Second-order ordinary differential equations with indefinite weight: the Neumann boundary value problem

We study the second-order nonlinear differential equation u\u2032\u2032+a(t)g(u)=0 , where g is a continuously differentiable function of constant sign defined on an open interval I 86R and a(t) is a sign-changing weight function. We look for solutions u(t) of the differential equation such that u(t) 08I, satisfying the Neumann boundary conditions. Special examples, considered in our model, are the equations with singularity, for I=R+0 and g(u) 3c 12u 12\u3c3, as well as the case of exponential nonlinearities, for I=R and g(u) 3cexp(u) . The proofs are obtained by passing to an equivalent equation of the form x\u2032\u2032=f(x)(x\u2032)2+a(t)

Gravitational waves from three-dimensional core-collapse supernova models: The impact of moderate progenitor rotation

We present predictions for the gravitational-wave (GW) emission of three-dimensional supernova (SN) simulations performed for a 15 solar-mass progenitor with the Prometheus-Vertex code using energy-dependent, three-flavor neutrino transport. The progenitor adopted from stellar evolution calculations including magnetic fields had a fairly low specific angular momentum (j_Fe <~ 10^{15} cm^2/s) in the iron core (central angular velocity ~0.2 rad/s), which we compared to simulations without rotation and with artificially enhanced rotation (j_Fe <~ 2*10^{16} cm^2/s; central angular velocity ~0.5 rad/s). Our results confirm that the time-domain GW signals of SNe are stochastic, but possess deterministic components with characteristic patterns at low frequencies (<~200 Hz), caused by mass motions due to the standing accretion shock instability (SASI), and at high frequencies, associated with gravity-mode oscillations in the surface layer of the proto-neutron star (PNS). Non-radial mass motions in the post-shock layer as well as PNS convection are important triggers of GW emission, whose amplitude scales with the power of the hydrodynamic flows. There is no monotonic increase of the GW amplitude with rotation, but a clear correlation with the strength of SASI activity. Our slowly rotating model is a fainter GW emitter than the non-rotating model because of weaker SASI activity and damped convection in the post-shock layer and PNS. In contrast, the faster rotating model exhibits a powerful SASI spiral mode during its transition to explosion, producing the highest GW amplitudes with a distinctive drift of the low-frequency emission peak from ~80-100 Hz to ~40-50 Hz. This migration signifies shock expansion, whereas non-exploding models are discriminated by the opposite trend.Comment: Added new figure, figure 9. Updated figure 9, now figure 10. Modified the discussion of the proto-neutron star convection. Added a figure showing the average rotation rate as a function of radius. Added a section discussing where the low-frequency gravitational waves are generated, this information is visualized in figure 9. We also made some minor changes to the text and selected plot

Uniqueness of positive solutions for boundary value problems associated with indefinite \u3c6-Laplacian-type equations

This paper provides a uniqueness result for positive solutions of the Neumann and periodic boundary value problems associated with the \u3c6-Laplacian equation 'Equation Presented', where \u3c6 is a homeomorphism with \u3c6(0) = 0, a(t) is a stepwise indefinite weight and g(u) is a continuous function. When dealing with the p-Laplacian differential operator \u3c6(s) = |s|p-2s with p > 1, and the nonlinear term g(u) = u\u3b3 with \u3b3 08 \u211d, we prove the existence of a unique positive solution when \u3b3 \u3f5 ]- 1e, (1 - 2p)/(p - 1)] 2a ]p - 1, + 1e[

Modeling Core-Collapse Supernovae Gravitational-Wave Memory in Laser Interferometric Data

We study the properties of the gravitational wave (GW) emission between $10^{-5}$ Hz and $50$ Hz (which we refer to as low-frequency emission) from core-collapse supernovae, in the context of studying such signals in laser interferometric data as well as performing multi-messenger astronomy. We pay particular attention to the GW linear memory, which is when the signal amplitude does not return to zero after the GW burst. Based on the long term simulation of a core-collapse supernova of a solar-metallicity star with a zero-age main sequence mass of 15 solar masses, we discuss the spectral properties, the memory's dependence on observer position and the polarization of low-frequency GWs from slowly non (or slowly) rotating core-collapse supernovae. We make recommendations on the angular spacing of the orientations needed to properly produce results that are averaged over multiple observer locations by investigating the angular dependence of the GW emission. We propose semi-analytical models that quantify the relationship between the bulk motion of the supernova shock-wave and the GW memory amplitude. We discuss how to extend neutrino generated GW signals from numerical simulations that were terminated before the neutrino emission has subsided. We discuss how the premature halt of simulations and the non-zero amplitude of the GW memory can induce artefacts during the data analysis process. Lastly, we also investigate potential solutions and issues in the use of taperings for both ground and space-based interferometers

Observing gravitational waves from core-collapse supernovae in the advanced detector era

