Solution of optimal continuous low-thrust transfer using Lie transforms

This paper addresses the problem of optimal constant continuous low-thrust transfer in the context of the restricted two-body problem (R2BP). Using the Pontryagin’s principle, the problem is formulated as a two point boundary value problem (TPBVP) for a Hamiltonian system. Lie transforms obtained through the Deprit method allow us to obtain the canonical mapping of the phase flow as a series in terms of the order of magnitude of the thrust applied. The reachable set of states starting from a given initial condition using optimal control policy is obtained analytically. In addition, a particular optimal transfer can be computed as the solution of a non-linear algebraic equation. Se investiga el uso de series y transformadas de Lie en problemas de optimización de trayectorias de satélites impulsados por motores de bajo empuje

El Problema de Lambert en el Contexto de Optimización de Trayectorias Espaciales

Esta tesis se basa en el estudio de la trayectoria que pasa por dos puntos en el problema de los dos cuerpos, inicialmente desarrollado por Lambert, del que toma su nombre. En el pasado, el Problema de Lambert se ha utilizado para la determinación de órbitas a partir de observaciones astronómicas de los cuerpos celestes. Actualmente, se utiliza continuamente en determinación de órbitas, misiones planetaria e interplanetarias, encuentro espacial e interceptación, o incluso en corrección de orbitas. Dada su gran importancia, se decide investigar especialmente sobre su solución y las aplicaciones en las misiones espaciales actuales. El campo de investigación abierto, es muy amplio, así que, es necesario determinar unos objetivos específicos realistas, en el contexto de ejecución de una Tesis, pero que sirvan para mostrar con suficiente claridad el potencial de los resultados aportados en este trabajo, e incluso poder extenderlos a otros campos de aplicación. Como resultado de este análisis, el objetivo principal de la Tesis se enfoca en el desarrollo de algoritmos para resolver el Problema de Lambert, que puedan ser aplicados de forma muy eficiente en las misiones reales donde aparece. En todos los desarrollos, se ha considerado especialmente la eficiencia del cálculo computacional necesario en comparación con los métodos existentes en la actualidad, destacando la forma de evitar la pérdida de precisión inherente a este tipo de algoritmos y la posibilidad de aplicar cualquier método iterativo que implique el uso de derivadas de cualquier orden. En busca de estos objetivos, se desarrollan varias soluciones para resolver el Problema de Lambert, todas ellas basadas en la resolución de ecuaciones transcendentes, con las cuales, se alcanzan las siguientes aportaciones principales de este trabajo: • Una forma genérica completamente diferente de obtener las diversas ecuaciones para resolver el Problema de Lambert, mediante desarrollo analítico, desde cero, a partir de las ecuaciones elementales conocidas de las cónicas (geométricas y temporal), proporcionando en todas ellas fórmulas para el cálculo de derivadas de cualquier orden. • Proporcionar una visión unificada de las ecuaciones más relevantes existentes, mostrando la equivalencia con variantes de las ecuaciones aquí desarrolladas. • Deducción de una nueva variante de ecuación, el mayor logro de esta Tesis, que destaca en eficiencia sobre todas las demás (tanto en coste como en precisión). • Estudio de la sensibilidad de la solución ante variación de los datos iniciales, y como aplicar los resultados a casos reales de optimización de trayectorias. • También, a partir de los resultados, es posible deducir muchas propiedades utilizadas en la literatura para simplificar el problema, en particular la propiedad de invariancia, que conduce al Problema Transformado Simplificado. ABSTRACT This thesis is based on the study of the two-body, two-point boundary-value problem, initially developed by Lambert, from who it takes its name. Since the past, Lambert's Problem has been used for orbit determination from astronomical observations of celestial bodies. Currently, it is continuously used in orbit determinations, for planetary and interplanetary missions, space rendezvous, and interception, or even in orbit corrections. Given its great importance, it is decided to investigate their solution and applications in the current space missions. The open research field is very wide, it is necessary to determine specific and realistic objectives in the execution context of a Thesis, but that these serve to show clearly enough the potential of the results provided in this work, and even to extended them to other areas of application. As a result of this analysis, the main aim of the thesis focuses on the development of algorithms to solve the Lambert’s Problem which can be applied very efficiently in real missions where it appears. In all these developments, it has been specially considered the efficiency of the required computational calculation compared to currently existing methods, highlighting how to avoid the loss of precision inherent in such algorithms and the possibility to apply any iterative method involving the use of derivatives of any order. Looking to meet these objectives, a number of solutions to solve the Lambert’s Problem are developed, all based on the resolution of transcendental equations, with which the following main contributions of this work are reached: • A completely different generic way to get the various equations to solve the Lambert’s Problem by analytical development, from scratch, from the known elementary conic equations (geometrics and temporal), by providing, in all cases, the calculation of derivatives of any order. • Provide a unified view of most existing relevant equations, showing the equivalence with variants of the equations developed here. • Deduction of a new variant of equation, the goal of this Thesis, which emphasizes efficiency (both computational cost and accuracy) over all other. • Estudio de la sensibilidad de la solución ante la variación de las condiciones iniciales, mostrando cómo aprovechar los resultados a casos reales de optimización de trayectorias. • Study of the sensitivity of the solution to the variation of the initial data, and how to use the results to real cases of trajectories’ optimization. • Additionally, from results, it is possible to deduce many properties used in literature to simplify the problem, in particular the invariance property, which leads to a simplified transformed problem.

