Neural Network Methods for Boundary Value Problems Defined in Arbitrarily Shaped Domains

Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geometry have been succesfuly treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the satisfaction of the boundary conditions. The method has been successfuly tested on two-dimensional and three-dimensional PDEs and has yielded accurate solutions

Selective Reflection Spectroscopy on the UV Third Resonance Line of Cs : Simultaneous Probing of a van der Waals Atom-Surface Interaction Sensitive to Far IR Couplings and of Interatomic Collisions

We report on the analysis of FM selective reflection experiments on the 6S1/2->8P3/2 transition of Cs at 388 nm, and on the measurement of the surface van der Waals interaction exerted by a sapphire interface on Cs(8P3/2). Various improvements in the systematic fitting of the experiments have permitted to supersede the major difficulty of a severe overlap of the hyperfine components, originating on the one hand in a relatively small natural structure, and on the other hand on a large pressure broadening imposed by the high atomic density needed for the observation of selective reflection on a weak transition. The strength of the van der Waals surface interaction is evaluated to be 73$\pm$10 kHz.$\mu$m3. An evaluation of the pressure shift of the transition is also provided as a by-product of the measurement. We finally discuss the significance of an apparent disagreement between the experimental measurement of the surface interaction, and the theoretical value calculated for an electromagnetic vacuum at a null temperature. The possible influence of the thermal excitation of the surface is evoked, because, the dominant contributions to the vW interaction for Cs(8P3/2) lie in the far infrared range.Comment: submitted to Laser Physics - issue in the memory of Herbert Walther

Benjamin-Ono Kadomtsev-Petviashvili’s models in interfacial electro-hydrodynamics

Three-dimensional nonlinear potential free surface flows in the presence of vertical electric fields are considered. Both the effects of gravity and surface tension are included in the dynamic boundary condition. An asymptotic analysis (based on the assumptions of small depth and small free surface displacements) is presented. It is shown that the problem can be modelled by a Benjamin-Ono Kadomtsev-Petviashvili equation. Furthermore a fifth order Benjamin-Ono Kadomtsev-Petviashvili equation is derived to describe the flows in the particular case of values of the Bond number close to 1/3

Evaluating the Effects of Match-Induced Fatigue on Landing Ability; the Case of the Basketball Game

International Journal of Exercise Science 14(6): 768-778, 2021. This paper examines the effect of match–induced fatigue on lower limb biomechanics, in the case of a basketball game. For this purpose, sixteen male basketball athletes, ages 18 to 22, performed a jump-landing task prior and post a recreational basketball game. The Landing Error Scoring System (LESS) was used to examine the biomechanics of landing. The Vertical jump (VJ) and the Borg Rating of Perceived Exertion (RPE) scale pre- and post-game were employed to assess the level of fatigue induced by the basketball game. In order to compare pre and post measurements, t-tests for dependent samples were used. The performance of the VJ test post-game was found to be significantly lower (t (15) = 3.83, p = 0.002) showing a large effect (Cohen’s d = 0.9) compared to pre-game measurements. Further, the LESS scores were significantly (t (15) = 2.33, p = 0.034) higher post-game with a medium effect (d = 0.5). The differences in LESS scores were due to errors in the landing technique which is bound to be influenced by biomechanics. Moreover, the Borg RPE scale was found to be significantly higher (t (15) = 10.77, p \u3c 0.001) post-game showing a very large effect (d =2.6). It is important to note, that these significant differences occurred with a merely medium level of fatigue (6.6 ± 0.3 pre-game vs 11.9 ± 1.0 post-game). The results of this study would be of great benefit to sports science teams and coaches for formulating effective strategies to improve athletes’ performance and reduce the likelihood of injury

Adaptive Memetic Particle Swarm Optimization with Variable Local Search Pool Size

We propose an adaptive Memetic Particle Swarm Optimization algorithm where local search is selected from a pool of different algorithms. The choice of local search is based on a probabilistic strategy that uses a simple metric to score the efficiency of local search. Our study investigates whether the pool size affects the memetic algorithm’s performance, as well as the possible benefit of using the adaptive strategy against a baseline static one. For this purpose, we employed the memetic algorithms framework provided in the recent MEMPSODE optimization software, and tested the proposed algorithms on the Benchmarking Black Box Optimization (BBOB 2012) test suite. The obtained results lead to a series of useful conclusions

Selective Reflection Spectroscopy at the Interface between a Calcium Fluoride Window and Cs Vapour

A special vapour cell has been built, that allows the measurement of the atom-surface van der Waals interaction exerted by a CaF2 window at the interface with Cs vapour. Mechanical and thermal fragility of fluoride windows make common designs of vapour cells unpractical, so that we have developed an all-sapphire sealed cell with an internal CaF2 window. Although impurities were accidentally introduced when filling-up the prototype cell, leading to a line-broadening and shift, the selective reflection spectrum on the Cs D1 line (894 nm) makes apparent the weak van der Waals surface interaction. The uncertainties introduced by the effects of these impurities in the van der Waals measurement are nearly eliminated when comparing the selective reflection signal at the CaF2 interface of interest, and at a sapphire window of the same cell. The ratio of the interaction respectively exerted by a sapphire interface and a CaF2 interface is found to be 0.55 $\pm$ 0.25, in good agreement with the theoretical evaluation of ~0.67.Comment: soumis \`a Appl Phys B MS 4734

Microwave Absorption of Surface-State Electrons on Liquid 3^3He

We have investigated the intersubband transitions of surface state electrons (SSE) on liquid $^3$He induced by microwave radiation at temperatures from 1.1 K down to 0.01 K. Above 0.4 K, the transition linewidth is proportional to the density of $^3$He vapor atoms. This proportionality is explained well by Ando's theory, in which the linewidth is determined by the electron - vapor atom scattering. However, the linewidth is larger than the calculation by a factor of 2.1. This discrepancy strongly suggests that the theory underestimates the electron - vapor atom scattering rate. At lower temperatures, the absorption spectrum splits into several peaks. The multiple peak structure is partly attributed to the spatial inhomogeneity of the static holding electric field perpendicular to the electron sheet.Comment: 15 pages, 7 figures, submitted to J. Phys. Soc. Jp

Calibration of the Herschel SPIRE Fourier Transform Spectrometer

The Herschel SPIRE instrument consists of an imaging photometric camera and an imaging Fourier Transform Spectrometer (FTS), both operating over a frequency range of 450-1550 GHz. In this paper, we briefly review the FTS design, operation, and data reduction, and describe in detail the approach taken to relative calibration (removal of instrument signatures) and absolute calibration against standard astronomical sources. The calibration scheme assumes a spatially extended source and uses the Herschel telescope as primary calibrator. Conversion from extended to point-source calibration is carried out using observations of the planet Uranus. The model of the telescope emission is shown to be accurate to within 6% and repeatable to better than 0.06% and, by comparison with models of Mars and Neptune, the Uranus model is shown to be accurate to within 3%. Multiple observations of a number of point-like sources show that the repeatability of the calibration is better than 1%, if the effects of the satellite absolute pointing error (APE) are corrected. The satellite APE leads to a decrement in the derived flux, which can be up to ~10% (1 sigma) at the high-frequency end of the SPIRE range in the first part of the mission, and ~4% after Herschel operational day 1011. The lower frequency range of the SPIRE band is unaffected by this pointing error due to the larger beam size. Overall, for well-pointed, point-like sources, the absolute flux calibration is better than 6%, and for extended sources where mapping is required it is better than 7%.Comment: 20 pages, 18 figures, accepted for publication in MNRA