Geometry preserving numerical methods for physical systems with finite-dimensional Lie algebras

In this paper we propose a geometric integrator to numerically approximate the flow of Lie systems. The highlight of this paper is to present a novel procedure that integrates the system on a Lie group intrinsically associated to the Lie system, and then generating the discrete solution of this Lie system through a given action of the Lie group on the manifold where the system evolves. One major result from the integration on the Lie group is that one is able to solve all automorphic Lie systems at the same time, and that they can be written as first-order systems of linear homogeneous ODEs in normal form. This brings a lot of advantages, since solving a linear ODE involves less numerical cost. Specifically, we use two families of numerical schemes on the Lie group, which are designed to preserve its geometrical structure: the first one based on the Magnus expansion, whereas the second is based on RKMK methods. Moreover, since the aforementioned action relates the Lie group and the manifold where the Lie system evolves, the resulting integrator preserves any geometric structure of the latter. We compare both methods for Lie systems with geometric invariants, particularly a class on Lie systems on curved spaces. As already mentioned, the milestone of this paper is to show that the method we propose preserves all the geometric invariants very faithfully, in comparison with nongeometric numerical methods.Comment: arXiv admin note: substantial text overlap with arXiv:2204.0004

Olive Actual “on Year” Yield Forecast Tool Based on the Tree Canopy Geometry Using UAS Imagery

Olive has a notable importance in countries of Mediterranean basin and its profitability depends on several factors such as actual yield, production cost or product price. Actual “on year” Yield (AY) is production (kg tree-1) in “on years”, and this research attempts to relate it with geometrical parameters of the tree canopy. Regression equation to forecast AY based on manual canopy volume was determined based on data acquired from different orchard categories and cultivars during different harvesting seasons in southern Spain. Orthoimages were acquired with unmanned aerial systems (UAS) imagery calculating individual crown for relating to canopy volume and AY. Yield levels did not vary between orchard categories; however, it did between irrigated orchards (7000–17,000 kg ha-1) and rainfed ones (4000–7000 kg ha-1). After that, manual canopy volume was related with the individual crown area of trees that were calculated by orthoimages acquired with UAS imagery. Finally, AY was forecasted using both manual canopy volume and individual tree crown area as main factors for olive productivity. AY forecast only by using individual crown area made it possible to get a simple and cheap forecast tool for a wide range of olive orchards. Finally, the acquired information was introduced in a thematic map describing spatial AY variability obtained from orthoimage analysis that may be a powerful tool for farmers, insurance systems, market forecasts or to detect agronomical problems

The second flight of the SUNRISE balloon-borne solar observatory: overview of instrument updates, the flight, the data and first results

The SUNRISE balloon-borne solar observatory, consisting of a 1~m aperture telescope that provided a stabilized image to a UV filter imager and an imaging vector polarimeter, carried out its second science flight in June 2013. It provided observations of parts of active regions at high spatial resolution, including the first high-resolution images in the Mg~{\sc ii}~k line. The obtained data are of very high quality, with the best UV images reaching the diffraction limit of the telescope at 3000~\AA\ after Multi-Frame Blind Deconvolution reconstruction accounting for phase-diversity information. Here a brief update is given of the instruments and the data reduction techniques, which includes an inversion of the polarimetric data. Mainly those aspects that evolved compared with the first flight are described. A tabular overview of the observations is given. In addition, an example time series of a part of the emerging active region NOAA AR~11768 observed relatively close to disk centre is described and discussed in some detail. The observations cover the pores in the trailing polarity of the active region, as well as the polarity inversion line where flux emergence was ongoing and a small flare-like brightening occurred in the course of the time series. The pores are found to contain magnetic field strengths ranging up to 2500~G and, while large pores are clearly darker and cooler than the quiet Sun in all layers of the photosphere, the temperature and brightness of small pores approach or even exceed those of the quiet Sun in the upper photosphere.Comment: Accepted for publication in The Astrophysical Journa

Magnetic and morphological characterization of Nd2Fe14B magnets with different quality grades at low temperature 5-300 K

