Range of validity of weakly non-linear theory in Rayleigh-Bénard convection

In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

Reversibility Iteration Method to Understand Reaction Networks and to Solve Micro-Kinetics in Heterogeneous Catalysis

Solving microkinetics of catalytic systems, which bridges microscopic processes and macroscopic reaction rates, is currently vital for understanding catalysis in silico. However, traditional microkinetic solvers possess several drawbacks that make the process slow and unreliable for complicated catalytic systems. In this paper, a new approach, the so-called reversibility iteration method (RIM), is developed to solve microkinetics for catalytic systems. Using the chemical potential notation we previously proposed to simplify the kinetic framework, the catalytic systems can be analytically illustrated to be logically equivalent to the electric circuit, and the reaction rate and coverage can be calculated by updating the values of reversibilities. Compared to the traditional modified Newton iteration method (NIM), our method is not sensitive to the initial guess of the solution and typically requires fewer iteration steps. Moreover, the method does not require arbitrary-precision arithmetic and has a higher probability of successfully solving the system. These features make it ∼1000 times faster than the modified Newton iteration method for the systems we tested. Moreover, the derived concept and the mathematical framework presented in this work may provide new insight into catalytic reaction networks.

Application of meta-analytical probabilistic approach for reliability benefits reflective optimal transmission costing – the case of India

In the deregulated Power markets it is necessary to have a appropriate Transmission Pricing methodology that also takes into account “Congestion and Reliability”, in order to ensure an economically viable, equitable, and congestion free power transfer capability, with high reliability and security. This thesis presents results of research conducted on the development of a Decision Making Framework (DMF) of concepts and data analytic and modelling methods for the Reliability benefits Reflective Optimal “cost evaluation for the calculation of Transmission Cost” for composite power systems, using probabilistic methods. The methodology within the DMF devised and reported in this thesis, utilises a full AC Newton-Raphson load flow and a Monte-Carlo approach to determine, Reliability Indices which are then used for the proposed Meta-Analytical Probabilistic Approach (MAPA) for the evaluation and calculation of the Reliability benefit Reflective Optimal Transmission Cost (ROTC), of a transmission system. This DMF includes methods for transmission line embedded cost allocation among transmission transactions, accounting for line capacity-use as well as congestion costing that can be used for pricing using application of Power Transfer Distribution Factor (PTDF) as well as Bialek’s method to determine a methodology which consists of a series of methods and procedures as explained in detail in the thesis for the proposed MAPA for ROTC. The MAPA utilises the Bus Data, Generator Data, Line Data, Reliability Data and Customer Damage Function (CDF) Data for the evaluation of Congestion, Transmission and Reliability costing studies using proposed application of PTDF and other established/proven methods which are then compared, analysed and selected according to the area/state requirements and then integrated to develop ROTC. Case studies involving standard 7-Bus, IEEE 30-Bus and 146-Bus Indian utility test systems are conducted and reported throughout in the relevant sections of the dissertation. There are close correlation between results obtained through proposed application of PTDF method with the Bialek’s and different MW-Mile methods. The novel contributions of this research work are: firstly the application of PTDF method developed for determination of Transmission and Congestion costing, which are further compared with other proved methods. The viability of developed method is explained in the methodology, discussion and conclusion chapters. Secondly the development of comprehensive DMF which helps the decision makers to analyse and decide the selection of a costing approaches according to their requirements. As in the DMF all the costing approaches have been integrated to achieve ROTC. Thirdly the composite methodology for calculating ROTC has been formed into suits of algorithms and MATLAB programs for each part of the DMF, which are further described in the methodology section. Finally the dissertation concludes with suggestions for Future work.

Algoritmo paralelo para determinação de autovalores de matrizes hermitianas

Dissertação (mestrado)–Universidade de Brasília, Universidade UnB de Planaltina, Programa de Pós-Graduação em Ciência de Materiais, 2015.

