3,438 research outputs found
Spectral Transformation Algorithms for Computing Unstable Modes of Large Scale Power Systems
In this paper we describe spectral transformation algorithms for the
computation of eigenvalues with positive real part of sparse nonsymmetric
matrix pencils , where is of the form \pmatrix{M&0\cr 0&0}. For
this we define a different extension of M\"obius transforms to pencils that
inhibits the effect on iterations of the spurious eigenvalue at infinity. These
algorithms use a technique of preconditioning the initial vectors by M\"obius
transforms which together with shift-invert iterations accelerate the
convergence to the desired eigenvalues. Also, we see that M\"obius transforms
can be successfully used in inhibiting the convergence to a known eigenvalue.
Moreover, the procedure has a computational cost similar to power or
shift-invert iterations with M\"obius transforms: neither is more expensive
than the usual shift-invert iterations with pencils. Results from tests with a
concrete transient stability model of an interconnected power system whose
Jacobian matrix has order 3156 are also reported here.Comment: 19 pages, 1 figur
Quantum Brownian motion in an analog Friedmann-Robertson-Walker geometry
In this paper we study the effects of quantum scalar field vacuum
fluctuations on scalar test particles in an analog model for the
Friedmann-Robertson-Walker spatially flat geometry. In this scenario, the cases
with one and two perfectly reflecting plane boundaries are considered as well
the case without boundary. We find that the particles can undergo Brownian
motion with a nonzero mean squared velocity induced by the quantum vacuum
fluctuations due to the time dependent background and the presence of the
boundaries. Typical singularities which appears due to the presence of the
boundaries in flat spacetime can be naturally regularized for an asymptotically
bounded expanding scale function. Thus, shifts in the velocity could be, at
least in principle, detectable experimentally. The possibility to implement
this observation in an analog cosmological model by the use of a Bose-Einstein
condensate is also discussed.Comment: 26 pages, 7 figures. Accepted for Publication in Phys. Rev.
Light-Cone Fluctuations in the Cosmic String Spacetime
In this paper we consider light-cone fluctuations arising as a consequence of
the nontrivial topology of the locally flat cosmic string spacetime. By setting
the light-cone along the z-direction we are able to develop a full analysis to
calculate the renormalized graviton two-point function, as well as the mean
square fluctuation in the geodesic interval function and the time delay (or
advance) in the propagation of a light-pulse. We found that all these
expressions depend upon the parameter characterizing the conical topology of
the cosmic string spacetime and vanish in the absence of it. We also point out
that at large distances from the cosmic string the mean square fluctuation in
the geodesic interval function is extremely small while in the opposite limit
it logarithmically increases, improving the signal and thus, making possible
the detection of such quantity.Comment: 19 pages, 1 figur
On the volume functional of compact manifolds with boundary with harmonic Weyl tensor
One of the main aims of this article is to give the complete classification
of critical metrics of the volume functional on a compact manifold with
boundary and with harmonic Weyl tensor, which improves the
corresponding classification for complete locally conformally flat case, due to
Miao and Tam [18]. In particular, we prove that a critical metric with harmonic
Weyl tensor on a simply connected compact manifold with boundary isometric to a
standard sphere must be isometric to a geodesic ball in a
simply connected space form and In order
to achieve our goal, firstly we shall conclude the classification of such
critical metrics under the Bach-flat assumption and then we will prove that
both geometric conditions are indeed equivalent.Comment: 20 page
Phonon induced Superconductivity of High Temperatures in Electrical Graphene Superlattices
We discuss the BCS theory for electrons in graphene with a superimposed
electrical unidirectional superlattice potential (SL). New Dirac points emerge
together with van Hove singularities (VHS) linking them. We obtain a
superconducting transition temperature for chemical potentials close to
the VHS assuming that acoustic phonon coupling should be the dominant
mechanism. Pairing of two onsite electrons with one electron close to the and the other close to the point is the most stable pair
formation. The resulting order parameter is almost constant over the entire SL.Comment: 10 pages, 2 figure
Acoustic black holes: massless scalar field analytic solutions and analogue Hawking radiation
We obtain the analytic solutions of the radial part of the massless
Klein-Gordon equation in the spacetime of both three dimensional rotating and
four dimensional canonical acoustic black holes, which are given in terms of
the confluent Heun functions. From these solutions, we obtain the scalar waves
near the acoustic horizon. We discuss the analogue Hawking radiation of
massless scalar particles and the features of the spectrum associated with the
radiation emitted by these acoustic black holes.Comment: 26 pages, with erratum. arXiv admin note: text overlap with
arXiv:1405.784
Lagrangian formulation of Newtonian cosmology
In this paper, we use the Lagrangian formalism of classical mechanics and
some assumptions to obtain cosmological differential equations analogous to
Friedmann and Einstein equations, obtained from the theory of general
relativity. This method can be used to a universe constituted of incoherent
matter, that is, the cosmologic substratum is comprised of dust.Comment: 5 pages. accepted for publication in Revista Brasileira de Ensino de
F\'{i}sica (RBEF). arXiv admin note: text overlap with arXiv:astro-ph/0309756
by other author
Confluent Heun functions and the physics of black holes: resonant frequencies, Hawking radiation and scattering of scalar waves
We apply the confluent Heun functions to study the resonant frequencies
(quasispectrum), the Hawking radiation and the scattering process of scalar
waves, in a class of spacetimes, namely, the ones generated by a
Kerr-Newman-Kasuya spacetime (dyon black hole) and a Reissner-Nordstr\"{o}m
black hole surrounded by a magnetic field (Ernst spacetime). In both
spacetimes, the solutions for the angular and radial parts of the corresponding
Klein-Gordon equations are obtained exactly, for massive and massless fields,
respectively. The special cases of Kerr and Schwarzschild black holes are
analyzed and the solutions obtained, as well as in the case of a Schwarzschild
black hole surrounded by a magnetic field. In all these special situations, the
resonant frequencies, Hawking radiation and scattering are studied.Comment: 18 pages. This paper was unified and published with arXiv:1603.0224
Class of solutions of the Wheeler-DeWitt equation in the Friedmann-Robertson-Walker universe
We show that the solutions of the Wheeler-DeWitt equation in a homogeneous
and isotropic universe are given by triconfluent Heun functions for the
spatially closed, flat, and open geometries of the Friedmann-Robertson-Walker
universe filled with different forms of energy. In a matter-dominated universe,
we find the polynomial solution and the energy density spectrum. In the cases
of radiation-dominated and vacuum universes, there are no polynomial solutions
as shown.Comment: 20 pages, 10 figure
Quantum Newtonian cosmology and the biconfluent Heun functions
We obtain the exact solution of the Schr\"odinger equation for a particle
(galaxy) moving in a Newtonian universe with a cosmological constant, which is
given in terms of the biconfluent Heun functions. The first six Heun
polynomials of the biconfluent function are written explicitly. The energy
spectrum which resembles the one corresponding to the isotropic harmonic
oscillator is also obtained. The wave functions as well as the energy levels
codify the role played by the cosmological constant.Comment: 15 pages, 2 figure
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