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

Free Versus Constrained Evolution of the 2+1 Equivariant Wave Map

We compare the numerical solutions of the 2+1 equivariant Wave Map problem computed with the symplectic, constraint respecting Rattle algorithm and the well known fourth order Runge-Kutta method. We show the advantages of the Rattle algorithm for constrained system compared to the free evolution with the Runge-Kutta method. We also present an expression, which represents the energy loss due to constraint violation. Taking this expression into account we can achieve energy conservation for the Runge-Kutta scheme, which is better than with the Rattle method. Using the symplectic scheme with constraint enforcement we can reproduce previous calculations of the equivariant case without imposing the symmetry explicitly, thereby confirming that the critical behaviour is stable.Comment: 16 pages, 8 figures. Formula for the scaling function on p. 13 corrected and two typos eliminated; otherwise agrees with the published pape

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

Total prompt γ

The total prompt γ-ray energy distributions for the neutron-induced fission of 235U, 239,241Pu at incident neutron energy of 0.025 eV ‒ 100 keV, and the spontaneous fission of 252Cf were measured using the Detector for Advanced Neutron Capture Experiments (DANCE) array in coincidence with the detection of fission fragments by a parallel-plate avalanche counter. DANCE is a highly segmented, highly efficient 4π γ-ray calorimeter. Corrections were made to the measured distribution by unfolding the two-dimension spectrum of total γ-ray energy vs multiplicity using a simulated DANCE response matrix. The mean values of the total prompt γ-ray energy, determined from the unfolded distributions, are ~ 20% higher than those derived from measurements using single γ-ray detector for all the fissile nuclei studied. This raises serious concern on the validity of the mean total prompt γ-ray energy obtained from the product of mean values for both prompt γ-ray energy and multiplicity

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

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