Formulação teórica dos fundamentos da otimização global topográfica com análise de desempenho e aplicações à estabilidade de fases de misturas termodinâmicas

Métodos de otimização que utilizam condições de otimalidade de primeira e/ou segunda ordem são conhecidos por serem eficientes. Comumente, esses métodos iterativos são desenvolvidos e analisados à luz da análise matemática do espaço euclidiano n-dimensional, cuja natureza é de caráter local. Consequentemente, esses métodos levam a algoritmos iterativos que executam apenas as buscas locais. Assim, a aplicação de tais algoritmos para o cálculo de minimizadores globais de uma função não linear,especialmente não-convexas e multimodais, depende fortemente da localização dos pontos de partida. O método de Otimização Global Topográfico é um algoritmo de agrupamento, que utiliza uma abordagem baseada em conceitos elementares da teoria dos grafos, a fim de gerar bons pontos de partida para os métodos de busca local, a partir de pontos distribuídos de modo uniforme no interior da região viável. Este trabalho tem dois objetivos. O primeiro é realizar uma nova abordagem sobre método de Otimização Global Topográfica, onde, pela primeira vez, seus fundamentos são formalmente descritos e suas propriedades básicas são matematicamente comprovadas. Neste contexto, propõe-se uma fórmula semi-empírica para calcular o parâmetro chave deste algoritmo de agrupamento, e, usando um método robusto e eficiente de direções viáveis por pontos-interiores, estendemos o uso do método de Otimização Global Topográfica a problemas com restrições de desigualdade. O segundo objetivo é a aplicação deste método para a análise de estabilidade de fase em misturas termodinâmicas,o qual consiste em determinar se uma dada mistura se apresenta em uma ou mais fases. A solução deste problema de otimização global é necessária para o cálculo do equilíbrio de fases, que é um problema de grande importância em processos da engenharia, como, por exemplo, na separação por destilação, em processos de extração e simulação da recuperação terciária de petróleo, entre outros. Além disso, afim de ter uma avaliação inicial do potencial dessa técnica, primeiro vamos resolver 70 problemas testes, e então comparar o desempenho do método proposto aqui com o solver MIDACO, um poderoso software recentemente introduzido no campo da otimização global.

Determinação experimental e modelagem termodinâmica do equilíbrio de fases em sistemas com CO2, n-hexano, n-hexadecano e tetralina

A descoberta de petróleo na camada de Pré-Sal possibilita a geração de ganhos em relação à dependência energética do país, mas também grandes desafios econômicos e tecnológicos. Os custos de extração são maiores devido a vários fatores como a exigência de equipamentos de exploração que suportem elevadas pressões, altas temperaturas e grandes concentrações de gases ácidos, tais quais, dióxido de carbono (CO2) e sulfeto de hidrogênio (H2S). Uma das principais preocupações com o CO2 é evitar liberá-lo para a atmosfera durante a produção. Com a modelagem termodinâmica de dados de equilíbrio de sistemas envolvendo CO2 supercrítico e hidrocarbonetos é possível projetar equipamentos utilizados em processos de separação. A principal motivação do trabalho é o levantamento de dados de equilíbrio de fases de sistemas compostos de CO2 e hidrocarbonetos, possibilitando assim prever o comportamento dessas misturas. Os objetivos específicos são a avaliação do procedimento experimental, a estimação e predição dos parâmetros de interação binários para assim prever o comportamento de fases dos sistemas ternários envolvendo CO2 e hidrocarbonetos. Duas metodologias foram utilizadas para obtenção dos dados de equilíbrio: método estático sintético (visual) e método dinâmico analítico (recirculação das fases). Os sistemas avaliados foram: CO2 + n-hexano, CO2 + tetralina, CO2 + n-hexadecano, CO2 + n-hexano + tetralina e CO2 + tetralina + n-hexadecano à alta pressão; tetralina + n-hexadecano à baixa pressão. Para o tratamento dos dados foi utilizada equação de estado cúbica de Peng-Robinson e a regra de mistura clássica

Motor coordination: when two have to act as one.

