A Mathematical Model for Simplifying Representations of Objects in a Geographic Information System

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.

BaTboT: a biologically inspired flapping and morphing bat robot actuated by SMA-based artificial muscles

Bats are animals that posses high maneuvering capabilities. Their wings contain dozens of articulations that allow the animal to perform aggressive maneuvers by means of controlling the wing shape during flight (morphing-wings). There is no other flying creature in nature with this level of wing dexterity and there is biological evidence that the inertial forces produced by the wings have a key role in the attitude movements of the animal. This can inspire the design of highly articulated morphing-wing micro air vehicles (not necessarily bat-like) with a significant wing-to-body mass ratio. This thesis presents the development of a novel bat-like micro air vehicle (BaTboT) inspired by the morphing-wing mechanism of bats. BaTboT’s morphology is alike in proportion compared to its biological counterpart Cynopterus brachyotis, which provides the biological foundations for developing accurate mathematical models and methods that allow for mimicking bat flight. In nature bats can achieve an amazing level of maneuverability by combining flapping and morphing wingstrokes. Attempting to reproduce the biological wing actuation system that provides that kind of motion using an artificial counterpart requires the analysis of alternative actuation technologies more likely muscle fiber arrays instead of standard servomotor actuators. Thus, NiTinol Shape Memory Alloys (SMAs) acting as artificial biceps and triceps muscles are used for mimicking the morphing wing mechanism of the bat flight apparatus. This antagonistic configuration of SMA-muscles response to an electrical heating power signal to operate. This heating power is regulated by a proper controller that allows for accurate and fast SMA actuation. Morphing-wings will enable to change wings geometry with the unique purpose of enhancing aerodynamics performance. During the downstroke phase of the wingbeat motion both wings are fully extended aimed at increasing the area surface to properly generate lift forces. Contrary during the upstroke phase of the wingbeat motion both wings are retracted to minimize the area and thus reducing drag forces. Morphing-wings do not only improve on aerodynamics but also on the inertial forces that are key to maneuver. Thus, a modeling framework is introduced for analyzing how BaTboT should maneuver by means of changing wing morphology. This allows the definition of requirements for achieving forward and turning flight according to the kinematics of the wing modulation. Motivated by the biological fact about the influence of wing inertia on the production of body accelerations, an attitude controller is proposed. The attitude control law incorporates wing inertia information to produce desired roll (φ) and pitch (θ) acceleration commands. This novel flight control approach is aimed at incrementing net body forces (Fnet) that generate propulsion. Mimicking the way how bats take advantage of inertial and aerodynamical forces produced by the wings in order to both increase lift and maneuver is a promising way to design more efficient flapping/morphing wings MAVs. The novel wing modulation strategy and attitude control methodology proposed in this thesis provide a totally new way of controlling flying robots, that eliminates the need of appendices such as flaps and rudders, and would allow performing more efficient maneuvers, especially useful in confined spaces. As a whole, the BaTboT project consists of five major stages of development: - Study and analysis of biological bat flight data reported in specialized literature aimed at defining design and control criteria. - Formulation of mathematical models for: i) wing kinematics, ii) dynamics, iii) aerodynamics, and iv) SMA muscle-like actuation. It is aimed at modeling the effects of modulating wing inertia into the production of net body forces for maneuvering. - Bio-inspired design and fabrication of: i) skeletal structure of wings and body, ii) SMA muscle-like mechanisms, iii) the wing-membrane, and iv) electronics onboard. It is aimed at developing the bat-like platform (BaTboT) that allows for testing the methods proposed. - The flight controller: i) control of SMA-muscles (morphing-wing modulation) and ii) flight control (attitude regulation). It is aimed at formulating the proper control methods that allow for the proper modulation of BaTboT’s wings. - Experiments: it is aimed at quantifying the effects of properly wing modulation into aerodynamics and inertial production for maneuvering. It is also aimed at demonstrating and validating the hypothesis of improving flight efficiency thanks to the novel control methods presented in this thesis. This thesis introduces the challenges and methods to address these stages. Windtunnel experiments will be oriented to discuss and demonstrate how the wings can considerably affect the dynamics/aerodynamics of flight and how to take advantage of wing inertia modulation that the morphing-wings enable to properly change wings’ geometry during flapping. Resumen: Los murciélagos son mamíferos con una alta capacidad de maniobra. Sus alas están conformadas por docenas de articulaciones que permiten al animal maniobrar gracias al cambio geométrico de las alas durante el vuelo. Esta característica es conocida como (alas mórficas). En la naturaleza, no existe ningún