18,918 research outputs found
Gravitational waveforms with controlled accuracy
A partially first-order form of the characteristic formulation is introduced
to control the accuracy in the computation of gravitational waveforms produced
by highly distorted single black hole spacetimes. Our approach is to reduce the
system of equations to first-order differential form on the angular
derivatives, while retaining the proven radial and time integration schemes of
the standard characteristic formulation. This results in significantly improved
accuracy over the standard mixed-order approach in the extremely nonlinear
post-merger regime of binary black hole collisions.Comment: Revised version, published in Phys. Rev. D, RevTeX, 16 pages, 4
figure
A conjecture on Exceptional Orthogonal Polynomials
Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of
Sturm-Liouville problems and generalize in this sense the classical families of
Hermite, Laguerre and Jacobi. They also generalize the family of CPRS
orthogonal polynomials. We formulate the following conjecture: every
exceptional orthogonal polynomial system is related to a classical system by a
Darboux-Crum transformation. We give a proof of this conjecture for codimension
2 exceptional orthogonal polynomials (X2-OPs). As a by-product of this
analysis, we prove a Bochner-type theorem classifying all possible X2-OPS. The
classification includes all cases known to date plus some new examples of
X2-Laguerre and X2-Jacobi polynomials
Gravitational Waves from a Fissioning White Hole
We present a fully nonlinear calculation of the waveform of the gravitational
radiation emitted in the fission of a vacuum white hole. At early times, the
waveforms agree with close-approximation perturbative calculations but they
reveal dramatic time and angular dependence in the nonlinear regime. The
results pave the way for a subsequent computation of the radiation emitted
after a binary black hole merger.Comment: 11 pages, 6 figures, RevTeX
Exceptional orthogonal polynomials and the Darboux transformation
We adapt the notion of the Darboux transformation to the context of
polynomial Sturm-Liouville problems. As an application, we characterize the
recently described Laguerre polynomials in terms of an isospectral
Darboux transformation. We also show that the shape-invariance of these new
polynomial families is a direct consequence of the permutability property of
the Darboux-Crum transformation.Comment: corrected abstract, added references, minor correction
Synchronization of networks with variable local properties
We study the synchronization transition of Kuramoto oscillators in scale-free
networks that are characterized by tunable local properties. Specifically, we
perform a detailed finite size scaling analysis and inspect how the critical
properties of the dynamics change when the clustering coefficient and the
average shortest path length are varied. The results show that the onset of
synchronization does depend on these properties, though the dependence is
smooth. On the contrary, the appearance of complete synchronization is
radically affected by the structure of the networks. Our study highlights the
need of exploring the whole phase diagram and not only the stability of the
fully synchronized state, where most studies have been done up to now.Comment: 5 pages and 3 figures. APS style. Paper to be published in IJBC
(special issue on Complex Networks' Structure and Dynamics
Surfactant effect in heteroepitaxial growth. The Pb - Co/Cu(111) case
A MonteCarlo simulations study has been performed in order to study the
effect of Pb as surfactant on the initial growth stage of Co/Cu(111). The main
characteristics of Co growing over Cu(111) face, i.e. the decorated double
layer steps, the multiple layer islands and the pools of vacancies, disappear
with the pre-evaporation of a Pb monolayer. Through MC simulations, a full
picture of these complex processes is obtained. Co quickly diffuses through the
Pb monolayer exchanging place with Cu atoms at the substrate. The exchange
process diffusion inhibits the formation of pure Co islands, reducing the
surface stress and then the formation of multilayer islands and the pools of
vacancies. On the other hand, the random exchange also suppress the nucleation
preferential sites generated by Co atoms at Cu steps, responsible of the step
decoration.Comment: 4 pages, latex, 2 figures embedded in the tex
A GIT interpretration of the Harder-Narasimhan filtration
An unstable torsion free sheaf on a smooth projective variety gives a GIT
unstable point in certain Quot scheme. To a GIT unstable point, Kempf
associates a "maximally destabilizing" 1-parameter subgroup, and this induces a
filtration of the torsion free sheaf. We show that this filtration coincides
with the Harder-Narasimhan filtration.Comment: 19 pages; Comments of the referees and references added. The
construction for holomorphic pairs (Sections 6 and 7 from previous version)
will appear in a further publication. To appear in Rev. Mat Complutens
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