Trying to pass someone walking toward you in a narrow corridor is a familiar example of a two-person motor game that requires coordination. In this study, we investigate coordination in sensorimotor tasks that correspond to classic coordination games with multiple Nash equilibria, such as "choosing sides," "stag hunt," "chicken," and "battle of sexes". In these tasks, subjects made reaching movements reflecting their continuously evolving "decisions" while they received a continuous payoff in the form of a resistive force counteracting their movements. Successful coordination required two subjects to "choose" the same Nash equilibrium in this force-payoff landscape within a single reach. We found that on the majority of trials coordination was achieved. Compared to the proportion of trials in which miscoordination occurred, successful coordination was characterized by several distinct features: an increased mutual information between the players' movement endpoints, an increased joint entropy during the movements, and by differences in the timing of the players' responses. Moreover, we found that the probability of successful coordination depends on the players' initial distance from the Nash equilibria. Our results suggest that two-person coordination arises naturally in motor interactions and is facilitated by favorable initial positions, stereotypical motor pattern, and differences in response times.

Nonsmooth geometry and collapse of flexible structures under smooth loads

While static equilibria of flexible strings subject to various load types (gravity, hydrostatic pressure, Newtonian wind) is well understood textbook material, the combinations of the very same loads can give rise to complex spatial behaviour at the core of which is the unilateral material constraint prohibiting compressive loads. While the effects of such constraints have been explored in optimisation problems involving straight cables, the geometric complexity of physical configurations has not yet been addressed. Here we show that flexible strings subject to combined smooth loads may not have smooth solutions in certain ranges of the load ratios. This non-smooth phenomenon is closely related to the collapse geometry of inflated tents. After proving the nonexistence of smooth solutions for a broad family of loadings we identify two alternative, critical geometries immediately preceding the collapse. We verify these analytical results by dynamical simulation of flexible chains as well as with simple table-top experiments with an inflated membrane.

Lyapunov-like conditions for the existence of zeno behavior in hybrid and lagrangian hybrid systems

Lyapunov-like conditions that utilize generalizations of energy and barrier functions certifying Zeno behavior near Zeno equilibria are presented. To better illustrate these conditions, we will study them in the context of Lagrangian hybrid systems. Through the observation that Lagrangian hybrid systems with isolated Zeno equilibria must have a onedimensional configuration space, we utilize our Lyapunov-like conditions to obtain easily verifiable necessary and sufficient conditions for the existence of Zeno behavior in systems of this form. © 2007 IEEE.

Delayed decision-making in bistable models

Switching between two modes of operation is a common property of biological systems. In continuous-time differential equation models, this is often realised by bistability, i.e. the existence of two asymptotically stable steadystates. Several biological models are shown to exhibit delayed switching, with a pronounced transient phase, in particular for near-threshold perturbations. This study shows that this delay in switching from one mode to the other in response to a transient input is reflected in local properties of an unstable saddle point, which has a one dimensional unstable manifold with a significantly slower eigenvalue than the stable ones. Thus, the trajectories first approximatively converge to the saddle point, then linger along the saddle's unstable manifold before quickly approaching one of the stable equilibria. ©2010 IEEE.

Consensus on homogeneous manifolds

The present paper considers distributed consensus algorithms for agents evolving on a connected compact homogeneous (CCH) manifold. The agents track no external reference and communicate their relative state according to an interconnection graph. The paper first formalizes the consensus problem for synchronization (i.e. maximizing the consensus) and balancing (i.e. minimizing the consensus); it thereby introduces the induced arithmetic mean, an easily computable mean position on CCH manifolds. Then it proposes and analyzes various consensus algorithms on manifolds: natural gradient algorithms which reach local consensus equilibria; an adaptation using auxiliary variables for almost-global synchronization or balancing; and a stochastic gossip setting for global synchronization. It closes by investigating the dependence of synchronization properties on the attraction function between interacting agents on the circle. The theory is also illustrated on SO(n) and on the Grassmann manifolds. ©2009 IEEE.