especimen volador con semejante grado de dexteridad de vuelo, y se ha demostrado, que las fuerzas inerciales producidas por el batir de las alas juega un papel fundamental en los movimientos que orientan al animal en vuelo. Estas características pueden inspirar el diseño de un micro vehículo aéreo compuesto por alas mórficas con redundantes grados de libertad, y cuya proporción entre la masa de sus alas y el cuerpo del robot sea significativa. Esta tesis doctoral presenta el desarrollo de un novedoso robot aéreo inspirado en el mecanismo de ala mórfica de los murciélagos. El robot, llamado BaTboT, ha sido diseñado con parámetros morfológicos muy similares a los descritos por su símil biológico Cynopterus brachyotis. El estudio biológico de este especimen ha permitido la definición de criterios de diseño y modelos matemáticos que representan el comportamiento del robot, con el objetivo de imitar lo mejor posible la biomecánica de vuelo de los murciélagos. La biomecánica de vuelo está definida por dos tipos de movimiento de las alas: aleteo y cambio de forma. Intentar imitar como los murciélagos cambian la forma de sus alas con un prototipo artificial, requiere el análisis de métodos alternativos de actuación que se asemejen a la biomecánica de los músculos que actúan las alas, y evitar el uso de sistemas convencionales de actuación como servomotores ó motores DC. En este sentido, las aleaciones con memoria de forma, ó por sus siglas en inglés (SMA), las cuales son fibras de NiTinol que se contraen y expanden ante estímulos térmicos, han sido usados en este proyecto como músculos artificiales que actúan como bíceps y tríceps de las alas, proporcionando la funcionalidad de ala mórfica previamente descrita. De esta manera, los músculos de SMA son mecánicamente posicionados en una configuración antagonista que permite la rotación de las articulaciones del robot. Los actuadores son accionados mediante una señal de potencia la cual es regulada por un sistema de control encargado que los músculos de SMA respondan con la precisión y velocidad deseada. Este sistema de control mórfico de las alas permitirá al robot cambiar la forma de las mismas con el único propósito de mejorar el desempeño aerodinámico. Durante la fase de bajada del aleteo, las alas deben estar extendidas para incrementar la producción de fuerzas de sustentación. Al contrario, durante el ciclo de subida del aleteo, las alas deben contraerse para minimizar el área y reducir las fuerzas de fricción aerodinámica. El control de alas mórficas no solo mejora el desempeño aerodinámico, también impacta la generación de fuerzas inerciales las cuales son esenciales para maniobrar durante el vuelo. Con el objetivo de analizar como el cambio de geometría de las alas influye en la definición de maniobras y su efecto en la producción de fuerzas netas, simulaciones y experimentos han sido llevados a cabo para medir cómo distintos patrones de modulación de las alas influyen en la producción de aceleraciones lineales y angulares. Gracias a estas mediciones, se propone un control de vuelo, ó control de actitud, el cual incorpora información inercial de las alas para la definición de referencias de aceleración angular. El objetivo de esta novedosa estrategia de control radica en el incremento de fuerzas netas para la adecuada generación de movimiento (Fnet). Imitar como los murciélagos ajustan sus alas con el propósito de incrementar las fuerzas de sustentación y mejorar la maniobra en vuelo es definitivamente un tópico de mucho interés para el diseño de robots aéros mas eficientes. La propuesta de control de vuelo definida en este trabajo de investigación podría dar paso a una nueva forma de control de vuelo de robots aéreos que no necesitan del uso de partes mecánicas tales como alerones, etc. Este control también permitiría el desarrollo de vehículos con mayor capacidad de maniobra. El desarrollo de esta investigación se centra en cinco etapas: - Estudiar y analizar el vuelo de los murciélagos con el propósito de definir criterios de diseño y control. - Formular modelos matemáticos que describan la: i) cinemática de las alas, ii) dinámica, iii) aerodinámica, y iv) actuación usando SMA. Estos modelos permiten estimar la influencia de modular las alas en la producción de fuerzas netas. - Diseño y fabricación de BaTboT: i) estructura de las alas y el cuerpo, ii) mecanismo de actuación mórfico basado en SMA, iii) membrana de las alas, y iv) electrónica abordo. - Contro de vuelo compuesto por: i) control de la SMA (modulación de las alas) y ii) regulación de maniobra (actitud). - Experimentos: están enfocados en poder cuantificar cuales son los efectos que ejercen distintos perfiles de modulación del ala en el comportamiento aerodinámico e inercial. El objetivo es demostrar y validar la hipótesis planteada al inicio de esta investigación: mejorar eficiencia de vuelo gracias al novedoso control de orientación (actitud) propuesto en este trabajo. A lo largo del desarrollo de cada una de las cinco etapas, se irán presentando los retos, problemáticas y soluciones a abordar. Los experimentos son realizados utilizando un túnel de viento con la instrumentación necesaria para llevar a cabo las mediciones de desempeño respectivas. En los resultados se discutirá y demostrará que la inercia producida por las alas juega un papel considerable en el comportamiento dinámico y aerodinámico del sistema y como poder tomar ventaja de dicha característica para regular patrones de modulación de las alas que conduzcan a mejorar la eficiencia del robot en futuros vuelos.

