Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Canine population dynamics: the potential effect of sterilization campaigns

Objective. To analyze, through mathematical modeling, the potential ability of sterilization campaigns to reduce the population density of pet dogs. Methods. Mathematical models were constructed to simulate the canine population dynamics and project the results of control strategies based on several sterilization rates. Results. Even at high sterilization rates (for example, 0.80 year(-1)), it would take approximately 5 years to reduce density by 20%. Even so, other sources of population growth, such as the importing of dogs from other geographic areas, could outweigh the effects of a sterilization program. Conclusions. A program`s effectiveness is contingent upon not only on the sterilization rate, but also the rate of population growth. Sterilization campaigns may potentially reduce population density, but this reduction may not be immediately evident.

Estimation of R(0) from the initial phase of an outbreak of a vector-borne infection

The magnitude of the basic reproduction ratio R(0) of an epidemic can be estimated in several ways, namely, from the final size of the epidemic, from the average age at first infection, or from the initial growth phase of the outbreak. In this paper, we discuss this last method for estimating R(0) for vector-borne infections. Implicit in these models is the assumption that there is an exponential phase of the outbreaks, which implies that in all cases R(0) > 1. We demonstrate that an outbreak is possible, even in cases where R(0) is less than one, provided that the vector-to-human component of R(0) is greater than one and that a certain number of infected vectors are introduced into the affected population. This theory is applied to two real epidemiological dengue situations in the southeastern part of Brazil, one where R(0) is less than one, and other one where R(0) is greater than one. In both cases, the model mirrors the real situations with reasonable accuracy.

The Galilean turn in population ecology

The standard mathematical models in population ecology assume that a population's growth rate is a function of its environment. In this paper we investigate an alternative proposal according to which the rate of change of the growth rate is a function of the environment and of environmental change. We focus on the philosophical issues involved in such a fundamental shift in theoretical assumptions, as well as on the explanations the two theories offer for some of the key data such as cyclic populations. We also discuss the relationship between this move in population ecology and a similar move from first-order to second-order differential equations championed by Galileo and Newton in celestial mechanics.

Estudo do processo de secagem em leito de espuma de cenoura, tomate, beterraba e morango

Em geral, produtos agrícolas são produzidos em larga escala e essa produtividade cresce proporcionalmente ao seu consumo. Entretanto, outro fator também cresce de forma proporcional, as perdas pós-colheita, o que sugere a utilização de tecnologias para aumentar a utilização desses produtos mitigando o desperdício e aumentando sua a vida de prateleira. Além disso, oferecer o produto durante o período de entressafra. No presente trabalho, foi utilizado à tecnologia de secagem em leito de espuma aplicada a cenoura, beterraba, tomate e morango, produtos amplamente produzidos e consumidos no Brasil. Neste trabalho, os quatros produtos foram submetidos à secagem em leito de espuma em secador com ar circulado em temperaturas controladas de 40, 50, 60, 70 e 80 °C. A descrição da cinética de secagem foi realizada pelo ajuste de modelos matemáticos para cada temperatura do ar de secagem. Além disso, foi proposto um modelo matemático generalizado ajustado por regressão não linear. O modelo de Page obteve o melhor ajuste sobre os dados de secagem em todos os produtos testados, com um coeficiente de determinação (R²) superior a 98% em todas as temperaturas avaliadas. Além disso, foi possível modelar a influência da temperatura do ar sobre o parâmetro k do modelo de Page através da utilização de um modelo exponencial. O coeficiente de difusão efetiva aumentou com a elevação da temperatura, apresentando valores entre 10-8e 10-7 m².s-¹ para as temperaturas de processo. A relação entre o coeficiente de difusão efetiva e a temperatura de secagem pôde ser descrita pela equação de Arrhenius.

Mathematical modelling of supercritical CO2 extraction of volatile oils from aromatic plants

The modelling of the experimental data of the extraction of the volatile oil from six aromatic plants (coriander, fennel, savoury, winter savoury, cotton lavender and thyme) was performed using five mathematical models, based on differential mass balances. In all cases the extraction was internal diffusion controlled and the internal mass transfer coefficienty (k(s)) have been found to change with pressure, temperature and particle size. For fennel, savoury and cotton lavender, the external mass transfer and the equilibrium phase also influenced the second extraction period, since k(s) changed with the tested flow rates. In general, the axial dispersion coefficient could be neglected for the conditions studied, since Peclet numbers were high. On the other hand, the solute-matrix interaction had to be considered in order to ensure a satisfactory description of the experimental data.

A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

Efeito do sombreamento nos painéis fotovoltaicos

Trabalho Final para obtenção do grau Mestre em Engenharia Electrotécnica

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

Aplicação de um modelo de programação linear inteira mista (PLIM) na expansão da rede de distribuição de energia elétrica em Angola

