Study of the ejection/collision orbits in the spatial RTBP using the McGehee regularization

In this paper we analyse the McGehee regularization of the collision in the spatial Restricted three-body problem (3D RTBP). As a particular application, we study the ejection (collision) orbits. The parameterization method is applied up to high order to obtain suitable initial conditions of ejection (collision) orbits. Moreover, assuming ejection orbits, different methods are discussed to detect which of them are also collision orbits. Finally we explore the so called ejection-collision (EC) orbits, that is, orbits where the particle ejects from one primary, reaches a maximum in the distance with respect to the same primary, and ends at collision with that primary. Some results concerning the existence of spatial EC orbits are described.M. Ollé and O. Rodríguez were supported by the Spanish MINECO/FEDER grant PGC2018-100928-B-I00 and the Catalan, Spain grant 2017SGR-1049. M. Ollé is also supported by the Spanish Maria de Maeztu grant R&D CEX2020-001084-M. J. Soler was supported by MTM2016-77278-P.Peer ReviewedPostprint (author's final draft

Analytical and numerical results on families of n-ejection-collision orbits in the RTBP

© 2020. ElsevierIn the planar RTBP with mass ratio µ we regularise the singularity at one of the primaries by means of Levi-Civita’s transformation in a rotating frame. We solve the variational equations in a neighbourhood of the ejection/collision orbits, giving analytic expressions for the first terms in µ of the convergent expansion for orbits with eccentricity e¿¿¿1. For high enough values of the Jacobi constant C we give analytic expressions for the coefficients of the above expansion in powers of the small parameter and we prove the existence of four families of the so called n-ejection-collision (EC) orbits, that are orbits which eject from the primary and reach n relative maxima in the distance with the primary before finally colliding with it. Moreover, massive numerical explorations extending the analytical result for any value of the mass ratio and bigger ranges of C are also shown and discussed.Peer ReviewedPostprint (author's final draft

Transit regions and ejection/collision orbits in the RTBP

In this paper we analyse the global behaviour of the whole set of ejection orbits in the planar circular RTBP. We consider ejection from the big or the small primary, that is we take the mass parameter µ, the mass traditionally associated with the small primary, in a range of values µ ¿ (0,1) (the other primary has mass 1-µ). A discussion on the relation between the Lyapunov periodic orbit around the collinear equilibrium point L1 and the ejection orbits is carried out in the range of values of the Jacobi constant such that the associated Hill regions permit only a bounded movement. In particular a chaotic in¿nity of heteroclinic connections between a primary and the LPO1 are obtained. As a consequence a chaotic in¿nity of ejection-collision orbits is also derived. Finally, 2D plots, called colour code diagrams, allow to describe the global dynamics of the ejection orbits given a range of time. Such diagrams provide a very accurate understanding of the dynamics of the orbits under discussion.M. Ollé and O. Rodríguez were supported by the Spanish MINECO/FEDER grant PGC2018-100928-B-100 and the Catalan grant 2017SGR-1049. J. Soler was supported by MTM2016-77278-P.Peer ReviewedPostprint (author's final draft

J2 effect and the collision restricted three–body problem

The existence of a new class of inclined periodic orbits of the collision restricted three–body problem is shown. The symmetric periodic solutions found are perturbations of elliptic kepler orbits and they exist only for special values of the inclination and are related to the motion of a satellite around an oblate planet

Hip-hop solutions of the 2N-body problem

Hip–Hop solutions of the 2N–body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N–gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three–imensional choreographies, with all the in the inertial frame.Peer ReviewedPostprint (author’s final draft

Highly eccentric hip-hop solutions of the 2N-body problem

We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter Є, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small Є ≠ 0, the topological transversality persists and Brouwer's fixed point theorem shows the existence of this kind of solutions in the full system.Postprint (author’s final draft

Generalized analytical results on n-ejection–collision orbits in the RTBP: analysis of bifurcations

In the planar circular restricted three-body problem and for any value of the mass parameter µ¿(0,1) and n=1 , we prove the existence of four families of n-ejection–collision (n-EC) orbits, that is, orbits where the particle ejects from a primary, reaches n maxima in the (Euclidean) distance with respect to it and finally collides with the primary. Such EC orbits have a value of the Jacobi constant of the form C=3µ+Ln2/3(1-µ)2/3 , where L>0 is big enough but independent of µ and n. In order to prove this optimal result, we consider Levi-Civita’s transformation to regularize the collision with one primary and a perturbative approach using an ad hoc small parameter once a suitable scale in the configuration plane and time has previously been applied. This result improves a previous work where the existence of the n-EC orbits was stated when the mass parameter µ>0 was small enough. Moreover, for decreasing values of C, there appear some bifurcations which are first numerically investigated and afterward explicit expressions for the approximation of the bifurcation values of C are discussed. Finally, a detailed analysis of the existence of n-EC orbits when µ¿1 is also described. In a natural way, Hill’s problem shows up. For this problem, we prove an analytical result on the existence of four families of n-EC orbits, and numerically, we describe them as well as the appearing bifurcations.Peer ReviewedPostprint (author's final draft

WebSurvCa: web-based estimation of death and survival probabilities in a cohort

La supervivencia relativa se ha utilizado habitualmente como medida de la evolución temporal del exceso de riesgo de mortalidad en cohortes de pacientes diagnosticados de cáncer, teniendo en cuenta la mortalidad de una población de referencia. Una vez estimado el exceso de riesgo de mortalidad pueden calcularse tres probabilidades acumuladas a un tiempo T: 1) la probabilidad de fallecer asociada a la causa de diagnóstico inicial (enfermedad en estudio), 2) la probabilidad de fallecer asociada a otras causas, y 3) la probabilidad de supervivencia absoluta en la cohorte a un tiempo T. Este trabajo presenta la aplicación WebSurvCa (https://shiny.snpstats.net/WebSurvCa/), mediante la cual los registros de cáncer de base hospitalaria y poblacional, y los registros de otras enfermedades, estiman dichas probabilidades en sus cohortes seleccionando como población de referencia la mortalidad de la comunidad autónoma que consideren

Epigenetic loss of RNA‑methyltransferase NSUN5 in glioma targets ribosomes to drive stress adaptive translational program

Tumors have aberrant proteomes that often do not match their corresponding transcriptome profiles. One possible cause of this discrepancy is the existence of aberrant RNA modification landscapes in the so-called epitranscriptome. Here, we report that human glioma cells undergo DNA methylation-associated epigenetic silencing of NSUN5, a candidate RNA methyltransferase for 5-methylcytosine. In this setting, NSUN5 exhibits tumor-suppressor characteristics in vivo glioma models. We also found that NSUN5 loss generates an unmethylated status at the C3782 position of 28S rRNA that drives an overall depletion of protein synthesis, and leads to the emergence of an adaptive translational program for survival under conditions of cellular stress. Interestingly, NSUN5 epigenetic inactivation also renders these gliomas sensitive to bioactivatable substrates of the stress-related enzyme NQO1. Most importantly, NSUN5 epigenetic inactivation is a hallmark of glioma patients with long-term survival for this otherwise devastating disease

Llums i ombres de la física: el projecte Manhattan

En aquesta xerrada es fa un repàs ràpid de l'evolució de la Física Nuclear fins a finals dels anys 30 i després es veuen les raons científiques, polítiques i militars que van portar al Projecte Manhattan: la fabricació de les dues bombes atòmiques que es van llençar contra el Japó el 1945. La barreja de recerca científica de primeríssima línia, activitat industrial secreta a gran escala i espionatge fan del Projecte Manhattan un tema fascinant que té encara algunes incògnites per resoldre