Análisis dinámico experimental de edificios esbeltos

Es conocido que la variación del comportamiento dinámico de las estructuras puede ser empleado dentro de un sistema de monitorización de su integridad estructural. Así, este estudio tiene como objetivo comprender el comportamiento dinámico de edificios esbeltos, frente a diferentes agentes ambientales como la temperatura y/o dirección y velocidad del viento. En el marco de esta investigación, se estudian dos edificios: la Torre de la ETSI (Escuela Técnica Superior de Ingenieros) de Caminos, Canales y Puertos de la UPM (Universidad Politécnica de Madrid) y un edificio de viviendas situado en la calle de Arturo Soria de Madrid. Los datos medioambientales antes mencionados, se registraron con sendas estacionales meteorológicas situadas en las azoteas de ambos edificios. Se realiza el análisis modal operacional de ambas estructuras. Este análisis se realiza a partir de las mediciones de las aceleraciones ante excitaciones ambientales, es un análisis basado sólo en la respuesta de la estructura. Por tanto, no es necesario interrumpir el funcionamiento en servicio de la instalación, obteniendo su comportamientos en este estado. A partir de este análisis, se obtienen las frecuencias naturales, los amortiguamientos modales y las formas modales. Así, en este trabajo se ha estudiado la relación existente entre la variación en la estimación de las frecuencias naturales y la variación de los agentes ambientales (fundamentalmente la temperatura). Los ensayos dinámicos en los dos edificios mencionados anteriormente, se han realizado utilizando acelerómetros de alta sensibilidad sincronizados inalámbricamente, lo cual ha simplificado el trabajo experimental si lo comparamos con los sistemas tradicionales. Como resultado del trabajo realizado se pueden destacar los siguientes puntos: (i) se ha visto que con el equipamiento disponible se pueden realizar análisis dinámicos de edificios, (ii) se ha mejorado el conocimiento dinámico de estas estructuras, y (iii) se ha visto la importancia que pueden tener los agentes ambientales dependiendo por un lado del tipo estructura del edificio. A partir del trabajo, se podrían actualizar modelos matemáticos que sirvan para la predicción de daños en las estructuras, y por otro, se podrán eliminar los efectos de los agentes ambientales, lo cual es un punto vital si se quiere emplear los parámetros modales para el cálculo de indices de daño. La aplicación de este tipo de investigación ayudará a tener una información mayor sobre el comportamiento de las estructuras y así, en el futuro, poder realizar distintos tipos de procesos, como la formulación de modelos matemáticos que reflejen con mayor fidelidad el comportamiento real. De esta forma, la monitorización de los agentes medioambientales permitirán valorar la influencia de estas variaciones sobre la estructura pudiéndose eliminar estos efectos. Con ello, se mejora la incertidumbre en la variación de frecuencias que puede ser utilizada como un sistema de activación de alarmas frente a la detección de daños estructurales. It is known that the variation of the dynamic behavior of structures can be used within a system to monitor structural integrity. So, this study aims to understand the dynamic behavior of slender buildings, against different environmental agents such as temperature and / or wind direction and velocity. As part of this investigation, two buildings are studied: the ETSI's (Escuela Técnica Superior de Ingenieros) main tower of Escuela de Caminos, Canales y Puertos of UPM (Universidad Politécnica de Madrid) and a residential building located in the streets Arturo Soria Madrid. The environmental data were recorded with weather stations located on the roof of both buildings. In both structures a modal operational analysis has been carried out. This analysis is performed from the measurements of the acceleration to the environmental excitation, this analysis is based only on the response of the structure. Therefore, it is not necessary to interrupt the operation of the structure, getting its behavior in this state. From this analysis, the natural frequencies, modal damping and mode shapes are obtained. So, in this work we have studied the existing relationship between the variation in the estimate of the natural frequencies and the variation of environmental agents (mainly temperature). The dynamic tests in the two buildings mentioned above, have been made using high-sensitivity accelerometers wirelessly synchronized, which has simplified the experimental work when compared to traditional systems. As a result of work performed can highlight the following points: (i) it has been found that with the available equipment can perform dynamic analysis of buildings, (ii) has improved dynamic knowledge of these structures, and, (iii) can be seen the potential importance of environmental agents depending on the type of building structure. From the work, mathematical models can be updated that serve to prediction of damage to structures, and on the other side, may eliminate the effects of environmental agents, which is a vital point if you want to use the modal parameters for calculating damage ratings. The application of this type of research will help to have more information about the behavior of structures and so, in the future, conduct various processes, as the formulation of mathematical models that reflect more accurately an actual behavior. In this way the monitoring of environmental agents will allow evaluate the influence of these variations on the structure being possible eliminate these effects. Thereby, improvement the uncertainty in the frequencies variation that can be used as an alarm activation system from detection of structural damage.

Estudio experimental sobre la reacción álcali-sílice en el hormigón producida por áridos de reacción lenta

