Searcharxiv⌕ Search

arXiv subjects

G. Gonzalez

Publications and source records attributed to G. Gonzalez.

At least 19 recordsLinked to original sources
arXiv2026

A family of non-autonomous hybrid Lienard oscillators based on a parametrically extended commutative factorization

We introduce a class of nonautonomous nonlinear oscillator equations of mixed Li\'{e}nard type that arises from a parametric deformation of the commutative factorization procedure applied to second-order ordinary differential equations with periodic solutions. Their solutions, in particular the isochronous waveforms, are obtained in closed form through a Riccati reduction scheme for the power-law choice of the factorization function, $\phi(x)=kx^{q}$, $k\in \mathbb{R}$, and $q\in\mathbb{N}$, corresponding to the so-called modified Emden oscillators, and do not depend on the arbitrary deformation parameter $A_1$. The variational structure of the equation is characterised by a Lagrangian supplemented with a generalised Rayleigh dissipation function that contains a non-standard cubic term in $\dot{x}$. We also show that multiplying the equation of motion by the Jacobi multiplier $M(x)=x^{-2A_1}$ a position-dependent-mass (PDM) form is obtained with related friction and restoring force.

nlin.SI↗
arXiv2026

LIGO Detector Characterization in the Second and Third Parts of the Fourth Observing Run

LIGO detector characterization efforts enabled the confident detection of gravitational waves from hundreds of compact binary coalescences during the fourth observing run. Reliable production of high quality detector data and rapid noise mitigation efforts allow the extraction of the most in-depth knowledge of gravitational wave sources and their progenitors. In this paper we describe LIGO detector characterization activities during the second and third parts of O4-O4b and O4c. We summarize changes in detector configuration and performance at the LIGO Hanford and LIGO Livingston Observatories between the end of the first part of O4a and the end of O4c, including upgrades made during the commissioning break preceding O4b and during repairs performed in O4c. We describe instrumental investigations carried out at both sites designed to understand and subsequently mitigate the effect on detector sensitivity of transient glitches, narrowband spectral lines, and vibration-driven noise, among other data quality concerns. We then review the tools and procedures used to validate gravitational wave candidates and the data quality products thus supplied to searches for gravitational waves from compact binary coalescences and unmodeled transients, continuous gravitational waves, and the stochastic gravitational wave background. The efforts of the detector characterization group are essential for maintaining and improving the sensitivity and reliability of the LIGO detectors especially as observing runs lengthen and more events are detected. We conclude with prospects for LIGO detector characterization activities in future observing runs.

astro-ph.IM↗
arXiv2026

Calibration and Performance of Germanium High Voltage Detectors for SuperCDMS SNOLAB

As SuperCDMS SNOLAB is getting ready to search for low mass dark matter particles, using cryogenic Ge and Si detectors, a set of six of the new SuperCDMS High Voltage (HV) detectors (four Ge and two Si) were tested in the Cryogenic Underground TEst facility (CUTE) at SNOLAB. This provided the first opportunity to gain experience with this new detector type and assess their performance thoroughly under low background conditions. Here we describe the SuperCDMS HV detector concept and discuss some of the newly developed analysis methods and approaches. Focusing on the Ge detectors, we investigate the detector performance under voltage bias (up to 90 V), exercise the low energy (keV to sub-keV range) calibration based on the electron capture peaks generated by the decay of $^{71}$Ge, assess the detector resolution, and demonstrate the unexpected (and encouraging) ability of these detectors to also measure high energy interactions in the hundreds of keV range with good resolution (better than 3% at 356 keV).

physics.ins-det↗
arXiv2024

Isochronous waveforms of Li\'enard equations via commutative factorization

Isochronous waveform solutions of homogeneous Li\'enard equations are obtained by a modification of the nonlinear factorization method of Rosu and Cornejo-P\'erez. The scheme is based on the assumption that the intermediate function $\Phi$ that can be introduced in this factorization method depends on both the dependent and independent variables of the nonlinear equation. The method is applied to three cases, a noted cubic anharmonic oscillator, a Li\'enard-reduced form of the Sharma-Tasso-Olver evolution equation, and the cubic-quintic Wilson's Li\'enard equation. All these cases are written in a commutative factored form that allows to obtain the general solutions as solutions of a certain type of Bernoulli differential equation. A theorem is also given asserting the general form of the Li\'enard equation, i.e., for given polynomial degree n of its coefficients, which can be solved by this method. The conditions under which these equations can be also approached by non-local transformations are established.

math.CA↗
arXiv2023

Stress evolution in plastically deformed austenitic and ferritic steels determined using angle- and energy-dispersive diffraction

