3,352 research outputs found
Birkhoff Normal Form and Long Time Existence for Periodic Gravity Water Waves
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and give a rigorous proof of a conjecture of Dyachenko-Zakharov [16] concerning the approximate integrability of these equations. More precisely, we prove a rigorous reduction of the water waves equations to its integrable Birkhoff normal form up to order 4. As a consequence, we also obtain a long-time stability result: periodic perturbations of a flat interface that are initially of size ε remain regular and small up to times of order (Formula presented.). This time scale is expected to be optimal. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC
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
Effects of Electromagnetic Field on the Dynamical Instability of Cylindrical Collapse
The objective of this paper is to discuss the dynamical instability in the
context of Newtonian and post Newtonian regimes. For this purpose, we consider
non-viscous heat conducting charged isotropic fluid as a collapsing matter with
cylindrical symmetry. Darmois junction conditions are formulated. The
perturbation scheme is applied to investigate the influence of dissipation and
electromagnetic field on the dynamical instability. We conclude that the
adiabatic index has smaller value for such a fluid in cylindrically
symmetric than isotropic sphere
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
Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow
We investigate the dynamics of the two-dimensional periodic Kolmogorov flow
of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct
numerical simulations. Above a critical Weissenberg number the flow displays a
transition from stationary to randomly fluctuating states, via periodic ones.
The increasing complexity of the flow in both time and space at progressively
higher values of elasticity accompanies the establishment of mixing features.
The peculiar dynamical behavior observed in the simulations is found to be
related to the appearance of filamental propagating patterns, which develop
even in the limit of very small inertial non-linearities, thanks to the
feedback of elastic forces on the flow.Comment: 10 pages, 14 figure
Explaining LIGO's observations via isolated binary evolution with natal kicks
We compare binary evolution models with different assumptions about
black-hole natal kicks to the first gravitational-wave observations performed
by the LIGO detectors. Our comparisons attempt to reconcile merger rate,
masses, spins, and spin-orbit misalignments of all current observations with
state-of-the-art formation scenarios of binary black holes formed in isolation.
We estimate that black holes (BHs) should receive natal kicks at birth of the
order of (50) km/s if tidal processes do (not) realign
stellar spins. Our estimate is driven by two simple factors. The natal kick
dispersion is bounded from above because large kicks disrupt too many
binaries (reducing the merger rate below the observed value). Conversely, the
natal kick distribution is bounded from below because modest kicks are needed
to produce a range of spin-orbit misalignments. A distribution of misalignments
increases our models' compatibility with LIGO's observations, if all BHs are
likely to have natal spins. Unlike related work which adopts a concrete BH
natal spin prescription, we explore a range of possible BH natal spin
distributions. Within the context of our models, for all of the choices of
used here and within the context of one simple fiducial parameterized
spin distribution, observations favor low BH natal spin.Comment: 19 pages, 14 figures, as published in PR
A post-Newtonian diagnosis of quasiequilibrium configurations of neutron star-neutron star and neutron star-black hole binaries
We use a post-Newtonian diagnostic tool to examine numerically generated
quasiequilibrium initial data sets for non-spinning double neutron star and
neutron star-black hole binary systems. The PN equations include the effects of
tidal interactions, parametrized by the compactness of the neutron stars and by
suitable values of ``apsidal'' constants, which measure the degree of
distortion of stars subjected to tidal forces. We find that the post-Newtonian
diagnostic agrees well with the double neutron star initial data, typically to
better than half a percent except where tidal distortions are becoming extreme.
We show that the differences could be interpreted as representing small
residual eccentricity in the initial orbits. In comparing the diagnostic with
preliminary numerical data on neutron star-black hole binaries, we find less
agreement.Comment: 17 pages, 6 tables, 8 figure
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
Double Compact Objects III: Gravitational Wave Detection Rates
The unprecedented range of second-generation gravitational-wave (GW)
observatories calls for refining the predictions of potential sources and
detection rates. The coalescence of double compact objects (DCOs)---i.e.,
neutron star-neutron star (NS-NS), black hole-neutron star (BH-NS), and black
hole-black hole (BH-BH) binary systems---is the most promising source of GWs
for these detectors. We compute detection rates of coalescing DCOs in
second-generation GW detectors using the latest models for their cosmological
evolution, and implementing inspiral-merger-ringdown (IMR) gravitational
waveform models in our signal-to-noise ratio calculations. We find that: (1)
the inclusion of the merger/ringdown portion of the signal does not
significantly affect rates for NS-NS and BH-NS systems, but it boosts rates by
a factor for BH-BH systems; (2) in almost all of our models BH-BH
systems yield by far the largest rates, followed by NS-NS and BH-NS systems,
respectively, and (3) a majority of the detectable BH-BH systems were formed in
the early Universe in low-metallicity environments. We make predictions for the
distributions of detected binaries and discuss what the first GW detections
will teach us about the astrophysics underlying binary formation and evolution.Comment: published in ApJ, 19 pages, 11 figure
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