La finalidad de esta investigación se enmarca dentro de los estudios sobre hormigones de presas llevados a cabo en el Laboratorio Central de Estructuras y Materiales del CEDEX. En España se han diagnosticado 18 obras afectadas tanto por la reacción álcali-sílice de tipo rápido como por la de tipo lento. Dos de de las obras, fabricadas con áridos graníticos, no presentan signos de deterioro pero en laboratorio se han hallado productos expansivos. En las 16 presas españolas restantes, el hormigón de 10 de ellas estaba fabricado con áridos graníticos, de las cuales, 7 están afectadas por la reacción de tipo lento. Sin embargo, en las clasificaciones internacionales de las rocas potencialmente reactivas se establece habitualmente que las rocas graníticas son inocuas o de reactividad muy baja. En los casos puntuales encontrados en la literatura, la reactividad de este tipo de áridos se encuentra frecuentemente asociada al cuarzo microcristalino que contienen y ocasionalmente se asocia esta reactividad también al cuarzo deformado y/o microfisurado. En la tesis doctoral de Víctor Daniel Lanza Fernández, también realizada en el CEDEX, se han tratado los áridos de reacción rápida, dando una descripción detallada de los componentes que intervienen en este tipo de reacción y presentando un ensayo eficaz para su detección en el laboratorio. La investigación desarrollada en la presente tesis doctoral se ha centrado en los áridos de reacción lenta, mucho menos estudiados. A partir del estudio bibliográfico realizado sobre este tipo de reacción se ha detectado ciertas lagunas, basadas principalmente en la falta de un método de detección en el laboratorio para los áridos de reacción lenta. No se ha encontrado un procedimiento en el estudio petrográfico que sea fiable y cuantificable para este tipo de áridos. El ensayo acelerado de barras de mortero, que para los áridos de reacción rápida supone un método rápido y fiable, falla en la detección de los áridos de reacción lenta al aplicar los límites normalizados. Si bien en publicaciones recientes se ha propuesto la posibilidad de ampliar el tiempo de tratamiento hasta los 90 días, la duración del ensayo es más larga de lo deseado. Para resolver estas lagunas, se han tomado áridos de obras reales afectadas por la reacción álcali-sílice (en algún caso también de las canteras de donde se extrajeron los áridos para la ejecución), con lo que la reactividad de estos áridos queda demostrada por su comportamiento en obra. Al objeto de aumentar la muestra de ensayo y utilizar también áridos inocuos, se han tomado muestras de canteras, tanto en uso como abandonadas. Sobre estos áridos se ha realizado una caracterización completa con los ensayos actualmente disponibles para el estudio de su reactividad con los álcalis del cemento: estudio petrográfico, ensayo acelerado de barras de mortero y Gel-Pat modificado. En la investigación se ha desarrollado una metodología de tinción de geles álcali-sílice para la cuantificación de los mismos en el interior de las barras de mortero. Se ha relacionado el volumen de gel generado en la reacción con la expansión producida, tanto para áridos lentos, como rápidos, estableciendo analogías y diferencias en el comportamiento de ambos. La cuantificación de este tipo de compuestos realizada en las barras de mortero, abre la posibilidad de estudiar la capacidad expansiva que presentan en testigos de hormigón de obras afectadas. Este dato podría ser una herramienta importante para