822 research outputs found
Quantization for uniform distributions on equilateral triangles
We approximate the uniform measure on an equilateral triangle by a measure
supported on points. We find the optimal sets of points (-means) and
corresponding approximation (quantization) error for , give numerical
optimization results for , and a bound on the quantization error for
. The equilateral triangle has particularly efficient quantizations
due to its connection with the triangular lattice. Our methods can be applied
to the uniform distributions on general sets with piecewise smooth boundaries
Black-Hole Solutions with Scalar Hair in Einstein-Scalar-Gauss-Bonnet Theories
In the context of the Einstein-scalar-Gauss-Bonnet theory, with a general
coupling function between the scalar field and the quadratic Gauss-Bonnet term,
we investigate the existence of regular black-hole solutions with scalar hair.
Based on a previous theoretical analysis, that studied the evasion of the old
and novel no-hair theorems, we consider a variety of forms for the coupling
function (exponential, even and odd polynomial, inverse polynomial, and
logarithmic) that, in conjunction with the profile of the scalar field, satisfy
a basic constraint. Our numerical analysis then always leads to families of
regular, asymptotically-flat black-hole solutions with non-trivial scalar hair.
The solution for the scalar field and the profile of the corresponding
energy-momentum tensor, depending on the value of the coupling constant, may
exhibit a non-monotonic behaviour, an unusual feature that highlights the
limitations of the existing no-hair theorems. We also determine and study in
detail the scalar charge, horizon area and entropy of our solutions.Comment: PdfLatex file, 29 Pages, 18 figures, the analysis was extended to
study the scalar charge, horizon area and entropy of our solutions, comments
added, typos corrected, version to appear in Physical Review
Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Ga XXX, Ge XXXI, As XXXII, Se XXXIII and Br XXXIV
We report calculations of energy levels, radiative rates and electron impact
excitation cross sections and rates for transitions in He-like Ga XXX, Ge XXXI,
As XXXII, Se XXXIII and Br XXXIV. The {\sc grasp} (general-purpose relativistic
atomic structure package) is adopted for calculating energy levels and
radiative rates. For determining the collision strengths, and subsequently the
excitation rates, the Dirac Atomic R-matrix Code ({\sc darc}) is used.
Oscillator strengths, radiative rates and line strengths are reported for all
E1, E2, M1 and M2 transitions among the lowest 49 levels of each ion.
Additionally, theoretical lifetimes are provided for all 49 levels of the above
five ions. Collision strengths are averaged over a Maxwellian velocity
distribution and the effective collision strengths obtained listed over a wide
temperature range up to 10 K. Comparisons are made with similar data
obtained using the Flexible Atomic Code ({\sc fac}) to highlight the importance
of resonances, included in calculations with {\sc darc}, in the determination
of effective collision strengths. Discrepancies between the collision strengths
from {\sc darc} and {\sc fac}, particularly for some forbidden transitions, are
also discussed. Finally, discrepancies between the present results for
effective collision strengths with the {\sc darc} code and earlier
semi-relativistic -matrix data are noted over a wide range of electron
temperatures for many transitions in all ions.Comment: 11 pages of Text, 11 Figures and 4 Tables. Ref: Physica Scripta 87
(2013) in press. arXiv admin note: substantial text overlap with
arXiv:1207.6525, arXiv:1209.2914, arXiv:1207.542
Hawking Radiation from a (4+n)-Dimensional Rotating Black Hole on the Brane
We study the emission of Hawking radiation in the form of scalar fields from
a (4+n)-dimensional, rotating black hole on the brane. We perform a numerical
analysis to solve both the radial and angular parts of the scalar field
equation, and derive exact results for the radial wavefunction and angular
eigenvalues, respectively. We then determine the Hawking radiation energy
emission rate, and find that, as the angular momentum increases, it is
suppressed in the low-energy regime but enhanced in the intermediate and
high-energy regimes. Our results agree with previous analytical studies,
derived in the low-angular momentum and low-energy approximation, and
generalize them to include angular momentum and energy regimes that were until
now unexplored. We also investigate the energy amplification due to
super-radiance and we find that, in the presence of extra dimensions, the
effect is significantly enhanced.Comment: 9 pages, Latex file, 5 figures, a new figure and a paragraph have
been added along with some clarifying comments, version to appear in Phys.
Lett.
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