Desenvolvimento do clube de história da matemática: um diálogo das ciências humanas com a matemática

Este trabalho apresenta uma pesquisa sobre a utilização da História da Matemática no ensino básico do Colégio Militar do Rio de Janeiro CMRJ através de manifestações artísticas, fazendo uso, principalmente, do teatro,para que alunos percebam a matemática como uma ciência temporal, humana e sujeita a interferências políticas e sociais e, dessa forma, desenvolver a criticidade, aumentar a sensibilidade e o senso de solidariedade. A partir de um tema da história envolvendo fatos matemáticos os alunos pesquisam, escrevem uma peça teatral e encenam para um público formado por pessoas da comunidade escolar. Como a intenção é tornar essa prática efetiva, a pesquisa culmina na fundação do Clube de História da Matemática, espaço onde, espera-se, atividades recorrentes sejamdesenvolvidas, atraindo alunos afetos tanto às ciências humanas e sociais como às ciências exatas. Realiza-se um estudo de caso com observação participante, por ser o autor também professor do CMRJ. Este estudo busca referência teórica principalmente em autores relacionados à História da Matemática, Arte na Educação, gestão democrática, relações de poder e na legislação vigente. A pesquisa aponta a importância do trabalho com a história e com a arte e nos leva a concluir que, para formar cidadãos participativos e críticos, o primeiro passo é a sociedade tornar-se participativa e crítica, sendo a escola o principal locuspara tal formação.

Modelo de Ginzburg-Landau a partir da teoria de campos a temperatura finita

Neste trabalho, utilizamos o formalismo de teorias quânticas de campos a temperatura finita, tal como desenvolvidas por Matsubara, aplicado a uma hamiltoniana de N campos escalares com autointeração quártica a N grande. Obtém-se uma expressão, na primeira aproximação quântica, para o coeficiente do termo quadrático da hamiltoniana ("massa quadrada"), renormalizado, como função da temperatura. A partir dela, estudamos o processo de quebra espontânea de simetria. Por outro lado, a mesma hamiltoniana é conhecida como modelo de Ginzburg-Landau na literatura de matéria condensada, e que permite o estudo de transições de fase em materiais ferromagnéticos. A temperatura é introduzida através do termo quadrático na hamiltoniana, de forma linear: é proporcional à diferença entre a variável de temperatura e a temperatura crítica. Tal modelo, porém, possui validade apenas na regi~ao de temperaturas próximas à criticalidade. Como resultado de nossos cálculos na teoria de campos a temperatura finita, observamos que, numa faixa de valores em torno da temperatura crítica, a massa quadrática pode ser aproximada por uma relação linear em relação à variável de temperatura. Isso evidencia a compatibilidade da abordagem de Ginzburg-Landau, na vizinhança da criticalidade, com respeito ao formalismo de campos a temperatura finita. Discutimos também os efeitos causados pela presença de um potencial químico no sistema.

Condições de contorno tipo albedo para cálculos globais de reatores nucleares com o modelo de dois grupos de energia na formulação de transporte SN em geometria bidimensional cartesiana

Os eventos de fissão nuclear, resultados da interação dos nêutrons com os núcleos dos átomos do meio hospedeiro multiplicativo, não estão presentes em algumas regiões dos reatores nucleares, e.g., moderador, refletor, e meios estruturais. Nesses domínios espaciais não há geração de potência nuclear térmica e, além disso, comprometem a eficiência computacional dos cálculos globais de reatores nucleares. Propomos nesta tese uma estratégia visando a aumentar a eficiência computacional dessas simulações eliminando os cálculos numéricos explícitos no interior das regiões não-multiplicativas (baffle e refletor) em torno do núcleo ativo. Apresentamos algumas modelagens e discutimos a eficiência da aplicação dessas condições de contorno aproximadas tipo albedo para uma e duas regiões nãomultiplicativas, na formulação de ordenadas discretas (SN) para problemas de autovalor a dois grupos de energia em geometria bidimensional cartesiana. A denominação Albedo, palavra de origem latina para alvura, foi originalmente definida como a fração da luz incidente que é refletida difusamente por uma superfície. Esta denominação latina permaneceu como o termo científico usual em astronomia e, nesta tese, este conceito é estendido para reflexão de nêutrons. Estas condições de contorno tipo albedo SN não-convencional substituem aproximadamente as regiões de baffle e refletor no em torno do núcleo ativo do reator, desprezando os termos de fuga transversal no interior dessas regiões. Se o problema, em particular, não possui termos de fuga transversal, i.e., trata-se de um problema unidimensional, então as condições de contorno albedo, como propostas nesta tese, são exatas. Por eficiência computacional entende-se a análise da precisão dos resultados numéricos em comparação com o tempo de execução computacional de cada simulação de um dado problema-modelo. Resultados numéricos considerando dois problemas-modelo com de simetria são considerados para ilustrar esta análise de eficiência.