In the presented research, the intergranular elastic interaction and the second-order plastic incompatibility stress in textured ferritic and austenitic steels were investigated by means of diffraction. The lattice strains were measured inside the samples by the multiple reflection method using high energy X-rays diffraction during uniaxial in situ tensile tests. Comparing experiment with various models of intergranular interaction, it was found that the Eshelby-Kr\"oner model correctly approximates the X-ray stress factors (XSFs) for different reflections hkl and scattering vector orientations. The verified XSFs were used to investigate the evolution of the first and second-order stresses in both austenitic and ferritic steels. It was shown that considering only the elastic anisotropy, the non-linearity of $\sin^2{\psi}$ plots cannot be explained by crystallographic texture. Therefore, a more advanced method based on elastic-plastic self-consistent modeling (EPSC) is required for the analysis. Using such methodology the non-linearities of $\cos^2{\phi}$ plots were explained, and the evolutions of the first and second-order stresses were determined. It was found that plastic deformation of about 1- 2% can completely exchange the state of second-order plastic incompatibility stresses.

cond-mat.mtrl-sci↗
arXiv2022

Factorization conditions for nonlinear second-order differential equations

For the case of nonlinear second-order differential equations with a constant coefficient of the first derivative term and polynomial nonlinearities, the factorization conditions of Rosu and Cornejo-Perez are approached in two ways: (i) by commuting the subindices of the factorization functions in the two factorization conditions and (ii) by leaving invariant only the first factorization condition achieved by using monomials or polynomial sequences. For the first case, the factorization brackets commute and the generated equations are only equations of Ermakov-Pinney type. The second modification is non commuting, leading to nonlinear equations with different nonlinear force terms, but the same first-order part as the initially factored equation. It is illustrated for monomials with the examples of the generalized Fisher and FitzHugh-Nagumo initial equations. A polynomial sequence example is also included.

nlin.SI↗
arXiv2021

Duality between Poisson and Schrödinger equations in three dimensions

A duality between an electrostatic problem in a three dimensional world and a quantum mechanical problem in a one dimensional world which allows one to obtain the ground state solution of the Schrödinger equation by using electrostatic results is generalized to three dimensions. Here, it is demonstrated that the same transformation technique is also applicable to the s-wave Schrödinger equation in three dimensions for central potentials. This approach leads to a general relationship between the electrostatic potential and the s-wave function and the electric energy density to the quantum mechanical energy.

quant-ph↗
arXiv2014

Environmental Influences on the LIGO Gravitational Wave Detectors during the 6th Science Run

We describe the influence of environmental noise on LIGO detectors in the sixth science run (S6), from July 2009 to October 2010. We show results from experimental investigations testing the coupling level and mechanisms for acoustic, electromagnetic/magnetic and seismic noise to the instruments. We argument the sensors' importance for vetoes of false positive detections, report estimates of the noise sources' contributions to the detector background, and discuss the ways in which environmental coupling should be reduced in the LIGO upgrade, Advanced LIGO.

astro-ph.IM↗
arXiv2012

Searching for gravitational waves from binary coalescence

We describe the implementation of a search for gravitational waves from compact binary coalescences in LIGO and Virgo data. This all-sky, all-time, multi-detector search for binary coalescence has been used to search data taken in recent LIGO and Virgo runs. The search is built around a matched filter analysis of the data, augmented by numerous signal consistency tests designed to distinguish artifacts of non-Gaussian detector noise from potential detections. We demonstrate the search performance using Gaussian noise and data from the fifth LIGO science run and demonstrate that the signal consistency tests are capable of mitigating the effect of non-Gaussian noise and providing a sensitivity comparable to that achieved in Gaussian noise.

gr-qc↗
arXiv2011

The two metallicity groups of the globular cluster M22: a chemical perspective

We present a detailed chemical composition analysis of 35 red giant stars in the globular cluster M22. High resolution spectra for this study were obtained at five observatories, and analyzed in a uniform manner. We have determined abundances of representative light proton-capture, alpha, Fe-peak and neutron-capture element groups. Our aim is to better understand the peculiar chemical enrichment history of this cluster, in which two stellar groups are characterized by a different content in iron, neutron capture elements Y, Zr and Ba, and alpha element Ca. The principal results of this study are: (i) substantial star-to-star metallicity scatter (-2.0<[Fe/H]<-1.6); (ii) enhancement of s-process/r-process neutron-capture abundance ratios in a fraction of giants, positively correlated with metallicity; (iii) sharp separation between the s-process rich and s-process poor groups by [La/Eu] ratio; (iv) possible increase of [Cu/Fe] ratios with increasing [Fe/H], suggesting that this element also has a significant s-process component; and (v) presence of Na-O and C-N anticorrelations in both the stellar groups.

