The need and desire to create robust and accurate joining of materials has been one of up most importance throughout the course of history. Many forms have often been employed, but none exhibit the strength or durability as the weld. This study endeavors to explore some of the aspects of welding, more specifically relating to the Double Sided Arc Welding process and how best to model the dynamic non-linear response of such a system. Concepts of the Volterra series, NARMAX approximation and neural networks are explored. Fundamental methods of the neural network, including radial basis functions, and Back-propagation are investigated.

We study diffusion-reaction-advection models describing population dynamics of aquatic organisms subject to a constant drift, with reflecting upstream and outflow downstream boundary conditions. We consider three different models: single logistically growing species, two and three competing species. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady-state solutions. We analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. We also introduce a spatially implicit ODE (nonspatial approximation) model which captures the essential behavior of the original PDE model. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and analytical techniques, in both the spatial and nonspatial approximation settings, we describe the effect of advection on competitive outcomes. Finally, in the case of three species, we use the nonspatial approximation approach to analyze and classify the possible scenarios as we change the flow speed in the habitat.

This research presents a complete review of signal processing techniques used, today, in vibration based industrial condition monitoring and diagnostics. It also introduces two novel techniques to this field, namely: the Kolmogorov-Smirnov test and Volterra series, which have not yet been applied to vibration based condition monitoring. The first technique, the Kolmogorov-Smirnov test, relies on a statistical comparison of the cumulative probability distribution functions (CDF) from two time series. It must be emphasised that this is not a moment technique, and it uses the whole CDF, in the comparison process. The second tool suggested in this research is the Volterra series. This is a non-linear signal processing technique, which can be used to model a time series. The parameters of this model are used for condition monitoring applications. Finally, this work also presents a comprehensive comparative study between these new methods and the existing techniques. This study is based on results from numerical and experimental applications of each technique here discussed. The concluding remarks include suggestions on how the novel techniques proposed here can be improved.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2008. / Submitted by Jaqueline Oliveira (jaqueoliveiram@gmail.com) on 2008-12-15T15:59:27Z No. of bitstreams: 1 DISSERTACAO_2008_KelemGomesLourenco.pdf: 1422115 bytes, checksum: 20a32fbf536b3c9518ef0a8601e1d847 (MD5) / Approved for entry into archive by Georgia Fernandes(georgia@bce.unb.br) on 2009-02-18T17:36:21Z (GMT) No. of bitstreams: 1 DISSERTACAO_2008_KelemGomesLourenco.pdf: 1422115 bytes, checksum: 20a32fbf536b3c9518ef0a8601e1d847 (MD5) / Made available in DSpace on 2009-02-18T17:36:21Z (GMT). No. of bitstreams: 1 DISSERTACAO_2008_KelemGomesLourenco.pdf: 1422115 bytes, checksum: 20a32fbf536b3c9518ef0a8601e1d847 (MD5) / Neste trabalho analisamos o sistema de equações differenciais com duas presas e um predador do tipo Lotka-Volterra, com e sem colheita. Inicialmente estudamos a estabilidade local e global dos pontos de equilíbrio no primeiro modelo. Posteriormente, no segundo modelo, estudamos o coeficiente de estabilidade das órbitas periódicas, através da forma normal e estimativas numéricas. Através do recurso Maple 11, verificamos o comportamento das soluções e o surgimento das órbitas periódicas. ________________________________________________________________________________________ ABSTRACT / In this work we analyzed the Lotka-Volterra system of diferential equations with two preys and a predator, with and without harvesting. Initially we studied the local and global stability of the points of equilibrium in the first model. Later, in the second model, we studied the coefficient of stability of the periodic orbits, by using normal form and numerical estimatives. By using Maple 11, we verified the behavior of the solutions and the appearance of the periodic orbits.

