Quasi-periodic solutions of completely resonant forced wave equations

We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number.Comment: 25 pages, 1 figur

Quasinormal Modes Beyond Kerr

The quasinormal modes (QNMs) of a black hole spacetime are the free, decaying oscillations of the spacetime, and are well understood in the case of Kerr black holes. We discuss a method for computing the QNMs of spacetimes which are slightly deformed from Kerr. We mention two example applications: the parametric, turbulent instability of scalar fields on a background which includes a gravitational QNM, and the shifts to the QNM frequencies of Kerr when the black hole is weakly charged. This method may be of use in studies of black holes which are deformed by external fields or are solutions to alternative theories of gravity.Comment: Proceedings of the Sant Cugat Forum on Astrophysics (2014). Session on 'Gravitational Wave Astrophysics.' 7 page

Fertimetro, a Principle and Device to Measure Soil Nutrient Availability for Plants by Microbial Degradation Rates on Differently-Spiked Buried Threads

A novel patented method (PCT/IB2012/001157: Squartini, Concheri, Tiozzo, University of Padova) and the corresponding application devices, suitable to measure soil fertility, are presented. The availability or deficiency of specific nutrients for crops is assessed by monitoring the kinetics of progressive weakening of cotton or silk threads due to in situ microbial activity. The method is based on a nutrient-primed incremented substrate degradation principle. Threads are buried as is or pre-impregnated with N or P solutions, and the acceleration of the degradation rate for the N-supplemented or P-supplemented thread, in comparison to the untreated thread, is proportional to the lack of the corresponding nutrient in that soil. Tests were validated on corn crops in plots receiving increasing fertilizer rates in a historical rotation that has been established since 1962. The measurement carried out in May significantly correlated with the subsequent crop yields recorded in October. The analysis allows an early, inexpensive, fast, and reproducible self-assessment at field level to improve fertilization rates. The device is envisaged as a user-friendly tool for agronomy, horticulture, and any environmental applications where organic matter cycling, soil quality, and specific nutrients excess or deficiency are critical considerations

Full description of Benjamin-Feir instability of stokes waves in deep water

Small-amplitude, traveling, space periodic solutions -called Stokes waves- of the 2 dimensional gravity water waves equations in deep water are linearly unstable with respect to long-wave perturbations, as predicted by Benjamin and Feir in 1967. We completely describe the behavior of the four eigenvalues close to zero of the linearized equations at the Stokes wave, as the Floquet exponent is turned on. We prove in particular the conjecture that a pair of non-purely imaginary eigenvalues depicts a closed figure "8", parameterized by the Floquet exponent, in full agreement with numerical simulations. Our new spectral approach to the Benjamin-Feir instability phenomenon uses a symplectic version of Kato's theory of similarity transformation to reduce the problem to determine the eigenvalues of a 4 x 4 complex Hamiltonian and reversible matrix. Applying a procedure inspired by KAM theory, we block-diagonalize such matrix into a pair of 2x2 Hamiltonian and reversible matrices, thus obtaining the full description of its eigenvalues

Effets de l’adoption de la technique du microdosage d’engrais sur la disponibilite et l’accessibilite cerealiere des exploitations agricoles a base de mil et de sorgho au Mali

Cette étude examine l’effet de l’adoption de la technique de microdosage d’engrais sur l’autosuffisance céréalière des exploitations agricoles à base de mil et de sorgho au Mali. Des données ont été collectées au cours de deux campagnes agricoles, à partir des enquêtes auprès de 108 exploitations agricoles. Les résultats montrent que l’application de la technique de microdosage par les producteurs sur les cultures de mil et de sorgho permet d’obtenir des rendements plus élevés comparativement à l’ancienne pratique des producteurs. Les résultats montrent aussi que l’adoption de la technique à grande échelle par les agriculteurs contribue l’amélioration de la sécurité alimentaire par la couverture des besoins céréaliers des exploitations agricoles. Des taux de couverture autonome et apparente des besoins céréaliers supérieurs ont été obtenus en moyenne pour les deux campagnes agricoles (2013-2014 et 2014-2015) avec les exploitations agricoles pratiquant le microdosage d’engrais sur le mil et le sorgho, comparés à celles en pratique paysanne.Mots- clés : microdosage d’engrais, effets, sécurité alimentaire, exploitations agricoles, mil, sorgho, Mal

On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA

Newly formed black holes are expected to emit characteristic radiation in the form of quasi-normal modes, called ringdown waves, with discrete frequencies. LISA should be able to detect the ringdown waves emitted by oscillating supermassive black holes throughout the observable Universe. We develop a multi-mode formalism, applicable to any interferometric detectors, for detecting ringdown signals, for estimating black hole parameters from those signals, and for testing the no-hair theorem of general relativity. Focusing on LISA, we use current models of its sensitivity to compute the expected signal-to-noise ratio for ringdown events, the relative parameter estimation accuracy, and the resolvability of different modes. We also discuss the extent to which uncertainties on physical parameters, such as the black hole spin and the energy emitted in each mode, will affect our ability to do black hole spectroscopy.Comment: 44 pages, 21 figures, 10 tables. Minor changes to match version in press in Phys. Rev.

LISA observations of massive black hole mergers: event rates and issues in waveform modelling

The observability of gravitational waves from supermassive and intermediate-mass black holes by the forecoming Laser Interferometer Space Antenna (LISA), and the physics we can learn from the observations, will depend on two basic factors: the event rates for massive black hole mergers occurring in the LISA best sensitivity window, and our theoretical knowledge of the gravitational waveforms. We first provide a concise review of the literature on LISA event rates for massive black hole mergers, as predicted by different formation scenarios. Then we discuss what (in our view) are the most urgent issues to address in terms of waveform modelling. For massive black hole binary inspiral these include spin precession, eccentricity, the effect of high-order Post-Newtonian terms in the amplitude and phase, and an accurate prediction of the transition from inspiral to plunge. For black hole ringdown, numerical relativity will ultimately be required to determine the relative quasinormal mode excitation, and to reduce the dimensionality of the template space in matched filtering.Comment: 14 pages, 2 figures. Added section with conclusions and outlook. Matches version to appear in the proceedings of 10th Annual Gravitational Wave Data Analysis Workshop (GWDAW 10), Brownsville, Texas, 14-17 Dec 200

Constraining properties of the black hole population using LISA

LISA should detect gravitational waves from tens to hundreds of systems containing black holes with mass in the range from 10 thousand to 10 million solar masses. Black holes in this mass range are not well constrained by current electromagnetic observations, so LISA could significantly enhance our understanding of the astrophysics of such systems. In this paper, we describe a framework for combining LISA observations to make statements about massive black hole populations. We summarise the constraints that LISA observations of extreme-mass-ratio inspirals might be able to place on the mass function of black holes in the LISA range. We also describe how LISA observations can be used to choose between different models for the hierarchical growth of structure in the early Universe. We consider four models that differ in their prescription for the initial mass distribution of black hole seeds, and in the efficiency of accretion onto the black holes. We show that with as little as 3 months of LISA data we can clearly distinguish between these models, even under relatively pessimistic assumptions about the performance of the detector and our knowledge of the gravitational waveforms.Comment: 12 pages, 3 figures, submitted to Class. Quantum Grav. for proceedings of 8th LISA Symposium; v2 minor changes for consistency with accepted versio