Experimental study of the flows in a non-axisymmetric ellipsoid under precession

Precession driven flows are of great interest for both, industrial and geophysical applications. While cylindrical, spherical and spheroidal geometries have been investigated in great detail, the numerically and theoretically more challenging case of a non-axisymmetric cavity has received less attention. We report experimental results on the flows in a precessing triaxial ellipsoid, with a focus on the base flow of uniform vorticity, which we show to be in good agreement with existing theoretical models. As predicted, the uniform vorticity component exhibits two branches of solutions leading to a hysteresis cycle as a function of the Poincaré number. The first branch is observed at low forcing and characterized by large amplitude of the total fluid rotation and a moderate tilt angle of the fluid rotation axis. In contrast, the second branch displays only a moderate fluid rotation and a large tilt angle of the fluid rotation axis, which tends to align with the precession axis. In addition, we observe the occurrence of parametric instabilities early in the first branch, which saturate in the second branch, where we observe the same order of the kinetic energy in the base flow and instabilities.

On the determination of a locally optimized Ellipsoidal model of the Geoid surface in sea areas

Deriving a local geoid model has drawn much research interest in the last decade, in an endeavour to minimize the errors in orthometric heights calculations, inherited by the use of global geoid reference models. In most parts of the earth, the local geoid surface may be tens of meters away from the Global Reference biaxial Ellipsoid (WGS84), which create numerus problems in topographic, environmental and navigational applications. Several methods have been developed for optimizing the precision of the calculation of the geoid heights undulations and the accuracy of the corresponding orthometric heights calculations. The optimization refers either to the method used for data acquisition, or to the geometrical method used for the determination of the best fit local geoid model. In the present work, we focus on the reference ellipsoid used for the geometric and geoid heights determination and develop a method to provide the one that fits best to the local geoid surface. Moreover, we consider relatively small sea regions and near to coast areas, where the usual methods for data acquisition fail more or less, and we pay attention in two directions: To obtain accurate measured data and to have the best possible reference ellipsoid for the area at hand. In this due, we use the “GNSS-on-boat” methodology to obtain direct sea level data, which we induce in a Moore Penrose pseudoinverse procedure to calculate the best fit triaxial ellipsoid. This locally optimized reference ellipsoid minimizes the geometric heights in the region at hand. The method is applied in two closed sea areas in Greece, namely Corinthian and Patra’s gulf and also in four regions in the Ionian Sea, which exhibit significant geoid alterations. Taking into account all factors of uncertainty, the precision of the mean sea level surface, produced by the “GNSS on boat” methodology, had been estimated at 5.43 cm for the gulf of Patras, at 3.76 cm for the Corinthian gulf and at 3.31 for the Ionian and Adriatic Sea areas. The average difference of this surface and the local triaxial reference ellipsoid, calculated in this work, is found to be less than 15 cm, whereas the corresponding difference with respect to WGS84 is of the order of 30m.

Gravitational waves from dynamical shape transition of protoneutron stars

We describe the dynamical behavior of newborn neutron stars modelled as homogeneous rotating spheroids. The dynamical evolution is triggered by the escape of trapped neutrinos, providing the initial equilibrium configuration. It is shown that for a given set of values of the initial angular momentum, a shape transition to a triaxial ellipsoid configuration occurs. Gravitational waves are then generated by the breaking of the axial symmetry, and some aspects of their observation are discussed. We found a narrow window for both, the initial values of the angular frequency and the eccentricity, able to enable a dynamical shape transition, with their upper bound determined by the Kepler frequency. The energy and angular momentum carried away by the gravitational wave are treated consistently with the solution of the equations of motion of the system.

A portrait of the Trans-Neptunian Object (143707) 2003 UY117 from a stellar occultation and photometry data.

<p>Within the Lucky Star international collaboration* on stellar occultations by TNOs and other outer solar system bodies, we predicted the occultation by the TNO (143707) 2003 UY117 of an mV ~ 14.6 mag star on 23 October 2020. Around a week before the occultation date, we updated and refined the prediction using high precision astrometry obtained using the 2 m Liverpool telescope located at El Roque de Los Muchachos Observatory on La Palma, Spain. The update resulted in a shadow path with good observability potential. We carried out a specific campaign involving 27 observing sites in the south of Spain and North of Africa to observe the occultation. We recorded 4 positive detections and several very close misses to the south of the body. With this information we determined the silhouette of 2003 UY117 at the moment of the occultation. We also obtained the geometric albedo and the size for this object. In addition to this, we carried out several photometric runs with large telescopes to determine the rotation period and rotational phase at the time of the occultation. The body presents a clear double-peaked rotational light curve consistent with a triaxial ellipsoid of considerable elongation, which means that a rotational light curve analysis is critical to correctly interpret the occultation results. The preliminary analysis indicates a larger equivalent diameter than that determined from Herschel thermal data, although consistent within the large error bars of the thermal determination. We will present the preliminary results and discuss their implications.</p> <p>*Lucky Star (LS) is an EU-funded research activity to obtain physical properties of distant Solar System objects using stellar occultations. LS collaboration agglomerates the efforts of the Paris, Granada, and Rio teams. https://lesia.obspm.fr/lucky-star/ </p> <p>Acknowledgements:</p> <p>JLO, PS-S, NM, MV, and RD acknowledge financial support from the State Agency for Research of the Spanish MCIU through the ‘Center of Excellence Severo Ochoa’ award for the Instituto de Astrofísica de Andalucía (SEV-2017-0709), they also acknowledge the financial support by the Spanish grant AYA-2017-84637-R and AYARTI2018- 098657-J-I00 ‘LEO-SBNAF’ (MCIU/AEI/FEDER, UE).</p>