Echo-delay resolution in sonar images of the big brown bat, Eptesicus fuscus

Echolocating big brown bats (Eptesicus fuscus) broadcast ultrasonic frequency-modulated (FM) biosonar sounds (20–100 kHz frequencies; 10–50 μs periods) and perceive target range from echo delay. Knowing the acuity for delay resolution is essential to understand how bats process echoes because they perceive target shape and texture from the delay separation of multiple reflections. Bats can separately perceive the delays of two concurrent electronically generated echoes arriving as little as 2 μs apart, thus resolving reflecting points as close together as 0.3 mm in range (two-point threshold). This two-point resolution is roughly five times smaller than the shortest periods in the bat’s sounds. Because the bat’s broadcasts are 2,000–4,500 μs long, the echoes themselves overlap and interfere with each other, to merge together into a single sound whose spectrum is shaped by their mutual interference depending on the size of the time separation. To separately perceive the delays of overlapping echoes, the bat has to recover information about their very small delay separation that was transferred into the spectrum when the two echoes interfered with each other, thus explicitly reconstructing the range profile of targets from the echo spectrum. However, the bat’s 2-μs resolution limit is so short that the available spectral cues are extremely limited. Resolution of delay seems overly sharp just for interception of flying insects, which suggests that the bat’s biosonar images are of higher quality to suit a wider variety of orientation tasks, and that biosonar echo processing is correspondingly more sophisticated than has been suspected.

Horizontal gene transfer and mutation: Ngrol genes in the genome of Nicotiana glauca

Ngrol genes (NgrolB, NgrolC, NgORF13, and NgORF14) that are similar in sequence to genes in the left transferred DNA (TL-DNA) of Agrobacterium rhizogenes have been found in the genome of untransformed plants of Nicotiana glauca. It has been suggested that a bacterial infection resulted in transformation of Ngrol genes early in the evolution of the genus Nicotiana. Although the corresponding four rol genes in TL-DNA provoked hairy-root syndrome in plants, present-day N. glauca and plants transformed with Ngrol genes did not exhibit this phenotype. Sequenced complementation analysis revealed that the NgrolB gene did not induce adventitious roots because it contained two point mutations. Single-base site-directed mutagenesis at these two positions restored the capacity for root induction to the NgrolB gene. When the NgrolB, with these two base substitutions, was positioned under the control of the cauliflower mosaic virus 35S promoter (P35S), transgenic tobacco plants exhibited morphological abnormalities that were not observed in P35s-RirolB plants. In contrast, the activity of the NgrolC gene may have been conserved after an ancient infection by bacteria. Discussed is the effect of the horizontal gene transfer of the Ngrol genes and mutations in the NgrolB gene on the phenotype of ancient plants during the evolution of N. glauca.

