3,674 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
Fusing Data with Correlations
Many applications rely on Web data and extraction systems to accomplish
knowledge-driven tasks. Web information is not curated, so many sources provide
inaccurate, or conflicting information. Moreover, extraction systems introduce
additional noise to the data. We wish to automatically distinguish correct data
and erroneous data for creating a cleaner set of integrated data. Previous work
has shown that a na\"ive voting strategy that trusts data provided by the
majority or at least a certain number of sources may not work well in the
presence of copying between the sources. However, correlation between sources
can be much broader than copying: sources may provide data from complementary
domains (\emph{negative correlation}), extractors may focus on different types
of information (\emph{negative correlation}), and extractors may apply common
rules in extraction (\emph{positive correlation, without copying}). In this
paper we present novel techniques modeling correlations between sources and
applying it in truth finding.Comment: Sigmod'201
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
Periodic solutions for a class of nonlinear partial differential equations in higher dimension
We prove the existence of periodic solutions in a class of nonlinear partial
differential equations, including the nonlinear Schroedinger equation, the
nonlinear wave equation, and the nonlinear beam equation, in higher dimension.
Our result covers cases where the bifurcation equation is infinite-dimensional,
such as the nonlinear Schroedinger equation with zero mass, for which solutions
which at leading order are wave packets are shown to exist.Comment: 34 page
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
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
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
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