Aspects of noncommutative Lorentzian geometry for globally hyperbolic spacetimes

Connes' functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d'Alembert operator and the causal functions of a globally hyperbolic spacetime. As a step of the presented machinery, a proof of the almost-everywhere smoothness of the Lorentzian distance considered as a function of one of the two arguments is given. Afterwards, using a $C^*$-algebra approach, the spacetime causal structure and the Lorentzian distance are generalized into noncommutative structures giving rise to a Lorentzian version of part of Connes' noncommutative geometry. The generalized noncommutative spacetime consists of a direct set of Hilbert spaces and a related class of $C^*$-algebras of operators. In each algebra a convex cone made of self-adjoint elements is selected which generalizes the class of causal functions. The generalized events, called {\em loci}, are realized as the elements of the inductive limit of the spaces of the algebraic states on the $C^*$-algebras. A partial-ordering relation between pairs of loci generalizes the causal order relation in spacetime. A generalized Lorentz distance of loci is defined by means of a class of densely-defined operators which play the r\^ole of a Lorentzian metric. Specializing back the formalism to the usual globally hyperbolic spacetime, it is found that compactly-supported probability measures give rise to a non-pointwise extension of the concept of events.Comment: 43 pages, structure of the paper changed and presentation strongly improved, references added, minor typos corrected, title changed, accepted for publication in Reviews in Mathematical Physic

Investigation of the Lightest Hybrid Meson Candidate with a Coupled-Channel Analysis of pˉp\bar{p}p-, π−p\pi^- p- and ππ\pi\pi-Data

Based on new insights from two recent coupled-channel analyses of $\bar{p}p$ annihilation together with $\pi\pi$-scattering data and of $\pi^- p$ data, this paper aims at a better understanding of the spin-exotic $\pi_1$ resonances in the light meson sector. The Crystal Barrel Collaboration observed the $\pi_1$-wave in $\bar{p}p$ annihilations in flight for the first time with the coupling to $\pi^0\eta$ in the reaction $\bar{p}p\,\rightarrow\,\pi^0\pi^0\eta$ with a sophisticated coupled-channel approach. Another refined coupled-channel analysis of the P- and D-waves in the $\pi\eta$ and $\pi\eta^\prime$ system based on data measured at COMPASS has been performed by the JPAC group. In that study the two spin-exotic signatures listed in the PDG, the $\pi_1(1400)$ and $\pi_1(1600)$, with a separate coupling to $\pi\eta$ and $\pi\eta^\prime$ can be described by a single pole. In this paper, both analyses, the one with the three $\bar{p}p$ annihilation channels into $\pi^0\pi^0\eta$, $\pi^0\eta\eta$ and $K^+K^-\pi^0$ and 11 different $\pi\pi$-scattering data sets and the one with the P- and D-wave data in the $\pi\eta$ and $\pi\eta^\prime$ systems measured at COMPASS, are subjected to a combined coupled channel analysis. By utilizing the K-matrix approach and realizing the analyticity via Chew-Mandelstam functions the $\pi_1$ wave can be well described by a single pole for both systems, $\pi\eta$ and $\pi\eta^\prime$. The mass and width of the $\pi_1$-pole are measured to be (1561.6 \, \pm \, 3.0 \, ^{+6.6}_{-2.6}\,)\, \mathrm{MeV/c}^2 and (388.1 \, \pm \, 5.4 \, ^{+0.2}_{-14.1}\,)\, \mathrm{MeV}.Comment: 5 pages, 2 figures, 1 tabl

Frictional strengthening explored during non-steady state shearing. Implications for fault stability and slip event recurrence time

On natural faults that host repeating slip events, the inter-event loading time is quite large compared to the slip event duration. Since most friction studies focus on steady-state frictional behavior, the fault loading phase is not typically examined. Here, we employ a method specifically designed to evaluate fault strength evolution during active loading, under shear driving rates as low as 10−10 m/s, on natural fault gouge samples from the Waikukupa Thrust in southern New Zealand. These tests reveal that in the early stages of loading following a slip event, there is a period of increased stability, which fades with accumulated slip. In the framework of rate- and state-dependent friction laws, this temporary stable phase exists as long as slip is less than the critical slip distance and the elapsed time is less than the value of the state variable at steady state. These observations indicate a minimum earthquake recurrence time, which depends on the field value of the critical slip distance and the background slip rate. We compare estimates of minimum earthquake recurrence times with the recurrence times of repeating large earthquakes on the Alpine Fault in southern New Zealand and repeating small-magnitude earthquakes on the San Andreas Fault system in California. We find that the observed recurrence times are mostly longer than the predicted minimum values, and exceptions in the San Andreas system may be explained by elevated slip rates due to larger earthquakes in this region

Centrifugation and capillarity integrated into a multiple analyte whole blood analyser

A unique clinical chemistry analyser is described which processes 90 μl of whole blood (fingerstick or venous) into multiple aliquots of diluted plasma and reports the results of 12 tests in 14 min. To perform a panel of tests, the operator applies the unmetered sample directly into a single use, 8 cm diameter plastic rotor which contains the required liquid diluent and dry reagents. Using centrifugal and capillary forces, the rotor meters the required amount of blood, separates the red cells, meters the plasma, meters the diluent, mixes the fluids, distributes the fluid to the reaction cuvettes and mixes the reagents and the diluted plasma in the cuvettes. The instrument monitors the reagent reactions simultaneously using nine wavelengths, calculates the results from the absorbance data, and reports the results

fulgeo-Design of an Intuitive User Interface for a Multimedia Search Engine

Multimedia documents like PowerPoint presentations or Flash documents are widely adopted in the Internet and exist in context of lots of different topics. However, so far there is no user friendly way to explore and search for this content. The aim of this work is to address this issue by developing a new, easy-to-use user interface approach and prototype search engine. Our system is called fulgeo and specifically focuses on a suitable multimedia interface for visualizing the query results of Flash documents. The prototype is available online as live demo at: http://fulgeo.komsys.org

Fulgeo - towards an intuitive user interface for a semantics-enabled multimedia search engine

Multimedia documents like PowerPoint presentations or Flash documents are widely adopted in the Internet and exist in context of lots of different topics. However, so far there is no user friendly way to explore and search for this content. The aim of this work is to address this issue by developing a new, easy-to-use user interface approach and prototype search engine. Our system is called fulgeo and specifically focuses on a suitable multimedia interface for visualizing the query results of semantically-enriched Flash documents