el desarrollo de modelos matemáticos que puedan predecir el futuro comportamiento de las estructuras afectadas por la reacción álcali-sílice. La tinción ha sido asimismo utilizada para establecer un método de detección de áridos reactivos basado en el ensayo de Gel-Pat modificado. La metodología de detección propuesta para estos áridos es cuantitativa y proporciona los resultados en 14 días, suponiendo una ventaja importante sobre los métodos actuales, que permiten detectarlos en 90 días (de forma orientativa en 56 días). This research is part of the studies on durability of concrete dams carried out in the Laboratorio Central de Estructuras y Materiales of CEDEX during the last years. At the present time, 18 public works affected by alkali-silica reaction have been diagnosed in Spain. In 12 of them the concrete was mixed with granitic aggregates, 7 of which were damaged by the slow alkali-silica reaction, 3 by the rapid alkali-silica reaction and in the other 2 cases, although there was no visual evidence of the reaction in field, the laboratory tests showed the presence of expansive products inside the concrete. However, in the international classifications of potentially reactive aggregates granitic rocks are pointed out as innocuous or as low reactivity and usually their reactivity is attributed to the presence of microcrystalline quartz and occasionally with the strained and microcracked quartz. The rapid reactive aggregates were deeply studied in a previous research (Víctor Daniel Lanza’s Thesis) also carried out in CEDEX. In this research, a detailed description of the components involved in the rapid alkali-silica reaction was given. Also, a fast method to detect them in the laboratory was developed. The research of the present PhD Thesis is focused in the slow-reactive aggregates, much less studied. The state of the art has shown some gaps in the knowledge about this reaction, mainly the absence of a reliable method to detect slow-reactive aggregates. On one side, there is no systematic and quantitative petrographic test for these aggregates. On the other side, the accelerated mortar bar test has been proved to be effective to detect rapid reactive aggregates but the standard limits fail in the detection of the slowreactive aggregates. In recent investigations it has been proposed extending the test until 90 days, but this period is considered too long. In this research, aggregates taken from affected structures have been used in the test, so their reactivity has been shown in practice. With the aim of increasing the number of samples aggregates from quarries have been also used. A method to stain alkali-silica gels has been applied to mortar bars, thereby quantifying the volume of gel generated inside. This volume has been related to the expansion of the bars, both for rapid for slow reactive aggregates, establishing similarities and differences. The quantification of the gel volume, applied to concrete cores extracted from affected structures, could be an important tool in mathematical models to predict the future behaviour of the structures affected by the alkali-silica reaction. The staining method has been also used to develop a method to detect slow reactive aggregates, based on the optimised Gel-Pat test, obtaining results in 14 days. This represents a major improvement compared to the actual methods (accelerated mortar bar test) which give an indicative value of reactivity at 56 days, and a final result at 90 days.

