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We report VI CCD photometry of the globular cluster cluster NGC 1851. We aim to study the membership of the variable stars detected in the field of the cluster as listed in the Catalogue of Variable stars in Globular Clusters (CVSGC; Clement et al. 2001) and reported by the Gaia mission. We cross match the two sets of variables to produce light curves that lead to the estimation of physical parameters. The resulting colour-magnitude diagram (CMD), free of likely field stars, enables to confirm the position of the variables, their type and evolutionary stage. We provide new estimations of the period using data acquired on a long timebase. The Fourier decomposition of cluster member RR Lyrae light curves lead to a mean metalicity and distance of \([Fe/H]_{ZW} = -1.35 \pm 0.22\) dex and \(11.9 \pm 0.6\) kpc. The variability and membership of stars reported by Gaia-DR3 as variables in the field of the cluster is discussed., Comment: 16 pages,10 figures, 5 table

We made a survey of the variable stars in a $13.2 \times 13.2$ arcmin$^2$ centered on the field of the Galactic bulge cluster NGC 6558. A total of 78 variables was found in the field of the cluster. Many of these variables are included in the Catalogue of Variable Stars in Galactic Globular Clusters (Clement et al. 2001), OGLE or Gaia-DR3 data releases. A membership analysis based on the proper motions of Gaia-DR3 revealed that many of these variables do not belong to the cluster. We employed the data from the aforementioned surveys and our own data in the VI photometric system to estimate the periods, which along with the light curves morphology and position in a deferentially dereddened colour-magnitude diagram(CMD), help classifying the variable types. Two new member variables were found; an eclipsing binary (V18) and a semi-regular SR/L (V19). In the end we conclude that only 9 variables are likely cluster members. Member variables were used to discuss the mean metallicity and distance of the parental cluster and find the average values.

Employing \emph{VI} images of NGC 2419 acquired over 17 years, light curves for most of the known variables in the field of the cluster are produced. A cluster membership analysis for about 3100 stars in the cluster field with proper motions from $Gaia$-DR3, revealed the presence of member stars as far as 140 pc from the cluster center and enabled the construction of a cleaner CMD free of field stars. It was found that RRab and RRc stars share the inter-order region in the instability strip, which is unusual for OoII clusters. Theoretical considerations confirm that Pop II cepheids are descendants of extreme ZAHB blue tail stars with very thin envelopes of about 10\% of the total mass. Member RR Lyrae stars were employed to calculate independent estimates of the mean cluster metallicity and distance; we found [Fe/H]$_{\rm UV}= -1.90 \pm 0.27$ and $D=86.3 \pm 5.0$ kpc from the RRab and [Fe/H]$_{\rm UV}= -1.88 \pm 0.30$ and $D=83.1 \pm 8.1$ kpc from the RRc light curves., Comment: 19 pages, 11 figures, 3 tables

We present a comprehensive analysis of the variable stars projected on the field of the Galactic bulge globular cluster NGC 6522, offering valuable insights into their characteristics. Using proper motions from Gaia DR3, we aim to distinguish between field stars and true cluster members. For an accurate color-magnitude diagram of the member stars, we produced a differential reddening map. We detect and discuss the peculiarities of variable stars of the types RR Lyrae, type II Cepheids, Long Period Variables (LPV) and eclipsing binaries, whose light curves are available through the OGLE III and IV databases. Notably, we explore the variable V24, which shows a prominent phase modulation resulting from period changes in a time scale of ~1100 days. The variable stars among the cluster members serve as indicators of the cluster metallicity and distance; these determinations are based on their light curves. With the Fourier light curve decomposition of three RRc stars, we have derived the following cluster parameters: the metallicity in the spectroscopic scale [Fe/H]$_{\rm UVES}$=--1.16 $\pm$0.09; and the mean distance $D=8.77 \pm 0.16$ kpc., Comment: 15 pages, 10 Figures, 3 tables

We present a CCD $VI$ time-series analysis of the globular cluster NGC 6139 and its variable star population. Using the astrometric data available in $Gaia$-DR3 we performed a membership analysis that enabled the construction of a clean Colour-Magnitude Diagram (CMD). Variable stars in the field of the cluster reported by $Gaia$-DR3 and newly discovered ones in this paper are classified and their membership is critically evaluated. We report two cluster member RRc (V12, V15) and four SR (V13, V14, V17, V18) not previously detected and assign variable names to V11 and V16 detected by $Gaia$ as they proof to be cluster members. Light curves and periods for non-member $Gaia$ eclipsing binaries, semi regular variables and newly detected RR Lyrae stars are provided. Fourier decomposition of the light curves of the cluster member RRab and RRc stars leads to the values [Fe/H]=$-1.63$ dex, and distance of 9.63$\pm$0.68 kpc. The Oosterhoff type II nature of the cluster is confirmed. We adopted the mean reddening $E(B-V)$=0.786 mag and performed a differential reddening analysis based on the dispersion of the red giant branch. The differential map allowed a mild correction of the CMD., Comment: 12 pages, 10 figures, 5 tables

