Alda Carvalho

Assessing the influence of material and geometrical uncertainty on the mechanical behavior of functionally graded material plates

ABSTRACT Composite materials possessing a functional gradient are becoming strong candidates to enhance the performance of structures when severe operating conditions are a reality. These types of conditions may, for example, range from situations where a high thermal gradient is present to others where it is imperative to minimize abrupt stresses transitions between material interfaces. The manufacturing achievement of the gradients determined for a specific application may in practice face some limitations, which can be due, among other factors, to technological process constraints, eventual operating condition deterioration of production stages, or to nonconforming raw materials. Regardless of the origin of such limitations, the reality is that the uncertainty is always present to some extent; this is clearly reflected in the scattering of material and geometrical properties of these composites. The understanding that deterministic analyses are not enough to provide a complete prediction of the composite structures u2009behavior emphasizes the crucial need to identify the effects that the variability in material and geometrical parameters will produce in the structural response. With the present work, one intends to study the influence of this variability in the static and free vibrations behavior of functionally graded plates. It is also an objective of this study to use regression models to predict these responses and to characterize the contribution of each model parameter to the explanation of the response variability. To this purpose, a set of numerical results is presented and discussed.

A generative power-law search tree model

It is now a well-established fact that search algorithms can exhibit heavy-tailed behavior. However, the reasons behind this fact are not well understood. We provide a generative search tree model whose distribution of the number of nodes visited during search is formally heavy-tailed. Our model allows us to generate search trees with any degree of heavy-tailedness. We also show how the different regimes observed for the runtime distributions of backtrack search methods across different constrainedness regions of random CSP models can be captured by a mixture of the so-called stable distributions.

Comparing wind generation profiles: A circular data approach

The importance of wind power energy for energy and environmental policies has been growing in past recent years. However, because of its random nature over time, the wind generation cannot be reliable dispatched and perfectly forecasted, becoming a challenge when integrating this production in power systems. In addition the wind energy has to cope with the diversity of production resulting from alternative wind power profiles located in different regions. In 2012, Portugal presented a cumulative installed capacity distributed over 223 wind farms [1]. In this work the circular data statistical methods are used to analyze and compare alternative spatial wind generation profiles. Variables indicating extreme situations are analyzed. The hour(s) of the day where the farm production attains its maximum daily production is considered. This variable was converted into circular variable, and the use of circular statistics enables to identify the daily hour distribution for different wind production profiles. This methodology was applied to a real case, considering data from the Portuguese power system regarding the year 2012 with a 15-minutes interval. Six geographical locations were considered, representing different wind generation profiles in the Portuguese system.In this work the circular data statistical methods are used to analyze and compare alternative spatial wind generation profiles. Variables indicating extreme situations are analyzed. The hour(s) of the day where the farm production attains its maximum daily production is considered. This variable was converted into circular variable, and the use of circular statistics enables to identify the daily hour distribution for different wind production profiles. This methodology was applied to a real case, considering data from the Portuguese power system regarding the year 2012 with a 15-minutes interval. Six geographical locations were considered, representing different wind generation profiles in the Portuguese system.

Ordinal sums of impartial games

Abstract In an ordinal sum of two combinatorial games G and H , denoted by G : H , a player may move in either G (base) or H (subordinate), with the additional constraint that any move on G completely annihilates the component H . It is well-known that the ordinal sum does not depend on the form of its subordinate, but depends on the form of its base. In this work, we analyze G ( G : H ) where G and H are impartial forms, observing that the G -values are related to the concept of minimum excluded value of order k . As a case study, we introduce the ruleset oak , a generalization of green hackenbush . By defining the operation gin sum, it is possible to determine the literal forms of the bases in polynomial time.

Adaptive empirical distributions in the framework of inverse problems

ABSTRACT This article presents an innovative framework regarding an inverse problem. One presents the extension of a global optimization algorithm to estimate not only an optimal set of modeling parameters, but also their optimal distributions. Regarding its characteristics, differential evolution algorithm is used to demonstrate this extension, although other population-based algorithms may be considered. The adaptive empirical distributions algorithm is here introduced for the same purpose. Both schemes rely on the minimization of the dissimilarity between the empirical cumulative distribution functions of two data sets, using a goodness-of-fit test to evaluate their resemblance.

The Geometer Dog Who Did Not Know Calculus

Summary We present a purely geometric solution for Elvis’s path problem. The geometric approach brings, for a constructible ratio of speeds, an easy compass-and-straightedge construction that visually explains some extreme cases. There is also a possible biological interpretation.

Allégorie de la Géométrie. A Mathematical Interpretation

Abstract In this work, we present a mathematical interpretation for the masterpiece Allégorie de la Géométrie (1649), painted by the French baroque artist Laurent de La Hyre (1606-1656)

On lattices from combinatorial game theory modularity and a representation theorem: Finite case

We show that a self-generated set of combinatorial games, S, may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question Is there a set which will give a non-distributive but modular lattice? appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented.

A Generator of Heavy-Tailed Search Trees

In theoretical computational statistics, the detection of heavy tails in computing costs of some random search algorithms generated an increased interest in the modeling of this heavy-tailed behavior. We propose a general model for these algorithms that reproduces this characteristic. The model represents the search for a solution as the descent of a search tree with regular branching factors and equiprobable nodes. In this work, we present a way to generate heavy-tailed search trees using very simple rules, and we show how a particular case relates to the famous Wallis product.

A recursive process related to a partisan variation of Wythoff

Abstract. Wythoff Queens is a classical combinatorial game related to very interesting mathematical results. An amazing one is the fact that the -positions are given by and where . In this paper, we analyze a different version where one player (Left) plays with a chess bishop and the other (Right) plays with a chess knight. The new game (call it Chessfights) lacks a Beatty sequence structure in the -positions as in Wythoff Queens. However, it is possible to formulate and prove some general results of a general recursive law which is a particular case of a Partizan Subtraction game.