591 research outputs found
An effectual template bank for the detection of gravitational waves from inspiralling compact binaries with generic spins
We report the construction of a three-dimensional template bank for the
search for gravitational waves from inspiralling binaries consisting of
spinning compact objects. The parameter space consists of two dimensions
describing the mass parameters and one "reduced-spin" parameter, which
describes the secular (non-precessing) spin effects in the waveform. The
template placement is based on an efficient stochastic algorithm and makes use
of the semi-analytical computation of a metric in the parameter space. We
demonstrate that for "low-mass" () binaries,
this template bank achieves effective fitting factors --
towards signals from generic spinning binaries in the advanced detector era
over the entire parameter space of interest (including binary neutron stars,
binary black holes, and black hole-neutron star binaries). This provides a
powerful and viable method for searching for gravitational waves from generic
spinning low-mass compact binaries. Under the assumption that spin magnitudes
of black-holes [neutron-stars] are uniformly distributed between 0--0.98 [0 --
0.4] and spin angles are isotropically distributed, the expected improvement in
the average detection volume (at a fixed signal-to-noise-ratio threshold) of a
search using this reduced-spin bank is , as compared to a search
using a non-spinning bank.Comment: Minor changes, version appeared in Phys. Rev.
Numerical simulations of the Fourier transformed Vlasov-Maxwell system in higher dimensions --- Theory and applications
We present a review of recent developments of simulations of the
Vlasov-Maxwell system of equations using a Fourier transform method in velocity
space. In this method, the distribution functions for electrons and ions are
Fourier transformed in velocity space, and the resulting set of equations are
solved numerically. In the original Vlasov equation, phase mixing may lead to
an oscillatory behavior and sharp gradients of the distribution function in
velocity space, which is problematic in simulations where it can lead to
unphysical electric fields and instabilities and to the recurrence effect where
parts of the initial condition recur in the simulation. The particle
distribution function is in general smoother in the Fourier transformed
velocity space, which is desirable for the numerical approximations. By
designing outflow boundary conditions in the Fourier transformed velocity
space, the highest oscillating terms are allowed to propagate out through the
boundary and are removed from the calculations, thereby strongly reducing the
numerical recurrence effect. The outflow boundary conditions in higher
dimensions including electromagnetic effects are discussed. The Fourier
transform method is also suitable to solve the Fourier transformed Wigner
equation, which is the quantum mechanical analogue of the Vlasov equation for
classical particles.Comment: 41 pages, 19 figures. To be published in Transport Theory and
Statistical Physics. Proceedings of the VLASOVIA 2009 Workshop, CIRM, Luminy,
Marseilles, France, 31 August - 4 September 200
A well-posedness theory in measures for some kinetic models of collective motion
We present existence, uniqueness and continuous dependence results for some
kinetic equations motivated by models for the collective behavior of large
groups of individuals. Models of this kind have been recently proposed to study
the behavior of large groups of animals, such as flocks of birds, swarms, or
schools of fish. Our aim is to give a well-posedness theory for general models
which possibly include a variety of effects: an interaction through a
potential, such as a short-range repulsion and long-range attraction; a
velocity-averaging effect where individuals try to adapt their own velocity to
that of other individuals in their surroundings; and self-propulsion effects,
which take into account effects on one individual that are independent of the
others. We develop our theory in a space of measures, using mass transportation
distances. As consequences of our theory we show also the convergence of
particle systems to their corresponding kinetic equations, and the
local-in-time convergence to the hydrodynamic limit for one of the models
Vlasov scaling for stochastic dynamics of continuous systems
We describe a general scheme of derivation of the Vlasov-type equations for
Markov evolutions of particle systems in continuum. This scheme is based on a
proper scaling of corresponding Markov generators and has an algorithmic
realization in terms of related hierarchical chains of correlation functions
equations. Several examples of the realization of the proposed approach in
particular models are presented.Comment: 23 page
A new interaction potential for swarming models
We consider a self-propelled particle system which has been used to describe
certain types of collective motion of animals, such as fish schools and bird
flocks. Interactions between particles are specified by means of a pairwise
potential, repulsive at short ranges and attractive at longer ranges. The
exponentially decaying Morse potential is a typical choice, and is known to
reproduce certain types of collective motion observed in nature, particularly
aligned flocks and rotating mills. We introduce a class of interaction
potentials, that we call Quasi-Morse, for which flock and rotating mills states
are also observed numerically, however in that case the corresponding
macroscopic equations allow for explicit solutions in terms of special
functions, with coefficients that can be obtained numerically without solving
the particle evolution. We compare thus obtained solutions with long-time
dynamics of the particle systems and find a close agreement for several types
of flock and mill solutions.Comment: 23 pages, 8 figure
Search for Gravitational Waves from Scorpius X-1 in LIGO O3 Data With Corrected Orbital Ephemeris
Improved observational constraints on the orbital parameters of the low-mass
X-ray binary Scorpius~X-1 were recently published in Killestein et al (2023).
In the process, errors were corrected in previous orbital ephemerides, which
have been used in searches for continuous gravitational waves from Sco~X-1
using data from the Advanced LIGO detectors. We present the results of a
re-analysis of LIGO detector data from the third observing run of Advanced LIGO
and Advanced Virgo using a model-based cross-correlation search. The corrected
region of parameter space, which was not covered by previous searches, was
about 1/3 as large as the region searched in the original O3 analysis, reducing
the required computing time. We have confirmed that no detectable signal is
present over a range of gravitational-wave frequencies from to
, analogous to the null result of Abbott et al (2022). Our
search sensitivity is comparable to that of Abbott et al (2022), who set upper
limits corresponding, between and , to an
amplitude of about when marginalized isotropically over the
unknown inclination angle of the neutron star's rotation axis, or less than
assuming the optimal orientation.Comment: 8 pages, 3 figures, 2 tables. Typeset with AASTeX 6.3.1. Accepted for
publication in The Astrophysical Journal. arXiv admin note: text overlap with
arXiv:2209.0286
Vlasov equation for long-range interactions on a lattice
We show that, in the continuum limit, the dynamics of Hamiltonian systems
defined on a lattice with long-range couplings is well described by the Vlasov
equation. This equation can be linearized around the homogeneous state and a
dispersion relation, that depends explicitly on the Fourier modes of the
lattice, can be derived. This allows one to compute the stability thresholds of
the homogeneous state, which turn out to depend on the mode number. When this
state is unstable, the growth rates are also function of the mode number.
Explicit calculations are performed for the -HMF model with , for which the zero mean-field mode is always found to dominate the
exponential growth. The theoretical predictions are successfully compared with
numerical simulations performed on a finite lattice
- …