Uniform Decay of Local Energy and the Semi-Linear Wave Equation on Schwarzchild Space

We provide a uniform decay estimate of Morawetz type for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzchild background. This estimate is both uniform in space and time, so in particular it implies a uniform bound on the sup norm of solutions which can be given in terms of certain inverse powers of the radial and advanced/retarded time coordinate variables. As a model application, we show these estimates give a very simple proof small amplitude scattering for nonlinear scalar fields with higher than cubic interactions.Comment: 24 page

A Multi-commodity network flow model for cloud service environments

Next-generation systems, such as the big data cloud, have to cope with several challenges, e.g., move of excessive amount of data at a dictated speed, and thus, require the investigation of concepts additional to security in order to ensure their orderly function. Resilience is such a concept, which when ensured by systems or networks they are able to provide and maintain an acceptable level of service in the face of various faults and challenges. In this paper, we investigate the multi-commodity flows problem, as a task within our D 2 R 2 +DR resilience strategy, and in the context of big data cloud systems. Specifically, proximal gradient optimization is proposed for determining optimal computation flows since such algorithms are highly attractive for solving big data problems. Many such problems can be formulated as the global consensus optimization ones, and can be solved in a distributed manner by the alternating direction method of multipliers (ADMM) algorithm. Numerical evaluation of the proposed model is carried out in the context of specific deployments of a situation-aware information infrastructure

Generalized and weighted Strichartz estimates

In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space $\mathbb{R}^n$. In particular, we prove the generalized and weighted Strichartz estimates for a large class of dispersive operators including the Schr\"odinger and wave equation. As a sample application of these new estimates, we are able to prove the Strauss conjecture with low regularity for dimension 2 and 3.Comment: Final version, to appear in the Communications on Pure and Applied Analysis. 33 pages. 2 more references adde

On the relation between mathematical and numerical relativity

The large scale binary black hole effort in numerical relativity has led to an increasing distinction between numerical and mathematical relativity. This note discusses this situation and gives some examples of succesful interactions between numerical and mathematical methods is general relativity.Comment: 12 page

Strichartz estimates on Schwarzschild black hole backgrounds

We study dispersive properties for the wave equation in the Schwarzschild space-time. The first result we obtain is a local energy estimate. This is then used, following the spirit of earlier work of Metcalfe-Tataru, in order to establish global-in-time Strichartz estimates. A considerable part of the paper is devoted to a precise analysis of solutions near the trapping region, namely the photon sphere.Comment: 44 pages; typos fixed, minor modifications in several place

Measurement of the Neutron Cross Section on Argon Between 95 and 720 MeV

We report an extended measurement of the neutron cross section on argon in the energy range of 95-720 MeV. The measurement was obtained with a 4.3-hour exposure of the Mini-CAPTAIN detector to the WNR/LANSCE beam at LANL. Compared to an earlier analysis of the same data, this extended analysis includes a reassessment of systematic uncertainties, in particular related to unused wires in the upstream part of the detector. Using this information we doubled the fiducial volume in the experiment and increased the statistics by a factor of 2.4. We also shifted the analysis from energy bins to time-of-flight bins. This change reduced the overall considered energy range, but improved the understanding of the energy spectrum of incoming neutrons in each bin. Overall, the new measurements are extracted from a fit to the attenuation of the neutron flux in five time-of-flight regions: 140 ns - 180 ns, 120 ns - 140 ns, 112 ns - 120 ns, 104 ns - 112 ns, 96 ns - 104 ns. The final cross sections are given for the flux-averaged energy in each time-of-flight bin: $\sigma(146~\rm{MeV})=0.60^{+0.14}_{-0.14}\pm0.08$(syst) b, $\sigma(236~\rm{MeV})=0.72^{+0.10}_{-0.10}\pm0.04$(syst) b, $\sigma(319~\rm{MeV})=0.80^{+0.13}_{-0.12}\pm0.040$(syst) b, $\sigma(404~\rm{MeV})=0.74^{+0.14}_{-0.09}\pm0.04$(syst) b, $\sigma(543~\rm{MeV})=0.74^{+0.09}_{-0.09}\pm0.04$(syst) b.Comment: 15 pages, 7 tables, 11 figures. Prepared for submission to PR

The Mini-CAPTAIN Liquid Argon Time Projection Chamber

This manuscript describes the commissioning of the Mini-CAPTAIN liquid argon detector in a neutron beam at the Los Alamos Neutron Science Center (LANSCE), which led to a first measurement of high-energy neutron interactions in argon. The Mini-CAPTAIN detector consists of a Time Projection Chamber (TPC) with an accompanying photomultiplier tube (PMT) array sealed inside a liquid-argon-filled cryostat. The liquid argon is constantly purified and recirculated in a closed-loop cycle during operation. The specifications and assembly of the detector subsystems and an overview of their performance in a neutron beam are reported.Comment: 21 pages, 27 figure

First Measurement of the Total Neutron Cross Section on Argon Between 100 and 800 MeV

We report the first measurement of the neutron cross section on argon in the energy range of 100-800 MeV. The measurement was obtained with a 4.3-hour exposure of the Mini-CAPTAIN detector to the WNR/LANSCE beam at LANL. The total cross section is measured from the attenuation coefficient of the neutron flux as it traverses the liquid argon volume. A set of 2,631 candidate interactions is divided in bins of the neutron kinetic energy calculated from time-of-flight measurements. These interactions are reconstructed with custom-made algorithms specifically designed for the data in a time projection chamber the size of the Mini-CAPTAIN detector. The energy averaged cross section is $0.91 \pm{} 0.10~\mathrm{(stat.)} \pm{} 0.09~\mathrm{(sys.)}~\mathrm{barns}$. A comparison of the measured cross section is made to the GEANT4 and FLUKA event generator packages.Comment: 5 pages, 1 table, 3 figures, submitted to Physical Review Letter