The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

The Sticky Information Macro Model: Beyond Perfect Foresight

Sticky information monetary models have been used in the macroeconomic literature to explain some of the observed features regarding inflation dynamics. In this paper, we explore the consequences of relaxing the rational expectations assumption usually taken in this type of model; in particular, by considering expectations formed through adaptive learning, it is possible to arrive to results other than the trivial convergence to a fixed point long-term equilibrium. The results involve the possibility of endogenous cyclical motion (periodic and a-periodic), which emerges essentially in scenarios of hyperinflation. In low inflation settings, the introduction of learning implies a less severe impact of monetary shocks that, nevertheless, tend to last for additional time periods relative to the pure perfect foresight setup.

Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

Dynamic equilibrium through reinforcement learning

Reinforcement Learning is an area of Machine Learning that deals with how an agent should take actions in an environment such as to maximize the notion of accumulated reward. This type of learning is inspired by the way humans learn and has led to the creation of various algorithms for reinforcement learning. These algorithms focus on the way in which an agent’s behaviour can be improved, assuming independence as to their surroundings. The current work studies the application of reinforcement learning methods to solve the inverted pendulum problem. The importance of the variability of the environment (factors that are external to the agent) on the execution of reinforcement learning agents is studied by using a model that seeks to obtain equilibrium (stability) through dynamism – a Cart-Pole system or inverted pendulum. We sought to improve the behaviour of the autonomous agents by changing the information passed to them, while maintaining the agent’s internal parameters constant (learning rate, discount factors, decay rate, etc.), instead of the classical approach of tuning the agent’s internal parameters. The influence of changes on the state set and the action set on an agent’s capability to solve the Cart-pole problem was studied. We have studied typical behaviour of reinforcement learning agents applied to the classic BOXES model and a new form of characterizing the environment was proposed using the notion of convergence towards a reference value. We demonstrate the gain in performance of this new method applied to a Q-Learning agent.

A Step-up mu-Power Converter for Solar Energy Harvesting Applications, using Hill Climbing Maximum Power Point Tracking

This paper presents a step-up micro-power converter for solar energy harvesting applications. The circuit uses a SC voltage tripler architecture, controlled by an MPPT circuit based on the Hill Climbing algorithm. This circuit was designed in a 0.13 mu m CMOS technology in order to work with an a-Si PV cell. The circuit has a local power supply voltage, created using a scaled down SC voltage tripler, controlled by the same MPPT circuit, to make the circuit robust to load and illumination variations. The SC circuits use a combination of PMOS and NMOS transistors to reduce the occupied area. A charge re-use scheme is used to compensate the large parasitic capacitors associated to the MOS transistors. The simulation results show that the circuit can deliver a power of 1266 mu W to the load using 1712 mu W of power from the PV cell, corresponding to an efficiency as high as 73.91%. The simulations also show that the circuit is capable of starting up with only 19% of the maximum illumination level.

Three-dimensional patchy lattice model for empty fluids

The phase diagram of a simple model with two patches of type A and ten patches of type B (2A10B) on the face centred cubic lattice has been calculated by simulations and theory. Assuming that there is no interaction between the B patches the behavior of the system can be described in terms of the ratio of the AB and AA interactions, r. Our results show that, similarly to what happens for related off-lattice and two-dimensional lattice models, the liquid-vapor phase equilibria exhibit reentrant behavior for some values of the interaction parameters. However, for the model studied here the liquid-vapor phase equilibria occur for values of r lower than 1/3, a threshold value which was previously thought to be universal for 2AnB models. In addition, the theory predicts that below r = 1/3 (and above a new condensation threshold which is < 1/3) the reentrant liquid-vapor equilibria are so extreme that it exhibits a closed loop with a lower critical point, a very unusual behavior in single-component systems. An order-disorder transition is also observed at higher densities than the liquid-vapor equilibria, which shows that the liquid-vapor reentrancy occurs in an equilibrium region of the phase diagram. These findings may have implications in the understanding of the condensation of dipolar hard spheres given the analogy between that system and the 2AnB models considered here. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4771591]

Sensing Cloud Optimization to Solve ED of Units with Valve-Point Effects and Multi-fuels

In this paper a solution to an highly constrained and non-convex economical dispatch (ED) problem with a meta-heuristic technique named Sensing Cloud Optimization (SCO) is presented. The proposed meta-heuristic is based on a cloud of particles whose central point represents the objective function value and the remaining particles act as sensors "to fill" the search space and "guide" the central particle so it moves into the best direction. To demonstrate its performance, a case study with multi-fuel units and valve- point effects is presented.

