On the analysis of the fractal basins of escape in the N‐body ring problem

This article summarizes the results of a numerical investigation of the phenomenon of escape in the N‐body ring configuration, focusing on the scenarios that result for N = 5, 6, 7, 8 peripheral bodies. There is a critical value of the Jacobi constant of the system such that for smaller values, the potential well opens and test particles may leave the potential through any of its N openings. By means of a surface of section, we show the results of the computation of the basins of escape towards the different directions of escape, analyzing the structures that appear in them

The 3D structure of an active region filament as extrapolated from photospheric and chromospheric observations

The 3D structure of an active region (AR) filament is studied using nonlinear force-free field (NLFFF) extrapolations based on simultaneous observations at a photospheric and a chromospheric height. To that end, we used the Si I 10827 \AA\ line and the He I 10830 \AA\ triplet obtained with the Tenerife Infrared Polarimeter (TIP) at the VTT (Tenerife). The two extrapolations have been carried out independently from each other and their respective spatial domains overlap in a considerable height range. This opens up new possibilities for diagnostics in addition to the usual ones obtained through a single extrapolation from, typically, a photospheric layer. Among those possibilities, this method allows the determination of an average formation height of the He I 10830 \AA\ signal of \approx 2 Mm above the surface of the sun. It allows, as well, to cross-check the obtained 3D magnetic structures in view of verifying a possible deviation from the force- free condition especially at the photosphere. The extrapolations yield a filament formed by a twisted flux rope whose axis is located at about 1.4 Mm above the solar surface. The twisted field lines make slightly more than one turn along the filament within our box, which results in 0.055 turns/Mm. The convex part of the field lines (as seen from the solar surface) constitute dips where the plasma can naturally be supported. The obtained 3D magnetic structure of the filament depends on the choice of the observed horizontal magnetic field as determined from the 180\circ solution of the azimuth. We derive a method to check for the correctness of the selected 180\circ ambiguity solution.Comment: 31 pages, 13 figures, ApJ Accepte

Analysis of the escape in systems with four exit channels

In this paper, we have performed a numerical investigation of the escape of a particle from two different dynamical systems with the same number of exit channels. We have chosen specific values of the parameters of the systems so that the openings of the potential well in both systems are approximately of the same size. We have found that, in the galactic system, the distribution of the times of escape follows a sequential pattern that has never been detected before. Moreover, we have proved that this pattern is directly related to the geometry of the stable manifolds to the Lyapunov orbits located at the openings of the potential. Finally, we have shown that the different nature of the two systems affects the way the escape occurs, due to the difference in the geometry of the manifolds to the Lyapunov orbits in both systems

Analysis of the geometry of the zero-velocity curves in the N-body ring problem depending on the mass ratio parameter

The purpose of the present study is the investigation of the effect of the mass ratio parameter, β, on the geometry of the zero-velocity curves, when there are N = 3, 4, . . . , 100 peripheral bodies. It is well known that there is a bifurcation value of the β parameter in the N-body ring problem that produces a change in the number of stationary solutions in the system from 5N to 3N. By examining the behavior of the critical values of the Jacobi constant that define each of the zones of stationary solutions, we have unveiled the existence of other bifurcations or critical values of β in the scenario with 5N stationary solutions, which cause different changes in the geometry of the zero-velocity curves, which in turn affect the threshold for the total opening of the curves of zero velocity.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work has been partially funded by the Algerian Ministry of Higher Education and Scientific Research, who awarded a grant for PhD training abroad in 2020 to the first author, Zahra Boureghda, at the University of Alicante

Study on the vibration characteristics of the telescope T80 in the Javalambre astrophysical observatory (JAO) aimed at detecting invalid images