A five year CCD photometric \emph{VI} time-series of NGC 7006 is employed to perform a detailed analysis of the known population of variable stars. In the process we have corrected inconsistent classifications, sky coordinates and found ten new cluster member variables. An independent reddening estimate with a value $E(B-V)=0.08\pm0.05$ is made. Using Fourier decompositions of RR Lyrae light curves and well established calibrations, the cluster mean metallicity and distance [Fe/H]$_{\rm ZW}= -1.53\pm0.15$ and $41.2\pm1.4$ kpc are estimated based on an extended sample of cluster member RRab stars. Using the $Gaia$-DR3 data we performed an extensive membership analysis which leads to a clean Colour-Magnitude diagram, and hence to the identification of variables that are likely field stars, and to considerations on the variables distribution in the Horizontal Branch (HB). A double mode RR Lyrae and three CW star are discussed. The origin of CW stars from precursors in the blue tail of the HB with very thin ($\sim 0.06 \pm 0.01 M_{\odot}$) envelopes is argued. Our models indicate that the Main Sequence predecessor of RR Lyrae stars had a mass of 0.82-0.85 $M_{\odot}$ and lost about 25-35\% of its mass during the red giant branch events before settling in the HB some 12-13.5 Gyrs later., Comment: 16 pages, 5 Tables, 8 Figures. Accepted by MNRAS November 8, 2022

We present a $VI$ CCD photometric study and a membership analysis of the globular cluster M56 (NGC 6779). This produced a decontaminated CMD from field stars, which enabled a better confrontation with theoretical isochrones; Zero-Age Horizontal Branches (ZAHB) and post-ZAHB evolutionary tracks. Post He-flash evolutionary models with a He-core mass of 0.5 M$_\odot$ and envelopes of 0.04 - 0.18 M$_\odot$, cover the complete Horizontal Branch. Models with total mass $\sim$ 0.68 M$_\odot$ explain the RR Lyrae, while those with a mass $\sim$ 0.56 M$_\odot$ and a very subtle envelope, explain the Pop II cepheids with a progenitor in the blue tail of the HB. %Using the mean $(V-I)$ at minimum color curve for the RRab stars, we derived a value for the reddening of $E(B-V)$ = 0.26 $\pm$ 0.02. Based on the Fourier decomposition of the $V$ light curve of a single cluster member RRc star, we determined a metallicity of $\rm [Fe/H]_{ ZW}$ = -1.96 $\pm$ 0.09. Several independent distance determination approaches lead to a mean distance to M56 of $\big< d \big>$ = 9.4 $\pm$ 0.4 kpc. Finally, we report 5 new variables: 1 SX Phe, 3 EB, and 1 RRc., Comment: 13 pages, 8 figures, To be published by Revista Mexicana de Astronomia y Astrofisica

We present a CCD $VI$ photometric study of the globular cluster M14. Particular attention is given to the variable stars. This allowed new classifications and cluster membership considerations. New variables are reported; 3 RRc, 18 SR and 1 SX Phe. The Fourier decomposition of RR Lyrae light curves lead to the mean cluster metallicity of [Fe/H]$_{\rm ZW}= -1.3 \pm 0.2$. Several independent methods yield a mean distance of $9.36 \pm 0.16$ kpc. A Colour-Magnitude diagram outlined by the cluster members enabled a matching with theoretical predictions of isochrones and zero-age horizontal branches, whose fitting to the observations is in good agreement with the above distance and metallicity. The Oosterhoff type of M14 is confirmed as Oo-int, and the pulsating mode distribution of RR Lyrae stars on the HB shows that the bimodal region of the instability strip is shared by RRab and RRc stars. By modelling the mass loss at the RGB after the He flash events, we were able to represent the blue tail of the HB, using a core mass of 0.48 $M_{\odot}$ and total masses of 0.52-0.55 $M_{\odot}$. A progenitor star on the MS of 0.84 $M_{\odot}$ reaches the HB in about 12.5 Gyrs, consonant with previous age determinations of the cluster. Type II Cepheids of M14 may be interpreted as products of post-HB evolution, driven by the complex processes involving the burning of the very thin low mass hydrogen and helium shells of these stars and their minuscule envelopes. No evidences were found in favor of M14 being of extragalactic origin., Comment: 18 pages, 16 figures, 6 tables