Two-dimensional direct rainfall hydraulic models applied to direct calculation of hydrologic events in dams to prevent overtopping

One of the main concerns when conducting a dam test is the acute determination of the hydrograph for a specific flood event. The use of 2D direct rainfall hydraulic mathematical models on a finite elements mesh, combined with the efficiency of vector calculus that provides CUDA (Compute Unified Device Architecture) technology, enables nowadays the simulation of complex hydrological models without the need for terrain subbasin and transit splitting (as in HEC-HMS). Both the Spanish PNOA (National Plan of Aereal Orthophotography) Digital Terrain Model GRID with a 5 x 5 m accuracy and the CORINE GIS Land Cover (Coordination of INformation of the Environment) that allows assessment of the ground roughness, provide enough data to easily build these kind of models

Control por modos deslizantes como estrategia de navegación en una flota de robots

En esta tesis se presenta el desarrollo de un esquema de cooperación entre vehículos terrestres (UGV) y aéreos (UAV) no tripulados, que sirve de base para conformar dos flotas de robots autónomos (denominadas FRACTAL y RoMA). Con el fin de comprobar, en diferentes escenarios y con diferente tareas, la validez de las estrategias de coordinación y cooperación propuestas en la tesis se utilizan los robots de la flota FRACTAL, que sirven como plataforma de prueba para tareas como el uso de vehículos aéreos y terrestres para apoyar labores de búsqueda y rescate en zonas de emergencia y la cooperación de una flota de robots para labores agrícolas. Se demuestra además, que el uso de la técnica de control no lineal conocida como Control por Modos Deslizantes puede ser aplicada no solo para conseguir la navegación autónoma individual de un robot aéreo o terrestre, sino también en tareas que requieren la navegación coordinada y sin colisiones de varios robots en un ambiente compartido. Para esto, se conceptualiza teóricamente el uso de la técnica de Control por Modos Deslizantes como estrategia de coordinación entre robots, extendiendo su aplicación a robots no-holonómicos en R2 y a robots aéreos en el espacio tridimensional. Después de dicha contextualización teórica, se analizan las condiciones necesarias para determinar la estabilidad del sistema multi-robot controlado y, finalmente, se comprueban las características de estabilidad y robustez ofrecidas por esta técnica de control. Tales comprobaciones se hacen simulando la navegación segura y eficiente de un grupo de UGVs para la detección de posibles riesgos ambientales, aprovechando la información aportada por un UAV. Para estas simulaciones se utilizan los modelos matemáticos de robots de la flota RoMA. Estas tareas coordinadas entre los robots se hacen posibles gracias a la efectividad, estabilidad y robustez de las estrategias de control que se desarrollan como núcleo fundamental de este trabajo de investigación. ABSTRACT This thesis presents the development of a cooperation scheme between unmanned ground (UGV) and aerial (UAV) vehicles. This scheme is the basis for forming two fleets of autonomous robots (called FRACTAL and RoMA). In order to assess, in different settings and on different tasks, the validity of the coordination and cooperation strategies proposed in the thesis, the FRACTAL fleet robots serves as a test bed for tasks like using coordinated aerial and ground vehicles to support search and rescue work in emergency scenarios or cooperation of a fleet of robots for agriculture. It is also shown that using the technique of nonlinear control known as Sliding Modes Control (SMC) can be applied not only for individual autonomous navigation of an aircraft or land robot, but also in tasks requiring the coordinated navigation of several robots, without collisions, in a shared environment. To this purpose, a strategy of coordination between robots using Sliding Mode Control technique is theoretically conceptualized, extending its application to non-holonomic robots in R2 and aerial robots in three-dimensional space. After this theoretical contextualization, the stability conditions of multi-robot system are analyzed, and finally, the stability and robustness characteristics are validated. Such validations are made with simulated experiments about the safe and efficient navigation of a group of UGV for the detection of possible environmental hazards, taking advantage of the information provided by a UAV. This simulations are made using mathematical models of RoMA fleet robots. These coordinated tasks of robots fleet are made possible thanks to the effectiveness, stability and robustness of the control strategies developed as core of this research.

