The role of rotation on Petersen Diagrams. The Pi1/0(Omega) Pi_{1/0}(Omega) period ratios

The present work explores the theoretical effects of rotation in calculating the period ratios of double-mode radial pulsating stars with special emphasis on high-amplitude delta Scuti stars (HADS). Diagrams showing these period ratios vs. periods of the fundamental radial mode have been employed as a good tracer of non-solar metallicities and are known as Petersen diagrams (PD).In this paper we consider the effect of moderate rotation on both evolutionary models and oscillation frequencies and we show that such effects cannot be completely neglected as it has been done until now. In particular it is found that even for low-to-moderate rotational velocities (15-50 km/s), differences in period ratios of some hundredths can be found. The main consequence is therefore the confusion scenario generated when trying to fit the metallicity of a given star using this diagram without a previous knowledge of its rotational velocity.Comment: A&A in pres

Integral relations and the adiabatic expansion method for 1+2 reactions above the breakup threshold: Helium trimers with soft-core potentials

The integral relations formalism introduced in \cite{bar09,rom11}, and designed to describe 1+$N$ reactions, is extended here to collision energies above the threshold for the target breakup. These two relations are completely general, and in this work they are used together with the adiabatic expansion method for the description of 1+2 reactions. The neutron-deuteron breakup, for which benchmark calculations are available, is taken as a test of the method. The s-wave collision between the $^4$He atom and $^4$He$_2$ dimer above the breakup threshold and the possibility of using soft-core two-body potentials plus a short-range three-body force will be investigated. Comparisons to previous calculations for the three-body recombination and collision dissociation rates will be shown.Comment: To be published in Physical Review

Verifying black hole orbits with gravitational spectroscopy

Gravitational waves from test masses bound to geodesic orbits of rotating black holes are simulated, using Teukolsky's black hole perturbation formalism, for about ten thousand generic orbital configurations. Each binary radiates power exclusively in modes with frequencies that are integer-linear-combinations of the orbit's three fundamental frequencies. The following general spectral properties are found with a survey of orbits: (i) 99% of the radiated power is typically carried by a few hundred modes, and at most by about a thousand modes, (ii) the dominant frequencies can be grouped into a small number of families defined by fixing two of the three integer frequency multipliers, and (iii) the specifics of these trends can be qualitatively inferred from the geometry of the orbit under consideration. Detections using triperiodic analytic templates modeled on these general properties would constitute a verification of radiation from an adiabatic sequence of black hole orbits and would recover the evolution of the fundamental orbital frequencies. In an analogy with ordinary spectroscopy, this would compare to observing the Bohr model's atomic hydrogen spectrum without being able to rule out alternative atomic theories or nuclei. The suitability of such a detection technique is demonstrated using snapshots computed at 12-hour intervals throughout the last three years before merger of a kludged inspiral. Because of circularization, the number of excited modes decreases as the binary evolves. A hypothetical detection algorithm that tracks mode families dominating the first 12 hours of the inspiral would capture 98% of the total power over the remaining three years.Comment: 18 pages, expanded section on detection algorithms and made minor edits. Final published versio

Classical Analog of Electromagnetically Induced Transparency

We present a classical analog for Electromagnetically Induced Transparency (EIT). In a system of just two coupled harmonic oscillators subject to a harmonic driving force we can reproduce the phenomenology observed in EIT. We describe a simple experiment performed with two linearly coupled RLC circuits which can be taught in an undergraduate laboratory class.Comment: 6 pages, two-column, 6 figures, submitted to the Am. J. Phy

Probabilistic Inference from Arbitrary Uncertainty using Mixtures of Factorized Generalized Gaussians

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both the joint probability density of the variables and the likelihood function of the (objective or subjective) observation are approximated by a special mixture model, in such a way that any desired conditional distribution can be directly obtained without numerical integration. We have developed an extended version of the expectation maximization (EM) algorithm to estimate the parameters of mixture models from uncertain training examples (indirect observations). As a consequence, any piece of exact or uncertain information about both input and output values is consistently handled in the inference and learning stages. This ability, extremely useful in certain situations, is not found in most alternative methods. The proposed framework is formally justified from standard probabilistic principles and illustrative examples are provided in the fields of nonparametric pattern classification, nonlinear regression and pattern completion. Finally, experiments on a real application and comparative results over standard databases provide empirical evidence of the utility of the method in a wide range of applications

Errors on the inverse problem solution for a noisy spherical gravitational wave antenna

A single spherical antenna is capable of measuring the direction and polarization of a gravitational wave. It is possible to solve the inverse problem using only linear algebra even in the presence of noise. The simplicity of this solution enables one to explore the error on the solution using standard techniques. In this paper we derive the error on the direction and polarization measurements of a gravitational wave. We show that the solid angle error and the uncertainty on the wave amplitude are direction independent. We also discuss the possibility of determining the polarization amplitudes with isotropic sensitivity for any given gravitational wave source.Comment: 13 pages, 4 figures, LaTeX2e, IOP style, submitted to CQ

General integral relations for the description of scattering states using the hyperspherical adiabatic basis

In this work we investigate 1+2 reactions within the framework of the hyperspherical adiabatic expansion method. To this aim two integral relations, derived from the Kohn variational principle, are used. A detailed derivation of these relations is shown. The expressions derived are general, not restricted to relative $s$ partial waves, and with applicability in multichannel reactions. The convergence of the ${\cal K}$-matrix in terms of the adiabatic potentials is investigated. Together with a simple model case used as a test for the method, we show results for the collision of a $^4$He atom on a \dimer dimer (only the elastic channel open), and for collisions involving a $^6$Li and two $^4$He atoms (two channels open).Comment: Accepted for publication in Physical Review

Variational description of continuum states in terms of integral relations

Two integral relations derived from the Kohn Variational Principle (KVP) are used for describing scattering states. In usual applications the KVP requires the explicit form of the asymptotic behavior of the scattering wave function. This is not the case when the integral relations are applied since, due to their short range nature, the only condition for the scattering wave function $\Psi$ is that it be the solution of $(H-E)\Psi=0$ in the internal region. Several examples are analyzed for the computation of phase-shifts from bound state type wave functions or, in the case of the scattering of charged particles, it is possible to obtain phase-shifts using free asymptotic conditions. As a final example we discuss the use of the integral relations in the case of the Hyperspherical Adiabatic method.Comment: 34 pages, 7 figures, accepted in Phys. Rev.