Estimativa de fontes externas uniformes de nêutrons em regiões combustíveis para uma distribuição prescrita de potência

Projetos de reatores nucleares foram classificados em quatro gerações (Gen) pelo Departamento de Energia dos Estados Unidos da América (DOE), quando o DOE introduziu o conceito de reatores de geração IV (Gen IV). Reatores Gen IV são um conjunto de projetos de reator nuclear, em sua maioria teóricos, atualmente sendo pesquisados. Entre os projetos Gen IV, incluem-se os projetos dos ADS (Accelerator Driven Systems), que são sistemas subcríticos estabilizados por fontes externas estacionárias de nêutrons. Estas fontes externas de nêutrons são normalmente geradas a partir da colisão de prótons com alta energia contra os núcleos de metais pesados presentes no núcleo do reator, fenômeno que é conhecido na literatura como spallation, e os prótons são acelerados num acelerador de partículas que é alimentado com parte da energia gerada pelo reator. A criticalidade de um sistema mantido por reações de fissão em cadeia depende do balanço entre a produção de nêutrons por fissão e a remoção por fuga pelos contornos e absorção de nêutrons. Um sistema está subcrítico quando a remoção por fuga e absorção ultrapassa a produção por fissão e, portanto, tende ao desligamento. Entretanto, qualquer sistema subcrítico pode ser estabilizado pela inclusão de fontes estacionárias de nêutrons em seu interior. O objetivo central deste trabalho é determinar as intensidades dessas fontes uniformes e isotrópicas de nêutrons, que se deve inserir em todas as regiões combustíveis do sistema, para que o mesmo estabilize-se gerando uma distribuição prescrita de potência elétrica. Diante do exposto, foi desenvolvido neste trabalho um aplicativo computacional em linguagem Java que estima as intensidades dessas fontes estacionárias de nêutrons, que devem ser inseridas em cada região combustível para que estabilizem o sistema subcrítico com uma dada distribuição de potência definida pelo usuário. Para atingir este objetivo, o modelo matemático adotado foi a equação unidimensional de transporte de nêutrons monoenergéticos na formulação de ordenadas discretas (SN) e o convencional método de malha fina diamond difference (DD) foi utilizado para resolver numericamente os problemas SN físicos e adjuntos. Resultados numéricos para dois problemas-modelos típicos são apresentados para ilustrar a acurácia e eficiência da metodologia proposta.

Safety implications of reactivity variations in fast thorium ADSRs

Nuclear power generation offers a reliable, low-impact and large-scale alternative to fossil fuels. However, concerns exist over the safety and sustainability of this method of power production, and it remains unpopular with some governments and pressure groups throughout the world. Fast thorium fuelled accelerator-driven sub-critical reactors (ADSRs) offer a possible route to providing further re-assurance regarding these concerns on account of their properties of enhanced safety through sub-critical operation combined with reduced actinide waste production from the thorium fuel source. The appropriate sub-critical margin at which these reactors should operate is the subject of continued debate. Commercial interests favour a small sub-critical margin in order to minimise the size of the accelerator needed for a given power output, whilst enhanced safety would be better satisfied through larger sub-critical margins to further minimise the possibility of a criticality excursion. Against this background, this paper examines some of the issues affecting reactor safety inherent within thorium fuel sources resulting from the essential Th90232→Th90233→Pa91233→U92233 breeding chain. Differences in the decay half-lives and fission and capture cross-sections of 233Pa and 233U can result in significant changes in the reactivity of the fuel following changes in the reactor power. Reactor operation is represented using a homogeneous lumped fast reactor model that can simulate the evolution of actinides and reactivity variations to first-order accuracy. The reactivity of the fuel is shown to increase significantly following a loss of power to the accelerator. Where the sub-critical operating margins are small this can result in a criticality excursion unless some form of additional intervention is made, for example through the insertion of control rods. © 2012 Elsevier Ltd. All rights reserved.

