Derivative-free high-order methods applied to preliminary orbit determination

From position and velocity coordinates for several given instants, it is possible to determine the orbital elements of the preliminary orbit, taking only into account mutual gravitational attraction forces between the Earth and the satellite. Nevertheless, it should be refined with later observations from ground stations, whose geographic coordinates are previously known. Different methods developed for this purpose need to find a solution of a nonlinear function. In some classical methods it is usual to employ fixed point or secant methods. The second iterative scheme is often used when it is not possible to obtain the derivative of the nonlinear function. Nowadays, there exist efficient numerical methods that are able to highly improve the results obtained by the classical schemes. We will focus our attention on the method of iteration of the true anomaly, in which the secant method is replaced by more efficient methods, such as the second-order Steffensen's method, as well as other high-order derivative-free methods. (C) 2011 Elsevier Ltd. All rights reserved.This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and by Vicerrectorado de Investigacion, Universitat Politecnica de Valencia PAID-06-2010-2285.Chicharro López, FI.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2013). Derivative-free high-order methods applied to preliminary orbit determination. Mathematical and Computer Modelling. 57(7-8):1795-1799. https://doi.org/10.1016/j.mcm.2011.11.045S17951799577-

Understanding the dynamics of segregation bands of simulated granular material in a rotating drum

Axial segregation of a binary mixture of grains in a rotating drum is studied using Molecular Dynamics (MD) simulations. A force scheme leading to a constant restitution coefficient is used and shows that axial segregation is possible between two species of grains made of identical material differing by size. Oscillatory motion of bands is investigated and the influence of the frictional properties elucidated. The mechanism of bands merging is explained using direct imaging of individual grains

Traveling Granular Segregation Patterns in a Long Drum Mixer

Mixtures of granular media often exhibit size segregation along the axis of a partially-filled, horizontal, rotating cylinder. Previous experiments have observed axial bands of segregation that grow from concentration fluctuations and merge in a manner analogous to spinodal decomposition. We have observed that a new dynamical state precedes this effect in certain mixtures: bi-directional traveling waves. By preparing initial conditions, we found that the wave speed decreased with wavelength. Such waves appear to be inconsistent with simple PDE models which are first order in time.Comment: 11 page

Evidence of Compton cooling during an X-ray flare supports a neutron star nature of the compact object in 4U1700-37

Based on new Chandra X-ray telescope data, we present empirical evidence of plasma Compton cooling during a flare in the non pulsating massive X-ray binary 4U1700-37. This behaviour might be explained by quasispherical accretion onto a slowly rotating magnetised neutron star. In quiescence, the neutron star in 4U1700-37 is surrounded by a hot radiatively cooling shell. Its presence is supported by the detection of mHz quasi periodic oscillations likely produced by its convection cells. The high plasma temperature and the relatively low X-ray luminosity observed during the quiescence, point to a small emitting area about 1 km, compatible with a hot spot on a NS surface. The sudden transition from a radiative to a significantly more efficient Compton cooling regime triggers an episode of enhanced accretion resulting in a flare. During the flare, the plasma temperature drops quickly. The predicted luminosity for such transitions, Lx = 3 x 10^35 erg s-1, is very close to the luminosity of 4U1700-37 during quiescence. The transition may be caused by the accretion of a clump in the stellar wind of the donor star. Thus, a magnetised NS nature of the compact object is strongly favoured.Comment: Accepted for publication in MNRA

Implications of zoonotic and vector-borne parasites to free-roaming cats in central Spain

Cats are definitive hosts and reservoirs for several parasites, some of which are responsible for serious zoonotic diseases. We conducted a case-control study of data from a trap-neuter-return (TNR) programme (years 2014-2017) designed to examine the prevalence of zoonotic parasites in free-roaming cats living in urban areas of central Spain. In the animal population tested (n = 263), we detected a 29.2% prevalence of endoparasites, including high rates of cestodes (12.9%) and Toxocara cati (11.7%). While faecal samples showed no Toxoplasma gondii oocysts, the seroprevalence of T. gondii infection was 24.2%. Antibodies to Leishmania infantum were detected in 4.8% of the animals, though all skin and blood samples analyzed were PCR negative for this parasite. Ectoparasites (ticks and fleas) were found in 4.6% of the cat population, and 10.6% of the cats were detected with Otodectes cynotis. Finally, 6.3% and 7.9% cats tested positive for feline leukaemia virus and feline immunodeficiency virus, respectively. Our study provides useful information for animal-welfare and public-health, as the parasites detected can affect native wild animals through predation, competition and disease transmission. Our detection of zoonotic parasites such as L. infantum, T. gondii, T. cati, Giardia duodenalis and several ectoparasites prompts an urgent need for health control measures in stray cats.S

King-Type Derivative-Free Iterative Families: Real and Memory Dynamics

A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stability analysis of the biparametric family without memory is made on quadratic polynomials, finding areas in the parametric plane with good performance. Moreover, in order to study the real behavior of the parametric class with memory, we associate it with a discrete multidimensional dynamical system. By analyzing the fixed and critical points of its vectorial rational function, we can select those methods with best stability properties

Stable high-order iterative methods for solving nonlinear models

[EN] There are several problems of pure and applied science which can be studied in the unified framework of the scalar and vectorial nonlinear equations. In this paper, we propose a sixth-order family of Jarratt type methods for solving nonlinear equations. Further, we extend this family to the multidimensional case preserving the order of convergence. Their theoretical and computational properties are fully investigated along with two main theorems describing the order of convergence. We use complex dynamics techniques in order to select, among the elements of this class of iterative methods, those more stable. This process is made by analyzing the conjugacy class, calculating the fixed and critical points and getting conclusions from parameter and dynamical planes. For the implementation of the proposed schemes for system of nonlinear equations, we consider some applied science problems namely, Van der Pol problem, kinematic syntheses, etc. Further, we compare them with existing sixth-order methods to check the validity of the theoretical results. From the numerical experiments, we find that our proposed schemes perform better than the existing ones. Further, we also consider a variety of nonlinear equations to check the performance of the proposed methods for scalar equations.This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P and by Generalitat Valenciana PROMETEO/2016/089.Behl, R.; Cordero Barbero, A.; Motsa, SS.; Torregrosa Sánchez, JR. (2017). Stable high-order iterative methods for solving nonlinear models. Applied Mathematics and Computation. 303:70-88. https://doi.org/10.1016/j.amc.2017.01.029S708830