Synchronization of physical oscillators

Tese de mestrado, Física (Física da Matéria Condensada e Nanomateriais) Universidade de Lisboa, Faculdade de Ciências, 2018The phenomenon of synchronization can be found in several biological and non-biological systems, such as, for example, in physical pendulum clocks, metronomes, pacemaker cells, firefly interaction and planet orbits. In this work we present a study concerning the synchronization of two coupled pendulum clocks. We use techniques of Dynamical Systems, in particular, when we study the Andronov model for an oscillator with impulses. We study the cases for a frequency relation of 1 : 1. We analyze the amplitude of the limit cycles of each oscillator and find an asymptotic stable fixed point for the velocity of an isolated clock. In a study of the phase, we construct the functions that map the phase difference between two coupled clocks and analyze its evolution, for a frequency relation of 1 : 1. We do the same study for a frequency relation of 2 : 1, which is a a study made by the first time in this work. We find one stable fixed point and one unstable fixed point, both for frequency relations of 1 : 1 and 2 : 1. We conclude that the system of coupled Andronov clocks tend to synchronize in phase opposition for the case 1 : 1 and in generalized phase opposition for the case 2 : 1. Also, we make a construction by phase approximation for the first order of the linear expansion, for frequency relations of N : 1. We then expand in second order the maps for a frequency relation of 1 : 1. With this approach, the results coincide with the more complicated technique of studying the original model, this technique is more suitable for numerical studies. Under the conditions of our problem, we conjecture that we have a master-slave relation for a frequency relation of N : 1, for N > 1, based on the observations of the maps of the phase difference and on the analysis of the linear expansions. We construct the regions of synchronization in the parameter space – the Arnold tongues – for two coupled Andronov clocks with frequency relations of 1 : 1, 2 : 1 and 3 : 1. We also analyze what effect does the friction have in these synchronization regions, which, in the synchronization of two Andronov clocks, is a new observation. Finally, we study the amplitude again, but now we do not assume the occurrence of phase locking. The orbits of the unperturbed system of coupled clocks can be described in the R2 surface of an invariant torus in phase space. We introduce the a Kolmogorov-Arnold-Moser like theory to verify that under a small limited perturbation to the system, the structure of the torus surface remains stable, which is, again, a new approach for the Andronov model

First-order periodic coupled systems with orderless lower and upper solutions

We present some existence and localization results for periodic solutions of first-order coupled nonlinear systems of two equations, without requiring periodicity for the nonlinearities. The arguments are based on Schauder's fixed point theorem together with not necessarily well-ordered upper and lower solutions. A real-case scenario shows the applicability of our results to some population dynamics models, describing the interaction between a criminal and a non-criminal population with a law enforcement component

Atividades investigativas: abordagem investigativa na aprendizagem da matemática

Este trabalho surge no âmbito do Mestrado no Ensino da Matemática no 3º Ciclo do Ensino Básico e Secundário, lecionado na Universidade da Madeira no ano letivo de 2011/2012 e tem como objetivo, estudar a prática das atividades investigativas em contexto de sala de aula e assim compreender de que forma estas contribuem para a aprendizagem da matemática. Uma vez que o ensino baseado na mecanização de conceitos pode inibir o desenvolvimento do pensamento dos alunos, como contribuir para uma atitude negativa em relação a esta disciplina, consideramos pertinente a realização deste estudo, onde as atividades de investigação constituem uma ferramenta matemática fundamental para a aquisição e desenvolvimento do espírito crítico, tão necessário na sociedade em que estão inseridos. Faremos em primeiro lugar, uma abordagem teórica, onde se identifica o conceito e os objetivos deste tipo de atividades, passando então para o estudo particular da aplicação destas atividades nas turmas lecionadas no referido ano letivo. Centramo-nos sobretudo no aluno, como agente ativo da sua própria aprendizagem e no professor, como um agente de inovação curricular, onde o seu trabalho se baseia numa abordagem metodológica inovadora do ensino-aprendizagem.Universidade da Madeir

Modelling forest fires using complex networks

Forest fires have been a major threat to the environment throughout history. In order to mitigate its consequences, we present, in a first of a series of works, a mathematical model with the purpose of predicting fire spreading in a given land portion divided into patches, considering the area and the rate of spread of each patch as inputs. The rate of spread can be estimated from previous knowledge on fuel availability, weather and terrain conditions. We compute the time duration of the spreading process in a land patch in order to construct and parametrize a landscape network, using cellular automata simulations. We use the multilayer network model to propose a network of networks at the landscape scale, where the nodes are the local patches, each with their own spreading dynamics. We compute some respective network measures and aim, in further work, for the establishment of a fire-break structure according to increasing accuracy simulation results.info:eu-repo/semantics/publishedVersio

A multi-scale network with percolation model to describe the spreading of forest fires

