Complex natural resonances of conducting planar objects buried in a dielectric half-space

A scheme is presented to incorporate a mixed potential integral equation (MPIE) using Michalski's formulation C with the method of moments (MoM) for analyzing the scattering of a plane wave from conducting planar objects buried in a dielectric half-space. The robust complex image method with a two-level approximation is used for the calculation of the Green's functions for the half-space. To further speed up the computation, an interpolation technique for filling the matrix is employed. While the induced current distributions on the object's surface are obtained in the frequency domain, the corresponding time domain responses are calculated via the inverse fast Fourier transform (FFT), The complex natural resonances of targets are then extracted from the late time response using the generalized pencil-of-function (GPOF) method. We investigate the pole trajectories as we vary the distance between strips and the depth and orientation of single, buried strips, The variation from the pole position of a single strip in a homogeneous dielectric medium was only a few percent for most of these parameter variations.

Historical trajectories of currently shrinking Portuguese cities: A typology of urban shrinkage

Cities develop according to different patterns, undergoing population growth during some periods and decline (shrinkage) during others. Theories attempting to understand these behaviours include: 1) shrinkage is a natural process in the life cycle of a city, alternating with periods of growth, or 2) shrinkage is an extreme event that places cities into a continuous decline process with no return to population growth. We use retrospective data over a period of 130 years to study 25 Portuguese cities currently facing population decline, and show that both theories coexist in time and space. Five types of shrinking city are revealed: “Persistent Early Shrinkage” due to exodus fromthe rural periphery, “Metropolitan Shrinkage” due to the challenges of urban sprawl, “Recent Shrinkage” in de-industrialisation hotspots, “Cyclic Shrinkage” occurring in political transformation cores, and “Mild Shrinkage” due to life-style disamenity. As diversity of city population trajectories appears to be the norm in both Portugal and other Western European countries, the incorporation of this range into the management of urban transitions is recommended in order to reinforce city resilience.

Sex-chromosome evolution of Palearctic tree frogs in space and time

Sexual reproduction is nearly universal in eukaryotes and genetic determination of sex prevails among animals. The astonishing diversity of sex-determining systems and sex chromosomes is yet bewildering. Some taxonomic groups possess conserved and dimorphic sex chromosomes, involving a functional copy (e.g. mammals' X, birds' Z) and a degenerated copy (mammals' Y, birds' W), implying that sex- chromosomes are expected to decay. In contrast, others like amphibians, reptiles and fishes yet maintained undifferentiated sex chromosomes. Why such different evolutionary trajectories? In this thesis, we empirically test and characterize the main hypotheses proposed to prevent the genetic decay of sex chromosomes, namely occasional X-Y recombination and frequent sex-chromosome transitions, using the Palearctic radiation of Hyla tree frogs as a model system. We take a phylogeographic and phylogenetic approach to relate sex-chromosome recombination, differentiation, and transitions in a spatial and temporal framework. By reconstructing the recent evolutionary history of the widespread European tree frog H. arborea, we showed that sex chromosomes can recombine in males, preventing their differentiation, a situation that potentially evolves rapidly. At the scale of the entire radiation, X-Y recombination combines with frequent transitions to prevent sex-chromosome degeneration in Hyla: we traced several turnovers of sex-determining system within the last 10My. These rapid changes seem less random than usually assumed: we gathered evidences that one chromosome pair is a sex expert, carrying genes with key role in animal sex determination, and which probably specialized through frequent reuse as a sex chromosome in Hyla and other amphibians. Finally, we took advantage of secondary contact zones between closely-related Hyla lineages to evaluate the consequences of sex chromosome homomorphy on the genetics of speciation. In comparison with other systems, the evolution of sex chromosomes in Hyla emphasized the existence of consistent evolutionary patterns within the chaotic diversity of flexibility of cold-blooded vertebrates' sex-determining systems, and provides insights into the evolution of recombination. Beyond sex-chromosome evolution, this work also significantly contributed to speciation, phylogeography and applied conservation research. -- La reproduction sexuée est quasi-universelle chez les eucaryotes et le sexe est le plus souvent déterminé génétiquement au sein du règne animal. L'incroyable diversité des systèmes de reproduction et des chromosomes sexuels est particulièrement étonnante. Certains groupes taxonomiques possèdent des chromosomes sexuels dimorphiques et très conservés, avec une copie entièrement fonctionnelle (ex : le X des mammifères, le Z des oiseaux) et une copie dégénérée (ex : le Y des mammifères, le W des oiseaux), suggérant que les chromosomes sexuels sont voués à se détériorer. Cependant les chromosomes sexuels d'autres groupes tels que les amphibiens, les reptiles et les poissons sont pour la plupart indifférenciés. Comment expliquer des trajectoires évolutives si différentes? Au cours de cette thèse, nous avons étudié empiriquement les processus évolutifs pouvant maintenir les chromosomes sexuels intacts, à savoir la recombinaison X-Y occasionnel ainsi que les substitutions fréquentes de chromosomes sexuels, en utilisant les rainettes Paléarctiques du genre Hyla comme modèle d'étude. Nous avons adopté une approche phylogéographique et phylogénétique pour appréhender les événements de recombinaison, de différenciation et de transitions de chromosomes sexuels dans un contexte spatio-temporel. En retraçant l'histoire évolutive récente de la rainette verte H. arborea, nous avons mis en évidence que les chromosomes sexuels pouvaient recombiner chez les mâles, empêchant ainsi leur différenciation, et que ce processus avait le potentiel d'évoluer très rapidement. A l'échelle plus globale de la radiation, il apparait que les phénomènes de recombinaison X-Y soient également accompagnés de substitutions de chromosomes sexuels, et participent de concert au maintien de chromosomes sexuels intacts dans les populations: le système de détermination du sexe des rainettes a changé plusieurs fois au cours des 10 derniers millions d'années. Ces transitions fréquentes ne semblent pas aléatoires: nous avons identifié une paire de chromosomes qui présente des caractéristiques présageant d'une spécialisation dans le déterminisme du sexe (notamment car elle possède des gènes importants pour cette fonction), et qui a été réutilisée plusieurs fois comme tel chez les rainettes ainsi que d'autres amphibiens. Enfin, nous avons étudié l'hybridation entre différentes espèces dans leurs zones de contact, afin d'évaluer si l'absence de différenciation entre X et Y jouaient un rôle dans les processus génétiques de spéciation. Outre son intérêt pour la compréhension de l'évolution des chromosomes sexuels, ce travail contribue de manière significative à d'autres domaines de recherche tels que la spéciation, la phylogéographie, ainsi que la biologie de la conservation.