Studies of cases in power systems by Sensitivity Analysis oriented by OPF

This paper presents studies of cases in power systems by Sensitivity Analysis (SA) oriented by Optimal Power Flow (OPF) problems in different operation scenarios. The studies of cases start from a known optimal solution obtained by OPF. This optimal solution is called base case, and from this solution new operation points may be evaluated by SA when perturbations occur in the system. The SA is based on Fiacco`s Theorem and has the advantage of not be an iterative process. In order to show the good performance of the proposed technique tests were carried out on the IEEE 14, 118 and 300 buses systems. (C) 2010 Elsevier Ltd. All rights reserved.

Loss minimization by the predictor-corrector modified barrier approach

This paper presents a new approach, predictor-corrector modified barrier approach (PCMBA), to minimize the active losses in power system planning studies. In the PCMBA, the inequality constraints are transformed into equalities by introducing positive auxiliary variables. which are perturbed by the barrier parameter, and treated by the modified barrier method. The first-order necessary conditions of the Lagrangian function are solved by predictor-corrector Newton`s method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, reaching the limits of the inequality constraints. The feasibility of the proposed approach is demonstrated using various IEEE test systems and a realistic power system of 2256-bus corresponding to the Brazilian South-Southeastern interconnected system. The results show that the utilization of the predictor-corrector method with the pure modified barrier approach accelerates the convergence of the problem in terms of the number of iterations and computational time. (C) 2008 Elsevier B.V. All rights reserved.

Distributed Estimation Over an Adaptive Incremental Network Based on the Affine Projection Algorithm

We study the problem of distributed estimation based on the affine projection algorithm (APA), which is developed from Newton`s method for minimizing a cost function. The proposed solution is formulated to ameliorate the limited convergence properties of least-mean-square (LMS) type distributed adaptive filters with colored inputs. The analysis of transient and steady-state performances at each individual node within the network is developed by using a weighted spatial-temporal energy conservation relation and confirmed by computer simulations. The simulation results also verify that the proposed algorithm provides not only a faster convergence rate but also an improved steady-state performance as compared to an LMS-based scheme. In addition, the new approach attains an acceptable misadjustment performance with lower computational and memory cost, provided the number of regressor vectors and filter length parameters are appropriately chosen, as compared to a distributed recursive-least-squares (RLS) based method.

Sobre o procedimento de Zippin para estimar populações de animais

O procedimento de Zippin é uma das técnicas mais precisas para estimar populações de animais, além de fornecer estimativas do erro padrão. Entretanto, a solução das equações de máxima verossimilhança não é algebricamente explícita. Sugere-se um procedimento iterativo utilizando a técnica de Newton Raphson para encontrar as soluções desejadas. Comparações com o procedimento clássico mostram sensíveis diferenças nas estimativas do erro padrão e diferenças menores nos demais parâmetros.

Formulação corrotacional para análise de vigas com elementos finitos

Dissertação apresentada na faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Mecânica

Modelagem numérica para o processo da evaporação da água do solo

Foram realizados vários ensaios laboratoriais para avaliar o desempenho de um modelo numérico em simular o processo unidimensional da evaporação da água do solo. Este modelo foi desenvolvido a partir da linearização da equação de Richards no espaço e do uso da técnica iterativa de Newton-Raphson, para resolver essa equação não-linear no tempo, e leva em conta o fluxo de vapor dentro do perfil de solo e a taxa de evaporação na sua superfície. Os resultados mostraram que o modelo foi capaz de simular satisfatoriamente o processo, tanto em meios porosos homogêneos quanto estratificados

Programa de ajuste multiparamétrico de curvas de titulação potenciométricas de ácidos húmicos