The location of large telescopes, generally far from the data processing centers, represents a logistical problem for the supervision of the capture of images. In this work, we carried out a preliminary study of the vibration signature of the T80 telescope at the Javalambre Astrophysical Observatory (JAO). The study analyzed the process of calculating the displacement that occurs because of the vibration in each of the frequencies in the range of interest. We analyzed the problems associated with very low frequencies by means of simulation, finding the most critical vibrations below 20 Hz, since they are the ones that generate greater displacements. The work also relates previous studies based on simulation with the real measurements of the vibration of the telescope taken remotely when it is subjected to different positioning movements (right ascension and/or declination) or when it performs movement actions such as those related to filter trays or mirror cover. The obtained results allow us to design a remote alarm system to detect invalid images (taken with excess vibration)

Modified filtered-x hierarchical lms algorithm with sequential partial updates for active noise control

In the field of active noise control (ANC), a popular method is the modified filtered-x LMS algorithm. However, it has two drawbacks: Its computational complexity higher than that of the conventional FxLMS, and its convergence rate that could still be improved. Therefore, we propose an adaptive strategy which aims at speeding up the convergence rate of an ANC system dealing with periodic disturbances. This algorithm consists in combining the organization of the filter weights in a hierarchy of subfilters of shorter length and their sequential partial updates (PU). Our contribution is threefold: (1) we provide the theoretical basis of the existence of a frequency-depend-ent parameter, called gain in step-size. (2) The theoretical upper bound of the step-size is compared with the limit obtained from simulations. (3) Additional experiments show that this strategy results in a fast algorithm with a computational complexity close to that of the conventional FxLMS

User-Guided System to Generate Spanish Popular Music

[EN]The automatic generation of music is an emerging field of research that has attracted wide attention in Computer Science. Additionally, the interaction between users and machines is nowadays very present in our daily lives, and influences fields such as Economy, Sports or Arts. Following this approach, this work develops an intelligent system that generates melodies based on Spanish popular music and some indications of the users through an interface. The system creates a melody by learning from the corpus selected through a Markov model, which is also influenced by the users’ preferences. Several experiments were carried out to evaluate the musical quality and the usefulness of the system to interact with the user and generate music. The results of the evaluation shows that the proposal is able to generate music adapted to the style standards of Spanish popular music and to the users’ indications

Financial Soundness Prediction Using a Multi-classification Model: Evidence from Current Financial Crisis in OECD Banks

The paper aims to develop an early warning model that separates previously rated banks (337 Fitch-rated banks from OECD) into three classes, based on their financial health and using a one-year window. The early warning system is based on a classification model which estimates the Fitch ratings using Bankscope bankspecific data, regulatory and macroeconomic data as input variables. The authors propose a “hybridization technique” that combines the Extreme learning machine and the Synthetic Minority Over-sampling Technique. Due to the imbalanced nature of the problem, the authors apply an oversampling technique on the data aiming to improve the classification results on the minority groups. The methodology proposed outperforms other existing classification techniques used to predict bank solvency. It proved essential in improving average accuracy and especially the performance of the minority groups

Four Decades of Studying Global Linear Instability: Progress and Challenges

Global linear instability theory is concerned with the temporal or spatial development of small-amplitude perturbations superposed upon laminar steady or time-periodic three-dimensional flows, which are inhomogeneous in two(and periodic in one)or all three spatial directions.After a brief exposition of the theory,some recent advances are reported. First, results are presented on the implementation of a Jacobian-free Newton–Krylov time-stepping method into a standard finite-volume aerodynamic code to obtain global linear instability results in flows of industrial interest. Second, connections are sought between established and more-modern approaches for structure identification in flows, such as proper orthogonal decomposition and Koopman modes analysis (dynamic mode decomposition), and the possibility to connect solutions of the eigenvalue problem obtained by matrix formation or time-stepping with those delivered by dynamic mode decomposition, residual algorithm, and proper orthogonal decomposition analysis is highlighted in the laminar regime; turbulent and three-dimensional flows are identified as open areas for future research. Finally, a new stable very-high-order finite-difference method is implemented for the spatial discretization of the operators describing the spatial biglobal eigenvalue problem, parabolized stability equation three-dimensional analysis, and the triglobal eigenvalue problem; it is shown that, combined with sparse matrix treatment, all these problems may now be solved on standard desktop computer