On chaos, transient chaos and ghosts in single populations models with allee effects

Density-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

A expressão dramática no desenvolvimento da formação pessoal e social da criança em idade pré-escolar

Relatório da Prática Profissional Supervisionada Mestrado em Educação Pré-Escolar

(E)xperimental study of the porosity and microstructure of self-compacting concrete (SCC) with binary and ternary mixes of fly ash and limestone filler

Self-compacting concrete (SCC) can soon be expected to replace conventional concrete due to its many advantages. Its main characteristics in the fresh state are achieved essentially by a higher volume of mortar (more ultrafine material) and a decrease of the coarse-aggregates. The use of over-large volumes of additions such as fly ash (FA) and/or limestone filler (LF) can substantially affect the concrete's pore structure and consequently its durability. In this context, an experimental programme was conducted to evaluate the effect on the concrete's porosity and microstructure of incorporating FA and LF in binary and ternary mixes of SCC. For this, a total of 11 SIX mixes were produced; 1 with cement only (C); 3 with C + FA in 30%, 60% and 70% substitution (fad); 3 with C + LF in 30%, 60% and 70% fad; 4 with C + FA + LF in combinations of 10-20%, 20-10%, 20-40% and 40-20% f(ad), respectively. The results enabled conclusions to be established regarding the SCC's durability, based on its permeability and the microstructure of its pore structure. The properties studied are strongly affected by the type and quantity of additions. The use of ternary mixes also proves to be extremely favourable, confirming the beneficial effect of the synergy between these additions. (C) 2015 Elsevier Ltd. All rights reserved.

Experimental study of the porosity and microstructure of self-compacting concrete (SCC) with binary and ternary mixes of fly ash and limestone filler

Abstract Self-compacting concrete (SCC) can soon be expected to replace conventional concrete due to its many advantages. Its main characteristics in the fresh state are achieved essentially by a higher volume of mortar (more ultrafine material) and a decrease of the coarse-aggregates. The use of over-large volumes of additions such as fly ash (FA) and/or limestone filler (LF) can substantially affect the concrete's pore structure and consequently its durability. In this context, an experimental programme was conducted to evaluate the effect on the concrete's porosity and microstructure of incorporating FA and LF in binary and ternary mixes of SCC. For this, a total of 11 SCC mixes were produced: 1 with cement only (C); 3 with C + FA in 30%, 60% and 70% substitution (fad); 3 with C + LF in 30%, 60% and 70% fad; 4 with C + FA + LF in combinations of 10-20%, 20-10%, 20-40% and 40-20% fad, respectively. The results enabled conclusions to be established regarding the SCC's durability, based on its permeability and the microstructure of its pore structure. The properties studied are strongly affected by the type and quantity of additions. The use of ternary mixes also proves to be extremely favourable, confirming the beneficial effect of the synergy between these additions. © 2015 Elsevier Ltd. All rights reserved.

Fresh-state properties of self-compacting mortar and concrete with combined use of limestone filler and fly ash

This paper presents the results of a study on the behaviour of self-compacting concrete (SCC) in the fresh and hardened states, produced with binary and ternary mixes of fly ash (FA) and limestone filler (LF), using the method proposed by Nepomuceno. His method determines the SCC composition parameters in the mortar phase (self-compacting mortar - SCM) easily and efficiently, whilst guaranteeing the SCC properties in both the fresh and hardened states. For this, 11 SCMs were studied: one with cement (C) only; three with FA at 30%, 60% and 70% C substitution; three with LF at 30%, 60% and 70% C substitution; four with FA + LF in combinations of 10-20%, 20-10%, 20-40% and 40-20% C substitution. Once the composition of these mortars was defined, 18 SCC mixes were produced: 14 binary SCC mixes were produced with the seven binary mortar mixes, and four ternary SCC mixes were produced with the four ternary mortar mixes. In addition to the methodology proposed by Nepomuceno, the combined use of FA and LF in ternary mixtures was tested. The results confirmed that the method could yield SCC with adequate properties in both the fresh and hardened states. It was also possible to determine the SCC composition parameters in the mortar phase (self-compacting mortar - SCM) that will guarantee the SCC properties in both the fresh and hardened states, as confirmed through the optimized behaviour of the SCC in the fresh state and the promising results in the hardened state (compressive strength). The potential demonstrated by the joint use of LF and FA through the synergetic interaction of both additions is emphasized.

Tudo no lugar certo: trabalho de projecto

Trabalho de Projecto submetido à Escola Superior de Teatro e Cinema para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Teatro - especialização em Teatro e Comunidade.

Relatório do trabalho de projecto Éter

Trabalho de Projecto submetido à Escola Superior de Teatro e Cinema para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Teatro - especialização em Artes Performativas/ Escritas de Cena.

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Partial classification of Lorenz knots: Syllable permutations of torus knots words

We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.

Nonautonomous Graphs and Topological Entropy of Nonautonomous Lorenz Systems

In this work, we associate a p-periodic nonautonomous graph to each p-periodic nonautonomous Lorenz system with finite critical orbits. We develop Perron-Frobenius theory for nonautonomous graphs and use it to calculate their entropy. Finally, we prove that the topological entropy of a p-periodic nonautonomous Lorenz system is equal to the entropy of its associated nonautonomous graph.