Forest fires have been a major threat to forest ecosystems and its biodiversity, as well as the environment in general, particularly in the Mediterranean regions. To mitigate fire spreading, this study aims at finding a fire-break solution for territories prone to fire occurrence. To the effect, here follows a model to map and predict phase transitions in fire regimes (spanning fires vs. penetrating fires) based on terrain morphology. The structure consists of a 2-scale network using site percolation and SIR epidemiology rules in a cellular automata to model local fire Dynamics. The target area for the application is the region of Serra de Ossa in Portugal, due to its wildfire incidence. The study considers the cases for a Moore neighbourhood of warm cells of radius 1 and 2 and also considers a heterogeneous terrain with 3 classes of vegetation. Phase transitions are found for different combinations of fire risk for each of these classes and use these values to parametrize the resulting landscape network.info:eu-repo/semantics/publishedVersio

CONCEÇÕES DE EDUCADORES DE INFÂNCIA E PROFESSORES DE 1. º CICLO DO ENSINO BÁSICO ACERCA DA EDUCAÇÃO AMBIENTALUm Estudo sobre a importância da Educação Ambiental

A Educação Ambiental assume um papel fundamental na sociedade e agrega variadíssimos temas que podem e devem ser abordados desde o jardim-de-infância. As vantagens a longo prazo para as crianças provenientes desta educação são diversas, tendo sido salientadas por Giordan e Souchon (1997) e Almeida (2006) no primeiro capítulo deste relatório. Destaca-se o papel que deverão ter os intervenientes neste processo de ensino - aprendizagem e a necessidade de educadores e professores reavaliarem o seu contributo para a formação ambiental dos seus alunos (Pelicioni, 2006), e para que as crianças, consideradas como “catalisadores ambientais” por Uzzel, et al., (1998), possam contribuir para essa mudança ambiental, não só através da sua atitude como também pela influência que exercem sobre as suas famílias. O propósito do presente trabalho foi realizar um estudo que tem como principal finalidade retratar as perspetivas de educadores de infância e professores de 1.º CEB em relação à Educação Ambiental, averiguar que fatores poderão influenciar a sua predisposição para esta temática, as dificuldades que sentem na sua prática e o tipo de estratégias e atividades que são implementadas pelos mesmos, com os principais objetivos de: 1) observar que importância dão os docentes à temática, 2) que vantagens os educadores e professores acham que poderão advir de uma abordagem precoce da mesma junto das crianças e, 3) de caracterizar as atividades realizadas e as dificuldades sentidas pelos pedagogos. Posto isto, criaram-se tabelas de contingência para verificar a influência na predisposição pessoal para o envolvimento em atividades relacionadas com a Educação Ambiental nos docentes: as suas formações académicas e as suas vivências pessoais (naturalidade e local de trabalho) como supôs Almeida (2006). O estudo envolveu 95 docentes (54 educadores e 41 professores). Os resultados obtidos, contrariamente ao esperado, remetem-nos para a inexistência de uma relação entre as variáveis em causa, na amostra estudada. Ou seja, neste caso, nem as vivências pessoais nem as formações académicas dos docentes são fatores que os fazem predispor no envolvimento de atividades relacionadas com a Educação Ambiental. Apesar destes fatores não serem determinantes na futura prática do investigador, foram sugeridos por Giordan e Souchon (1997) e Almeida (2006) portanto, decidiu-se aprofundar os mesmos. Contudo pairam dúvidas em relação a este assunto, o qual será debatido no terceiro capítulo deste relatórioEnvironmental Education assumes a fundamental role in society and it aggregates many topics that can and should be approached since kindergarden. The long term advantages of this education for the children are several referred by Giordan e Souchon, (1997) and Almeida (2006). Stand out the role that the participants in this learning process should have and the need for educators and teachers re-evaluate their contribution in their students environmental education (Pelicioni, 2006), and the important role of children, considered as “environmental catalysts” by Uzzel, et al., (1998), in the contribution to the environmental change, not only by their own attitudes but also by the influence they have on their families. The main purpose of this work was to realize a study that has as main objective, exploring what perspectives kindergarten teachers and primary school teachers have regarding Environmental Education, which factors may influence their predisposition to this theme, the difficulties felt in their practice and the type of strategies and activities that are implemented by them, having as main objectives: 1) the observation of the importance given by teachers to the subject, 2) the understanding of which advantages can come from an early approach to this education next to the children and, 3) the characterization of the activities they do and the difficulties they have when trying to implement this education. In this order of ideas, contingency tables were created in order to check the influence of the personal predisposition in the participation of activities related to Environmental Education by the teachers: their academic backgrounds and their personal experiences (birth place and workplace). The study involved 95 teachers (54 educators and 41 primary teachers). The results obtained, against what was expected, showed us a total absence of a relationship between the variables in question, at least in the studied sample. Which means that neither the personal experiences nor the teachers academic backgrounds were factors that made them predispose in the involvement of activities related to Environmental Education. Although these factors don’t be determinant in the future of the investigator, they were suggested by Giordan and Souchon (1997) and Almeida (2006) so, we decided to study this factors in details. But, some questions remain concerning this subject, which will be debated in the 3rd chapter of this report

