5,000 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
Phase separation in quasi incompressible fluids: Cahn-Hilliard model in the Cattaneo-Maxwell framework
In this paper we propose a mathematical model of phase separation for a
quasi-incompressible binary mixture where the spinodal decomposition is induced
by an heat flux governed by the Cattaneo-Maxwell equation. As usual, the phase
separation is considered in the framework of phase field modeling so that the
transition is described by an additional field, the concentration c. The
evolution of concentration is described by the Cahn-Hilliard equation and in
our model is coupled with the Navier-Stokes equation. Since thermal effect are
included, the whole set of evolution equations is set up for the velocity, the
concentration, the temperature and the heat flux. The model is compatible with
thermodynamics and a maximum theorem holds.Comment: Submitted to ZAM
Considerations on the excitation of black hole quasinormal modes
We provide some considerations on the excitation of black hole quasinormal
modes (QNMs) in different physical scenarios. Considering a simple model in
which a stream of particles accretes onto a black hole, we show that resonant
QNM excitation by hyperaccretion requires a significant amount of fine-tuning,
and is quite unlikely to occur in nature. Then we summarize and discuss present
estimates of black hole QNM excitation from gravitational collapse, distorted
black holes and head-on black hole collisions. We emphasize the areas that, in
our opinion, are in urgent need of further investigation from the point of view
of gravitational wave source modeling.Comment: 11 pages, 2 figures, proceedings of the 7th International Conference
of the Hellenic Astronomical Society. Complements section VB of gr-qc/051216
Estimating spinning binary parameters and testing alternative theories of gravity with LISA
We investigate the effect of spin-orbit and spin-spin couplings on the
estimation of parameters for inspiralling compact binaries of massive black
holes, and for neutron stars inspiralling into intermediate-mass black holes,
using hypothetical data from the proposed Laser Interferometer Space Antenna
(LISA). We work both in Einstein's theory and in alternative theories of
gravity of the scalar-tensor and massive-graviton types. We restrict the
analysis to non-precessing spinning binaries, i.e. to cases where the spins are
aligned normal to the orbital plane. We find that the accuracy with which
intrinsic binary parameters such as chirp mass and reduced mass can be
estimated within general relativity is degraded by between one and two orders
of magnitude. We find that the bound on the coupling parameter omega_BD of
scalar-tensor gravity is significantly reduced by the presence of spin
couplings, while the reduction in the graviton-mass bound is milder. Using fast
Monte-Carlo simulations of 10^4 binaries, we show that inclusion of spin terms
in massive black-hole binaries has little effect on the angular resolution or
on distance determination accuracy. For stellar mass inspirals into
intermediate-mass black holes, the angular resolution and the distance are
determined only poorly, in all cases considered. We also show that, if LISA's
low-frequency noise sensitivity can be extrapolated from 10^-4 Hz to as low as
10^-5 Hz, the accuracy of determining both extrinsic parameters (distance, sky
location) and intrinsic parameters (chirp mass, reduced mass) of massive
binaries may be greatly improved.Comment: 29 pages, 9 figures. Matches version accepted in Physical Review D.
More stringent checks in the inversion of the Fisher matri
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
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
Assessing the Fundraising Impact of power2give on Local Arts Councils
Nonprofit arts organizations, like all nonprofit organizations, are always in search of a fundraising “silver bullet.” Does a program or product exist that raises more money, engages more donors, and minimizes effort and expense? The Arts & Science Council in Charlotte, North Carolina launched a new online crowdfunding platform in 2011 hoping to do just that. Power2give was designed specifically for nonprofit arts organizations to add crowdfunding to their fundraising arsenal. The platform was designed to be an inexpensive and easy to use option for local arts councils to adopt for their communities. Now four years later, power2give has expanded to 24 communities and raised over $6 million for arts organizations. This thesis offers the first in-depth look at how power2give is being used by arts organizations and local arts councils across the nation. Is it a fundraising “silver bullet,” or just another passing trend
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