Forced nutations of a two-layer Earth in canonical formulation with dissipative Hori-like kernel

[EN] In this research, a modification of the Lie-Hori perturbation method developed by the authors in a recent investigation is used to compute the forced nutations of a non-rigid Earth model, including dissipative processes at the core-mantle boundary. The study is tackled within the Hamiltonian formalism of a two-layer Earth, where the viscous and electromagnetic couplings between mantle and core are introduced via generalized forces. The modified Lie-Hori method is introduced within the framework of the generalized Hamiltonian formalism. It, therefore, allows for calculating first-order perturbations in both conservative and non-conservative systems, while the classical Lie-Hori procedure is not designed to include generalized forces in the kernel to account for dissipative processes. Unlike other methods, this one presents the advantage of keeping the same dimensionality of the original problem, avoiding the doubling of the dimension of the phase space. With this mathematical refinement, differences in the derived nutation amplitudes at the microarcsecond level have been found when compared with the former, first approximation for dissipative systems based on damped oscillators —the only existing previous solution. Those figures are of relevance according to recent recommendations of the International Astronomical Union (IAU) and the International Association of Geodesy (IAG) based on the final report of the Joint Working Group on Theory of Earth rotation and validation.SIThis research has been partially supported by the Spanish project AYA2016-79775-P (AEI/FEDER, UE)

Precession of the non-rigid Earth: Effect of the mass redistribution

[EN] This research is focused on determining the contribution to the precession of the Earth’s equator due to the mass redistribution stemming from the gravitational action of the Moon and the Sun on a rotating solid Earth. In the IAU2006 precession theory, this effect is taken into account through a contribution of −0.960 mas cy−1 for the precession in longitude (with the unspecific name of non-linear effect). In this work, the revised value of that second-order contribution reaches −37.847 mas cy−1 when using the Love numbers values given in IERS Conventions, and −43.945 mas cy−1 if those values are supplemented with the contributions of the oceanic tides. Such variations impose a change of the first-order precession value that induces relative changes of the Earth’s dynamical ellipticity of about 7.3 and 8.5 ppm, respectively. The corresponding values for the obliquity rate are 0.0751 and 0.9341 mas cy−1, respectively, in contrast to 0.340 mas cy−1 considered in IAU2006. The fundamentals of the modeling have been revisited by giving a clear construction of the redistribution potential of the Earth through the corresponding changes in the Earth tensor of inertia. The dynamical problem is tackled within the Hamiltonian framework of a two-layer Earth model, introduced and developed by Getino and Ferrándiz. This approach allows for the achievement of closed-analytical formulae for the precession in longitude and obliquity. It makes it possible to obtain numerical values for different Earth models once a set of associated Love numbers is selected. The research is completed with a discussion on the permanent tide and the related estimation of the variation of the second degree zonal Stokes parameter, J2, and also the indirect effects on nutations arising from the relative change of the Earth’s dynamicalSIThis work has been partially supported by the Spanish project AYA2016-79775-P (AEI/FEDER, UE)

Secular changes in length of day: Effect of the mass redistribution

[EN] In this paper the secular change in the length of day due to mass redistribution effects is revisited using the Hamiltonian formalism of the Earth rotation theories. The framework is a two-layer deformable Earth model including dissipative effects at the core–mantle boundary, which are described through a coupling torque formulated by means of generalized forces. The theoretical development leads to the introduction of an effective time-averaged polar inertia moment, which allows us to quantify the level of core–mantle coupling throughout the secular evolution of the Earth. Taking advantage of the canonical procedure, we obtain a closed analytical formula for the secular deceleration of the rotation rate, numerical evaluation of which is performed using frequency-dependent Love numbers corresponding to solid and oceanic tides. With this Earth modeling, under the widespread assumption of totally coupled core and mantle layers in the long term response, a secular angular acceleration of − 1328.6′′ cy−2 is obtained, which is equivalent to an increase of 2.418 ms cy−1 in the length of day. The ocean tides and the semidiurnal band of the mass-redistribution-perturbing potential, mostly induced by the Moon, constitute the main part of this deceleration. This estimate is shown to be in very good agreement with recent observational values, and with other theoretical predictions including comparable modeling features.SIThis research has been developed within the framework of the IAU/IAG Joint Working Group 3.1: Improving Theories and Models of the Earth’s Rotation (ITMER)

Nutation of the non-rigid Earth: Effect of the mass redistribution

[EN] In this research, we computed the nutation of the figure axis for a non-rigid Earth model due to the mass redistribution resulting from the lunisolar attraction on the deformable Earth, thus extending our previous work on the precessional motion. The basic Earth model is a two-layer structure composed of a fluid core and an anelastic mantle. We used the Hamiltonian approach, leading to closed-form analytical formulae that describe the nutations in longitude and obliquity of the figure axis as a sum of Poisson and Oppolzer terms. Those formulae were evaluated assuming different Earth rheologies by means of the Love number formalism. In particular, we first computed the effect using the standard model of the International Earth Rotation and Reference Systems Service Conventions (2010) solid tides, and then the Love numbers computed by Williams and Boggs, accounting for the complete oceanic tide contribution, which should provide more consistent and updated values for the nutations. The main amplitudes correspond to the 18.6 yr nutation component and reach 201 μas and −96 μas in the in-phase components in longitude and obliquity, respectively. The obtained values differ greatly from those considered in the current nutation model, IAU2000, of the International Astronomical Union (IAU) – and later similar studies – which includes this effect under the denomination of non-linear terms and derives its numerical contribution on the basis of the Sasao, Okubo, and Saito framework. The differences are significant and reach more than 30 μas for some nutation amplitudes. They can be likely attributed to several factors: an incomplete modelling of the redistribution potential; a different treatment of the permanent tide; and the use of different oceanic tide models.S

