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 ($^{67}\mathrm{Ga}$, $^{111}\mathrm{In}$, $^{123}\mathrm{I}$, $^{125}\mathrm{I}$ and $^{125}\mathrm{Xe}$). 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]