Top Management Involvement in New Product Development: A Review and Synthesis

Established literature on new product development (NPD) management recognizes top management involvement (TMI) as one of the most critical success factors. With increasing pressure to sustain competitive advantage and growth, NPD activities remain the focus of close interest from top management in many organizations. TMI in the NPD domain is receiving increasing academic attention. Despite its criticality, there is no systematic review of the existing literature to inform and stimulate researchers in the field for further investigation. This paper introduces the current state of literature on TMI in NPD, synthesizes important findings, and identifies the gaps and deficiencies in this research stream. The contents of the selected articles, which investigated TMI in NPD, are analyzed based on the type of the study, level of analysis, research methodology, operationalization of TMI, and main findings. Additionally, other studies, which did not directly investigate TMI and support in NPD, but were sufficiently related, are briefly summarized. As a result of this detailed literature review, it can be stated that both exploratory and relational studies provide rich evidence on the critical role of top management in NPD. However, the identified gaps and deficiencies in this research stream call for a better theoretical understanding and well-defined constructs of TMI in the NPD domain for different levels of analysis for future studies.

Numerical stability of the predictor-corrector method in Monte Carlo burnup calculations of critical reactors

Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the simplest methods, such as the beginning-of-step and middle-of-step constant flux approximations, are numerically unstable in fuel cycle calculations of critical reactors. Here we show that even the predictor-corrector methods that are implemented in established Monte Carlo burnup codes can be numerically unstable in cycle calculations of large systems. © 2013 Elsevier Ltd. All rights reserved.

Effect of95 241Am(n, γ) reaction branching ratio on fuel cycle and reactor design characteristics

The growing interest in innovative reactors and advanced fuel cycle designs requires more accurate prediction of various transuranic actinide concentrations during irradiation or following discharge because of their effect on reactivity or spent-fuel emissions, such as gamma and neutron activity and decay heat. In this respect, many of the important actinides originate from the 241Am(n,γ) reaction, which leads to either the ground or the metastable state of 242Am. The branching ratio for this reaction depends on the incident neutron energy and has very large uncertainty in the current evaluated nuclear data files. This study examines the effect of accounting for the energy dependence of the 241Am(n,γ) reaction branching ratio calculated from different evaluated data files for different reactor and fuel types on the reactivity and concentrations of some important actinides. The results of the study confirm that the uncertainty in knowing the 241Am(n,γ) reaction branching ratio has a negligible effect on the characteristics of conventional light water reactor fuel. However, in advanced reactors with large loadings of actinides in general, and 241Am in particular, the branching ratio data calculated from the different data files may lead to significant differences in the prediction of the fuel criticality and isotopic composition. Moreover, it was found that neutron energy spectrum weighting of the branching ratio in each analyzed case is particularly important and may result in up to a factor of 2 difference in the branching ratio value. Currently, most of the neutronic codes have a single branching ratio value in their data libraries, which is sometimes difficult or impossible to update in accordance with the neutron spectrum shape for the analyzed system.

Efficient generation of one-group cross sections for coupled Monte Carlo depletion calculations

Coupled Monte Carlo depletion systems provide a versatile and an accurate tool for analyzing advanced thermal and fast reactor designs for a variety of fuel compositions and geometries. The main drawback of Monte Carlo-based systems is a long calculation time imposing significant restrictions on the complexity and amount of design-oriented calculations. This paper presents an alternative approach to interfacing the Monte Carlo and depletion modules aimed at addressing this problem. The main idea is to calculate the one-group cross sections for all relevant isotopes required by the depletion module in a separate module external to Monte Carlo calculations. Thus, the Monte Carlo module will produce the criticality and neutron spectrum only, without tallying of the individual isotope reaction rates. The onegroup cross section for all isotopes will be generated in a separate module by collapsing a universal multigroup (MG) cross-section library using the Monte Carlo calculated flux. Here, the term "universal" means that a single MG cross-section set will be applicable for all reactor systems and is independent of reactor characteristics such as a neutron spectrum; fuel composition; and fuel cell, assembly, and core geometries. This approach was originally proposed by Haeck et al. and implemented in the ALEPH code. Implementation of the proposed approach to Monte Carlo burnup interfacing was carried out through the BGCORE system. One-group cross sections generated by the BGCORE system were compared with those tallied directly by the MCNP code. Analysis of this comparison was carried out and led to the conclusion that in order to achieve the accuracy required for a reliable core and fuel cycle analysis, accounting for the background cross section (σ0) in the unresolved resonance energy region is essential. An extension of the one-group cross-section generation model was implemented and tested by tabulating and interpolating by a simplified σ0 model. A significant improvement of the one-group cross-section accuracy was demonstrated.

