FM carrier deviation measured by differential probability method

Differential probability FM system measures deviation of a carrier modulated by a complex signal. The peak-to-peak amplitude is measured and related to the frequency shift of the carrier signal. The deviation is described in terms of a probability as well as a peak value

Drift and its mediation in terrestrial orbits

The slow deformation of terrestrial orbits in the medium range, subject to lunisolar resonances, is well approximated by a family of Hamiltonian flow with $2.5$ degree-of-freedom. The action variables of the system may experience chaotic variations and large drift that we may quantify. Using variational chaos indicators, we compute high-resolution portraits of the action space. Such refined meshes allow to reveal the existence of tori and structures filling chaotic regions. Our elaborate computations allow us to isolate precise initial conditions near specific zones of interest and study their asymptotic behaviour in time. Borrowing classical techniques of phase- space visualisation, we highlight how the drift is mediated by the complement of the numerically detected KAM tori.Comment: 22 pages, 11 figures, 1 table, 52 references. Comments and feedbacks greatly appreciated. This article is part of the Research Topic `The Earth-Moon System as a Dynamical Laboratory', confer https://www.frontiersin.org/research-topics/5819/the-earth-moon-system-as-a-dynamical-laborator

From order to chaos in Earth satellite orbits

We consider Earth satellite orbits in the range of semi-major axes where the perturbing effects of Earth's oblateness and lunisolar gravity are of comparable order. This range covers the medium-Earth orbits (MEO) of the Global Navigation Satellite Systems and the geosynchronous orbits (GEO) of the communication satellites. We recall a secular and quadrupolar model, based on the Milankovitch vector formulation of perturbation theory, which governs the long-term orbital evolution subject to the predominant gravitational interactions. We study the global dynamics of this two-and-a-half degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator (FLI), used in a statistical sense. Specifically, we characterize the degree of chaoticity of the action space using angle-averaged normalized FLI maps, thereby overcoming the angle dependencies of the conventional stability maps. Emphasis is placed upon the phase-space structures near secular resonances, which are of first importance to the space debris community. We confirm and quantify the transition from order to chaos in MEO, stemming from the critical inclinations, and find that highly inclined GEO orbits are particularly unstable. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors, and, from a mathematical perspective, have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.Comment: 30 pages, 9 figures. Accepted for publication in the Astronomical Journa

Drift and Its Mediation in Terrestrial Orbits

The slow deformation of terrestrial orbits in the medium range, subject to lunisolar resonances, is well approximated by a family of Hamiltonian flow with 2.5 degree-of-freedom. The action variables of the system may experience chaotic variations and large drift that we may quantify. Using variational chaos indicators, we compute high-resolution portraits of the action space. Such refined meshes allow to reveal the existence of tori and structures filling chaotic regions. Our elaborate computations allow us to isolate precise initial conditions near specific zones of interest and study their asymptotic behaviour in time. Borrowing classical techniques of phase-space visualization, we highlight how the drift is mediated by the complement of the numerically detected KAM tori

The dynamical structure of the MEO region: long-term stability, chaos, and transport

It has long been suspected that the Global Navigation Satellite Systems exist in a background of complex resonances and chaotic motion; yet, the precise dynamical character of these phenomena remains elusive. Recent studies have shown that the occurrence and nature of the resonances driving these dynamics depend chiefly on the frequencies of nodal and apsidal precession and the rate of regression of the Moon's nodes. Woven throughout the inclination and eccentricity phase space is an exceedingly complicated web-like structure of lunisolar secular resonances, which become particularly dense near the inclinations of the navigation satellite orbits. A clear picture of the physical significance of these resonances is of considerable practical interest for the design of disposal strategies for the four constellations. Here we present analytical and semi-analytical models that accurately reflect the true nature of the resonant interactions, and trace the topological organization of the manifolds on which the chaotic motions take place. We present an atlas of FLI stability maps, showing the extent of the chaotic regions of the phase space, computed through a hierarchy of more realistic, and more complicated, models, and compare the chaotic zones in these charts with the analytical estimation of the width of the chaotic layers from the heuristic Chirikov resonance-overlap criterion. As the semi-major axis of the satellite is receding, we observe a transition from stable Nekhoroshev-like structures at three Earth radii, where regular orbits dominate, to a Chirikov regime where resonances overlap at five Earth radii. From a numerical estimation of the Lyapunov times, we find that many of the inclined, nearly circular orbits of the navigation satellites are strongly chaotic and that their dynamics are unpredictable on decadal timescales.Comment: Submitted to Celestial Mechanics and Dynamical Astronomy. Comments are greatly appreciated. 28 pages, 15 figure

