On the stability of classical orbits of the hydrogen ground state in Stochastic Electrodynamics

de la Pe\~na 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics are stable. Though the Cole-Zou 2003 simulations support the stability, our recent numerics always lead to self-ionisation. Here the de la Pe\~na-Puthoff argument is extended to elliptic orbits. For very eccentric orbits with energy close to zero and angular momentum below some not-small value, there is on the average a net gain in energy for each revolution, which explains the self-ionisation. Next, an $1/r^2$ potential is added, which could stem from a dipolar deformation of the nuclear charge by the electron at its moving position. This shape retains the analytical solvability. When it is enough repulsive, the ground state of this modified hydrogen problem is predicted to be stable. The same conclusions hold for positronium.Comment: 18 pages latex, 1 figur

Classification of Low Velocity Impactors Using Spiral Sensing of Acousto-Ultrasonic Waves

The non-linear elastodynamics of a flat plate subjected to low velocity foreign body impacts is studied, resembling the space debris impacts on the space structure. The work is based on a central hypothesis that in addition to identifying the impact locations, the material properties of the foreign objects can also be classified using acousto-ultrasonic signals (AUS). Simultaneous localization of impact point and classification of impact object is quite challenging using existing state-of-the-art structural health monitoring (SHM) approaches. Available techniques seek to report the exact location of impact on the structure, however, the reported information is likely to have errors from nonlinearity and variability in the AUS signals due to materials, geometry, boundary conditions, wave dispersion, environmental conditions, sensor and hardware calibration etc. It is found that the frequency and speed of the guided wave generated in the plate can be quantized based on the impactor\u27s relationship with the plate (i.e. the wave speed and the impactor\u27s mechanical properties are coupled). In this work, in order to characterize the impact location and mechanical properties of imapctors, nonlinear transient phenomenon is empirically studied to decouple the understanding using the dominant frequency band (DFB) and Lag Index (LI) of the acousto-ultrasonic signals. Next the understanding was correlated with the elastic modulus of the impactor to predict transmitted force histories. The proposed method presented in this thesis is especially applicable for SHM where sensors cannot be widely or randomly distributed. Thus a strategic organization and localization of the sensors is achieved by implementing the geometric configuration of Theodorous Spiral Sensor Cluster (TSSC). The performance of TSSC in characterizing the impactor types are compared with other conventional sensor clusters (e.g. square, circular, random etc.) and it is shown that the TSSC is advantageous over conventional localized sensor clusters. It was found that the TSSC provides unbiased sensor voting that boosts sensitivity towards classification of impact events. To prove the concept, a coupled field (multiphysics) finite element model (CFFEM) is developed and a series of experiments were performed. The dominant frequency band (DBF) along with a Lag Index (LI) feature extraction technique was found to be suitable for classifying the impactors. Results show that TSSC with DBF features increase the sensitivity of impactor\u27s elastic modulus, if the covariance of the AUS from the TSSC and other conventional sensor clusters are compared. It is observe that for the impact velocity, geometric and mechanical properties studied herein, longitudinal and flexural waves are excited, and there are quantifiable differences in the Lamb wave signatures excited for different impactor materials. It is found that such differences are distinguishable only by the proposed TSSC, but not by other state-of-the-art sensor configurations used in SHM. This study will be useful for modeling an inverse problem needed for classifying impactor materials and the subsequent reconstruction of force histories via neural network or artificial intelligence. Finally an alternative novel approach is proposed to describe the Probability Map of Impact (PMOI) over the entire structure. PMOI could serve as a read-out tool for simultaneously identifying the impact location and the type of the impactor that has impacted the structure. PMOI is intended to provide high risk areas of the space structures where the incipient damage could exist (e.g. area with PMOI \u3e 95%) after an impact

Summation of series and Gaussian quadratures

Abstract. In 1985, Gautschi and the author constructed Gaussian quadrature formulae on (0, +∞) involving Einstein and Fermi functions as weights and applied then to the summation of slowly convergent series which can be represented in terms of the derivative of a Laplace transform, or in terms of the Laplace transform itself. A problem that may arise in this procedure is the determination of the respective inverse Laplace transform. For the class of slowly convergent series and R(s) is a rational function, Gautschi recently solved this problem. In the present paper, using complex integration and constructing Gauss-Christoffel quadratures on (0, +∞) with respect to the weight functions w 1 (t) = 1/ cosh 2 t and w 2 (t) = sinh t/ cosh 2 t, we reduce the and w 2 , respectively. We illustrate this method with a few numerical examples

