arXiv subjects

José Marques

Publications and source records attributed to José Marques.

5 recordsLinked to original sources

arXiv2025

The Kawahara equation on star graphs

In this paper, we establish local well-posedness for the Cauchy problem associated with the Kawahara equation on a general metric star graph. Initially, we identify suitable boundary conditions that produce a well-behaved dynamics for the linear equation. Subsequently, we derive the integral formula using the forcing operator method, previously applied to the Kawahara equation on the half-line by Cavalcante and Kwak (NoDEA 2020), and the Fourier restriction method of Bourgain (GAFA 1993). This work has the potential to be extended to other fifth-order nonlinear dispersive equations on star graphs.

math.AP↗

arXiv2025

The Korteweg-de Vries Equation on general star graphs

In this paper, we establish local well-posedness for the Cauchy problem associated with the Korteweg-de Vries (KdV) equation on a general metric star graph. The graph comprises m + k semi-infinite edges: k negative half-lines and m positive half-lines, all joined at a common vertex. The choice of boundary conditions is compatible with the conditions determined by the semigroup theory. The crucial point in this work is to obtain the integral formula using the forcing operator method and the Fourier restriction method of Bourgain. This work extends the results obtained by Cavalcante for the specific case of the Y junction to a more general class of star graphs.

math.AP↗

arXiv2024

Measurement of differential collisional excitation cross sections for the K$α$ emission of He-like oxygen

We measure the energy-differential cross sections for collisional excitation of the soft X-ray electric-dipole K$α$ ($x+y+w$) emission from He-like oxygen (O VII), using an electron beam ion trap. Values near their excitation thresholds were extracted from the observed emissivity by rapidly cycling the energy of the exciting electron beam. This allows us to subtract time-dependent contributions of the forbidden $z$-line emission to the multiplet. We develop a time-dependent collisional-radiative model to further demonstrate the method and predict all spectral features. We then compare the extracted $x+y+w$ cross-sections with calculations based on distorted-wave and R-matrix methods from the literature and our own predictions using the Flexible Atomic Code (FAC). All R-matrix results are validated by our measurements of direct and resonant excitation, supporting the use of such state-of-the-art codes for astrophysical and plasma physics diagnostics.

physics.atom-ph↗

arXiv2023

NSOAMT -- New Search Only Approach to Machine Translation

Translation automation mechanisms and tools have been developed for several years to bring people who speak different languages together. A "new search only approach to machine translation" was adopted to tackle some of the slowness and inaccuracy of the other technologies. The idea is to develop a solution that, by indexing an incremental set of words that combine a certain semantic meaning, makes it possible to create a process of correspondence between their native language record and the language of translation. This research principle assumes that the vocabulary used in a given type of publication/document is relatively limited in terms of language style and word diversity, which enhances the greater effect of instantaneously and rigor in the translation process through the indexing process. A volume of electronic text documents where processed and loaded into a database, and analyzed and measured in order confirm the previous premise. Although the observed and projected metric values did not give encouraging results, it was possible to develop and make available a translation tool using this approach.

cs.CL↗

arXiv2019

Revisiting the Fe XVII line emission problem: laboratory measurements of the 3s-2p and 3d-2p line-formation channels

We determined relative X-ray photon emission cross sections in Fe XVII ions that were mono-energetically excited in an electron beam ion trap. Line formation for the 3s (3s-2p) and 3d (3d-2p) transitions of interest proceeds through dielectronic recombination (DR), direct electron-impact excitation (DE), resonant excitation (RE), and radiative cascades. By reducing the electron-energy spread to a sixth of that of previous works and increasing counting statistics by three orders of magnitude, we account for hitherto unresolved contributions from DR and the little-studied RE process to the 3d transitions, and also for cascade population of the 3s line manifold through forbidden states. We found good agreement with state-of-the-art many-body perturbation theory (MBPT) and distorted-wave (DW) method for the 3s transition, while in the 3d transitions known discrepancies were confirmed. Our results show that DW calculations overestimate the 3d line emission due to DE by ~20%. Inclusion of electron-electron correlation effects through the MBPT method in the DE cross section calculations reduces this disagreement by ~11%. The remaining ~9% in 3d and ~11% in 3s/3d discrepancies are consistent with those found in previous laboratory measurements, solar, and astrophysical observations. Meanwhile, spectral models of opacity, temperature, and turbulence velocity should be adjusted to these experimental cross sections to optimize the accuracy of plasma diagnostics based on these bright soft X-ray lines of Fe XVII.

astro-ph.HE↗