Tendo em vista a dificuldade de determinação dos pontos de inflexão na curva de titulação potenciométrica de ácidos húmicos, por metodologias tradicionais, foi desenvolvido foi desenvolvido um programa na linguagem Delphi para ajuste multiparamétrico de dados de titulação potenciométrica. Para isso um processo iterativo para estimar as raízes de um polinômio, com base no método de Newton-Raphson, foi utilizado. Os dados das titulações potenciométricas de ácidos húmicos usados nas regressões foram obtidos em um sistema automatizado de titulação potenciométrica. O programa desenvolvido na linguagem Delphi permite maior versatilidade e facilidade de operação, com uma interação mais amigável com o usuário. As curvas de titulação potenciométricas ajustadas sobrepuseram-se quase que totalmente às curvas experimentais. Os valores de pKa e as percentagens de grupos tituláveis dos ácidos húmicos, parâmetros ajustáveis na regressão multiparamétrica, apresentaram valores comparáveis com dados da literatura.

On the Connectivity of the Julia sets of meromorphic functions

We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.

Aplicação de métodos numéricos para estimativa de variáveis psicrométricas

O ar atmosférico é formado por uma composição de ar seco e vapor d'água, cujos valores da quantidade de vapor, em termos quantitativos, são variáveis em função dos elementos climáticos, tais como: temperatura e pressão. Portanto, para estimar os valores de umidade relativa do ar, são necessárias informações completas de séries de dados de temperatura do ar (Tar), pressão atual de vapor (e a) e temperatura de bulbo úmido (Tu). O trabalho apresenta como objetivo a elaboração de rotina computacional para encontrar valores da temperatura do termômetro de bulbo úmido (Tu) em função de outras variáveis, para uma série de dados obtidos, mediante a aplicação de métodos numéricos (Método de Newton-Raphson e Método da Secante), para fins de complementação de uma série de dados diários para Piracicaba - SP. Verificou-se que os métodos numéricos de Newton-Raphson e da Secante apresentaram bom desempenho na simulação dos resultados, porém o método da Secante apresentou-se como o melhor para encontrar os valores de Tu, mediante a resolução numérica da equação psicrométrica.

Étude numérique des origines hémodynamiques des oscillations dans des réseaux de capillaires

En simulant l’écoulement du sang dans un réseau de capillaires (en l’absence de contrôle biologique), il est possible d’observer la présence d’oscillations de certains paramètres comme le débit volumique, la pression et l’hématocrite (volume des globules rouges par rapport au volume du sang total). Ce comportement semble être en concordance avec certaines expériences in vivo. Malgré cet accord, il faut se demander si les fluctuations observées lors des simulations de l’écoulement sont physiques, numériques ou un artefact de modèles irréalistes puisqu’il existe toujours des différences entre des modélisations et des expériences in vivo. Pour répondre à cette question de façon satisfaisante, nous étudierons et analyserons l’écoulement du sang ainsi que la nature des oscillations observées dans quelques réseaux de capillaires utilisant un modèle convectif et un modèle moyenné pour décrire les équations de conservation de masse des globules rouges. Ces modèles tiennent compte de deux effets rhéologiques importants : l’effet Fåhraeus-Lindqvist décrivant la viscosité apparente dans un vaisseau et l’effet de séparation de phase schématisant la distribution des globules rouges aux points de bifurcation. Pour décrire ce dernier effet, deux lois de séparation de phase (les lois de Pries et al. et de Fenton et al.) seront étudiées et comparées. Dans ce mémoire, nous présenterons une description du problème physiologique (rhéologie du sang). Nous montrerons les modèles mathématiques employés (moyenné et convectif) ainsi que les lois de séparation de phase (Pries et al. et Fenton et al.) accompagnés d’une analyse des schémas numériques implémentés. Pour le modèle moyenné, nous employons le schéma numérique explicite traditionnel d’Euler ainsi qu’un nouveau schéma implicite qui permet de résoudre ce problème d’une manière efficace. Ceci est fait en utilisant une méthode de Newton- Krylov avec gradient conjugué préconditionné et la méthode de GMRES pour les itérations intérieures ainsi qu’une méthode quasi-Newton (la méthode de Broyden). Cette méthode inclura le schéma implicite d’Euler et la méthode des trapèzes. Pour le schéma convectif, la méthode explicite de Kiani et al. sera implémentée ainsi qu’une nouvelle approche implicite. La stabilité des deux modèles sera également explorée. À l’aide de trois différentes topologies, nous comparerons les résultats de ces deux modèles mathématiques ainsi que les lois de séparation de phase afin de déterminer dans quelle mesure les oscillations observées peuvent être attribuables au choix des modèles mathématiques ou au choix des méthodes numériques.

