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We present a timing study of the gamma and X-ray observations and analysis of a sample of bright gamma-ray bursts (GRBs; i.e. GRB 180720B, GRB 181222B, GRB 211211A and GRB 220910A), including the very bright and long GRB 211211A (a.k.a. kilonova candidate). They have been detected and observed by the Atmosphere-Space Interactions Monitor (ASIM) installed on the International Space Station (ISS) and the Gamma-ray Burst Monitor (GBM) on-board the Fermi mission. The early (T-T0=s) and high-energy (0.3-20 MeV) ASIM High Energy Detector (HED) and (150 keV-30 MeV) Fermi (BGO) light curves show well-defined peaks with a low quasi-periodic oscillation (QPO) frequency between 2.5-3.5 Hz that could be identified with the spin of the neutron star in the binary mergers (coinciding with the orbital frequency of the binary merger) originating these GRBs. These QPOs consist on the first detection of low-frequency QPOs (<10 Hz) detected in magnetars so far. We also detect a strong QPO at 21.8-22 Hz in GRB 181222B together with its (less significant) harmonics. The low-frequency QPO would correspond to the signal of the orbiting neutron star (NS) previous to the final coalescence giving rise to the gravitational-wave (GW) signal., Comment: Accepted for publication in MNRAS Letters (14-Feb.-2025)

Measuring the eye's mechanical properties in vivo and with minimally invasive techniques can be the key for individualized solutions to a number of eye pathologies. The development of such techniques largely relies on a computational modelling of the eyeball and, it optimally requires the synergic interplay between experimentation and numerical simulation. In Astrophysics and Geophysics the remote measurement of structural properties of the systems of their realm is performed on the basis of (helio-)seismic techniques. As a biomechanical system, the eyeball possesses normal vibrational modes encompassing rich information about its structure and mechanical properties. However, the integral analysis of the eyeball vibrational modes has not been performed yet. Here we develop a new finite difference method to compute both the spheroidal and, specially, the toroidal eigenfrequencies of the human eye. Using this numerical model, we show that the vibrational eigenfrequencies of the human eye fall in the interval 100 Hz - 10 MHz. We find that compressible vibrational modes may release a trace on high frequency changes of the intraocular pressure, while incompressible normal modes could be registered analyzing the scattering pattern that the motions of the vitreous humour leave on the retina. Existing contact lenses with embebed devices operating at high sampling frequency could be used to register the microfluctuations of the eyeball shape we obtain. We advance that an inverse problem to obtain the mechanical properties of a given eye (e.g., Young's modulus, Poisson ratio) measuring its normal frequencies is doable. These measurements can be done using non-invasive techniques, opening very interesting perspectives to estimate the mechanical properties of eyes in vivo. Future research might relate various ocular pathologies with anomalies in measured vibrational frequencies of the eye., Comment: Published in PLoS ONE as Open Access Research Article. 17 pages, 5 color figures

In this technical note we show how to reach a remarkable speed up when solving elliptic partial differential equations with finite differences thanks to the joint use of the Chebyshev-Jacobi method with high order discretizations and its parallel implementation over GPUs., Comment: 18 pages, 4 figures, 3 tables, submitted to JCP

The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations ($Au=b$) associated with elliptic problems. It inherits its robustness and accelerates its convergence rate computing a set of $P$ relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of $M$ consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method. Our method to estimate the weights has the advantage that the explicit computation of the maximum and minimum eigenvalues of the matrix $A$ is replaced by the (much easier) calculation of the maximum and minimum frequencies derived from a von Neumann analysis. This set of weights is also optimal for the general problem, resulting in the fastest convergence of all possible SRJ schemes for a given grid structure. We also show that with the set of weights computed for the optimal SRJ scheme for a fixed cycle size it is possible to estimate numerically the optimal value of the parameter $\omega$ in the Successive Overtaxation (SOR) method in some cases. Finally, we demonstrate with practical examples that our method also works very well for Poisson-like problems in which a high-order discretization of the Laplacian operator is employed. This is of interest since the former discretizations do not yield consistently ordered $A$ matrices. Furthermore, the optimal SRJ schemes here deduced, are advantageous over existing SOR implementations for high-order discretizations of the Laplacian operator in as much as they do not need to resort to multi-coloring schemes for their parallel implementation. (abridged), Comment: 28 pages, 5 figures, submitted to JCP

Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficiency in the reduction of the residual increases with the number of levels employed in the algorithm. Applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal SRJ schemes, as the mixed (non-linear) algebraic-differential equations from which they result become notably stiff. Here we present a new methodology for obtaining the parameters of SRJ schemes that overcomes the limitations of the original algorithm and provide parameters for SRJ schemes with up to 15 levels and resolutions of up to $2^{15}$ points per dimension, allowing for acceleration factors larger than several hundreds with respect to the Jacobi method for typical resolutions and, in some high resolution cases, close to 1000. Furthermore, we extend the original algorithm to apply it to certain systems of non-linear ePDEs., Comment: 37 pages, 8 figures, submitted to JCP