Esta tese é composta por três ensaios. No primeiro, mostramos em nosso modelo básico que economias formadas exclusivamente por produtores e parasitas podem cair em armadilhas de pobreza, desde que ambos grupos se comportem de acordo com a dinâmica de Lotka-Volterra. Contudo, a introdução de um limite para o crescimento do produto e de expectativas por parte dos agentes exclui o resultado de armadilha em seus múltiplos equilíbrios. Nossa conclusão, entretanto, é similar para ambos modelos estudados: melhora na proteção aos direitos de propriedade por parte do Estado pode fazer com que a armadilha de pobreza seja superada, no modelo básico; e afetar a estabilidade dos equilíbrios, no modificado, fazendo com que resultados econômicos com maior produto tornem-se estáveis. No segundo ensaio, obtemos condições sob as quais a função perda do banco central é estritamente convexa em quatro estados distintos da economia: economia aquecida, em recessão, inação alta e produto alto. Encontramos, ainda, que quando in- ação e produto são funções lineares do instrumento de política monetária, a convexidade é garantida para qualquer um dos quatro estados citados. Ao estendermos nossa análise a vários instrumentos, encontramos que apenas linearidade já não é mais suficiente para a garantia do formato da função perda. Nossos resultados fornecem, ainda, condições sob as quais existirá dependência entre os instrumentos de política monetária. Por fim, o terceiro ensaio estuda regimes de metas de inação, nos quais agentes podem influenciar a política monetária através das expectativas de mercado reportadas ao banco central. Este, por sua vez, deve formular a política monetária considerando que tal influência pode ser usada em benefício dos próprios agentes. Modelamos essa relação estratégica como um jogo sequencial entre uma instituição financeira representativa e o banco central. Mostramos que quando a autoridade monetária escolhe apenas o nível da taxa de juros, existe um potencial viés inflacionário na economia. Esse viés é superado quando a oferta de moeda torna-se um segundo instrumento de política. Ainda mostramos que penalização de instituições más previsoras também pode ser um mecanismo eficiente de ancoragem de expectativas. / This thesis consists of three essays. In the first one, we show in our basic model that economies consisted exclusively by producers and parasites may fall into poverty traps, assuming that both groups behave according to the dynamics of Lotka-Volterra. However, the introduction of an upper bound on the output growth and expectations for the agents excludes the result of trap in its multiple equilibria. Our conclusion, nevertheless, is similiar for both studied models: improved protection of property rights by the state can mitigate the poverty trap possibility in the basic model, and affect the stability of equilibria in the modified one, making that economic outcomes with higher output become stable. In the second essay, we obtain conditions under which the central bank's loss function is strictly convex in four different states of the economy: booming economy, recession, high inflation and high output. Moreover, we found that when inaction and output are linear functions of monetary policy instruments, convexity is guaranteed for any of the four states mentioned. When we extend our analysis to the case of many instruments, we found that only linearity is not sufficient to guarantee the shape of loss function. Our results also provide conditions under which there exists dependence between instruments of monetary policy. Finally, the third essay studies the ination targeting regimes, in which agents can influence the monetary policy through market expectations reported to the central bank. Monetary authority, in its turn, should formulate the monetary policy considering that this influence may be used for the benefit of agents themselves. We model this strategic relationship as a sequential game between a representative financial institution and the central bank. We show that when the monetary authority chooses only the level of interest rates, there is a potential inflationary bias in the economy. This bias is solved when the money supply becomes a second instrument of policy. In addition, we show that to impose penalty on the worse predictor institutions may also be an efficient anchoring expectations mechanism.