The Rotation of the Nonrigid Earth at the Second Order. II. The Poincaré Model: Nonsingular Complex Canonical Variables and Poisson Terms

[EN] We develop a Hamiltonian analytical theory for the rotation of a Poincaré Earth model (rigid mantle and liquid core) at the second order with respect to the lunisolar potential and moving ecliptic term. Since the Andoyer variables considered in the first-order solution present virtual singularities, i.e., vanishing divisors, we introduce a set of nonsingular complex canonical variables. This choice allows for applying the Hori canonical perturbation method in a standard way. We derive analytical expressions for the first- and second-order solutions of the precession and nutation of the angular momentum axis (Poisson terms). Contrary to first-order theories, there is a part of the Poisson terms that does depend on the Earth's structure. The resulting numerical amplitudes, not incorporated in the International Astronomical Union nutation standard, are not negligible considering current accuracies. They are at the microarcsecond level for a few terms, with a very significant contribution in obliquity of about 40 μas for the nutation argument with period −6798.38 days. The structure-dependent amplitudes present a large amplification with respect to the rigid model due to the fluid core resonance. The features of such resonance, however, are different from those found in first-order solutions. The most prominent is that it does not depend directly on the second-order nutation argument but rather on the combination of first-order arguments generating it. It entails that some first-order approaches, like those based on the transfer function, cannot be applied to obtain the second-order contributions.S

Limitations of the IAU2000 nutation model accuracy due to the lack of Oppolzer terms of planetary origin

[EN] Context. The current IAU2000 nutation model performed different approximations, one of them being that the Oppolzer terms associated to the planetary perturbations of the nutations were assumed to be smaller than 5 μas and thus were neglected. At present, the uncertainties of the amplitudes of individual components of the observed nutations are better, and the conventional nutation model does not fit the accuracy requirements pursued by the International Astronomical Union (IAU) and the International Association of Geodesy (IAG). Aims. The objective of this work is to estimate the magnitude of the lacking Oppolzer terms of the planetary nutations and find out whether they are still negligible or not. Methods. The Oppolzer terms resulting from the direct and indirect planetary perturbations of the Earth’s rotation have been computed for a two-layer Earth model following the Hamiltonian theory of the non-rigid-Earth. Results. The planetary Oppolzer terms for the non-rigid Earth are not really negligible as believed, and some of them have amplitudes larger than 10 μas, therefore significantly above the current level of uncertainty of individual harmonic constituents. Conclusions. In the short term, the IAU2000 nutation model must be supplemented with suitable corrections accounting for those missing components; its planetary component must be thoroughly revised in the medium term.SIThis work was partly supported by grant AYA2016-79775-P (AEI/FEDER, UE)

A First Assessment of the Corrections for the Consistency of the IAU2000 and IAU2006 Precession-Nutation Models

[EN] The Earth precession-nutation model endorsed by resolutions of each the International Astronomical Union and the International Union of Geodesy and Geophysics is composed of two theories developed independently, namely IAU2006 precession and IAU2000A nutation. The IAU2006 precession was adopted to supersede the precession part of the IAU 2000A precession-nutation model and tried to get the new precession theory dynamically consistent with the IAU2000A nutation. However, full consistency was not reached, and slight adjustments of the IAU2000A nutation amplitudes at the micro arcsecond level were required to ensure consistency. The first set of formulae for these corrections derived by Capitaine et al. (Astrophys 432(1):355–367, 2005), which was not included in IAU2006 but provided in some standards and software for computing nutations. Later, Escapa et al. showed that a few additional terms of the same order of magnitude have to be added to the 2005 expressions to get complete dynamical consistency between the official precession and nutation models. In 2018 Escapa and Capitaine made a joint review of the problem and proposed three alternative ways of nutation model and its parameters to achieve consistency to certain different extents, although no estimation of their respective effects could be worked out to illustrate the proposals. Here we present some preliminary results on the assessment of the effects of each of the three sets of corrections suggested by Escapa and Capitaine (Proceedings of the Journées, des Systémes de Référence et de la Rotation Terrestre: Furthering our Knowledge of Earth Rotation, Alicante, 2018) by testing them in conjunction with the conventional celestial pole offsets given in the IERS EOP14C04 time series