The next galactic core-collapse supernova (CCSN) has already exploded, and its electromagnetic (EM) waves, neutrinos, and gravitational waves (GWs) may arrive at any moment. We present an extensive study on the potential sensitivity of prospective detection scenarios for GWs from CCSNe within 5 Mpc, using realistic noise at the predicted sensitivity of the Advanced LIGO and Advanced Virgo detectors for 2015, 2017, and 2019. We quantify the detectability of GWs from CCSNe within the Milky Way and Large Magellanic Cloud, for which there will be an observed neutrino burst. We also consider extreme GW emission scenarios for more distant CCSNe with an associated EM signature. We find that a three-detector network at design sensitivity will be able to detect neutrino-driven CCSN explosions out to ∼5.5  kpc, while rapidly rotating core collapse will be detectable out to the Large Magellanic Cloud at 50 kpc. Of the phenomenological models for extreme GW emission scenarios considered in this study, such as long-lived bar-mode instabilities and disk fragmentation instabilities, all models considered will be detectable out to M31 at 0.77 Mpc, while the most extreme models will be detectable out to M82 at 3.52 Mpc and beyond

A First Comparison Between LIGO and Virgo Inspiral Search Pipelines

This article reports on a project that is the first step the LIGO Scientific Collaboration and the Virgo Collaboration have taken to prepare for the mutual search for inspiral signals. The project involved comparing the analysis pipelines of the two collaborations on data sets prepared by both sides, containing simulated noise and injected events. The ability of the pipelines to detect the injected events was checked, and a first comparison of how the parameters of the events were recovered has been completed.Comment: GWDAW-9 proceeding

A first comparison of search methods for gravitational wave bursts using LIGO and Virgo simulated data

We present a comparative study of 6 search methods for gravitational wave bursts using simulated LIGO and Virgo noise data. The data's spectra were chosen to follow the design sensitivity of the two 4km LIGO interferometers and the 3km Virgo interferometer. The searches were applied on replicas of the data sets to which 8 different signals were injected. Three figures of merit were employed in this analysis: (a) Receiver Operator Characteristic curves, (b) necessary signal to noise ratios for the searches to achieve 50 percent and 90 percent efficiencies, and (c) variance and bias for the estimation of the arrival time of a gravitational wave burst.Comment: GWDAW9 proceeding

Performance validity tests in nonlitigant patients with functional motor disorder

Background: Performance Validity Tests (PVTs) are used in neuropsychological assessments to detect patterns of performance suggesting that the broader evaluation may be an invalid reflection of an individual's abilities. Data on Functional motor disorder (FMD) are currently poor and conflicting. Objectives: We aimed to examine the rate of failure at three different PVTs of non-litigant, non-compensation seeking FMD patients, and we compared their performance to that of healthy controls and controls asked to simulate malingering (healthy simulators). Methods: We enrolled 29 non-litigant, non-compensation seeking patients with a clinical diagnosis of FMD, 29 healthy controls and 29 healthy simulators. Three PVTs, the Coin in the Hand Test (CIH), the Rey 15-item Test (REY) and the Finger Tapping Test (FTT), were employed. Results: FMD Patients showed low rates of failure at the CIH and REY tests (7% and 10%, respectively) and slightly higher at the FTT (15%, n=26) test, which implies a motor task. Their performance was statistically comparable to that of healthy controls but statistically different from that of healthy simulators (p&lt;0.001). 93% of FMD patients, 7% of healthy simulators, and 100% of healthy controls passed at least two of the three tests. Conclusions: PVT performance of non-litigant, non-compensation seeking patients with FMD ranged from 7 to 15%. Patient's performance was comparable to controls and significantly differed from that of simulators. This simple battery of three PVTs could be of practical utility and routinely used in clinical practice

Environmental pre-exploitation monitoring of Torre Alfina geothermal system (Central Italy)

An interesting project of geothermal pilot plant, with no-gas emission in atmosphere, has been submitted for approval in the medium-enthalpy geothermal field of Torre Alfina. This prompted us to develop a geochemical and geophysical monitoring of the area with the aim of establishing a background information to reco-gnize anomalous gas emission, induced seismicity and subsidence, possibly related to the field exploitation. The exploration conducted by Enel in the years ‘70 - '80, including the drilling of 9 deep wells, has shown the existence of a medium-enthalpy geothermal field in the Torre Alfina zone, in central Italy. The area has been affected by a very complex geological evolution during the Neogene. It was affected by the Quaternary volcanism of the Tyrrhenian margin which, reached its climax between 0.6 and 0.3 Ma. The present stress field around Quaternary volcanoes of central Italy has a NE to ENE direction of extension, in agreement with the alignment of Quaternary volcanoes and earthquake fault plane solutions, with T axes preferentially oriented between NE and ENE.PublishedPrague, Czech Republic, June 22 to July 2, 20156T. Sismicità indotta e caratterizzazione sismica dei sistemi naturaliope