Stability estimates for resolvents, eigenvalues and eigenfunctions of elliptic operators on variable domains

We consider general second order uniformly elliptic operators subject to homogeneous boundary conditions on open sets $\phi (\Omega)$ parametrized by Lipschitz homeomorphisms $\phi$ defined on a fixed reference domain $\Omega$. Given two open sets $\phi (\Omega)$, $\tilde \phi (\Omega)$ we estimate the variation of resolvents, eigenvalues and eigenfunctions via the Sobolev norm $\|\tilde \phi -\phi \|_{W^{1,p}(\Omega)}$ for finite values of $p$, under natural summability conditions on eigenfunctions and their gradients. We prove that such conditions are satisfied for a wide class of operators and open sets, including open sets with Lipschitz continuous boundaries. We apply these estimates to control the variation of the eigenvalues and eigenfunctions via the measure of the symmetric difference of the open sets. We also discuss an application to the stability of solutions to the Poisson problem.Comment: 34 pages. Minor changes in the introduction and the refercenes. Published in: Around the research of Vladimir Maz'ya II, pp23--60, Int. Math. Ser. (N.Y.), vol. 12, Springer, New York 201

Search for the decay K+→π+ννˉK^+\to \pi^+ \nu \bar\nu in the momentum region Pπ<195 MeV/cP_\pi < 195 {\rm ~MeV/c}

We have searched for the decay $K^+ \to \pi^+ \nu \bar\nu$ in the kinematic region with pion momentum below the $K^+ \to \pi^+ \pi^0$ peak. One event was observed, consistent with the background estimate of $0.73\pm 0.18$. This implies an upper limit on $B(K^+ \to \pi^+ \nu \bar\nu)< 4.2\times 10^{-9}$ (90% C.L.), consistent with the recently measured branching ratio of $(1.57^{+1.75}_{-0.82}) \times 10^{-10}$, obtained using the standard model spectrum and the kinematic region above the $K^+ \to \pi^+ \pi^0$ peak. The same data were used to search for $K^+ \to \pi^+ X^0$, where $X^0$ is a weakly interacting neutral particle or system of particles with $150 < M_{X^0} < 250 {\rm ~MeV/c^2}$.Comment: 4 pages, 2 figure

The extended-track reconstruction for MiniBooNE

The Booster Neutrino Experiment (MiniBooNE) searches for muon neutrino to electron neutrino oscillations using the ~1 GeV neutrino beam produced by the FNAL Booster synchrotron. The array of photomultiplier tubes (PMTs) lining the MiniBooNE detector records Cherenkov and scintillation photons from the charged particles produced in neutrino interactions. We describe a maximum likelihood fitting algorithm used to reconstruct the basic properties (position, direction, energy) of these particles from the charges and times measured by the PMTs. The likelihoods returned from fitting an event to different particle hypotheses are used to categorize it as a signal electron neutrino event or as one of the background muon neutrino processes, in particular charged current quasi-elastic scattering and neutral current $\pi^0$ production. The reconstruction and event selection techniques described here can be applied to current and future neutrino experiments using similar Cherenkov-based detection.Comment: 39 pages, 25 figures. Version 2 includes minor editorial change

Further search for the decay K+→π+ννˉK^+ \to \pi^+ \nu \bar \nu in the momentum region P < 195 MeV/c

We report the results of a search for the decay $K^+ \to \pi^+ \nu \bar \nu$ in the kinematic region with $\pi^+$ momentum $140 < P < 195$ MeV/c using the data collected by the E787 experiment at BNL. No events were observed. When combined with our previous search in this region, one candidate event with an expected background of $1.22 \pm 0.24$ events results in a 90% C.L. upper limit of $2.2 \times 10^{-9}$ on the branching ratio of $K^+ \to \pi^+ \nu \bar \nu$. We also report improved limits on the rates of $K^+ \to \pi^+ X^0$ and $K^+ \to \pi^+ X^1 X^2$ where $X^0, X^1, X^2$ are hypothetical, massless, long-lived neutral particles.Comment: 5 pages, 3 figures, Accepted for publication in Phys. Rev.

Diving into the vertical dimension of elasmobranch movement ecology

Knowledge of the three-dimensional movement patterns of elasmobranchs is vital to understand their ecological roles and exposure to anthropogenic pressures. To date, comparative studies among species at global scales have mostly focused on horizontal movements. Our study addresses the knowledge gap of vertical movements by compiling the first global synthesis of vertical habitat use by elasmobranchs from data obtained by deployment of 989 biotelemetry tags on 38 elasmobranch species. Elasmobranchs displayed high intra- and interspecific variability in vertical movement patterns. Substantial vertical overlap was observed for many epipelagic elasmobranchs, indicating an increased likelihood to display spatial overlap, biologically interact, and share similar risk to anthropogenic threats that vary on a vertical gradient. We highlight the critical next steps toward incorporating vertical movement into global management and monitoring strategies for elasmobranchs, emphasizing the need to address geographic and taxonomic biases in deployments and to concurrently consider both horizontal and vertical movements

Light Yield in DarkSide-10: a Prototype Two-phase Liquid Argon TPC for Dark Matter Searches

As part of the DarkSide program of direct dark matter searches using liquid argon TPCs, a prototype detector with an active volume containing 10 kg of liquid argon, DarkSide-10, was built and operated underground in the Gran Sasso National Laboratory in Italy. A critically important parameter for such devices is the scintillation light yield, as photon statistics limits the rejection of electron-recoil backgrounds by pulse shape discrimination. We have measured the light yield of DarkSide-10 using the readily-identifiable full-absorption peaks from gamma ray sources combined with single-photoelectron calibrations using low-occupancy laser pulses. For gamma lines of energies in the range 122-1275 keV, we get consistent light yields averaging 8.887+-0.003(stat)+-0.444(sys) p.e./keVee. With additional purification, the light yield measured at 511 keV increased to 9.142+-0.006(stat) p.e./keVee.Comment: 10 pages, 7 figures, Accepted for publication in Astroparticle Physic