Genome scan of human systemic lupus erythematosus: Evidence for linkage on chromosome 1q in African-American pedigrees

Systemic lupus erythematosus (SLE) is an autoimmune disorder characterized by production of autoantibodies against intracellular antigens including DNA, ribosomal P, Ro (SS-A), La (SS-B), and the spliceosome. Etiology is suspected to involve genetic and environmental factors. Evidence of genetic involvement includes: associations with HLA-DR3, HLA-DR2, Fcγ receptors (FcγR) IIA and IIIA, and hereditary complement component deficiencies, as well as familial aggregation, monozygotic twin concordance >20%, λs > 10, purported linkage at 1q41–42, and inbred mouse strains that consistently develop lupus. We have completed a genome scan in 94 extended multiplex pedigrees by using model-based linkage analysis. Potential [log10 of the odds for linkage (lod) > 2.0] SLE loci have been identified at chromosomes 1q41, 1q23, and 11q14–23 in African-Americans; 14q11, 4p15, 11q25, 2q32, 19q13, 6q26–27, and 12p12–11 in European-Americans; and 1q23, 13q32, 20q13, and 1q31 in all pedigrees combined. An effect for the FcγRIIA candidate polymorphism) at 1q23 (lod = 3.37 in African-Americans) is syntenic with linkage in a murine model of lupus. Sib-pair and multipoint nonparametric analyses also support linkage (P < 0.05) at nine loci detected by using two-point lod score analysis (lod > 2.0). Our results are consistent with the presumed complexity of genetic susceptibility to SLE and illustrate racial origin is likely to influence the specific nature of these genetic effects.

Factores asociados a la predisposición a vacunarse contra la gripe pandémica A/H1N1 en población adulta del Departamento de Salud de Elche (España): influencia de las fuentes de información

Fundamento. Evaluar en población general las fuentes de información, actitudes y predisposición hacia la vacunación contra la gripe pandémica A/H1N1 de 2009. Métodos. Estudio descriptivo de carácter transversal realizado entre el 25 de noviembre y 30 de diciembre de 2009 mediante entrevista personal cara a cara a una muestra aleatoria (826) de adultos residentes en el Departamento de Salud de Elche (España). Resultados. Los encuestados manifestaron que la televisión (57%) y el médico de familia (47,9%) eran su fuente principal de información sobre vacunas. El 82,2% tenía una buena opinión sobre las vacunas, un 30,5% percibía la gripe A/H1N1 como más grave que la estacional, siendo esta percepción creciente entre los de mayor edad y con menos estudios. Un 25,4% de encuestados sentía preocupación por padecerla, sobre todo los de menor nivel educativo. Un 42,1% manifiesta su buena predisposición para vacunarse contra la gripe estacional, disminuyendo hasta un 18,4% la intención hacia la gripe A/H1N1. La predisposición hacia la vacunación crece con la edad y en el caso de la gripe A/H1N1 decrece a mayor nivel educativo. El médico de familia es la fuente de información más determinante para inmunizarse frente a gripe estacional (OR 1,43) y gripe A/H1N1 (OR 2,47). Conclusiones. Existe baja aceptabilidad de la vacuna pandémica y baja percepción de gravedad sobre la gripe A/H1N1. La experiencia previa de vacunación ante gripe estacional predispone hacia la inmunización contra gripe A/H1N1. Aunque los medios de comunicación encabezan la fuente de información más usual durante este episodio, la influencia del médico de familia en la decisión de vacunarse resulta significativa.

