Analysis and selection of the simulation environment

This document provides the initial report of the Simulation work package (Work Package 4,WP4) of the CATNETS project. It contains an analisys of the requirements for a simulation tool to be used in CATNETS and an evaluation of a number of grid and general purpose simulators with respect to the selected requirements. A reasoned choice of a suitable simulator is performed based on the evaluation conducted. -- Diese Arbeit analysiert die Anforderungen an eine Simulationsumgebung für die Analyse der Katallaxie. Anhand von Kennzahlen wird die Auswahl der Simulationsumgebung bestimmt.Grid Computing

Competencia matemática plantear y resolver problemas: el caso de la mediana como medida de tendencia central

La siguiente comunicación presenta un avance de investigación, en el cual se pretende caracterizar los niveles de la competencia matemática plantear y resolver problemas que se caracterizan en los desempeños de los estudiantes de 9° grado de la Institución Educativa Jorge Eliécer Gaitán, a partir de actividades con secuencias didácticas que involucren el objeto matemático la mediana. El trabajo hace parte del proyecto de investigación “Formación y desarrollo de competencias matemáticas en estudiantes de educación básica y media del Departamento del Caquetá, del grupo de investigación Desarrollo Institucional Integrado, de la Universidad de la Amazonia (Florencia-Caquetá), en la línea Didáctica de la Matemática

Phase Equilibria of Lattice Polymers from Histogram Reweighting Monte Carlo Simulations

Histogram-reweighting Monte Carlo simulations were used to obtain polymer / solvent phase diagrams for lattice homopolymers of chain lengths up to r=1000 monomers. The simulation technique was based on performing a series of grand canonical Monte Carlo calculations for a small number of state points and combining the results to obtain the phase behavior of a system over a range of temperatures and densities. Critical parameters were determined from mixed-field finite-size scaling concepts by matching the order parameter distribution near the critical point to the distribution for the three-dimensional Ising universality class. Calculations for the simple cubic lattice (coordination number z=6) and for a high coordination number version of the same lattice (z=26) were performed for chain lengths significantly longer than in previous simulation studies. The critical temperature was found to scale with chain length following the Flory-Huggins functional form. For the z=6 lattice, the extrapolated infinite chain length critical temperature is 3.70+-0.01, in excellent agreement with previous calculations of the temperature at which the osmotic second virial coefficient is zero and the mean end-to-end distance proportional to the number of bonds. This confirms that the three alternative definitions of the Theta-temperature are equivalent in the limit of long chains. The critical volume fraction scales with chain length with an exponent equal to 0.38+-0.01, in agreement with experimental data but in disagreement with polymer solution theories. The width of the coexistence curve prefactor was tentatively found to scale with chain length with an exponent of 0.20+-0.03 for z = 6 and 0.22+-0.03 for z = 26. These values are near the lower range of values obtained from experimental data.Comment: 23 pages, including 7 figure

Representations in the learning of the derivative of a function by secondary school students

Este estudo tem como objetivo averiguar o contributo das representações na aprendizagem da derivada de uma função de alunos do 11.º ano. Adotando uma abordagem qualitativa e interpretativa, recolheram-se os dados através das resoluções de tarefas realizadas pelos alunos. Os resultados apontam que, apesar da tendência para a representação algébrica, as representações numérica, tabelar e gráfica também foram usadas. A representação numérica e a algébrica foram usadas essencialmente para determinar a imagem de um dado objeto, em particular, no caso de extremos relativos. A representação gráfica foi utilizada no estudo comparativo da função com a sua função derivada ou sempre que os alunos pretendiam uma imagem global do comportamento da função. A representação tabelar foi usada essencialmente para estudar a monotonia e os extremos relativos de uma função, e, em alguns casos, na conversão entre a representação algébrica e gráfica.The main goal of this study is to verify the contribution that representations give to the learning of the derivate of a function by 11th grade students. Adopting a qualitative and interpretative approach, the data was collected through the students’ resolution of tasks. The results indicate that, in spite generalized use of the algebraic representation, the numerical, the tabular, and the graphic representations were also used. The numerical and algebraic representations were used essentially to determine the image of a given object, in particular, in the case of relative extremes. The graphic representation was used to compare a function with its derivate function or whenever the students wanted a global image of the function behaviour. The tabular representation was used essentially to study the monotony and the relative extremes of a function and, in some cases, in the conversion between the algebraic and the graphic representation.info:eu-repo/semantics/publishedVersio