An increasing number of cryogenic devices may benefit from the use of Nd2Fe14B permanent magnets. However, it is necessary to precisely know their behavior because magnetization varies significantly due to Spin Reorientation Transition. In this work, magnetic and morphological characterization of Nd2Fe14B commercial polycrystalline magnets with different quality grades from 5 to 300 K is provided. A set of magnets ranging from N35 to N52 quality have been analyzed. Mean grain dimension as well as material composition elements are provided. Higher quality magnets show smaller mean grain dimensions. Regarding cryogenic temperatures, the well know spin transition effect appears in all the magnets as expected, however, the transition temperature occurs at different temperatures in a range from 112 to 120 K which is lower than those obtained for single crystal samples. Moreover, the relative variation of the remanence from 300 to 5 K is lower than 4% while the maximum expected variation is in average 11%. As extra information, the same analyzes are provided for additional quality grades N40M, N40S, N40SH and N40UH.The research leading to these results has received funding from the European Community's Seventh Framework Programme ([FP7/2007-2013]) under grant agreement n° 263014

Multifocal ERG signal analysis using structural pattern and wavelet packet analysis

Abstrac

FAP- Anion Ionic Liquids Used in the Lubrication of a Steel–Steel Contact

This study compares the tribological behavior of two ionic liquids ([BMP][FAP] and [(NEMM)MOE][FAP]) used as oil additive for the lubrication of a steel–steel contact. Friction and wear experiments were performed using a HFRR test machine. Friction coefficient and electrical contact resistance were measured during the tests, and the wear surface was analyzed by confocal microscopy and XPS. The tribological results showed that both ionic liquids used as additive decrease friction and wear but the [BMP][FAP] had a better performance than the [(NEMM)MOE][FAP] due to its higher reactivity with the steel

The ratio of horizontal to vertical displacement in solar oscillations estimated from combined SO/PHI and SDO/HMI observations

In order to make accurate inferences about the solar interior using helioseismology, it is essential to understand all the relevant physical effects on the observations. One effect to understand is the (complex-valued) ratio of the horizontal to vertical displacement of the p- and f-modes at the height at which they are observed. Unfortunately, it is impossible to measure this ratio directly from a single vantage point, and it has been difficult to disentangle observationally from other effects. In this paper we attempt to measure the ratio directly using 7.5 hours of simultaneous observations from the Polarimetric and Helioseismic Imager on board Solar Orbiter and the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. While image geometry problems make it difficult to determine the exact ratio, it appears to agree well with that expected from adiabatic oscillations in a standard solar model. On the other hand it does not agree with a commonly used approximation, indicating that this approximation should not be used in helioseismic analyses. In addition, the ratio appears to be real-valued.Comment: Accepted for publication in Astronomy & Astrophysics. 8 pages, 8 figure

Magnetic fields inferred by Solar Orbiter: A comparison between SO/PHI-HRT and SDO/HMI

The High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager on board the Solar Orbiter spacecraft (SO/PHI) and the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) both infer the photospheric magnetic field from polarised light images. SO/PHI is the first magnetograph to move out of the Sun--Earth line and will provide unprecedented access to the Sun's poles. This provides excellent opportunities for new research wherein the magnetic field maps from both instruments are used simultaneously. We aim to compare the magnetic field maps from these two instruments and discuss any possible differences between them. We used data from both instruments obtained during Solar Orbiter's inferior conjunction on 7 March 2022. The HRT data were additionally treated for geometric distortion and degraded to the same resolution as HMI. The HMI data were re-projected to correct for the $3^{\circ}$ separation between the two observatories. SO/PHI-HRT and HMI produce remarkably similar line-of-sight magnetograms, with a slope coefficient of $0.97$, an offset below $1$ G, and a Pearson correlation coefficient of $0.97$. However, SO/PHI-HRT infers weaker line-of-sight fields for the strongest fields. As for the vector magnetic field, SO/PHI-HRT was compared to both the $720$-second and $90$-second HMI vector magnetic field: SO/PHI-HRT has a closer alignment with the $90$-second HMI vector. In the weak signal regime ($< 600$ G), SO/PHI-HRT measures stronger and more horizontal fields than HMI, very likely due to the greater noise in the SO/PHI-HRT data. In the strong field regime ($\gtrsim 600$ G), HRT infers lower field strengths but with similar inclinations (a slope of $0.92$) and azimuths (a slope of $1.02$). The slope values are from the comparison with the HMI $90$-second vector.Comment: 10 pages, 5 figures, accepted for publication in A&A; manuscript is a part of Astronomy & Astrophysics special issue: Solar Orbiter First Results (Nominal Mission Phase