of method components, such as substructures and coarse degrees of freedom. It is then shown that P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC preconditioned operators are of the same algebraic form, and the standard condition number bound carries over to arbitrary abstract operators of this form. The equality of eigenvalues of BDDC and FETI-DP also holds in the minimalist abstract setting. The abstract framework is explained on a standard substructuring example.Comment: 11 pages, 1 figure, also available at http://www-math.cudenver.edu/ccm/reports

Refined saddle-point preconditioners for discretized Stokes problems

This paper is concerned with the implementation of efficient solution algorithms for elliptic problems with constraints. We establish theory which shows that including a simple scaling within well-established block diagonal preconditioners for Stokes problems can result in significantly faster convergence when applying the preconditioned MINRES method. The codes used in the numerical studies are available online

Microbial community dynamics in soil depth profiles over 120,000 years of ecosystem development

Along a long-term ecosystem development gradient, soil nutrient contents and mineralogical properties change, therefore probably altering soil microbial communities. However, knowledge about the dynamics of soil microbial communities during long-term ecosystem development including progressive and retrogressive stages is limited, especially in mineral soils. Therefore, microbial abundances (quantitative PCR) and community composition (pyrosequencing) as well as their controlling soil properties were investigated in soil depth profiles along the 120,000 years old Franz Josef chronosequence (New Zealand). Additionally, in a microcosm incubation experiment the effects of particular soil properties, i.e., soil age, soil organic matter fraction (mineral-associated vs. particulate), O2 status, and carbon and phosphorus additions, on microbial abundances (quantitative PCR) and community patterns (T-RFLP) were analyzed. The archaeal to bacterial abundance ratio not only increased with soil depth but also with soil age along the chronosequence, coinciding with mineralogical changes and increasing phosphorus limitation. Results of the incubation experiment indicated that archaeal abundances were less impacted by the tested soil parameters compared to Bacteria suggesting that Archaea may better cope with mineral-induced substrate restrictions in subsoils and older soils. Instead, archaeal communities showed a soil age-related compositional shift with the Bathyarchaeota, that were frequently detected in nutrient-poor, low-energy environments, being dominant at the oldest site. However, bacterial communities remained stable with ongoing soil development. In contrast to the abundances, the archaeal compositional shift was associated with the mineralogical gradient. Our study revealed, that archaeal and bacterial communities in whole soil profiles are differently affected by long-term soil development with archaeal communities probably being better adapted to subsoil conditions, especially in nutrient-depleted old soils

Cross Section Measurements of Charged Pion Photoproduction in Hydrogen and Deuterium from 1.1 to 5.5 GeV

The differential cross section for the gamma +n --> pi- + p and the gamma + p --> pi+ n processes were measured at Jefferson Lab. The photon energies ranged from 1.1 to 5.5 GeV, corresponding to center-of-mass energies from 1.7 to 3.4 GeV. The pion center-of-mass angles varied from 50 degree to 110 degree. The pi- and pi+ photoproduction data both exhibit a global scaling behavior at high energies and high transverse momenta, consistent with the constituent counting rule prediction and the existing pi+ data. The data suggest possible substructure of the scaling behavior, which might be oscillations around the scaling value. The data show an enhancement in the scaled cross section at center-of-mass energy near 2.2 GeV. The differential cross section ratios at high energies and high transverse momenta can be described by calculations based on one-hard-gluon-exchange diagrams.Comment: 18 pages, 19 figure

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

The HADES Tracking System

The tracking system of the dielectron spectrometer HADES at GSI Darmstadt is formed out of 24 low-mass, trapezoidal multi-layer drift chambers providing in total about 30 square meter of active area. Low multiple scattering in the in total four planes of drift chambers before and after the magnetic field is ensured by using helium-based gas mixtures and aluminum cathode and field wires. First in-beam performance results are contrasted with expectations from simulations. Emphasis is placed on the energy loss information, exploring its relevance regarding track recognition.Comment: 6 pages, 4 figures, presented at the 10th Vienna Conference on Instrumentation, Vienna, February 2004, to be published in NIM A (special issue

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

Deep sub-threshold Ξ−\Xi^- production in Ar+KCl reactions at 1.76A GeV

We report first results on a deep sub-threshold production of the doubly strange hyperon $\Xi^-$ in a heavy-ion reaction. At a beam energy of 1.76A GeV the reaction Ar+KCl was studied with the High Acceptance Di-Electron Spectrometer (HADES) at SIS18/GSI. A high-statistics and high-purity $\Lambda$ sample was collected, allowing for the investigation of the decay channel $\Xi^- \to \Lambda \pi^-$. The deduced $\Xi^-/(\Lambda+\Sigma^0)$ production ratio of $(5.6 \pm 1.2 ^{+1.8}_{-1.7})\cdot 10^{-3}$ is significantly larger than available model predictions.Comment: 4 pages, including 4 figure

An upper limit on hypertriton production in collisions of Ar(1.76 AGeV)+KCl

A high-statistic data sample of Ar(1.76 AGeV)+KCl events recorded with HADES is used to search for a hypertriton signal. An upper production limit per centrality-triggered event of $1.04$ x $10^{-3}$ on the $3\sigma$ level is derived. Comparing this value with the number of successfully reconstructed $\Lambda$ hyperons allows to determine an upper limit on the ratio $N_{_{\Lambda}^3H}/N_{\Lambda}$, which is confronted with statistical and coalescence-type model calculations