The activity of 9th grade students with modeling tasks in the study of functions

A natureza das tarefas determina a dinâmica das atividades da sala de aula. Entre a tipologia de tarefas, as características das de modelação proporcionam aos alunos a oportunidade de se envolverem na construção do conhecimento matemático. Partindo deste pressuposto, pretende-se caracterizar a atividade que os alunos do 9.º ano de escolaridade realizam com tarefas de modelação, com recurso à calculadora gráfica e a sensores, no estudo de funções e as dificuldades que revelam nessas atividades. Trata-se de um estudo qualitativo de natureza interpretativa que recolheu a informação através da gravação de aulas, da análise de produções dos alunos e de um questionário. Os resultados mostram que os alunos realizam uma diversidade de atividades com tarefas de modelação, tais como interpretação das situações dadas, recolha de dados e sua organização em tabelas, tradução da informação desses dados através de gráficos e de expressões analíticas. Nestas atividades emerge algumas dificuldades, tais como distinguir a variável dependente da independente, utilizar escalas na subdivisão dos eixos cartesianos, restringir o domínio que contextualiza as situações dadas, encontrar o melhor modelo que se ajuste à situação dada e em distinguir os conceitos de proporcionalidade direta e inversa.The nature of tasks constrains the dynamic of the activities in the class. Among the typology of tasks, those of modelling, by their characteristics, give students the opportunity to engage in the construction of mathematical knowledge. Based on this assumption, we aim to characterize the activities that 9th grade students perform with modelling tasks in the study of functions, using the graphic calculator and sensors. We also aim to identify students’ difficulties in these activities. In this study, of qualitative and interpretative nature, data were collected by recording the classes, by analysing students’ productions, and by a questionnaire. Results show that students perform a diversity of activities with modelling tasks, such as interpretation of the situations provided, data collection and its organization in tables, and translation of those data into graphics and analytical expressions. In these activities, students reveal some difficulties, such as to differentiate dependent from independent variable, to use of scales in the subdivision of cartesians axes, to restrict the domain to one that contextualize the situations given, to find the better model that adjusts to the situation provided, and to differentiate the concepts of direct and inverse proportionality.info:eu-repo/semantics/publishedVersio

Direct calculation of parton distribution functions (PDFs) on the lattice

In dieser Arbeit befassen wir uns mit einer Reihe von entscheidenden Schritten, um die unpolarisierten Helizitäts- und Trasversitäts-Parton-Verteilungsfunktionen der Nukleonen im Rahmen der Gitter-QCD zu bewerten. Diskretisierungsartefakte werden unter Verwendung eines N_f=2+1+1 Eichensembles von Fermionen mit verdrillter Wilson-Masse untersucht, die bei einer Pionenmasse von ungefähr M=37 MeV simuliert werden. Die unpolarisierten und Helizitäts Partonverteilungsfunktionen weisen eine nicht vernachlässigbare Abhängigkeit vom Gitterabstand auf, und die Kontinuumsextrapolation ergibt eine bessere Übereinstimmung mit Phänomenologie. Die direkte Berechnung der Fourier-Transformation mit diskreten Gitterdaten kann Artefakte verursachen. Daher arbeiten wir mit einer neuen datengesteuerten Methode, die auf Gauß-Prozess-Regression basiert, die sogenannte Bayes-Gauß-Fourier-Transformation, um die Einschränkungen der diskreten Fourier-Transformation zu überwinden. Wir sind der Meinung, dass dieser datengesteuerte Ansatz die durch die Diskretisierung der Fourier-Transformation eingeführten Artefakte drastisch reduzieren kann, jedoch ist der endgültige Effekt auf die Lichtkegel-PDFs gering. Darüber hinaus präsentieren wir die Ergebnisse der ersten ab initio Berechnung der individuellen up, down und strange unpolarisierten, Helizitäts- und Transversitäts-Partonverteilungsfunktionen für das Proton. Die Analyse wird an einem durch N_f=2+1+1 verdrillten Kleeblatt-verbesserten Fermionen-Ensemble durchgeführt, das bei einer Pionenmasse von 260 MeV simuliert wird. Wir verwenden den hierarchischen Sondierungsalgorithmus, um die unzusammenhängenden Quarkschleifen auszuwerten. Dadurch erhalten wir Ergebnisse ungleich Null für den unbegundenen isoskalaren Beitrag und die strange Quark-Matrixelemente.In this work, we address a number of crucial steps in order to evaluate the nucleon unpolarized helicity and trasversity parton distribution functions within the framework of lattice QCD. Discretization artifacts are investigated using an N_f=2+1+1 gauge ensemble of Wilson twisted mass fermions simulated at a pion mass of approximately M=370 MeV. The unpolarized and helicity parton distribution functions show a non-negligible dependence on the lattice spacing, with the continuum extrapolation producing a better agreement with phenomenology. The direct computation of the Fourier transform using discrete lattice data may introduce artifacts and we, therefore, use a new data-driven method based on Gaussian process regression, the so-called Bayes-Gauss Fourier transform to overcome the limitations of the discrete Fourier transform. We find that this data-driven approach can drastically reduce the artifacts introduced by the discretization of the Fourier transform, however, the final effect on the light-cone PDFs is small. Furthermore, we present results of the first ab initio calculation of the individual up, down, and strange unpolarized, helicity, and transversity parton distribution functions for the proton. The analysis is performed on an N_f=2+1+1 twisted mass clover-improved fermion ensemble simulated at a pion mass of 260 MeV. We employ the hierarchical probing algorithm to evaluate the disconnected quark loops, allowing us to obtain non-zero results for the disconnected isoscalar contribution and the strange quark matrix elements

Book reviews

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