We present a new time-series VI CCD photometry of the globular cluster NGC 6397, from which we obtained and analysed the light curves of 35 variables carefully identified in the cluster field. We assessed the membership of the variables with an astrometric analysis based on \emph{Gaia} DR2 data. The cluster colour-magnitude diagram was differentially dereddened and cleaned of non members, which allowed us to fit isochrones for [Fe/H]$ = -2.0$ dex in the range 13.0--13.5 Gyr, for a mean reddening $E(B-V)=0.19$, and a distance of 2.5 kpc. This distance was confirmed using the period-luminosity relation for the cluster's five SX Phoenicis variables (V10, V11, V15, V21, and V23) present among its blue stragglers, yielding $2.24\pm0.13$ kpc. We also modelled the light curves of four eclipsing binaries (V4, V5, V7, and V8), and gave the parameters of the systems; the contact binaries V7 and V8 have distances consistent with that of the cluster. NGC 6397 appears to harbour no RR Lyrae stars, being its horizontal branch remarkably blue, much like that of its analogous cluster, M10. To match the blue tail of the horizontal branch population, models of 0.64--0.66 $M_\odot$ with mass loss at the RGB are required, indicating rather thin shell masses for the HB stars., Comment: 19 pages, 9 figures

Time-series VI CCD photometry of the globular cluster M10 (NGC 6254) is employed to perform a detailed identification, inspection of their light curves, their classification and their cluster membership, of all the known variables reported up to 2018. The membership analysis is based on the Gaia-DR2 positions and proper motions. The metallicity of the cluster is estimated based on the sole RRc star known in the cluster. The Fourier decomposition of its light curve leads to [Fe/H]ZW=-1:59 $\pm$ 0:23 dex. The mean cluster distance, estimated by several independent methods is 5.0 $\pm$ 0.3 kpc. A multi-approach search in a region of about 10x10 arcmin2 around the cluster revealed three new variables, one SX Phe (V35) and two sinusoidal variables on the red giant branch of unclear classification (V36,V37). Modelling the HB stars is very sensitive to the stellar hydrogen shell mass, which surrounds the 0.50 M$_\odot$ helium core. To match the full stretch of the HB population, a range of total mass of 0.56 to 0.62 M$_\odot$ is required. These models support a distance of 5.35 kpc and an age of about 13 Gyrs, and hints to some individual variation of the mass loss on the uppper RGB, perhaps caused by the presence of closed magnetic field in red giants., Comment: 14 pages, 7 Figures, 6 Tables. Manuscript accepted for publication in MNRAS Sept. 23, 2020

We present an analysis of \emph{VI} CCD time-series photometry of the Oo II type globular cluster M92. The variable star population of the cluster is studied with the aim of revising their classifications, identifications, frequency spectra and to select indicators of the parental cluster metallicity and distance. The Fourier decomposition of RR Lyrae light curves lead to the estimation of mean [Fe/H]$_{\rm spec}=-2.20\pm 0.18$, and distance of $8.3\pm0.2$ kpc. Four new variables are reported; one RRd (V40), a multimode SX Phe (V41), a SR (V42) and one RRc (F1) that is most likely not a cluster member. The AC nature of V7 is confirmed. The double mode nature of the RRc star V11 is not confirmed and its amplitude modulations are most likely due to the Blazhko effect. Two modes are found in the known RRc variable V13. It is argued that the variable V30, previously classified as RRab is, in fact, an BL Her-type star not belonging to the cluster. Making use of the $Gaia$-DR2 proper motions, we identified 5012 stars in the field of the cluster, that are very likely cluster members, and for which we possess photometry, enabling the production of a refined Colour-Magnitude Diagram. This also allowed us to identify a few variable stars that do not belong to the cluster. The RR Lyrae pulsation modes on the HB are cleanly separated by the first overtone red edge, a common feature in all Oo II type clusters., Comment: 15 pages, 17 figures, 6 tables, accepted for publication in MNRAS 2020 February 27

We report an analysis of new $V$ and $I$ CCD time-series photometry of the globular cluster NGC 6934. Through the Fourier decomposition of the RR Lyrae light curves, the mean values of [Fe/H] and the distance of the cluster were estimated, we found; [Fe/H]$_{UVES}$=-1.48$\pm$0.14 and $d$=16.03$\pm$0.42 kpc, and [Fe/H]$_{UVES}$=-1.43$\pm$0.11 and $d$=15.91$\pm$0.39 kpc, from the calibrations of RRab and RRc stars respectively. Independent distance estimations from SX Phe and SR stars are also discussed. Individual absolute magnitudes, radii and masses are also reported for RR Lyrae stars. We found 12 new variables: 4 RRab, 3 SX Phe, 2 W Virginis (CW)and 3 semi-regular (SR). The inter-mode or "either-or" region in the instability strip is shared by the RRab and RRc stars. This characteristic, observed only in some OoI clusters and never seen in an OoII, is discussed in terms of mass distribution in the ZAHB., Comment: 25 pages, 16 figures, 6 tables