Nichtüberlappende Gebietszerlegungsmethoden für lineare und quasilineare (monotone und nichtmonotone) Probleme

In dieser Arbeit werden nichtüberlappende Gebietszerlegungsmethoden einerseits hinsichtlich der zu lösenden Problemklassen verallgemeinert und andererseits in bisher nicht untersuchten Kontexten betrachtet. Dabei stehen funktionalanalytische Untersuchungen zur Wohldefiniertheit, eindeutigen Lösbarkeit und Konvergenz im Vordergrund. Im ersten Teil werden lineare elliptische Dirichlet-Randwertprobleme behandelt, wobei neben Problemen mit dominantem Hauptteil auch solche mit singulärer Störung desselben, wie konvektions- oder reaktionsdominante Probleme zugelassen sind. Der zweite Teil befasst sich mit (gleichmäßig) monotonen koerziven quasilinearen elliptischen Dirichlet-Randwertproblemen. In beiden Fällen wird das Lipschitz-Gebiet in endlich viele Lipschitz-Teilgebiete zerlegt, wobei insbesondere Kreuzungspunkte und Teilgebiete ohne Außenrand zugelassen sind. Anschließend werden Transmissionsprobleme mit frei wählbaren $L^{\infty}$-Parameterfunktionen hergeleitet, wobei die Konormalenableitungen als Funktionale auf geeigneten Funktionenräumen über den Teilrändern ($H_{00}^{1/2}(\Gamma)$) interpretiert werden. Die iterative Lösung dieser Transmissionsprobleme mit einem Ansatz von Deng führt auf eine Substrukturierungsmethode mit Robin-artigen Transmissionsbedingungen, bei der eine Auswertung der Konormalenableitungen aufgrund einer geschickten Aufdatierung der Robin-Daten nicht notwendig ist (insbesondere ist die bekannte Robin-Robin-Methode von Lions als Spezialfall enthalten). Die Konvergenz bezüglich einer partitionierten $H^1$-Norm wird für beide Problemklassen gezeigt. Dabei werden keine über $H^1$ hinausgehende Regularitätsforderungen an die Lösungen gestellt und die Gebiete müssen keine zusätzlichen Glattheitsvoraussetzungen erfüllen. Im letzten Kapitel werden nichtmonotone koerzive quasilineare Probleme untersucht, wobei das Zugrunde liegende Gebiet nur in zwei Lipschitz-Teilgebiete zerlegt sein soll. Das zugehörige nichtlineare Transmissionsproblem wird durch Kirchhoff-Transformation in lineare Teilprobleme mit nichtlinearen Kopplungsbedingungen überführt. Ein optimierungsbasierter Lösungsansatz, welcher einen geeigneten Abstand der rücktransformierten Dirichlet-Daten der linearen Teilprobleme auf den Teilrändern minimiert, führt auf ein optimales Kontrollproblem. Die dabei entstehenden regularisierten freien Minimierungsprobleme werden mit Hilfe eines Gradientenverfahrens unter minimalen Glattheitsforderungen an die Nichtlinearitäten gelöst. Unter zusätzlichen Glattheitsvoraussetzungen an die Nichtlinearitäten und weiteren technischen Voraussetzungen an die Lösung des quasilinearen Ausgangsproblems, kann zudem die quadratische Konvergenz des Newton-Verfahrens gesichert werden.