Stabilization of planar collective motion with limited communication

This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and time-invariant or time-varying. The emphasis of this paper is to show how previous results assuming all-to-all communication can be extended to a general communication framework. © 2008 IEEE.

Stabilization of collective motion in three dimensions: A consensus approach

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the stabilization problem is reduced to a consensus problem. We first derive the stabilizing control laws in the presence of all-to-all communication. Providing each agent with a consensus estimator, we then extend the results to a general setting that allows for unidirectional and time-varying communication topologies. © 2007 IEEE.

Stabilization of planar collective motion: All-to-all communication

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level. © 2007 IEEE.

Group coordination and cooperative control of steered particles in the plane

The paper overviews recent and ongoing efforts by the authors to develop a design methodology to stabilize isolated relative equilibria in a kinematic model of identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles about the same center with fixed relative headings. © Springer-Verlag Berlin Heidelberg 2006.

Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria

This paper presents some new criteria for uniform and nonuniform asymptotic stability of equilibria for time-variant differential equations and this within a Lyapunov approach. The stability criteria are formulated in terms of certain observability conditions with the output derived from the Lyapunov function. For some classes of systems, this system theoretic interpretation proves to be fruitful since - after establishing the invariance of observability under output injection - this enables us to check the stability criteria on a simpler system. This procedure is illustrated for some classical examples.

Delayed-decision making in noisy bistable switches

Bistable switches are frequently encountered in biological systems. Typically, a bistable switch models a binary decision where each decision corresponds to one of the two stable equilibria. Recently, we showed that the global decision-making process in bistable switches strongly depends on a particular equilibrium point of these systems, their saddle point. In particular, we showed that a saddle point with a time-scale separation between its attractive and repulsive directions can delay the decision-making process. In this paper, we study the effects of white Gaussian noise on this mechanism of delayed decision-making induced by the saddle point. Results show that the mean decision-time strongly depends on the balance between the initial distance to the separatrix and the noise strength. © IFAC.

Effect of growth conditions on the GaN thin film by sputtering deposition

The phase transition between thermodynamically stable hexagonal wurtzite (h-WZ) gallium nitride (GaN) and metastable cubic zinc-blende (c-ZB) GaN during growth by radio-frequency planar magnetron sputtering is studied. GaN films grown on substrates with lower mismatches tend to have a h-WZ structure, but when grown on substrates with higher mismatches, a c-ZB structure is preferred. GaN films grown under high nitrogen pressure also tend to have a h-WZ structure, whereas a c-ZB structure is preferred when grown under low nitrogen pressure. In addition, low target-power growth not only helps to improve hexagonal GaN (h-GaN) crystalline quality at high nitrogen pressure on low-mismatch substrates, but also enhances cubic GaN (c-GaN) quality at low nitrogen pressure on high-mismatch substrates. (c) 2007 Elsevier B.V. All rights reserved.

Investigation of Interfacial Tensions for Carbon Dioxide Aqueous Solutions by Perturbed-Chain Statistical Associating Fluid Theory Combined with Density-Gradient Theory

The perturbed-chain statistical associating fluid theory and density-gradient theory are used to construct an equation of state (EOS) applicable for the phase behaviors of carbon dioxide aqueous solutions. With the molecular parameters and influence parameters respectively regressed from bulk properties and surface tensions of pure fluids as input, both the bulk and interfacial properties of carbon dioxide aqueous solutions are satisfactorily correlated by adjusting the binary interaction parameter (k(ij)). Our results show that the constructed EOS is able to describe the interfacial properties of carbon dioxide aqueous solutions in a wide temperature range, and illustrate the influences of temperature, pressure, and densities in each phase on the interfacial properties.