Models of immune memory: On the role of cross-reactive stimulation, competition, and homeostasis in maintaining immune memory

There has been much debate on the contribution of processes such as the persistence of antigens, cross-reactive stimulation, homeostasis, competition between different lineages of lymphocytes, and the rate of cell turnover on the duration of immune memory and the maintenance of the immune repertoire. We use simple mathematical models to investigate the contributions of these various processes to the longevity of immune memory (defined as the rate of decline of the population of antigen-specific memory cells). The models we develop incorporate a large repertoire of immune cells, each lineage having distinct antigenic specificities, and describe the dynamics of the individual lineages and total population of cells. Our results suggest that, if homeostatic control regulates the total population of memory cells, then, for a wide range of parameters, immune memory will be long-lived in the absence of persistent antigen (T1/2 > 1 year). We also show that the longevity of memory in this situation will be insensitive to the relative rates of cross-reactive stimulation, the rate of turnover of immune cells, and the functional form of the term for the maintenance of homeostasis.

Identificação de sistemas para o estudo de controle motor.

Qualquer tarefa motora ativa se dá pela ativação de uma população de unidades motoras. Porém, devido a diversas dificuldades, tanto técnicas quanto éticas, não é possível medir a entrada sináptica dos motoneurônios em humanos. Por essas razões, o uso de modelos computacionais realistas de um núcleo de motoneurônios e as suas respectivas fibras musculares tem um importante papel no estudo do controle humano dos músculos. Entretanto, tais modelos são complexos e uma análise matemática é difícil. Neste texto é apresentada uma abordagem baseada em identificação de sistemas de um modelo realista de um núcleo de unidades motoras, com o objetivo de obter um modelo mais simples capaz de representar a transdução das entradas do núcleo de unidades motoras na força do músculo associado ao núcleo. A identificação de sistemas foi baseada em um algoritmo de mínimos quadrados ortogonal para achar um modelo NARMAX, sendo que a entrada considerada foi a condutância sináptica excitatória dendrítica total dos motoneurônios e a saída foi a força dos músculos produzida pelo núcleo de unidades motoras. O modelo identificado reproduziu o comportamento médio da saída do modelo computacional realista, mesmo para pares de sinal de entrada-saída não usados durante o processo de identificação do modelo, como sinais de força muscular modulados senoidalmente. Funções de resposta em frequência generalizada do núcleo de motoneurônios foram obtidas do modelo NARMAX, e levaram a que se inferisse que oscilações corticais na banda-beta (20 Hz) podem influenciar no controle da geração de força pela medula espinhal, comportamento do núcleo de motoneurônios até então desconhecido.

Modelagem de sinais neuronais utilizando filtros lineares de tempo discreto.