Classification of the triaxial ellipsoid projections

There are generally accepted classifications of cartographic projections of a sphere and an ellipsoid of revolution according to various criteria. The projections of a triaxial ellipsoid have a number of differences from those of a sphere and an ellipsoid of revolution; therefore, the existing classifications need to be clarified. The definitions of the main classes of cartographic projections of a sphere and an ellipsoid of revolution by the type of cartographic grid cannot be extended to those of a triaxial ellipsoid. At the same time, the traditional approach with the auxiliary surface is maintained. To obtain projections of a triaxial ellipsoid in transverse orientation, there is no need to recalculate through polar spherical coordinates as is done for those of a sphere and an ellipsoid of revolution. The transition is carried out by rotating the ellipsoid around the axes, which is much easier. In the classification of the projections of a triaxial ellipsoid according to the distortions, it is necessary to distinguish conformal, quasiconformal, equal-area projections and the ones which preserve lengths along the meridians.

SANS STUDIES ON THE BOVINE SERUM ALBUMIN DENATURATION IN THE PRESENCE OF SDS

The effect of the presence of sodium dodecyl sulfate (SDS) on the denaturation of bovine serum albumin (BSA) has been studied using 36 m small-angle neutron scattering (SANS) BATAN spectrometer (SMARTer). The neutron scattering data reduction used the Graphical Reduction and Analysis SANS Program (GRASP) software, and the fitting process used the IGOR SANS Analysis software. The denaturation process was identified by observing the changes BSA globular structure. The experimental results showed the addition of SDS at low concentrations (2 mM, 5 mM, 10 mM) into BSA solution at pH 7 do not cause a significant change in the size of the BSA globular structure. The SANS scattering profile of BSA fitted with the triaxial ellipsoid model, a simple shape approach for protein globular structure. The fitting result showed the semi-axis B for BSA in the addition of 2 mM, 5 mM, 10 mM SDS were 33.8 Å, 33.8 Å, and 37.8 Å, respectively. While the semi-axis A and semi-axis C were constant for those three variations at 14.6 Å and 32.2 Å, respectively. In higher addition of SDS, the globular structure of BSA unfolded into flexible cylinder structure with the radius of 14.4 Å and length of 83.5 Å. The denaturation of BSA was clearly showed by the addition of 40 mM SDS. The structure of BSA in this condition fitted to fractal structure with fractal dimension of 1.1, the block radius of 16.7 Å and the correlation length of 42.5 Å. These results indicated that the addition of SDS at low concentrations has not caused the denaturation of BSA. Meanwhile, the addition of SDS at high concentrations made BSA to unfold that lead to the denaturation of BSA.

Meridian section projections: a new class of the triaxial ellipsoid projections

Historically the conformal projections have been used for mapping not only the Earth, but other celestial bodies as well. Their application enables preserving the shape of the relief features on the maps, which is extremely important for various analyses of celestial bodies’ surfaces. For many small bodies of the Solar system the International Astronomical Union recommends to apply a triaxial ellipsoid as a reference surface. But if the conformal projections for the reference surfaces of a sphere and an ellipsoid of revolution already exist, obtaining these projections for a triaxial ellipsoid will be significantly complicated, and the task of preserving the shape of relief features still actual. In general, the article deals with cylindrical and azimuthal projections of the meridian section for global mapping the celestial body surface in accordance with the idea formulated by prof. L. M. Bugaevsky. The projections are implemented for mapping of Phobos, moon of Mars.

Experimental investigation of precession driven flows in a triaxial ellipsoid

<p>Precession driven flows are relevant for geo- and astrophysical fluid dynamics as well as industrial applications. In the context of planetary core dynamics, they are attributed to the generation of magnetic fields and/or anomalous dissipation. While precession driven flows have been frequently studied in a cylindrical, spherical or spheroidal container shape, the geometry of a triaxial ellipsoid, representing the geophysical case of core mantle boundary deformation in a tidally locked planet, has received less attention.</p><p>Here, we present results from an experimental study in a triaxial ellipsoid. The main focus of our study is on the base flow of uniform vorticity and we report a good agreement between experimental data and existing semi-analytical models. The amplitude of the time averaged uniform vorticity displays a hysteresis loop as a function of the precession forcing and we demonstrate that this observation depends on the ellipticity of the container. Our study also comprises experiments where the boundary layer is expected to be in a turbulent state. Therefore, we discuss the applicability of an effective damping coefficient in the semi-analytical models to account for the dissipation in a turbulent boundary layer. </p>

Performance of a solution of the direct geodetic problem by Taylor series of Cartesian coordinates

The direct geodetic problem is regarded on the biaxial and triaxial ellipsoid. A known solution method suitable for low eccentricities, which uses differential equations in Cartesian coordinates and Taylor series expansions of these coordinates, is advanced in view of its practical application. According to previous works, this approach has the advantages that no singularities occur in the determination of the coordinates, its mathematical formulation is simple and it is not computationally intensive. The formulas of the solution method are simplified in the present contribution. A test of this method using an extensive test data set on a biaxial earth ellipsoid shows its accuracy and practicability for distances of any length. Based on the convergence behavior of the series of the test data set, a truncation criterion for the series expansions is compiled taking into account accuracy requirements of the coordinates. Furthermore, a procedure is shown which controls the truncation of the series expansions by accuracy requirements of the direction to be determined in the direct problem. The conducted tests demonstrate the correct functioning of the methods for the series truncation. However, the considered solution method turns out to be significantly slower than another current method for biaxial ellipsoids, which makes it more relevant for triaxial ellipsoids.