astro-ph.SR↗
arXiv2009

Parent Stars of Extrasolar Planets. X. Lithium Abundances and vsini Revisited

We determine Li abundances and vsini values from new spectra of 53 stars with Doppler-detected planets not included in our previous papers in this series. We also examine two sets of stars without detected planets, which together serve as our comparison sample. Using the method of comparison of Li abundances and vsini values between two sets of stars we introduced in Gonzalez (2008), we confirm that these two quantities are smaller among stars with planets compared to stars without detected planets near the solar temperature. The transition from low to high Li abundance among SWPs occurs near 5850 K, a revision of about 50 K from our previous determination. The transition from low to high vsini occurs near 6000 K, but this temperature is not as well constrained.

astro-ph.SR↗
arXiv2009

Accurate calibration of test mass displacement in the LIGO interferometers

We describe three fundamentally different methods we have applied to calibrate the test mass displacement actuators to search for systematic errors in the calibration of the LIGO gravitational-wave detectors. The actuation frequencies tested range from 90 Hz to 1 kHz and the actuation amplitudes range from 1e-6 m to 1e-18 m. For each of the four test mass actuators measured, the weighted mean coefficient over all frequencies for each technique deviates from the average actuation coefficient for all three techniques by less than 4%. This result indicates that systematic errors in the calibration of the responses of the LIGO detectors to differential length variations are within the stated uncertainties.

gr-qc↗
arXiv2009

Precise calibration of LIGO test mass actuators using photon radiation pressure

Precise calibration of kilometer-scale interferometric gravitational wave detectors is crucial for source localization and waveform reconstruction. A technique that uses the radiation pressure of a power-modulated auxiliary laser to induce calibrated displacements of one of the ~10 kg arm cavity mirrors, a so-called photon calibrator, has been demonstrated previously and has recently been implemented on the LIGO detectors. In this article, we discuss the inherent precision and accuracy of the LIGO photon calibrators and several improvements that have been developed to reduce the estimated voice coil actuator calibration uncertainties to less than 2 percent (1-sigma). These improvements include accounting for rotation-induced apparent length variations caused by interferometer and photon calibrator beam centering offsets, absolute laser power measurement using temperature-controlled InGaAs photodetectors mounted on integrating spheres and calibrated by NIST, minimizing errors induced by localized elastic deformation of the mirror surface by using a two-beam configuration with the photon calibrator beams symmetrically displaced about the center of the optic, and simultaneously actuating the test mass with voice coil actuators and the photon calibrator to minimize fluctuations caused by the changing interferometer response. The photon calibrator is able to operate in the most sensitive interferometer configuration, and is expected to become a primary calibration method for future gravitational wave searches.

gr-qc↗
arXiv2005

Relativistic motion with linear dissipation

A general formalism for obtaining the Lagrangian and Hamiltonian for a one dimensional dissipative system is developed. The formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The relativistic wave equation is solved for a free particle with linear dissipation.

quant-ph↗
arXiv2005

Habitable Zones in the Universe

Habitability varies dramatically with location and time in the universe. This was recognized centuries ago, but it was only in the last few decades that astronomers began to systematize the study of habitability. The introduction of the concept of the habitable zone was key to progress in this area. The habitable zone concept was first applied to the space around a star, now called the Circumstellar Habitable Zone. Recently, other, vastly broader, habitable zones have been proposed. We review the historical development of the concept of habitable zones and the present state of the research. We also suggest ways to make progress on each of the habitable zones and to unify them into a single concept encompassing the entire universe.

astro-ph↗
arXiv2004

Lagrangians and Hamiltonians for one-dimensional systems

An equation is obtained to find the Lagrangian for a one-dimensional autonomous system. The continuity of the first derivative of its constant of motion is assumed. This equation is solved for a generic nonconservative autonomous system that has certain quasi-relativistic properties. A new method based on a Taylor series expansion is used to obtain the associated Hamiltonian for this system. These results have the usual expression for a conservative system when the dissipation parameter goes to zero. An example of this approach is given.

math-ph↗
arXiv2003

Effects on the eigenvalues of the quantum bouncer due to dissipation

Effects on the spectra of the quantum bouncer due to dissipation are given when a linear or quadratic dissipation is taken into account. Classical constant of motions and Hamiltonians are deduced for these systems and their quantized eigenvalues are estimated through perturbation theory. we found some differences when we compare the eigenvalues of these two quantities.

quant-ph↗