Basic dyestuffs removal from textile effluents using feathers: equilibrium, kinetic and column studies

This research work has been focused in the study of gallinaceous feathers, a waste that may be valorised as sorbent, to remove the Dark Blue Astrazon 2RN (DBA) from Dystar. This study was focused on the following aspects: optimization of experimental conditions through factorial design methodology, kinetic studies into a continuous stirred tank adsorber (at pH 7 and 20ºC), equilibrium isotherms (at pH 5, 7 and 9 at 20 and 45ºC) and column studies (at 20ºC, at pH 5, 7 and 9). In order to evaluate the influence of the presence of other components in the sorption of the dyestuff, all experiments were performed both for the dyestuff in aqueous solution and in real textile effluent. The pseudo-first and pseudo-second order kinetic models were fitted to the experimental data, being the latter the best fit for the aqueous solution of dyestuff. For the real effluent both models fit the experimental results and there is no statistical difference between them. The Central Composite Design (CCD) was used to evaluate the effects of temperature (15 - 45ºC) and pH (5 - 9) over the sorption in aqueous solution. The influence of pH was more significant than temperature. The optimal conditions selected were 45ºC and pH 9. Both Langmuir and Freundlich models could fit the equilibrium data. In the concentration range studied, the highest sorbent capacity was obtained for the optimal conditions in aqueous solution, which corresponds to a maximum capacity of 47± 4 mg g-1. The Yoon-Nelson, Thomas and Yan’s models fitted well the column experimental data. The highest breakthrough time for 50% removal, 170 min, was obtained at pH 9 in aqueous solution. The presence of the dyeing agents in the real wastewater decreased the sorption of the dyestuff mostly for pH 9, which is the optimal pH. The effect of pH is less pronounced in the real effluent than in aqueous solution. This work shows that feathers can be used as sorbent in the treatment of textile wastewaters containing DBA.

Caraterização dos habitats propícios à conservação da Estrelinha-de-Santa-Maria (Regulus regulus sanctaemariae)

Dissertação de Mestrado, Gestão e Conservação da Natureza, 11 de Junho de 2014, Universidade dos Açores.

Colloidal dipolar interactions in 2D smectic-C films

We use a two-dimensional (2D) elastic free energy to calculate the effective interaction between two circular disks immersed in smectic-C films. For strong homeotropic anchoring, the distortion of the director field caused by the disks generates topological defects that induce an effective interaction between the disks. We use finite elements, with adaptive meshing, to minimize the 2D elastic free energy. The method is shown to be accurate and efficient for inhomogeneities on the length scales set by the disks and the defects, that differ by up to 3 orders of magnitude. We compute the effective interaction between two disk-defect pairs in a simple (linear) configuration. For large disk separations, D, the elastic free energy scales as similar to D-2, confirming the dipolar character of the long-range effective interaction. For small D the energy exhibits a pronounced minimum. The lowest energy corresponds to a symmetrical configuration of the disk-defect pairs, with the inner defect at the mid-point between the disks. The disks are separated by a distance that, is twice the distance of the outer defect from the nearest disk. The latter is identical to the equilibrium distance of a defect nucleated by an isolated disk.

How patchy can one get and still condense? The role of dissimilar patches in the interactions of colloidal particles

We investigate the influence of strong directional, or bonding, interactions on the phase diagram of complex fluids, and in particular on the liquid-vapour critical point. To this end we revisit a simple model and theory for associating fluids which consist of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the interactions between each pair of spots have strengths [image omitted], [image omitted] and [image omitted]. The theory is applied over the whole range of bonding strengths and results are interpreted in terms of the equilibrium cluster structures of the coexisting phases. In systems where unlike sites do not interact (i.e. where [image omitted]), the critical point exists all the way to [image omitted]. By contrast, when [image omitted], there is no critical point below a certain finite value of [image omitted]. These somewhat surprising results are rationalised in terms of the different network structures of the two systems: two long AA chains are linked by one BB bond (X-junction) in the former case, and by one AB bond (Y-junction) in the latter. The vapour-liquid transition may then be viewed as the condensation of these junctions and we find that X-junctions condense for any attractive [image omitted] (i.e. for any fraction of BB bonds), whereas condensation of the Y-junctions requires that [image omitted] be above a finite threshold (i.e. there must be a finite fraction of AB bonds).

Criticality of colloids with distinct interaction patches: The limits of linear chains, hyperbranched polymers, and dimers

We use a simple model of associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the bonding interactions between each pair of spots have strengths epsilon(AA), epsilon(BB), and epsilon(AB). The theory is applied over the whole range of bonding strengths and the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains (epsilon(AA)not equal 0, epsilon(AB)=epsilon(BB)=0), hyperbranched polymers (epsilon(AB)not equal 0, epsilon(AA)=epsilon(BB)=0), and dimers (epsilon(BB)not equal 0, epsilon(AA)=epsilon(AB)=0). These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains (AA clusters connected by a few AB or BB bonds); of hyperbranched polymers (AB clusters connected by AA bonds); or of dimers (BB clusters connected by AA bonds). Interestingly, there is no critical point when epsilon(AA) vanishes despite the fact that AA bonds alone cannot drive condensation.

