The Hamiltonian tube of a cotangent-lifted action

The Marle-Guillemin-Sternberg (MGS) form is local model for a neighborhood of an orbit of a Hamiltonian Lie group action on a symplectic manifold. One of the main features of the MGS form is that it puts simultaneously in normal form the existing symplectic structure and momentum map. The main drawback of the MGS form is that it does not have an explicit expression. We will obtain a MGS form for cotangent-lifted actions on cotangent bundles that, in addition to its defining features, respects the additional fibered structure present. This model generalizes previous results obtained by T. Schmah for orbits with fully-isotropic momentum. In addition, our construction is explicit up to the integration of a differential equation on G. This equation can be easily solved for the groups SO(3) or SL(2), thus giving explicit symplectic coordinates for arbitrary canonical actions of these groups on any cotangent bundle.Peer ReviewedPostprint (author's final draft

Nonlinear Stability of Riemann Ellipsoids withSymmetric Configurations

Using modern differential geometric methods, we study the relative equilibria for Dirichlet's model of a self-gravitating fluid mass having at least two equal axes. We show that the only relative equilibria of this type correspond to Riemann ellipsoids for which the angular velocity and vorticity are parallel to the same principal axis of the body configuration. The two solutions found are MacLaurin and transversal spheroids. The singular reduced energy-momentum method developed in Rodríguez-Olmos (Nonlinearity 19(4):853-877, 2006) is applied to study their nonlinear stability and instability. We found that the transversal spheroids are nonlinearly stable for all eccentricities while for the MacLaurin spheroids, we recover the classical results. Comparisons with other existing results and methods in the literature are also mad

On the stability of Hamiltonian relative equilibria with non-trivial isotropy

We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subspace of the Lie algebra of the symmetry group, with different splittings giving different criteria. In this note we remove this splitting construction and so provide a more general and more easily computed criterion for stability. The result is also extended to apply to systems whose momentum map is not coadjoint equivariant

Portable multispectral imaging system based on Raspberry Pi

Purpose In this work, the authors aim to present a compact low-cost and portable spectral imaging system for general purposes. The developed system provides information that can be used for a fast in situ identification and classification of samples based on the analysis of captured images. The connectivity of the instrument allows a deeper analysis of the images in an external computer. Design/methodology/approach The wavelength selection of the system is carried out by light multiplexing through a light-emitting diode panel where eight wavelengths covering the spectrum from ultraviolet (UV) to near-infrared region (NIR) have been included. The image sensor used is a red green blue – infrared (RGB-IR) micro-camera controlled by a Raspberry Pi board where a basic image processing algorithm has been programmed. It allows the visualization in an integrated display of the reflectance and the histogram of the images at each wavelength, including UV and NIRs. Findings The prototype has been tested by analyzing several samples in a variety of applications such as detection of damaged, over-ripe and sprayed fruit, classification of different type of plastic materials and determination of properties of water. Originality/value The designed system presents some advantages as being non-expensive and portable in comparison to other multispectral imaging systems. The low-cost and size of the camera module connected to the Raspberry Pi provides a compact instrument for general purposes.Project CTQ2013-44545-R from the Ministry of Economy and Competitiveness (Spain)Junta de Andalucía (Proyecto de Excelencia P10-FQM-5974)European Regional Development Funds (ERDF

Non-Invasive Oxygen Determination in Intelligent Packaging Using a Smartphone

Here, we present a technique for the determination of the gaseous oxygen concentration 2 inside packed food. It is based on the use of a luminescent membrane sensitive to O2 that is optically excited and read by a smartphone. The flash of the smartphone along with an optical filter is used as the light source for the optical stimulation of the membrane. The luminescence generated, which is quenched by the surrounding gaseous oxygen, is registered by the rear camera of the same device. The response parameter is defined by combining the registered intensities at two different wavelength ranges corresponding to the emission and the absorption peaks of the sensitive membrane. Thanks to this novel response parameter, the sensitivity is increased and, more importantly, the thermal dependence of the membrane is significantly reduced. This approach allows the use of a luminescent O2-sensitive membrane for intelligent packaging with no need of any associated electronics for its excitation and reading. This means that an oxygen sensor is developed, where a luminescent compound acts as an indicator, therefore combining the advantages of both schemes, that is, the simplicity and reduced cost of indicators with the high sensitivity and accuracy of selective sensors.This work was supported by the Spanish Ministry of Economics and Competivity through the Project CTQ2016-78754-C2-1-R. The work P. Escobedo Araque was supported by the Spanish Ministry of Education, Culture and Sport under Grant FPU13/05032. The work of I. Pérez de Vargas-Sansalvador was supported in part by the European Union’s Horizon 2020 Research and Innovation Program (Multisens) under Grant 706303, in part by the Talentia Postdoc Program launched by the Andalusian Knowledge Agency, in part by the European Union’s Seventh Framework Program, in part by the Marie Skłodowska-Curie actions (COFUND) under Grant 267226, and in part by the Ministry of Economy, Innovation, Science and Employment of the Junta de Andalucía

Stability of relative equilibria with singular momentum values in simple mechanical systems

A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group actions and singular momentum values. A normal form for the symplectic matrix at a relative equilibrium is also obtained.Comment: Partially rewritten. Some mistakes fixed. Exposition improve

Novel Resorbable and Osteoconductive Calcium Silicophosphate Scaffold Induced Bone Formation

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).Abstract: This aim of this research was to develop a novel ceramic scaffold to evaluate the response of bone after ceramic implantation in New Zealand (NZ) rabbits. Ceramics were prepared by the polymer replication method and inserted into NZ rabbits. Macroporous scaffolds with interconnected round-shaped pores (0.5–1.5 mm = were prepared). The scaffold acted as a physical support where cells with osteoblastic capability were found to migrate, develop processes, and newly immature and mature bone tissue colonized on the surface (initially) and in the material’s interior. The new ceramic induced about 62.18% ± 2.28% of new bone and almost complete degradation after six healing months. An elemental analysis showed that the gradual diffusion of Ca and Si ions from scaffolds into newly formed bone formed part of the biomaterial’s resorption process. Histological and radiological studies demonstrated that this porous ceramic scaffold showed biocompatibility and excellent osteointegration and osteoinductive capacity, with no interposition of fibrous tissue between the implanted material and the hematopoietic bone marrow interphase, nor any immune response after six months of implantation. No histological changes were observed in the various organs studied (para-aortic lymph nodes, liver, kidney and lung) as a result of degradation products being released.Odontologí

El modelo semi-presencial y virtual a examen en el área de ingeniería

Durante los dos últimos cursos, la educación universitaria se ha visto obligada a cambiar de forma precipitada debido a la pandemia mundial que nos ha afectado. A pesar de los esfuerzos de las instituciones por adaptarse de una forma adecuada a un modelo semi-presencial o virtual a lo largo del curso, la percepción de los estudiantes no siempre corresponde con la que se pretende desde los organismos oficiales. En este estudio se ha realizado una encuesta voluntaria al alumnado de diferentes titulaciones de grado y másteres del área de ingeniería con el objetivo de someter a examen las medidas adoptadas por la Universidad de Granada (UGR) y comprobar si son aceptadas por los estudiantes y si, desde su punto de vista, se podrían mantener a largo plazo