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.

The Solar Stormwatch CME catalogue: results from the first space weather citizen science project

Solar Stormwatch was the first space weather citizen science project, the aim of which was to identify and track coronal mass ejections (CMEs) observed by the Heliospheric Imagers aboard the STEREO satellites. The project has now been running for approximately 4 years, with input from >16000 citizen scientists, resulting in a dataset of >38000 time-elongation profiles of CME trajectories, observed over 18 pre-selected position angles. We present our method for reducing this data set into aCME catalogue. The resulting catalogue consists of 144 CMEs over the period January-2007 to February-2010, of which 110 were observed by STEREO-A and 77 were observed by STEREO-B. For each CME, the time-elongation profiles generated by the citizen scientists are averaged into a consensus profile along each position angle that the event was tracked. We consider this catalogue to be unique, being at present the only citizen science generated CME catalogue, tracking CMEs over an elongation range of 4 degrees out to a maximum of approximately 70 degrees. Using single spacecraft fitting techniques, we estimate the speed, direction, solar source region and latitudinal width of each CME. This shows that, at present, the Solar Stormwatch catalogue (which covers only solar minimum years) contains almost exclusively slow CMEs, with a mean speed of approximately 350 kms−1. The full catalogue is available for public access at www.met.reading.ac.uk/spate/stormwatch. This includes, for each event, the unprocessed time-elongation profiles generated by Solar Stormwatch, the consensus time-elongation profiles and a set of summary plots, as well as the estimated CME properties.

Evasive Maneuvers in Space Debris Environment and Technological Parameters

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Collisional semiclassical approximations in phase-space representation

The Gaussian wave-packet phase-space representation is used to show that the expansion in powers of a of the quantum Liouville propagator leads, in the zeroth-order term, to results close to those obtained in the statistical quasiclassical method of Lee and Scully in the Weyl-Wigner picture. It is also verified that, propagating the Wigner distribution along the classical trajectories, the amount of error is less than that coming from propagating the Gaussian distribution along classical trajectories.

Alternative Transfers to the NEOs 99942 Apophis, 1994 WR12, and 2007 UW1 via Derived Trajectories from Periodic Orbits of Family G

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Searching for capture and escape trajectories around Jupiter using its Galilean satellites

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Coding of reaching in 3-D space

Many psychophysical studies suggest that target depth and direction during reaches are processed independently, but the neurophysiological support to this view is so far limited. Here, we investigated the representation of reach depth and direction by single neurons in an area of the medial posterior parietal cortex (V6A). Single-unit activity was recorded from V6A in two Macaca fascicularis monkeys performing a fixation-to-reach task to targets at different depths and directions. We found that in a substantial percentage of V6A neurons depth and direction signals jointly influenced fixation, planning and arm movement-related activity in 3D space. While target depth and direction were equally encoded during fixation, depth tuning became stronger during arm movement planning, execution and target holding. The spatial tuning of fixation activity was often maintained across epochs, and this occurred more frequently in depth. These findings support for the first time the existence of a common neural substrate for the encoding of target depth and direction during reaching movements in the posterior parietal cortex. Present results also highlight the presence in V6A of several types of cells that process independently or jointly eye position and arm movement planning and execution signals in order to control reaches in 3D space. It is possible that depth and direction influence also the metrics of the reach action and that this effect on the reach kinematic variables can account for the spatial tuning we found in V6A neural activity. For this reason, we recorded and analyzed behavioral data when one monkey performed reaching movements in 3-D space. We evaluated how the target spatial position, in particular target depth and target direction, affected the kinematic parameters and trajectories describing the motor action properties.

