3,770 research outputs found
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
Quasi-T\"oplitz functions in KAM theorem
We define and describe the class of Quasi-T\"oplitz functions. We then prove
an abstract KAM theorem where the perturbation is in this class. We apply this
theorem to a Non-Linear-Scr\"odinger equation on the torus , thus proving
existence and stability of quasi-periodic solutions and recovering the results
of [10]. With respect to that paper we consider only the NLS which preserves
the total Momentum and exploit this conserved quantity in order to simplify our
treatment.Comment: 34 pages, 1 figur
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
Turbulence and coarsening in active and passive binary mixtures
Phase separation between two fluids in two-dimensions is investigated by
means of Direct Numerical Simulations of coupled Navier-Stokes and
Cahn-Hilliard equations. We study the phase ordering process in the presence of
an external stirring acting on the velocity field. For both active and passive
mixtures we find that, for a sufficiently strong stirring, coarsening is
arrested in a stationary dynamical state characterized by a continuous rupture
and formation of finite domains. Coarsening arrest is shown to be independent
of the chaotic or regular nature of the flow.Comment: 4 pages, 5 figures; discussion on the dependence of the arrest scale
on the shear rate has been added; figures have been modified accordingl
Massive Black Holes: formation and evolution
Supermassive black holes are nowadays believed to reside in most local
galaxies. Observations have revealed us vast information on the population of
local and distant black holes, but the detailed physical properties of these
dark massive objects are still to be proven. Accretion of gas and black hole
mergers play a fundamental role in determining the two parameters defining a
black hole: mass and spin. We briefly review here the basic properties of the
population of supermassive black holes, focusing on the still mysterious
formation of the first massive black holes, and their evolution from early
times to now.Comment: review to appear in Proc. IAU Symp. 238, "Black Holes: from stars to
galaxies - across the range of masses
Non-radial oscillation modes as a probe of density discontinuities in neutron stars
A phase transition occurring in the inner core of a neutron star could be
associated to a density discontinuity that would affect the frequency spectrum
of the non-radial oscillation modes in two ways. Firstly, it would produce a
softening of the equation of state, leading to more compact equilibrium
configurations and changing the frequency of the fundamental and pressure modes
of the neutron star. Secondly, a new non-zero frequency g-- mode would appear,
associated to each discontinuity. These discontinuity g--modes have typical
frequencies larger than those of g--modes previously studied in the literature
(thermal, core g-- modes, or g--modes due to chemical inhomogeneities in the
outer layers), and smaller than that of the fundamental mode; therefore they
should be distinguishable from the other modes of non radial oscillation. In
this paper we investigate how high density discontinuities change the frequency
spectrum of the non-radial oscillations, in the framework of the general
relativistic theory of stellar perturbations. Our purpose is to understand
whether a gravitational signal, emitted at the frequencies of the quasi normal
modes, may give some clear information on the equation of state of the neutron
star and, in particular, on the parameters that characterize the density
discontinuity. We discuss some astrophysical processes that may be associated
to the excitation of these modes, and estimate how much gravitational energy
should the modes convey to produce a signal detectable by high frequency
gravitational detectors.Comment: submitted to MNRA
Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity
We study the transition from inspiral to plunge in general relativity by
computing gravitational waveforms of non-spinning, equal-mass black-hole
binaries. We consider three sequences of simulations, starting with a
quasi-circular inspiral completing 1.5, 2.3 and 9.6 orbits, respectively, prior
to coalescence of the holes. For each sequence, the binding energy of the
system is kept constant and the orbital angular momentum is progressively
reduced, producing orbits of increasing eccentricity and eventually a head-on
collision. We analyze in detail the radiation of energy and angular momentum in
gravitational waves, the contribution of different multipolar components and
the final spin of the remnant. We find that the motion transitions from
inspiral to plunge when the orbital angular momentum L=L_crit is about 0.8M^2.
For L<L_crit the radiated energy drops very rapidly. Orbits with L of about
L_crit produce our largest dimensionless Kerr parameter for the remnant,
j=J/M^2=0.724. Generalizing a model recently proposed by Buonanno, Kidder and
Lehner to eccentric binaries, we conjecture that (1) j=0.724 is the maximal
Kerr parameter that can be obtained by any merger of non-spinning holes, and
(2) no binary merger (even if the binary members are extremal Kerr black holes
with spins aligned to the orbital angular momentum, and the inspiral is highly
eccentric) can violate the cosmic censorship conjecture.Comment: Added sequence of long inspirals to the study. To match published
versio
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
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