A aquisição experimental de sinais neuronais é um dos principais avanços da neurociência. Por meio de observações da corrente e do potencial elétricos em uma região cerebral, é possível entender os processos fisiológicos envolvidos na geração do potencial de ação, e produzir modelos matemáticos capazes de simular o comportamento de uma célula neuronal. Uma prática comum nesse tipo de experimento é obter leituras a partir de um arranjo de eletrodos posicionado em um meio compartilhado por diversos neurônios, o que resulta em uma mistura de sinais neuronais em uma mesma série temporal. Este trabalho propõe um modelo linear de tempo discreto para o sinal produzido durante o disparo do neurônio. Os coeficientes desse modelo são calculados utilizando-se amostras reais dos sinais neuronais obtidas in vivo. O processo de modelagem concebido emprega técnicas de identificação de sistemas e processamento de sinais, e é dissociado de considerações sobre o funcionamento biofísico da célula, fornecendo uma alternativa de baixa complexidade para a modelagem do disparo neuronal. Além disso, a representação por meio de sistemas lineares permite idealizar um sistema inverso, cuja função é recuperar o sinal original de cada neurônio ativo em uma mistura extracelular. Nesse contexto, são discutidas algumas soluções baseadas em filtros adaptativos para a simulação do sistema inverso, introduzindo uma nova abordagem para o problema de separação de spikes neuronais.

USLE and WEPP Soil Erosion Models: Their Applicability and Use in Generating Cover Values to Stabilize Soil in the Los Alamos, New Mexico Area

Soil erosion is a naturally occurring process that involves the detachment, transport, and deposition of soil particles. Disturbances such as thinning and wildfire can reduce cover greatly and increase erosion rates. Forest managers may use erosion prediction tools, such as the Universal Soil Loss Equation (USLE) and Water Erosion Prediction Project (WEPP) to estimate erosion rates and develop techniques to manage erosion. However, it is important to understand the differences and the applications of each model. Erosion rates were generated by each model and the model most applicable to the study site, Los Alamos, New Mexico was determined. It was also used to find the amount of cover needed to stabilize soil. The USLE is a simpler model and less complicated than a computer model like WEPP, and thus easier to manipulate to estimate cover values. Predicted cover values were compared to field cover values. Cover is necessary to establish effective erosion control guidelines.

Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.

Development of a novel pyrolysis-gas chromatography/mass spectrometry method for the analysis of poly(lactic acid) thermal degradation products

Thermal degradation of PLA is a complex process since it comprises many simultaneous reactions. The use of analytical techniques, such as differential scanning calorimetry (DSC) and thermogravimetry (TGA), yields useful information but a more sensitive analytical technique would be necessary to identify and quantify the PLA degradation products. In this work the thermal degradation of PLA at high temperatures was studied by using a pyrolyzer coupled to a gas chromatograph with mass spectrometry detection (Py-GC/MS). Pyrolysis conditions (temperature and time) were optimized in order to obtain an adequate chromatographic separation of the compounds formed during heating. The best resolution of chromatographic peaks was obtained by pyrolyzing the material from room temperature to 600 °C during 0.5 s. These conditions allowed identifying and quantifying the major compounds produced during the PLA thermal degradation in inert atmosphere. The strategy followed to select these operation parameters was by using sequential pyrolysis based on the adaptation of mathematical models. By application of this strategy it was demonstrated that PLA is degraded at high temperatures by following a non-linear behaviour. The application of logistic and Boltzmann models leads to good fittings to the experimental results, despite the Boltzmann model provided the best approach to calculate the time at which 50% of PLA was degraded. In conclusion, the Boltzmann method can be applied as a tool for simulating the PLA thermal degradation.

Saint Mathew Law and Bonini Paradox in Textual Theory of Complex Models

The mathematical models of the complex reality are texts belonging to a certain literature that is written in a semi-formal language, denominated L(MT) by the authors whose laws linguistic mathematics have been previously defined. This text possesses linguistic entropy that is the reflection of the physical entropy of the processes of real world that said text describes. Through the temperature of information defined by Mandelbrot, the authors begin a text-reality thermodynamic theory that drives to the existence of information attractors, or highly structured point, settling down a heterogeneity of the space text, the same one that of ontologic space, completing the well-known law of Saint Mathew, of the General Theory of Systems and formulated by Margalef saying: “To the one that has more he will be given, and to the one that doesn't have he will even be removed it little that it possesses.

Comparisons of models predicting ambient lake phosphorus concentrations /

Mode of access: Internet.

Comparison of numerical and physical hydraulic models, Masonboro Inlet, North Carolina /

"June 1977."