Esta tese é composta por três ensaios. No primeiro, mostramos em nosso modelo básico que economias formadas exclusivamente por produtores e parasitas podem cair em armadilhas de pobreza, desde que ambos grupos se comportem de acordo com a dinâmica de Lotka-Volterra. Contudo, a introdução de um limite para o crescimento do produto e de expectativas por parte dos agentes exclui o resultado de armadilha em seus múltiplos equilíbrios. Nossa conclusão, entretanto, é similar para ambos modelos estudados: melhora na proteção aos direitos de propriedade por parte do Estado pode fazer com que a armadilha de pobreza seja superada, no modelo básico; e afetar a estabilidade dos equilíbrios, no modificado, fazendo com que resultados econômicos com maior produto tornem-se estáveis. No segundo ensaio, obtemos condições sob as quais a função perda do banco central é estritamente convexa em quatro estados distintos da economia: economia aquecida, em recessão, inação alta e produto alto. Encontramos, ainda, que quando in- ação e produto são funções lineares do instrumento de política monetária, a convexidade é garantida para qualquer um dos quatro estados citados. Ao estendermos nossa análise a vários instrumentos, encontramos que apenas linearidade já não é mais suficiente para a garantia do formato da função perda. Nossos resultados fornecem, ainda, condições sob as quais existirá dependência entre os instrumentos de política monetária. Por fim, o terceiro ensaio estuda regimes de metas de inação, nos quais agentes podem influenciar a política monetária através das expectativas de mercado reportadas ao banco central. Este, por sua vez, deve formular a política monetária considerando que tal influência pode ser usada em benefício dos próprios agentes. Modelamos essa relação estratégica como um jogo sequencial entre uma instituição financeira representativa e o banco central. Mostramos que quando a autoridade monetária escolhe apenas o nível da taxa de juros, existe um potencial viés inflacionário na economia. Esse viés é superado quando a oferta de moeda torna-se um segundo instrumento de política. Ainda mostramos que penalização de instituições más previsoras também pode ser um mecanismo eficiente de ancoragem de expectativas. / This thesis consists of three essays. In the first one, we show in our basic model that economies consisted exclusively by producers and parasites may fall into poverty traps, assuming that both groups behave according to the dynamics of Lotka-Volterra. However, the introduction of an upper bound on the output growth and expectations for the agents excludes the result of trap in its multiple equilibria. Our conclusion, nevertheless, is similiar for both studied models: improved protection of property rights by the state can mitigate the poverty trap possibility in the basic model, and affect the stability of equilibria in the modified one, making that economic outcomes with higher output become stable. In the second essay, we obtain conditions under which the central bank's loss function is strictly convex in four different states of the economy: booming economy, recession, high inflation and high output. Moreover, we found that when inaction and output are linear functions of monetary policy instruments, convexity is guaranteed for any of the four states mentioned. When we extend our analysis to the case of many instruments, we found that only linearity is not sufficient to guarantee the shape of loss function. Our results also provide conditions under which there exists dependence between instruments of monetary policy. Finally, the third essay studies the ination targeting regimes, in which agents can influence the monetary policy through market expectations reported to the central bank. Monetary authority, in its turn, should formulate the monetary policy considering that this influence may be used for the benefit of agents themselves. We model this strategic relationship as a sequential game between a representative financial institution and the central bank. We show that when the monetary authority chooses only the level of interest rates, there is a potential inflationary bias in the economy. This bias is solved when the money supply becomes a second instrument of policy. In addition, we show that to impose penalty on the worse predictor institutions may also be an efficient anchoring expectations mechanism.

abstract: There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels. / Dissertation/Thesis / Ph.D. Applied Mathematics 2014

Esta tese é composta por três ensaios. No primeiro, mostramos em nosso modelo básico que economias formadas exclusivamente por produtores e parasitas podem cair em armadilhas de pobreza, desde que ambos grupos se comportem de acordo com a dinâmica de Lotka-Volterra. Contudo, a introdução de um limite para o crescimento do produto e de expectativas por parte dos agentes exclui o resultado de armadilha em seus múltiplos equilíbrios. Nossa conclusão, entretanto, é similar para ambos modelos estudados: melhora na proteção aos direitos de propriedade por parte do Estado pode fazer com que a armadilha de pobreza seja superada, no modelo básico; e afetar a estabilidade dos equilíbrios, no modificado, fazendo com que resultados econômicos com maior produto tornem-se estáveis. No segundo ensaio, obtemos condições sob as quais a função perda do banco central é estritamente convexa em quatro estados distintos da economia: economia aquecida, em recessão, inação alta e produto alto. Encontramos, ainda, que quando in- ação e produto são funções lineares do instrumento de política monetária, a convexidade é garantida para qualquer um dos quatro estados citados. Ao estendermos nossa análise a vários instrumentos, encontramos que apenas linearidade já não é mais suficiente para a garantia do formato da função perda. Nossos resultados fornecem, ainda, condições sob as quais existirá dependência entre os instrumentos de política monetária. Por fim, o terceiro ensaio estuda regimes de metas de inação, nos quais agentes podem influenciar a política monetária através das expectativas de mercado reportadas ao banco central. Este, por sua vez, deve formular a política monetária considerando que tal influência pode ser usada em benefício dos próprios agentes. Modelamos essa relação estratégica como um jogo sequencial entre uma instituição financeira representativa e o banco central. Mostramos que quando a autoridade monetária escolhe apenas o nível da taxa de juros, existe um potencial viés inflacionário na economia. Esse viés é superado quando a oferta de moeda torna-se um segundo instrumento de política. Ainda mostramos que penalização de instituições más previsoras também pode ser um mecanismo eficiente de ancoragem de expectativas. / This thesis consists of three essays. In the first one, we show in our basic model that economies consisted exclusively by producers and parasites may fall into poverty traps, assuming that both groups behave according to the dynamics of Lotka-Volterra. However, the introduction of an upper bound on the output growth and expectations for the agents excludes the result of trap in its multiple equilibria. Our conclusion, nevertheless, is similiar for both studied models: improved protection of property rights by the state can mitigate the poverty trap possibility in the basic model, and affect the stability of equilibria in the modified one, making that economic outcomes with higher output become stable. In the second essay, we obtain conditions under which the central bank's loss function is strictly convex in four different states of the economy: booming economy, recession, high inflation and high output. Moreover, we found that when inaction and output are linear functions of monetary policy instruments, convexity is guaranteed for any of the four states mentioned. When we extend our analysis to the case of many instruments, we found that only linearity is not sufficient to guarantee the shape of loss function. Our results also provide conditions under which there exists dependence between instruments of monetary policy. Finally, the third essay studies the ination targeting regimes, in which agents can influence the monetary policy through market expectations reported to the central bank. Monetary authority, in its turn, should formulate the monetary policy considering that this influence may be used for the benefit of agents themselves. We model this strategic relationship as a sequential game between a representative financial institution and the central bank. We show that when the monetary authority chooses only the level of interest rates, there is a potential inflationary bias in the economy. This bias is solved when the money supply becomes a second instrument of policy. In addition, we show that to impose penalty on the worse predictor institutions may also be an efficient anchoring expectations mechanism.