Validation of the resilience scale to Physical Education classes

[Resumen] Las clases de Educación Física se caracterizan por la continua exposición por parte del alumnado de una serie de circunstancias adversas y estresantes ante las cuales en mayor o menor medida deben de enfrentarse en algún momento. Por ello, el objetivo de este estudio fue validar y adaptar la Escala de Resiliencia en el contexto Deportivo de Trigueros, Álvarez, Aguilar-Parra y Rosado (2017) al contexto de la Educación Física. En el estudio participaron 515 estudiantes de secundaria con edades comprendidas entre los 13 y 19 años (M = 15.65; DT = 1.28) pertenecientes a varios centros educativos del sur-este de España. El análisis factorial exploratorio y confirmatorio reveló unos índices de ajuste adecuados para la nueva versión de la escala, mostrándose la estructura factorial invariante respecto al generó. Los dos factores que integran la escala, competencia personal y aceptación de uno mismo y de la vida, obtuvieron una alta consistencia interna y estabilidad temporal. La versión española de la Escala de Resiliencia en el contexto Educación Física se mostró como un instrumento con adecuadas propiedades psicométricas para medir la resiliencia en el contexto de la Educación Física en adolescentes[Abstract] Physical Education classes are characterized by the continuous exposure of students to a series of adverse and stressful circumstances which they must face at some point. Therefore, the objective of this study was to validate and adapt the Resilience Scale in the Sport context of Trigueros, Álvarez, Aguilar-Parra and Rosado (2017) to the context of Physical Education. The study involved 515 high school students aged between 13 and 19 (M = 15.65, SD = 1.28) belonging to several educational centers in the south-east of Spain. The exploratory and confirmatory factor analysis revealed adequate adjustment indices for the new version of the scale, showing the factorial structure invariant with respect to the generated one. The two factors that make up the scale, personal competence and acceptance of oneself and life, obtained a high internal consistency and temporary stability. The Spanish version of the Resilience Scale in the Physical Education context was shown as an instrument with adequate psychometric properties to measure resilience in the context of Physical Education in adolescents

Alginate-Agarose Hydrogels Improve the In Vitro Differentiation of Human Dental Pulp Stem Cells in Chondrocytes. A Histological Study

[EN] Matrix-assisted autologous chondrocyte implantation (MACI) has shown promising results for cartilage repair, combining cultured chondrocytes and hydrogels, including alginate. The ability of chondrocytes for MACI is limited by different factors including donor site morbidity, dedifferentiation, limited lifespan or poor proliferation in vitro. Mesenchymal stem cells could represent an alternative for cartilage regeneration. In this study, we propose a MACI scaffold consisting of a mixed alginate-agarose hydrogel in combination with human dental pulp stem cells (hDPSCs), suitable for cartilage regeneration. Scaffolds were characterized according to their rheological properties, and their histomorphometric and molecular biology results. Agarose significantly improved the biomechanical behavior of the alginate scaffolds. Large scaffolds were manufactured, and a homogeneous distribution of cells was observed within them. Although primary chondrocytes showed a greater capacity for chondrogenic differentiation, hDPSCs cultured in the scaffolds formed large aggregates of cells, acquired a rounded morphology and expressed high amounts of type II collagen and aggrecan. Cells cultured in the scaffolds expressed not only chondral matrix-related genes, but also remodeling proteins and chondrocyte differentiation factors. The degree of differentiation of cells was proportional to the number and size of the cell aggregates that were formed in the hydrogels.This work was funded by the Ministry of Economy and Competitiveness of the Spanish Government (PID2019-106099RB-C42, MM) and by the Generalitat Valenciana, Spain (PROMETEO/2020/069, CC). CIBER-BBN and CIBER-ER are financed by the VI National R&D&I Plan 2008-2011, Iniciativa Ingenio 2010, Consolider Program, CIBER Actions and the Instituto de Salud Carlos III, with assistance of the European Regional Development Fund.Oliver-Ferrándiz, M.; Milián, L.; Sancho-Tello, M.; Martín De Llano, JJ.; Gisbert-Roca, F.; Martínez-Ramos, C.; Carda, C.... (2021). Alginate-Agarose Hydrogels Improve the In Vitro Differentiation of Human Dental Pulp Stem Cells in Chondrocytes. A Histological Study. Biomedicines. 9(7):1-22. https://doi.org/10.3390/biomedicines9070834S1229

Centaurea aspera subsp. geladensis, subsp. nov. (C. sect. Seridia (Juss.) DC., Asteraceae), a new taxon for the Valencian flora

Se describe una nueva subespecie de Centaurea aspera L. (sect. Seridia (Juss.) DC., Asteraceae) procedente de las dunas fósiles del Parque Natural de Serra Gelada (L’Alfàs del Pi y Benidorm, Alicante, España). Se proporcionan datos morfológicos y ecológicos que permiten la diferenciación de la nueva subespecie con sus dos parientes cercanos C. aspera subsp. aspera y C. aspera subsp. stenophylla.A new subspecies of Centaurea aspera L. (sect. Seridia (Juss.) DC., Asteraceae) is described from the fossil dunes of Serra Gelada Natural Park (L’Alfàs del Pi and Benidorm, Alicante, Spain). Morphological and ecological data are provided which allow differentiation from the close relatives C. aspera subsp. aspera and C. aspera subsp. stenophylla