1,802 research outputs found
Efficient Enumeration of Non-Equivalent Squares in Partial Words with Few Holes
International audienceA partial word is a word with holes (also called don't cares: special symbols which match any symbol). A p-square is a partial word matching at least one standard square without holes (called a full square). Two p-squares are called equivalent if they match the same sets of full squares. Denote by psquares(T) the number of non-equivalent p-squares which are subwords of a partial word T. Let PSQUARES k (n) be the maximum value of psquares(T) over all partial words of length n with k holes. We show asympthotically tight bounds: c1 · min(nk 2 , n 2) ≤ PSQUARES k (n) ≤ c2 · min(nk 2 , n 2) for some constants c1, c2 > 0. We also present an algorithm that computes psquares(T) in O(nk 3) time for a partial word T of length n with k holes. In particular, our algorithm runs in linear time for k = O(1) and its time complexity near-matches the maximum number of non-equivalent p-squares
Introductory lectures on the Effective One Body formalism
The Effective One Body (EOB) formalism is an analytical approach which aims
at providing an accurate description of the motion and radiation of coalescing
binary black holes. We present a brief review of the basic elements of this
approach.Comment: 22 pages, 3 figures, lectures given at the Second ICRANet
Stueckelberg Workshop on Relativistic Field Theories (Pescara, Italy,
September 3-8, 2007); to be published in the International Journal of Modern
Physics
Hadamard Regularization
Motivated by the problem of the dynamics of point-particles in high
post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a
certain class of functions which are smooth except at some isolated points
around which they admit a power-like singular expansion. We review the concepts
of (i) Hadamard ``partie finie'' of such functions at the location of singular
points, (ii) the partie finie of their divergent integral. We present and
investigate different expressions, useful in applications, for the latter
partie finie. To each singular function, we associate a partie-finie (Pf)
pseudo-function. The multiplication of pseudo-functions is defined by the
ordinary (pointwise) product. We construct a delta-pseudo-function on the class
of singular functions, which reduces to the usual notion of Dirac distribution
when applied on smooth functions with compact support. We introduce and analyse
a new derivative operator acting on pseudo-functions, and generalizing, in this
context, the Schwartz distributional derivative. This operator is uniquely
defined up to an arbitrary numerical constant. Time derivatives and partial
derivatives with respect to the singular points are also investigated. In the
course of the paper, all the formulas needed in the application to the physical
problem are derived.Comment: 50 pages, to appear in Journal of Mathematical Physic
Gravitational-Wave Recoil from the Ringdown Phase of Coalescing Black Hole Binaries
The gravitational recoil or "kick" of a black hole formed from the merger of
two orbiting black holes, and caused by the anisotropic emission of
gravitational radiation, is an astrophysically important phenomenon. We combine
(i) an earlier calculation, using post-Newtonian theory, of the kick velocity
accumulated up to the merger of two non-spinning black holes, (ii) a
"close-limit approximation" calculation of the radiation emitted during the
ringdown phase, and based on a solution of the Regge-Wheeler and Zerilli
equations using initial data accurate to second post-Newtonian order. We prove
that ringdown radiation produces a significant "anti-kick". Adding the
contributions due to inspiral, merger and ringdown phases, our results for the
net kick velocity agree with those from numerical relativity to 10-15 percent
over a wide range of mass ratios, with a maximum velocity of 180 km/s at a mass
ratio of 0.38.Comment: 9 pages, 5 figures; to appear in Class. Quant. Gra
Wash-Out in N_2-dominated leptogenesis
We study the wash-out of a cosmological baryon asymmetry produced via
leptogenesis by subsequent interactions. Therefore we focus on a scenario in
which a lepton asymmetry is established in the out-of-equilibrium decays of the
next-to-lightest right-handed neutrino. We apply the full classical Boltzmann
equations without the assumption of kinetic equilibrium and including all
quantum statistical factors to calculate the wash-out of the lepton asymmetry
by interactions of the lightest right-handed state. We include scattering
processes with top quarks in our analysis. This is of particular interest since
the wash-out is enhanced by scatterings and the use of mode equations with
quantum statistical distribution functions. In this way we provide a
restriction on the parameter space for this scenarios.Comment: 26 pages, 4 figures, profound revision, exposition is now in flavor
notation, one plot and discussion added, numerical error corrected, three
plots changed, text polished, main results remain unchanged, reference
added,matches published versio
A template bank to search for gravitational waves from inspiralling compact binaries: II. Phenomenological model
Matched filtering is used to search for gravitational waves emitted by
inspiralling compact binaries in data from ground-based interferometers. One of
the key aspects of the detection process is the deployment of a set of
templates, also called a template bank, to cover the astrophysically
interesting region of the parameter space. In a companion paper, we described
the template-bank algorithm used in the analysis of LIGO data to search for
signals from non-spinning binaries made of neutron star and/or stellar-mass
black holes; this template bank is based upon physical template families. In
this paper, we describe the phenomenological template bank that was used to
search for gravitational waves from non-spinning black hole binaries (from
stellar mass formation) in the second, third and fourth LIGO science runs. We
briefly explain the design of the bank, whose templates are based on a
phenomenological detection template family. We show that this template bank
gives matches greater than 95% with the physical template families that are
expected to be captured by the phenomenological templates.Comment: 10 pages, 9 figure
Post-Newtonian expansion of gravitational waves from a particle in circular orbits around a rotating black hole: Up to beyond the quadrupole formula
Extending a method developed by Sasaki in the Schwarzschild case and by
Shibata, Sasaki, Tagoshi, and Tanaka in the Kerr case, we calculate the
post-Newtonian expansion of the gravitational wave luminosities from a test
particle in circular orbit around a rotating black hole up to beyond
the quadrupole formula. The orbit of a test particle is restricted on the
equatorial plane. We find that spin dependent terms appear in each
post-Newtonian order, and that at they have a significant effect on
the orbital phase evolution of coalescing compact binaries. By comparing the
post-Newtonian formula of the luminosity with numerical results we find that,
for , the spin dependent terms at and
improve the accuracy of the post-Newtonian formula significantly, but
those at do not improve.Comment: 27 pages, revtex, 6 figures, submitted to Physical Review
Full Boltzmann equations for leptogenesis including scattering
We study the evolution of a cosmological baryon asymmetry produced via
leptogenesis by means of the full classical Boltzmann equations, without the
assumption of kinetic equilibrium and including all quantum statistical
factors. Beginning with the full mode equations we derive the usual equations
of motion for the right-handed neutrino number density and integrated lepton
asymmetry, and show explicitly the impact of each assumption on these
quantities. For the first time, we investigate also the effects of scattering
of the right-handed neutrino with the top quark to leading order in the Yukawa
couplings by means of the full Boltzmann equations. We find that in our full
Boltzmann treatment the final lepton asymmetry can be suppressed by as much as
a factor of 1.5 in the weak wash-out regime (K<1), compared to the usual
integrated approach which assumes kinetic equilibrium and neglects quantum
statistics. This suppression is in contrast with the enhancement seen in some
previous studies that considered only decay and inverse decay of the
right-handed neutrino. However, this suppression quickly decreases as we
increase K. In the strong wash-out regime (K>1), the full Boltzmann treatment
and the integrated approach give nearly identical final lepton asymmetries
(within 10 % of each other at K>3). Finally, we show that the opposing effects
of quantum statistics on decays/inverse decays and the scattering processes
tend to reduce the net importance of scattering on leptogenesis in the full
treatment compared to the integrated approach.Comment: 39 pages, 8 figures, typos corrected, replaced to match published
versio
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