Effectiveness of GNSS disposal strategies

The management of the Global Navigation Satellite Systems (GNSS) and of the Medium Earth Orbit (MEO) region as a whole is a subject that cannot be deferred, due to the growing exploitation and launch rate in that orbital regime. The advent of the European Galileo and the Chinese Beidou constellations significantly added complexity to the system and calls for an adequate global view on the four constellations present in operation. The operation procedures, including maintenance and disposal practices, of the constellations currently deployed were analyzed in order to asses a proper reference simulation scenario. The complex dynamics of the MEO region with all the geopotential and lunisolar resonances was studied to better identify the proper end-of-life orbit for every proposed strategy, taking into account and, whenever possible, exploiting the orbital dynamics in this peculiar region of space. The possibility to exploit low thrust propulsion or non gravitational perturbations with passive de-orbiting devices (and a combination of the two) was analyzed, in view of possible applications in the design of the future generations of the constellations satellites. Several upgrades in the long-term evolution software SDM and DAMAGE were undertaken to properly handle the constellation simulations in every aspect from constellation maintenance to orbital dynamics. A thorough approach considering the fulltime evolving covariance matrix associated with every object was implemented in SDM to compute the collision risk and associated maneuver rate for the constellation satellites. Once the software upgrades will be completed, the effectiveness of the different disposal strategies will be analyzed in terms of residual collision risk and avoidance maneuvers rate

Neuropsychological patterns following lesions of the anterior insula in a series of forty neurosurgical patients

In the present study we investigated the effects of lesions affecting mainly the anterior insula in a series of 22 patients with lesions in the left hemisphere (LH), and 18 patients with lesions involving the right hemisphere (RH). The site of the lesion was established by performing an overlap of the probabilistic cytoarchitectonic maps of the posterior insula. Here we report the patients\u2019 neuropsychological profile and an analysis of their pre-surgical symptoms. We found that pre-operatory symptoms significantly differed in patients depending on whether the lesion affected the right or left insula and a strict parallelism between the patterns emerged in the pre-surgery symptoms analysis, and the patients\u2019 cognitive profile. In particular, we found that LH patients showed cognitive deficits. By contrast, the RH patients, with the exception of one case showing an impaired performance at the visuo-spatial planning test were within the normal range in performing all the tests. In addition, a sub-group of patients underwent to the post-surgery follow-up examination

Incidental sounds of locomotion in animal cognition

The highly synchronized formations that characterize schooling in fish and the flight of certain bird groups have frequently been explained as reducing energy expenditure. I present an alternative, or complimentary, hypothesis that synchronization of group movements may improve hearing perception. Although incidental sounds produced as a by-product of locomotion (ISOL) will be an almost constant presence to most animals, the impact on perception and cognition has been little discussed. A consequence of ISOL may be masking of critical sound signals in the surroundings. Birds in flight may generate significant noise; some produce wing beats that are readily heard on the ground at some distance from the source. Synchronization of group movements might reduce auditory masking through periods of relative silence and facilitate auditory grouping processes. Respiratory locomotor coupling and intermittent flight may be other means of reducing masking and improving hearing perception. A distinct border between ISOL and communicative signals is difficult to delineate. ISOL seems to be used by schooling fish as an aid to staying in formation and avoiding collisions. Bird and bat flocks may use ISOL in an analogous way. ISOL and interaction with animal perception, cognition, and synchronized behavior provide an interesting area for future study