Quantification of relativistic perturbation forces on spacecraft trajectories

The intent of the work presented in this thesis is to show that relativistic perturbations should be considered in the same manner as well known perturbations currently taken into account in planet-satellite systems. It is also the aim of this research to show that relativistic perturbations are comparable to standard perturbations in speciffc force magnitude and effects. This work would have been regarded as little more then a curiosity to most engineers until recent advancements in space propulsion methods { e.g. the creation of a artiffcial neutron stars, light sails, and continuous propulsion techniques. These cutting-edge technologies have the potential to thrust the human race into interstellar, and hopefully intergalactic, travel in the not so distant future. The relativistic perturbations were simulated on two orbit cases: (1) a general orbit and (2) a Molniya type orbit. The simulations were completed using Matlab's ODE45 integration scheme. The methods used to organize, execute, and analyze these simulations are explained in detail. The results of the simulations are presented in graphical and statistical form. The simulation data reveals that the speciffc forces that arise from the relativistic perturbations do manifest as variations in the classical orbital elements. It is also apparent from the simulated data that the speciffc forces do exhibit similar magnitudes and effects that materialize from commonly considered perturbations that are used in trajectory design, optimization, and maintenance. Due to the similarities in behavior of relativistic versus non-relativistic perturbations, a case is made for the development of a fully relativistic formulation for the trajectory design and trajectory optimization problems. This new framework would afford the possibility of illuminating new more optimal solutions to the aforementioned problems that do not arise in current formulations. This type of reformulation has already showed promise when the previously unknown Space Superhighways arose as a optimal solution when classical astrodynamics was reformulated using geometric mechanics.

RAPID SPACE TRAJECTORY GENERATION USING A FOURIER SERIES SHAPE-BASED APPROACH

With the insatiable curiosity of human beings to explore the universe and our solar system, it is essential to benefit from larger propulsion capabilities to execute efficient transfers and carry more scientific equipment. In the field of space trajectory optimization the fundamental advances in using low-thrust propulsion and exploiting the multi-body dynamics has played pivotal role in designing efficient space mission trajectories. The former provides larger cumulative momentum change in comparison with the conventional chemical propulsion whereas the latter results in almost ballistic trajectories with negligible amount of propellant. However, the problem of space trajectory design translates into an optimal control problem which is, in general, time-consuming and very difficult to solve. Therefore, the goal of the thesis is to address the above problem by developing a methodology to simplify and facilitate the process of finding initial low-thrust trajectories in both two-body and multi-body environments. This initial solution will not only provide mission designers with a better understanding of the problem and solution but also serves as a good initial guess for high-fidelity optimal control solvers and increases their convergence rate. Almost all of the high-fidelity solvers enjoy the existence of an initial guess that already satisfies the equations of motion and some of the most important constraints. Despite the nonlinear nature of the problem, it is sought to find a robust technique for a wide range of typical low-thrust transfers with reduced computational intensity. Another important aspect of our developed methodology is the representation of low-thrust trajectories by Fourier series with which the number of design variables reduces significantly. Emphasis is given on simplifying the equations of motion to the possible extent and avoid approximating the controls. These facts contribute to speeding up the solution finding procedure. Several example applications of two and three-dimensional two-body low-thrust transfers are considered. In addition, in the multi-body dynamic, and in particular the restricted-three-body dynamic, several Earth-to-Moon low-thrust transfers are investigated.

Differential algebra techniques for space applications

This project investigates the utility of differential algebra (DA) techniques applied to the problem of orbital dynamics with initial uncertainties in the orbital determination of the involved bodies. The use of DA theory allows the splitting of a common Monte Carlo simulation in two parts: the generation of a Taylor map of the final states with regard to the perturbation in the initial coordinates, and the evaluation of the map for many points. A propagator is implemented exploiting DA techniques, and tested in the field of asteroid impact risk monitoring with the potentially hazardous 2011 AG5 and 2007 VK184 as test cases. Results show that the new method is able to simulate 2.5 million trajectories with a precision good enough for the impact probability to be accurately reproduced, while running much faster than a traditional Monte Carlo approach (in 1 and 2 days, respectively).

A method for revealing phase space structures of general time dependent dynamical systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a “heuristic argument” that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper “side-by-side” comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (“time averages”) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

Camera localization using trajectories and maps

We propose a new Bayesian framework for automatically determining the position (location and orientation) of an uncalibrated camera using the observations of moving objects and a schematic map of the passable areas of the environment. Our approach takes advantage of static and dynamic information on the scene structures through prior probability distributions for object dynamics. The proposed approach restricts plausible positions where the sensor can be located while taking into account the inherent ambiguity of the given setting. The proposed framework samples from the posterior probability distribution for the camera position via data driven MCMC, guided by an initial geometric analysis that restricts the search space. A Kullback-Leibler divergence analysis is then used that yields the final camera position estimate, while explicitly isolating ambiguous settings. The proposed approach is evaluated in synthetic and real environments, showing its satisfactory performance in both ambiguous and unambiguous settings.