LEMA: Towards a Language for Reliable Arithmetic

Generating certified and efficient numerical codes requires information ranging from the mathematical level to the representation of numbers. Even though the mathematical semantics can be expressed using the content part of MathML, this language does not encompass the implementation on computers. Indeed various arithmetics may be involved, like floating-point or fixed-point, in fixed precision or arbitrary precision, and current tools cannot handle all of these. Therefore we propose in this paper LEMA (Langage pour les Expressions Mathématiques Annotées), a descriptive language based on MathML with additional expressiveness. LEMA will be used during the automatic generation of certified numerical codes. Such a generation process typically involves several steps, and LEMA would thus act as a glue to represent and store the information at every stage. First, we specify in the language the characteristics of the arithmetic as described in the IEEE 754 floating-point standard: formats, exceptions, rounding modes. This can be generalized to other arithmetics. Then, we use annotations to attach a specific arithmetic context to an expression tree. Finally, considering the evaluation of the expression in this context allows us to deduce several properties on the result, like being exact or being an exception. Other useful properties include numerical ranges and error bounds

System Level Synthesis Beyond Finite Impulse Response Using Approximation by Simple Poles

Optimal linear feedback control design is valuable but challenging. The system level synthesis approach uses a reparameterization to expand the class of problems that can be solved using convex reformulations, among other benefits. However, to solve system level synthesis problems prior work relies on finite impulse response approximations that lead to deadbeat control, and that can experience infeasibility and increased suboptimality, especially in systems with large separation of time scales. This work develops a new technique by combining system level synthesis with a new approximation based on simple poles. The result is a new design method which does not result in deadbeat control, is convex and tractable, always feasible, can incorporate prior knowledge, and works well for systems with large separation of time scales. A general suboptimality result is provided which bounds the approximation error based on the geometry of the pole selection. The bound is then specialized to a particularly interesting pole selection to obtain a non-asymptotic convergence rate. An example demonstrates superior performance of the method.Comment: 25 page

