Symplectic Regularization of Binary Collisions in the Circular N+2 Sitnikov Problem

We present a brief overview of the regularizing transformations of the Kepler problem and we relate the Euler transformation with the symplectic structure of the phase space of the N-body problem. We show that any particular solution of the N-body problem where two bodies have rectilinear dynamics can be regularized by a linear symplectic transformation and the inclusion of the Euler transformation into the group of symplectic local diffeomorphisms over the phase space. As an application we regularize a particular configuration of the circular N+2 Sitnikov problem.Comment: 23 pages, 5 figures. References to algorithmic regularization included, changes in References and small typographic corrections. Accepted in J. of Phys. A: Math. Theor 44 (2011) 265204 http://stacks.iop.org/1751-8121/44/26520

Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature

We extend here results for escapes in any given direction of the configuration space of a mechanical system with a non singular bounded at infinity homogeneus potential of degree -1, when the energy is positive. We use geometrical methods for analyzing the parallel and asymptotic escapes of this type of systems. By using Riemannian geometry methods we prove under suitable conditions on the potential that all the orbits escaping in a given direction are asymptotically parallel among themselves. We introduce a conformal Riemannian metric with negative curvature in the interior of the Hill's region for a fixed positive energy level and we consider the boundary as a singular part of the infinity. The associated geodesic flow has as solution curves those of the problem for a fixed energy. We perform the compactification of the region via the limiting directions of the geodesic flow, obtaining a closed unit disk with a quasi-complete metric of negative curvature

Erratum for "Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature"

Fe d'errade

Energy levels of periodic solutions of the circular 2+2 Sitnikov problem

We study a 2+2 body problem introduced in a previous paper as the circular double Sitnikov problem. Since the secondary bodies are moving on the same perpendicular line where evolve the primaries, almost every solution is a collision orbit. We extend the solutions beyond collisions with a symplectic regularization and study the set of energy surfaces that contain periodic orbits and their foliations .Comment: 20 pages, 5 figures. This is not the final version

Hidrogeles multicomponentes basados en vinilpirrolidona y su aplicación en ingeniería de tejidos y/o medicina regenerativa

Hidrogel con estructura de red polimérica multicomponente entrecruzada, caracterizado porque comprende: a) unidades derivadas de vinilpirrolidona (V) y unidades derivadas de un monómero alquénico aniónico o anionizable (A), donde las relaciones de reactividad en copolimerización radical binaria de (V) y (A) tienen valores máximo y mínimo de 0.5 respectivamente; y b) unidades derivadas de al menos un entrecruzante; siempre que el o los entrecruzantes sean i) dos entrecruzantes E1 y E2, donde E1 presenta homología al menos parcial respecto a (A) y E2 presenta homología al menos parcial respecto a (V); o ii) un entrecruzante E3 que presenta homología respecto a (A) y (V). Procedimiento de obtención del mencionado hidrogel que comprende poner en contacto los monómeros (A) y (V) con los entrecruzantes E1 y E2, o el entrecruzante E3, en condiciones de polimerización radicalaria. Uso del hidrogel en aplicaciones biológicas, biomédicas o biotecnológicas que requieran una interacción no tóxica hidrogel-célula.Peer reviewedConsejo Superior de investigaciones Científicas, Universidad Complutense de MadridB1 Patente sin examen previ

Sports, morality and body. The voices of sportswomen under Franco's dictatorship

The aim of this research is to study sportswomen's perceptions and experiences of women's sport in Francoist Spain (1939-1975). The main objective is to analyse the social, moral and aesthetic elements that are present in the experience of these athletes. This study was carried out with an intentional sample of 24 women from Andalusia, Aragon, Asturias, Basque Country, Catalonia and Valencia. They were interviewed by a network of researchers from six universities. Outstanding results show the existence of social limitations to start sports practice (particularly in the post-war period); the importance of sport as a character-building aspect; sport's remarkable influence on their body self-concept; and the incidence on sports of the mainstream moral discourse, which created a female model that even affected sports clothing. The main conclusion is that sportswomen in that period were pioneers and had to fight against most of society in order to develop their facet as athletes, as they would not follow the established model

Urban heritages: how history and housing finance matter to housing form and homeownership rates

Contemporary Western cities are not uniform but display a variety of different housing forms and tenures, both between and within countries. We distinguish three general city types in this paper: low rise, single-family dwelling cities where owner-occupation is the most prevalent tenure form; multi-dwelling building cities where tenants comprise the majority and; multi-dwelling building cities where owner occupation is the principal tenure form. We argue that historical developments beginning in the nineteenth century are crucial to understanding this diversity in urban form and tenure composition across Western cities. Our path-dependent argument is twofold. First, we claim that different housing finance institutions engendered different forms of urban development during the late-nineteenth century and had helped to establish the difference between single-family dwelling cities and multi-dwelling building cities by 1914. Second, rather than stemming from countries’ welfare systems or ‘variety of capitalism’, we argue that these historical distinctions have a significant and enduring impact on today’s urban housing forms and tenures. Our argument is supported by a unique collection of data of 1095 historical cities across 27 countries

Phase behaviour of Ag2CrO4 under compression: Structural, vibrational, and optical properties

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Journal of Physical Chemistry C, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://dx.doi.org/10.1021/jp401524sWe have performed an experimental study of the crystal structure, lattice dynamics, and optical properties of silver chromate (Ag2CrO4) at ambient temperature and high pressures. In particular, the crystal structure, Raman-active phonons, and electronic band gap have been accurately determined. When the initial orthorhombic Pnma Ag2CrO4 structure (phase I) is compressed up to 4.5 GPa, a previously undetected phase (phase II) has been observed with a 0.95% volume collapse. The structure of phase II can be indexed to a similar orthorhombic cell as phase I, and the transition can be considered to be an isostructural transition. This collapse is mainly due to the drastic contraction of the a axis (1.3%). A second phase transition to phase III occurs at 13 GPa to a structure not yet determined. First-principles calculations have been unable to reproduce the isostructural phase transition, but they propose the stabilization of a spinel-type structure at 11 GPa. This phase is not detected in experiments probably because of the presence of kinetic barriers. Experiments and calculations therefore seem to indicate that a new structural and electronic description is required to model the properties of silver chromate.This study was supported by the Spanish government MEC under grants MAT2010-21270-C04-01/03/04 and CTQ2009-14596-C02-01, by the Comunidad de Madrid and European Social Fund (S2009/PPQ1551 4161893), by the MALTA Consolider Ingenio 2010 project (CSD2007-00045), and by the Vicerrectorado de Investigacion y Desarrollo of the Universidad Politecnica de Valencia (UPV2011-0914 PAID-05-11 and UPV2011-0966 PAID-06-11). A.M. and P.R.-H. acknowledge computing time provided by Red Espanola de Supercomputacion (RES) and MALTA-Cluster. J.A.S. acknowledges Juan de la Cierva Fellowship Program for its financial support. Diamond and ALBA Synchrotron Light Sources are acknowledged for provisions of beam time. We also thank Drs. Peral, Popescu, and Fauth for technical support.Santamaría Pérez, D.; Bandiello, E.; Errandonea, D.; Ruiz-Fuertes, J.; Gomis Hilario, O.; Sans, JÁ.; Manjón Herrera, FJ.... (2013). Phase behaviour of Ag2CrO4 under compression: Structural, vibrational, and optical properties. Journal of Physical Chemistry C. 117(23):12239-12248. https://doi.org/10.1021/jp401524sS12239122481172