Limitations of microbial hydrocarbon degradation at the Amon Mud Volcano (Nile Deep Sea Fan)

The Amon mud volcano (MV), located at 1250 m water depth on the Nile Deep Sea Fan, is known for its active emission of methane and non-methane hydrocarbons into the hydrosphere. Previous investigations showed a low efficiency of hydrocarbon-degrading anaerobic microbial communities inhabiting the Amon MV center in the presence of sulphate and hydrocarbons in the seeping subsurface fluids. By comparing spatial and temporal patterns of in situ biogeochemical fluxes, temperature gradients, pore water composition and microbial activities over three years, we investigated why the activity of anaerobic hydrocarbon degraders can be low despite high energy supplies. We found that the central dome of the Amon MV, as well as a lateral mud flow at its base, showed signs of recent exposure of hot subsurface muds lacking active hydrocarbon degrading communities. In these highly disturbed areas, anaerobic degradation of methane was less than 2% of the methane flux. Rather high oxygen consumption rates compared to low sulphide production suggest a faster development of more rapidly growing aerobic hydrocarbon degraders in highly disturbed areas. In contrast, the more stabilized muds surrounding the central gas and fluid conduits hosted active anaerobic hydrocarbon-degrading microbial communities. Furthermore, within three years, cell numbers and hydrocarbon degrading activity increased at the gas-seeping sites. The low microbial activity in the hydrocarbon-vented areas of Amon mud volcano is thus a consequence of kinetic limitations by heat and mud expulsion, whereas most of the outer mud volcano area is limited by hydrocarbon transport.

On the existence of solutions to boundary value problems on time scales

This work formulates existence theorems for solutions to two-point boundary value problems on time scales. The methods used include maximum principles, a priori bounds and topological degree theory.

A note on bifurcation from an interval

We study the global bifurcation of nonlinear Sturm-Liouville problems of the form -(pu')' + qu = lambda a(x)f(u), b(0)u(0) - c(0)u' (0) = 0, b(1)u(1) + c(1)u'(1) = 0 which are not linearizable in any neighborhood of the origin. (c) 2005 Published by Elsevier Ltd.

On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

Properties and performance of polymer modified cements and mortars

Polymer modified cements and mortars have become popular for use as patch repair materials. General evidence suggests that these materials offer considerable improvements compared to traditional mortars although the mechanisms for this are not fully understood. This work elucidates the factors which govern some properties and performance of different polymer systems. In view of the wide range of commercial systems available, investigations concentrated on the use of three of the most commonly available groups of polymers. These were: (1) Styrene Butadiene Rubber (SBR), (2) Acrylics and, (3) Ethylene Vinyl Acetates (EVA). The later two were in the form of both emulsions and redispersible powders. Experiments concentrated on: (1) Rheological behaviour of polymer modified cement pastes; (2) Workability of polymer modified mortars; (3) Influence of curing conditions on the pore size distribution and diffusion of chloride ions; (4) Bond strength of polymer modified cement and mortar patches; and (5) Microscopic examination and semi-quantitative analyses of the bulk and interfacial microstructures. The following main conclusions were reached: (1) The addition of polymer emulsions have a considerable influence on the workability of fresh cement pastes, the extent of this depending on the type of system used. (2) The rheological parameters of fresh polymer modified mortars can be established using a two-point workability test which may be used when comparing the properties of different systems at constant workability. (3) Curing conditions affect the properties of polymer modified systems and a wet/dry curing regime was essential for good adhesion of these materials to mortar substrates. (4) In contrast, the wet/dry curing regime resulted in a curing affected zone at the surface of patch materials. This can result in a much coarser pore structure and enhanced diffusion of e.g. chloride ions. (5) The microstructure of polymer modified systems was very different compared with the unmodified cement/mortar and varied depending on curing conditions.