Evolutionary Robot Swarms Under Real-World Constraints

Tese de doutoramento em Engenharia Electrotécnica e de Computadores, na especialidade de Automação e Robótica, apresentada ao Departamento de Engenharia Electrotécnica e de Computadores da Faculdade de Ciências e Tecnologia da Universidade de CoimbraNas últimas décadas, vários cientistas e engenheiros têm vindo a estudar as estratégias provenientes da natureza. Dentro das arquiteturas biológicas, as sociedades que vivem em enxames revelam que agentes simplistas, tais como formigas ou pássaros, são capazes de realizar tarefas complexas usufruindo de mecanismos de cooperação. Estes sistemas abrangem todas as condições necessárias para a sobrevivência, incorporando comportamentos de cooperação, competição e adaptação. Na “batalha” sem fim em prol do progresso dos mecanismos artificiais desenvolvidos pelo homem, a ciência conseguiu simular o primeiro comportamento em enxame no final dos anos oitenta. Desde então, muitas outras áreas, entre as quais a robótica, beneficiaram de mecanismos de tolerância a falhas inerentes da inteligência coletiva de enxames. A área de investigação deste estudo incide na robótica de enxame, consistindo num domínio particular dos sistemas robóticos cooperativos que incorpora os mecanismos de inteligência coletiva de enxames na robótica. Mais especificamente, propõe-se uma solução completa de robótica de enxames a ser aplicada em contexto real. Nesta ótica, as operações de busca e salvamento foram consideradas como o caso de estudo principal devido ao nível de complexidade associado às mesmas. Tais operações ocorrem tipicamente em cenários dinâmicos de elevadas dimensões, com condições adversas que colocam em causa a aplicabilidade dos sistemas robóticos cooperativos. Este estudo centra-se nestes problemas, procurando novos desafios que não podem ser ultrapassados através da simples adaptação da literatura da especialidade em algoritmos de enxame, planeamento, controlo e técnicas de tomada de decisão. As contribuições deste trabalho sustentam-se em torno da extensão do método Particle Swarm Optimization (PSO) aplicado a sistemas robóticos cooperativos, denominado de Robotic Darwinian Particle Swarm Optimization (RDPSO). O RDPSO consiste numa arquitetura robótica de enxame distribuída que beneficia do particionamento dinâmico da população de robôs utilizando mecanismos evolucionários de exclusão social baseados na sobrevivência do mais forte de Darwin. No entanto, apesar de estar assente no caso de estudo do RDPSO, a aplicabilidade dos conceitos aqui propostos não se encontra restrita ao mesmo, visto que todos os algoritmos parametrizáveis de enxame de robôs podem beneficiar de uma abordagem idêntica. Os fundamentos em torno do RDPSO são introduzidos, focando-se na dinâmica dos robôs, nos constrangimentos introduzidos pelos obstáculos e pela comunicação, e nas suas propriedades evolucionárias. Considerando a colocação inicial dos robôs no ambiente como algo fundamental para aplicar sistemas de enxames em aplicações reais, é assim introduzida uma estratégia de colocação de robôs realista. Para tal, a população de robôs é dividida de forma hierárquica, em que são utilizadas plataformas mais robustas para colocar as plataformas de enxame no cenário de forma autónoma. Após a colocação dos robôs no cenário, é apresentada uma estratégia para permitir a criação e manutenção de uma rede de comunicação móvel ad hoc com tolerância a falhas. Esta estratégia não considera somente a distância entre robôs, mas também a qualidade do nível de sinal rádio frequência, redefinindo assim a sua aplicabilidade em cenários reais. Os aspetos anteriormente mencionados estão sujeitos a uma análise detalhada do sistema de comunicação inerente ao algoritmo, para atingir uma implementação mais escalável do RDPSO a cenários de elevada complexidade. Esta elevada complexidade inerente à dinâmica dos cenários motivaram a ultimar o desenvolvimento do RDPSO, integrando para o efeito um mecanismo adaptativo baseado em informação contextual (e.g., nível de atividade do grupo). Face a estas considerações, o presente estudo pode contribuir para expandir o estado-da-arte em robótica de enxame com algoritmos inovadores aplicados em contexto real. Neste sentido, todos os métodos propostos foram extensivamente validados e comparados com alternativas, tanto em simulação como com robôs reais. Para além disso, e dadas as limitações destes (e.g., número limitado de robôs, cenários de dimensões limitadas, constrangimentos reais limitados), este trabalho contribui ainda para um maior aprofundamento do estado-da-arte, onde se propõe um modelo macroscópico capaz de capturar a dinâmica inerente ao RDPSO e, até certo ponto, estimar analiticamente o desempenho coletivo dos robôs perante determinada tarefa. Em suma, esta investigação pode ter aplicabilidade prática ao colmatar a lacuna que se faz sentir no âmbito das estratégias de enxames de robôs em contexto real e, em particular, em cenários de busca e salvamento.Over the past decades, many scientists and engineers have been studying nature’s best and time-tested patterns and strategies. Within the existing biological architectures, swarm societies revealed that relatively unsophisticated agents with limited capabilities, such as ants or birds, were able to cooperatively accomplish complex tasks necessary for their survival. Those simplistic systems embrace all the conditions necessary to survive, thus embodying cooperative, competitive and adaptive behaviours. In the never-ending battle to advance artificial manmade mechanisms, computer scientists simulated the first swarm behaviour designed to mimic the flocking behaviour of birds in the late eighties. Ever since, many other fields, such as robotics, have benefited from the fault-tolerant mechanism inherent to swarm intelligence. The area of research presented in this Ph.D. Thesis focuses on swarm robotics, which is a particular domain of multi-robot systems (MRS) that embodies the mechanisms of swarm intelligence into robotics. More specifically, this Thesis proposes a complete swarm robotic solution that can be applied to real-world missions. Although the proposed methods do not depend on any particular application, search and rescue (SaR) operations were considered as the main case study due to their inherent level of complexity. Such operations often occur in highly dynamic and large scenarios, with harsh and faulty conditions, that pose several problems to MRS applicability. This Thesis focuses on these problems raising new challenges that cannot be handled appropriately by simple adaptation of state-of-the-art swarm algorithms, planning, control and decision-making techniques. The contributions of this Thesis revolve around an extension of the Particle Swarm Optimization (PSO) to MRS, denoted as Robotic Darwinian Particle Swarm Optimization (RDPSO). The RDPSO is a distributed swarm robotic architecture that benefits from the dynamical partitioning of the whole swarm of robots by means of an evolutionary social exclusion mechanism based on Darwin’s survival-of-the-fittest. Nevertheless, although currently applied solely to the RDPSO case study, the applicability of all concepts herein proposed is not restricted to it, since all parameterized swarm robotic algorithms may benefit from a similar approach The RDPSO is then proposed and used to devise the applicability of novel approaches. The fundamentals around the RDPSO are introduced by focusing on robots’ dynamics, obstacle avoidance, communication constraints and its evolutionary properties. Afterwards, taking the initial deployment of robots within the environment as a basis for applying swarm robotics systems into real-world applications, the development of a realistic deployment strategy is proposed. For that end, the population of robots is hierarchically divided, wherein larger support platforms autonomously deploy smaller exploring platforms in the scenario, while considering communication constraints and obstacles. After the deployment, a way of ensuring a fault-tolerant multi-hop mobile ad hoc communication network (MANET) is introduced to explicitly exchange information needed in a collaborative realworld task execution. Such strategy not only considers the maximum communication range between robots, but also the minimum signal quality, thus refining the applicability to real-world context. This is naturally followed by a deep analysis of the RDPSO communication system, describing the dynamics of the communication data packet structure shared between teammates. Such procedure is a first step to achieving a more scalable implementation by optimizing the communication procedure between robots. The highly dynamic characteristics of real-world applications motivated us to ultimate the RDPSO development with an adaptive strategy based on a set of context-based evaluation metrics. This thesis contributes to the state-of-the-art in swarm robotics with novel algorithms for realworld applications. All of the proposed approaches have been extensively validated in benchmarking tasks, in simulation, and with real robots. On top of that, and due to the limitations inherent to those (e.g., number of robots, scenario dimensions, real-world constraints), this Thesis further contributes to the state-of-the-art by proposing a macroscopic model able to capture the RDPSO dynamics and, to some extent, analytically estimate the collective performance of robots under a certain task. It is the author’s expectation that this Ph.D. Thesis may shed some light into bridging the reality gap inherent to the applicability of swarm strategies to real-world scenarios, and in particular to SaR operations.FCT - SFRH/BD /73382/201