Ultra-thin 242mAm fuel elements in nuclear reactors

There is a growing interest in using 242mAm as a nuclear fuel. The advantages of 242mAm as a nuclear fuel derive from the fact that 242mAm has the highest thermal fission cross section. The thermal capture cross section is relatively low and the number of neutrons per thermal fission is high. These nuclear properties make it possible to obtain nuclear criticality with ultra-thin fuel elements. The possibility of having ultra-thin fuel elements enables the use of these fission products directly, without the necessity of converting their energy to heat, as is done in conventional reactors. There are three options of using such highly energetic and highly ionized fission products. 1. Using the fission products themselves for ionic propulsion. 2. Using the fission products in an MHD generator, in order to obtain electricity directly. 3. Using the fission products to heat a gas up to a high temperature for propulsion purposes. In this work, we are not dealing with a specific reactor design, but only calculating the minimal fuel elements' thickness and the energy of the fission products emerging from these fuel elements. It was found that it is possible to design a nuclear reactor with a fuel element of less than 1 μm of 242mAm. In such a fuel element, 90% of the fission products' energy can escape.

Application of axial discontinuity factors for high conversion water reactors

The paper shows that generating cross sections using three-dimensional geometry and application of axial discontinuity factors are essential requirements for obtaining accurate prediction of criticality and zone average reaction rates in highly heterogeneous RBWR-type systems using computer codes based on diffusion theory approximation. The same methodology as presented here will be used to generate discontinuity factors for each axial interface between fuel assembly zones to ensure preservation of reaction rates in each zone and global multiplication factor. The use of discontinuity factors and three-dimensional cross sections may allow for a coarser energy group structure which is desirable to simplify and speed up transient calculations.

The stochastic implicit Euler method - A stable coupling scheme for Monte Carlo burnup calculations

Existing Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the coupling schemes of the existing Monte Carlo burnup codes can be numerically unstable. Here we develop the Stochastic Implicit Euler method - a stable and efficient new coupling scheme. The implicit solution is obtained by the stochastic approximation at each time step. Our test calculations demonstrate that the Stochastic Implicit Euler method can provide an accurate solution to problems where the methods in the existing Monte Carlo burnup codes fail. © 2013 Elsevier Ltd. All rights reserved.

Classical two-site fidelity and quantum phase transitions in the Ising model and the extended Hubbard model

In this Letter, the classical two-site-ground-state fidelity (CTGF) is exploited to identify quantum phase transitions (QPTs) for the transverse field Ising model (TFIM) and the one-dimensional extended Hubbard model (EHM). Our results show that the CTGF exhibits an abrupt change around the regions of criticality and can be used to identify QPTs in spin and fermionic systems. The method is especially convenient when it is connected with the density-matrix renormalization group (DMRG) algorithm. (C) 2008 Elsevier B.V. All rights reserved.

Density matrix Loschmidt echo and quantum phase transitions

We introduce the concept of the Loschmidt echo (LE) to the space of the reduced density matrix of spin and fermionic systems to study the density matrix LEs (DMLEs) of the one-dimensional extended Hubbard model and the transverse field Ising model. Our results show that the DMLEs are remarkably influenced by the criticality of the system, and the method is a convenient way to study quantum phase transitions.

Loschmidt echo and Berry phase of a quantum system coupled to an XY spin chain: Proximity to a quantum phase transition

We study the Loschmidt echo (LE) of a coupled system consisting of a central spin and its surrounding environment described by a general XY spin-chain model. The quantum dynamics of the LE is shown to be remarkably influenced by the quantum criticality of the spin chain. In particular, the decaying behavior of the LE is found to be controlled by the anisotropy parameter of the spin chain. Furthermore, we show that due to the coupling to the spin chain, the ground-state Berry phase for the central spin becomes nonanalytical and its derivative with respect to the magnetic parameter lambda in spin chain diverges along the critical line lambda=1, which suggests an alternative measurement of the quantum criticality of the spin chain.