Copper and lead removal by peanut hulls: equilibrium and kinetic studies

This research work aims to study the use of peanut hulls, an agricultural and food industry waste, for copper and lead removal through equilibrium and kinetic parameters evaluation. Equilibrium batch studies were performed in a batch adsorber. The influence of initial pH was evaluated (3–5) and it was selected between 4.0 and 4.5. The maximum sorption capacities obtained for the Langmuir model were 0.21 ± 0.03 and 0.18 ± 0.02 mmol/g, respectively for copper and lead. In bi-component systems, competitive sorption of copper and lead was verified, the total amount adsorbed being around 0.21 mmol of metal per gram of material in both mono and bi-component systems. In the kinetic studies equilibrium was reached after 200 min contact time using a 400 rpm stirring rate, achieving 78% and 58% removal, in mono-component system, for copper and lead respectively. Their removal follows a pseudo-second-order kinetics. These studies show that most of the metals removal occurred in the first 20 min of contact, which shows a good uptake rate in all systems.

Exploração da Point Cloud Library aplicada à percepção em sistemas autónomos

A navegação e a interpretação do meio envolvente por veículos autónomos em ambientes não estruturados continua a ser um grande desafio na actualidade. Sebastian Thrun, descreve em [Thr02], que o problema do mapeamento em sistemas robóticos é o da aquisição de um modelo espacial do meio envolvente do robô. Neste contexto, a integração de sistemas sensoriais em plataformas robóticas, que permitam a construção de mapas do mundo que as rodeia é de extrema importância. A informação recolhida desses dados pode ser interpretada, tendo aplicabilidade em tarefas de localização, navegação e manipulação de objectos. Até à bem pouco tempo, a generalidade dos sistemas robóticos que realizavam tarefas de mapeamento ou Simultaneous Localization And Mapping (SLAM), utilizavam dispositivos do tipo laser rangefinders e câmaras stereo. Estes equipamentos, para além de serem dispendiosos, fornecem apenas informação bidimensional, recolhidas através de cortes transversais 2D, no caso dos rangefinders. O paradigma deste tipo de tecnologia mudou consideravelmente, com o lançamento no mercado de câmaras RGB-D, como a desenvolvida pela PrimeSense TM e o subsequente lançamento da Kinect, pela Microsoft R para a Xbox 360 no final de 2010. A qualidade do sensor de profundidade, dada a natureza de baixo custo e a sua capacidade de aquisição de dados em tempo real, é incontornável, fazendo com que o sensor se tornasse instantaneamente popular entre pesquisadores e entusiastas. Este avanço tecnológico deu origem a várias ferramentas de desenvolvimento e interacção humana com este tipo de sensor, como por exemplo a Point Cloud Library [RC11] (PCL). Esta ferramenta tem como objectivo fornecer suporte para todos os blocos de construção comuns que uma aplicação 3D necessita, dando especial ênfase ao processamento de nuvens de pontos de n dimensões adquiridas a partir de câmaras RGB-D, bem como scanners laser, câmaras Time-of-Flight ou câmaras stereo. Neste contexto, é realizada nesta dissertação, a avaliação e comparação de alguns dos módulos e métodos constituintes da biblioteca PCL, para a resolução de problemas inerentes à construção e interpretação de mapas, em ambientes indoor não estruturados, utilizando os dados provenientes da Kinect. A partir desta avaliação, é proposta uma arquitectura de sistema que sistematiza o registo de nuvens de pontos, correspondentes a vistas parciais do mundo, num modelo global consistente. Os resultados da avaliação realizada à biblioteca PCL atestam a sua viabilidade, para a resolução dos problemas propostos. Prova da sua viabilidade, são os resultados práticos obtidos, da implementação da arquitectura de sistema proposta, que apresenta resultados de desempenho interessantes, como também boas perspectivas de integração deste tipo de conceitos e tecnologia em plataformas robóticas desenvolvidas no âmbito de projectos do Laboratório de Sistemas Autónomos (LSA).

Stochastic short-term maintenance scheduling of GENCOs in an oligopolistic electricity market

In the proposed model, the independent system operator (ISO) provides the opportunity for maintenance outage rescheduling of generating units before each short-term (ST) time interval. Long-term (LT) scheduling for 1 or 2 years in advance is essential for the ISO and the generation companies (GENCOs) to decide their LT strategies; however, it is not possible to be exactly followed and requires slight adjustments. The Cournot-Nash equilibrium is used to characterize the decision-making procedure of an individual GENCO for ST intervals considering the effective coordination with LT plans. Random inputs, such as parameters of the demand function of loads, hourly demand during the following ST time interval and the expected generation pattern of the rivals, are included as scenarios in the stochastic mixed integer program defined to model the payoff-maximizing objective of a GENCO. Scenario reduction algorithms are used to deal with the computational burden. Two reliability test systems were chosen to illustrate the effectiveness of the proposed model for the ST decision-making process for future planned outages from the point of view of a GENCO.