Typicality assessment of onions (Allium cepa) from different geographical regions based on the volatile signature and chemometric tools

Onion (Allium cepa L.) is one of the main agricultural commodities produced and consumed around the world. In the present work, for the first time, the volatile signature of onions from different geographical regions of Madeira Island (Caniço, Santa Cruz, Ribeira Brava, and Porto Moniz) was tested with headspace solid-phase microextraction (HS-SPME/GC-qMS) and chemometric tools, showing that the volatile signature was affected by the geographical region of cultivation. Sulfur compounds, furanic compounds, and aldehydes are the most dominant chemical groups. Some of the identified volatile organic metabolites (VOMs) were detected only in onions cultivated in specific regions; 17 VOMs were only identified in onions cultivated at Caniço, eight in Porto Moniz, two in Santa Cruz, two in Ribeira Brava, while 12 VOMs are common to all samples from the four regions. Moreover, some VOMs belonging to sulfur compounds (dipropyl disulfide, 3-(acetylthio)-2-methylfuran), furanic compounds (dimethylmethoxyfuranone, ethyl furanone, acetyloxy-dimethylfuranone), and lactones (whiskey lactone isomer), could be applied as potential geographical markers of onions, providing a useful tool to authenticate onions by farming regions where the influence of latitude seems to be an important factor for yielding the chemical profile and may contribute to geographical protection of food and simultaneously benefiting both consumers and farmers.info:eu-repo/semantics/publishedVersio

Modelling Forest Fires Using Complex Networks

Forest fires have been a major threat to the environment throughout history. In order to mitigate its consequences, we present, in a first of a series of works, a mathematical model with the purpose of predicting fire spreading in a given land portion divided into patches, considering the area and the rate of spread of each patch as inputs. The rate of spread can be estimated from previous knowledge on fuel availability, weather and terrain conditions. We compute the time duration of the spreading process in a land patch in order to construct and parametrize a landscape network, using cellular automata simulations. We use the multilayer network model to propose a network of networks at the landscape scale, where the nodes are the local patches, each with their own spreading dynamics. We compute some respective network measures and aim, in further work, for the establishment of a fire-break structure according to increasing accuracy simulation results

Building an International One Health Strain Level Database to Characterise the Epidemiology of AMR Threats: ESBL—AmpC Producing E. coli as An Example—Challenges and Perspectives

(This article belongs to the Special Issue Epidemiology of ESBL-Producing Enterobacteriaceae)Antimicrobial resistance (AMR) is one of the top public health threats nowadays. Among the most important AMR pathogens, Escherichia coli resistant to extended spectrum cephalosporins (ESC-EC) is a perfect example of the One Health problem due to its global distribution in animal, human, and environmental sources and its resistant phenotype, derived from the carriage of plasmid-borne extended-spectrum and AmpC β-lactamases, which limits the choice of effective antimicrobial therapies. The epidemiology of ESC-EC infection is complex as a result of the multiple possible sources involved in its transmission, and its study would require databases ideally comprising information from animal (livestock, companion, wildlife), human, and environmental sources. Here, we present the steps taken to assemble a database with phenotypic and genetic information on 10,763 ESC-EC isolates retrieved from multiple sources provided by 13 partners located in eight European countries, in the frame of the DiSCoVeR Joint Research project funded by the One Health European Joint Programme (OH-EJP), along with its strengths and limitations. This database represents a first step to help in the assessment of different geographical and temporal trends and transmission dynamics in animals and humans. The work performed highlights aspects that should be considered in future international efforts, such as the one presented here.This research was funded by Promoting One Health in Europe through joint actions on foodborne zoonoses, antimicrobial resistance, and emerging microbiological hazards–One Health EJP, grant number 773830 (DiSCoVeR). Research at the German Federal Institute for Risk Assessment, Germany, was partially supported by the internal project BfR-BIOS-08-43-001. Research at the National Institute for Agrarian and Veterinary Research (INIAV) was partially supported by the project PTDC/CVT-CVT/28469/2017 financed by the “Fundação para a Ciência e Tecnologia” (FCT), Portugal. Research at the National Veterinary Research Institute (PIWet), Poland, was also partially supported by the Polish Ministry of Education and Science from the funds for science in the years 2018–2022 allocated for the implementation of a co-financed international project. The environmental isolates from Ireland were collected as part of the AREST project, which is jointly funded by the Environmental Protection Agency, under the EPA Research Programme 2014–2020, and the Health Service Executive (2017-HW-LS-1). The isolates collected from pig farms in Ireland were collected as part of a Walsh Scholarship project funded by Teagasc (ref 2018027). Research at the VISAVET Health Surveillance Centre (Spain) was partially supported by the project Antimicrobial resistance transmission dynamics in the human-animal interface: Shaping the risk posed by epidemic plasmids (PID2021-125136OB-I00, Ministerio de Ciencia, Innovación y Universidades, MICINN).info:eu-repo/semantics/publishedVersio