Made available in DSpace on 2014-06-12T18:28:11Z (GMT). No. of bitstreams: 2 arquivo4027_1.pdf: 921557 bytes, checksum: b9e672cafb3172f4a3c1624ed82bd20f (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho estudamos uma teoria assintótica para um sistema homogêneo de equações em diferenças funcionais. O enfoque é na existência de soluções convergentes, comportamento assintótico e propriedades desta classe de soluções para perturbações não lineares do sistema homogêneo. O problema é abordado via teoria das dicotomias. Especi- ficamente estudamos o caso no qual a equação homogênea, possui um determinado tipo de dicotomia. Alguns dos resultados usados para demonstrar os teoremas de convergência são os teoremas de Krasnoselky e o critério de compacidade. Também analisaremos informações com respeito ao conjunto das soluções convergentes

Abstract The modern wireless communication techniques are aiming on increasing bandwidth and the number of carriers for higher data rate. This sets challenging linearity requirements for RF power amplifiers (PAs). Unfortunately, high linearity can only be obtained at the cost of efficiency. In order to improve the performance of the PA, in-depth understanding of nonlinear behaviour is mandatory. This calls for techniques that can give componentwise information of the causes of the distortion. The aim of this thesis is to develop a technique that can provide such information. This thesis proposes a detailed distortion analysis technique that is based on frequency domain fitting of polynomial models. Simulated large-signal spectra are used for fitting as these contain the necessary information about the large-signal bias point and amplitude range. Moreover, in the frequency domain the delays are easy to compensate, and detailed analysis to any fitted tone can be performed. The fitting procedure as such is simple but becomes difficult in multi-dimensional nonlinearities if the controlling voltages correlate strongly. In this thesis the solvability and reliability of the fitting procedure is increased by numerical operations, model-degree reduction and by using different excitations. A simplified Volterra method is used to calculate the distortion contributions by using the fitted model. The overall distortion is analysed by calculating the voltage response of the contributions of each nonlinearity to the terminal nodes of the device by the use of linear transfer functions of the circuit. The componentwise analysis is performed by phasor presentation enabling the cancelling mechanisms to be seen. The proposed technique is implemented on top of harmonic balance simulation in an APLAC circuit simulator in which extensive distortion simulations are performed. The technique relies on the existing device model and thus the fitted model can be only as accurate as the particular simulation model. However, two different RF PAs are analysed that show a good agreement between measurements and simulations. The proposed technique is verified with several test cases including amplitude dependent amplitude and phase distortion, intermodulation distortion sweet spots, bandwidth dependent memory effects and impedance optimization. The main finding of the detailed analysis is that the distortion is a result of several cancelling mechanisms. In general, cubic nonlinearity of transconductance is dominating the in-band distortion but is cancelled by the 2nd-degree nonlinearity that is mixed to the fundamental band from envelope and 2nd harmonic bands that is usually the main cause of memory effects.