The statistical scattering properties of wave transport in disordered waveguides are derived perturbatively within the transition matrix formalism. The limiting macroscopic statistic of the wave transport, emerges as a consequence of a generalized central-limit-theorem: the expectation values of macroscopic observables depend only on the first and second moments of the reflection matrix of individual scatterers. This theoretical approach does not consider any statistical assumption on the scattering properties of the individual scatterers and it is fully consistent with the optical theorem. The results are found in the so called dense-weak-scattering limit and in the ballistic regime., Comment: Submitted for Phys. Rev. B publication. 12 pages 1 Figure

In this work, we present a theoretical study of the statistical properties of wave scattering in a disordered ballistic waveguide of length L; we have called this system the "building block". The building block is interesting as a physical system because its statistical properties could be studied experimentally in the laboratory. In order to study the building block, as a physical system in itself, we have developed a perturbative method based on Born series. This method is valid only in the ballistic regime, when the length of the system L is smaller than the mean free path l, and in the short-wave-length approximation, when the the wave number k and the mean free path l satisfy kl >> 1. This method has allowed to find, analytically, the behavior of quantities of interest that we have not been able to find from the diffusion equation. In contrast with the diffusion equation method, which takes into account approximately the contribution of closed channels, this method takes them explicitly. In earlier works numerical evidence was found that the expectation values of some interesting quantities are insensitive to the number of closed channels that were used on the calculations; with this method, we could show that closed channels are relevant for the expectation values of amplitudes but irrelevant for the intensities and conductance expectation values. The results of this method show a good agreement with numerical simulations., Comment: 4 Figures

We study the wave transport through a disordered system inside a waveguide. The expectation value of the complex reflection and transmission coefficients (the coherent fields) as well as the transmittance and reflectance are obtained numerically. The numerical results show that the averages of the coherent fields are only relevant for direct processes, while the transmittance and reflectance are mainly dominated by the diffuse intensities, which come from the statistical fluctuations of the fields., Comment: 6 Figures. arXiv admin note: text overlap with arXiv:1407.5617

We establish a relationship between the electric magnetic dipole interaction force from a plane wave on a small magnetodielectric particle, the transport cross-section and the scattering asymmetry parameter, g. In this way, we predict negative g that minimize the transport mean free-path below values of the scattering mean free path of a dilute suspension of both perfectly reflecting spheres as well as of those that satisfy the so-called Kerker conditions, like high permittivity dielectric ones.

An amazingly simple model of correlated disorder is a one-dimensional chain of n potential steps with a fixed width lc and random heights. A theoretical analysis of the average transmission coefficient and Landauer resistance as functions of n and klc predicts two distinct regimes of behavior, one marked by extreme sensitivity and the other associated with exponential behavior of the resistance. The sensitivity arises in n and klc for klc approximately pi, where the system is nearly transparent. Numerical simulations match the predictions well, and they suggest a strong motivation for experimental study., Comment: A6 pages. 5 figures. Accepted in EPL

We study the statistical properties of wave scattering in a disordered waveguide. The statistical properties of a "building block" of length (delta)L are derived from a potential model and used to find the evolution with length of the expectation value of physical quantities. In the potential model the scattering units consist of thin potential slices, idealized as delta slices, perpendicular to the longitudinal direction of the waveguide; the variation of the potential in the transverse direction may be arbitrary. The sets of parameters defining a given slice are taken to be statistically independent from those of any other slice and identically distributed. In the dense-weak-scattering limit, in which the potential slices are very weak and their linear density is very large, so that the resulting mean free paths are fixed, the corresponding statistical properties of the full waveguide depend only on the mean free paths and on no other property of the slice distribution. The universality that arises demonstrates the existence of a generalized central-limit theorem. Our final result is a diffusion equation in the space of transfer matrices of our system, which describes the evolution with the length L of the disordered waveguide of the transport properties of interest. In contrast to earlier publications, in the present analysis the energy of the incident particle is fully taken into account., Comment: 75 pages, 10 figures, submitted to Phys. Rev E

The statistical theory of certain complex wave interference phenomena, like the statistical fluctuations of transmission and reflection of waves, is of considerable interest in many fields of physics. In this article we shall be mainly interested in those situations where the complexity derives from the quenched randomness of scattering potentials, as in the case of disordered conductors, or, more in general, disordered waveguides. In studies performed in such systems one has found remarkable statistical regularities, in the sense that the probability distribution for various macroscopic quantities involves a rather small number of relevant physical parameters, while the rest of the microscopic details serves as mere "scaffolding". We shall review past work in which this feature was captured following a maximum-entropy approach, as well as later studies in which the existence of a limiting distribution, in the sense of a generalized central-limit theorem, has been actually demonstrated. We then describe a microscopic potential model that was developed recently, which gives rise to a further generalization of the central-limit theorem and thus to a limiting macroscopic statistics., Comment: To be published in Physica A