Ethanol intake of paediatric intensive care patients

Background - Limiting the amount of alcohol in children's medicines is advisable but as alcohol is the second most common solvent used in liquid preparations, paediatric patients with increased medication intake may be exposed to a considerable alcohol intake. Few medicines are specifically designed for children in Paediatric Intensive Care (PICU), and therefore adult formulations are frequently administered, with high medication use further exposing a PICU patient to undesired alcohol intake. Aims - This small pilot study aimed to examiine the intake of a sample of PICU patients, highlight common medicines used on PICU containing alcohol, provide alternatives where possible and where alternatives are not possible, provide the prescriber with a list of the higher alcohol containing medicines. Method - A retrospective medication chart review was undertaken as a two point snap shot. Data collected included age, weight, medications prescribed and the formulations used at time of the study. The patients' sedation score was recorded. The electronic medicine compendium (EMC) was consulted for any ethanol content for the commercially available products. The manufacturer was contacted for ethanol content of all ‘specials’ and any commercial products found to contain ethanol from the EMC. The PICU patient's daily intake of ethanol was calculated. The calculation was converted to an adult equivalent alcohol unit intake and although this method of conversion is crude and does not take physiological differences of adult and children into account, it was done in order to provide the clinician with commonly used terminology in deciding the risk to the patient. Results - Twenty-eight patients were prescribed a range of 69 different medications. Of the 69 medicines, 12 products were found to contain ethanol. Patient ages ranged from a 26 week premature infant to 15 years old, weights ranges from 0.7 kg to 45 kg. Only 2 out of the 28 patients did not receive ethanol containing medications, and most patients were prescribed at least two medicines containing ethanol. Daily ethanol intake uncorrected for weight ranged from 0.006 ml to 2.18 ml (median 0.26 ml). Converting this to adult units per week, alcohol intake ranged from 0.07 to 15.2 units (median 1.4 units). The two patients receiving above 15 units/week adult equivalent were prescribed an oral morphine weaning regimen, therefore the high alcohol exposure was short term. The most common drugs prescribed containing alcohol were found to be nystatin, ranitidine, furosemide and morphine. No commercially available alcohol-free oral liquid preparations were found for ranitidine, furosemide or morphine at the time of the study. Correlation of the sedation score against ethanol intake was difficult to analyse as most patients were actively sedated. Conclusions - Polypharmacy in PICU patients increases the exposure to alcohol. Some commercially available medicines provide excessive ethanol intake, providing the clinician with ethical, potentially economical dilemmas of prescribing an unlicensed medicine to minimise ethanol exposure. Further research is required to evaluate the scope of the problem, effects of exposure and provision of alcohol free formulations.

Applications of Subordination Principle to Log-Harmonic Mappings

MSC 2010: 30C45, 30C55

Self-adaptive probabilistic roadmap generation for intelligent virtual agents

Agents inhabiting large scale environments are faced with the problem of generating maps by which they can navigate. One solution to this problem is to use probabilistic roadmaps which rely on selecting and connecting a set of points that describe the interconnectivity of free space. However, the time required to generate these maps can be prohibitive, and agents do not typically know the environment in advance. In this paper we show that the optimal combination of different point selection methods used to create the map is dependent on the environment, no point selection method dominates. This motivates a novel self-adaptive approach for an agent to combine several point selection methods. The success rate of our approach is comparable to the state of the art and the generation cost is substantially reduced. Self-adaptation therefore enables a more efficient use of the agent's resources. Results are presented for both a set of archetypal scenarios and large scale virtual environments based in Second Life, representing real locations in London.

Seawater carbonate chemistry and calcification rate of eastern oyster Crassostrea virginica, 2011

Anthropogenic carbon dioxide (CO2) emissions reduce pH of marine waters due to the absorption of atmospheric CO2 and formation of carbonic acid. Estuarine waters are more susceptible to acidification because they are subject to multiple acid sources and are less buffered than marine waters. Consequently, estuarine shell forming species may experience acidification sooner than marine species although the tolerance of estuarine calcifiers to pH changes is poorly understood. We analyzed 23 years of Chesapeake Bay water quality monitoring data and found that daytime average pH significantly decreased across polyhaline waters although pH has not significantly changed across mesohaline waters. In some tributaries that once supported large oyster populations, pH is increasing. Current average conditions within some tributaries however correspond to values that we found in laboratory studies to reduce oyster biocalcification rates or resulted in net shell dissolution. Calcification rates of juvenile eastern oysters, Crassostrea virginica, were measured in laboratory studies in a three-way factorial design with 3 pH levels, two salinities, and two temperatures. Biocalcification declined significantly with a reduction of ~0.5 pH units and higher temperature and salinity mitigated the decrease in biocalcification.