1,706 research outputs found
The Geometry of Warped Product Singularities
In this article the degenerate warped products of singular semi-Riemannian
manifolds are studied. They were used recently by the author to handle
singularities occurring in General Relativity, in black holes and at the
big-bang. One main result presented here is that a degenerate warped product of
semi-regular semi-Riemannian manifolds with the warping function satisfying a
certain condition is a semi-regular semi-Riemannian manifold. The connection
and the Riemann curvature of the warped product are expressed in terms of those
of the factor manifolds. Examples of singular semi-Riemannian manifolds which
are semi-regular are constructed as warped products. Applications include
cosmological models and black holes solutions with semi-regular singularities.
Such singularities are compatible with a certain reformulation of the Einstein
equation, which in addition holds at semi-regular singularities too.Comment: 14 page
Self-consistent calculations for atomic electron capture
We present a comprehensive investigation of electron capture (EC) ratios
spanning a broad range of atomic numbers. The study employs a self-consistent
computational method that incorporates electron screening, electron
correlations, overlap and exchange corrections, as well as shake-up and
shake-off atomic effects. The electronic wave functions are computed with the
Dirac-Hartree-Fock-Slater (DHFS) method, chosen following a systematic
comparison of binding energies, atomic relaxation energies and Coulomb
amplitudes against other existing methods and experimental data. A novel
feature in the calculations is the use of an energy balance employing atomic
masses, which avoids approximating the electron total binding energy and allows
a more precise determination of the neutrino energy. This leads to a better
agreement of our predictions for capture ratios in comparison with the
experimental ones, especially for low-energy transitions. We expand the
assessment of EC observables uncertainties by incorporating atomic relaxation
energy uncertainties, in contrast to previous studies focusing only on Q-value
and nuclear level energies. Detailed results are presented for nuclei of
practical interest in both nuclear medicine and exotic physics searches
involving liquid Xenon detectors (, ,
, and ). Our study can
be relevant for astrophysical, nuclear, and medical applications.Comment: 16 pages, 9 figures, 4 table
Fully-Renormalized QRPA fulfills Ikeda sum rule exactly
The renormalized quasiparticle-RPA is reformulated for even-even nuclei using
restrictions imposed by the commutativity of the phonon creation operator with
the total particle number operator. This new version, Fully-Renormalized QRPA
(FR-QRPA), is free from the spurious low-energy solutions. Analytical proof is
given that the Ikeda sum rule is fullfiled within the FR-QRPA.Comment: 9 page
Study of the acoustic signature of UHE neutrino interactions in water and ice
The production of acoustic signals from the interactions of ultra-high energy
(UHE) cosmic ray neutrinos in water and ice has been studied. A new
computationally fast and efficient method of deriving the signal is presented.
This method allows the implementation of up to date parameterisations of
acoustic attenuation in sea water and ice that now includes the effects of
complex attenuation, where appropriate. The methods presented here have been
used to compute and study the properties of the acoustic signals which would be
expected from such interactions. A matrix method of parameterising the signals,
which includes the expected fluctuations, is also presented. These methods are
used to generate the expected signals that would be detected in acoustic UHE
neutrino telescopes.Comment: 21 pages and 13 figure
GaN and InN nanowires grown by MBE: a comparison
Morphological, optical and transport properties of GaN and InN nanowires
grown by molecular beam epitaxy (MBE) have been studied. The differences
between the two materials in respect to growth parameters and optimization
procedure was stressed. The nanowires crystalline quality has been investigated
by means of their optical properties. A comparison of the transport
characteristics was given. For each material a band schema was shown, which
takes into account transport and optical features and is based on Fermi level
pinning at the surface.Comment: 5 pages, 5 figure
Spectral Simplicity of Apparent Complexity, Part I: The Nondiagonalizable Metadynamics of Prediction
Virtually all questions that one can ask about the behavioral and structural
complexity of a stochastic process reduce to a linear algebraic framing of a
time evolution governed by an appropriate hidden-Markov process generator. Each
type of question---correlation, predictability, predictive cost, observer
synchronization, and the like---induces a distinct generator class. Answers are
then functions of the class-appropriate transition dynamic. Unfortunately,
these dynamics are generically nonnormal, nondiagonalizable, singular, and so
on. Tractably analyzing these dynamics relies on adapting the recently
introduced meromorphic functional calculus, which specifies the spectral
decomposition of functions of nondiagonalizable linear operators, even when the
function poles and zeros coincide with the operator's spectrum. Along the way,
we establish special properties of the projection operators that demonstrate
how they capture the organization of subprocesses within a complex system.
Circumventing the spurious infinities of alternative calculi, this leads in the
sequel, Part II, to the first closed-form expressions for complexity measures,
couched either in terms of the Drazin inverse (negative-one power of a singular
operator) or the eigenvalues and projection operators of the appropriate
transition dynamic.Comment: 24 pages, 3 figures, 4 tables; current version always at
http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt1.ht
Double beta decay to excited states in Nd150
The pseudo SU(3) model is used to study the double beta decay of Nd150 to the
ground and excited states of Sm150 . Low lying collective excitations of Sm150
and its BE(2) intensities are well reproduced. Expressions for the two neutrino
double beta decay to excited states are developed and used to describe the
decay of Nd150 . The existence of selection rules which strongly restrict the
decay is discussed.Comment: 22 pages, LaTeX, 1 figure with Postscript file available under
request at [email protected]
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