Em Angola, apenas cerca de 30% da população tem acesso à energia elétrica, nível que decresce para valores inferiores a 10% em zonas rurais mais remotas. Este problema é agravado pelo facto de, na maioria dos casos, as infraestruturas existentes se encontrarem danificadas ou não acompanharem o desenvolvimento da região. Em particular na capital angolana, Luanda que, sendo a menor província de Angola, é a que regista atualmente a maior densidade populacional. Com uma população de cerca de 5 milhões de habitantes, não só há frequentemente problemas relacionados com a falha do fornecimento de energia elétrica como há ainda uma percentagem considerável de municípios onde a rede elétrica ainda nem sequer chegou. O governo de Angola, no seu esforço de crescimento e aproveitamento das suas enormes potencialidades, definiu o setor energético como um dos fatores críticos para o desenvolvimento sustentável do país, tendo assumido que este é um dos eixos prioritários até 2016. Existem objetivos claros quanto à reabilitação e expansão das infraestruturas do setor elétrico, aumentando a capacidade instalada do país e criando uma rede nacional adequada, com o intuito não só de melhorar a qualidade e fiabilidade da rede já existente como de a aumentar. Este trabalho de dissertação consistiu no levantamento de dados reais relativamente à rede de distribuição de energia elétrica de Luanda, na análise e planeamento do que é mais premente fazer relativamente à sua expansão, na escolha dos locais onde é viável localizar novas subestações, na modelação adequada do problema real e na proposta de uma solução ótima para a expansão da rede existente. Depois de analisados diferentes modelos matemáticos aplicados ao problema de expansão de redes de distribuição de energia elétrica encontrados na literatura, optou-se por um modelo de programação linear inteira mista (PLIM) que se mostrou adequado. Desenvolvido o modelo do problema, o mesmo foi resolvido por recurso a software de otimização Analytic Solver e CPLEX. Como forma de validação dos resultados obtidos, foi implementada a solução de rede no simulador PowerWorld 8.0 OPF, software este que permite a simulação da operação do sistema de trânsito de potências.

Distribuição de Contaminantes Orgânicos em Solos Calcários – Influência dos minerais de Argila

O solo é um recurso multifuncional e vital para a humanidade, apresentando funções ecológicas, técnico-industriais, socioeconómicas e culturais, estabelecendo um vasto capital natural insubstituível. Face à sua taxa de degradação potencialmente rápida que, devido ao crescente desenvolvimento económico e incremento da população mundial, tem vindo a aumentar nas últimas décadas, o solo é, atualmente, um recurso finito e limitado. Devido a esta problemática, o presente documento visa abordar a progressiva preocupação sobre as questões geoambientais e toda a investigação que as envolvem, avaliando o modo como os contaminantes se dispersam pelo solo nas diferentes fases do mesmo (fases sólida, líquida e gasosa). A parte experimental centrou-se na análise da adsorção do benzeno, a partir da determinação das isotérmicas de adsorção. Para tal, foram previamente preparados reatores com calcário, sendo alguns deles previamente contaminados com um biocombustível, biodiesel, a uma concentração constante. Este processo foi monitorizado com base na evolução temporal da concentração na fase gasosa, através da cromatografia gasosa. De entre os objetivos, procurou-se analisar a distribuição dos contaminantes pelas fases constituintes do solo, ajustar os dados experimentais obtidos os modelos matemáticos de Langmuir, Freundlich e Polinomial, e verificar e discutir as soluções mais adequadas.

MAC regenerative analysis of wireless Ad-Hoc networks

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Electrotécnica e de Computadores

Modeling AIDS vaccines: the cellular level

This paper discuses current strategies for the development of AIDS vaccines wich allow immunzation to disturb the natural course of HIV at different detailed stages of its life cycle. Mathematical models describing the main biological phenomena (i.e. virus and vaccine induced T4 cell growth; virus and vaccine induced activation latently infected T4 cells; incremental changes immune response as infection progress; antibody dependent enhancement and neutralization of infection) and allowing for different vaccination strategies serve as a backgroud for computer simulations. The mathematical models reproduce updated information on the behavior of immune cells, antibody concentrations and free viruses. The results point to some controversial outcomes of an AIDS vaccine such as an early increase in virus concentration among vaccinated when compared to nonvaccinated individuals.

Growth in a Cross-Section of Cities: Location, Increasing Returns or Random Growth?

This article analyzes empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we implement a threshold nonlinearity test that extends standard linear growth regression models to a dataset on urban, climatological and macroeconomic variables on 1,175 U.S. cities. Our analysis reveals the existence of increasing returns when per-capita income levels are beyond $19; 264. Despite this, income growth is mostly explained by social and locational fundamentals. Population growth also exhibits two distinct equilibria determined by a threshold value of 116,300 inhabitants beyond which city population grows at a higher rate. Income and population growth do not go hand in hand, implying an optimal level of population beyond which income growth stagnates or deteriorates

Study and implementation of some quantitative trading models

Quantitative or algorithmic trading is the automatization of investments decisions obeying a fixed or dynamic sets of rules to determine trading orders. It has increasingly made its way up to 70% of the trading volume of one of the biggest financial markets such as the New York Stock Exchange (NYSE). However, there is not a signi cant amount of academic literature devoted to it due to the private nature of investment banks and hedge funds. This projects aims to review the literature and discuss the models available in a subject that publications are scarce and infrequently. We review the basic and fundamental mathematical concepts needed for modeling financial markets such as: stochastic processes, stochastic integration and basic models for prices and spreads dynamics necessary for building quantitative strategies. We also contrast these models with real market data with minutely sampling frequency from the Dow Jones Industrial Average (DJIA). Quantitative strategies try to exploit two types of behavior: trend following or mean reversion. The former is grouped in the so-called technical models and the later in the so-called pairs trading. Technical models have been discarded by financial theoreticians but we show that they can be properly cast into a well defined scientific predictor if the signal generated by them pass the test of being a Markov time. That is, we can tell if the signal has occurred or not by examining the information up to the current time; or more technically, if the event is F_t-measurable. On the other hand the concept of pairs trading or market neutral strategy is fairly simple. However it can be cast in a variety of mathematical models ranging from a method based on a simple euclidean distance, in a co-integration framework or involving stochastic differential equations such as the well-known Ornstein-Uhlenbeck mean reversal ODE and its variations. A model for forecasting any economic or financial magnitude could be properly defined with scientific rigor but it could also lack of any economical value and be considered useless from a practical point of view. This is why this project could not be complete without a backtesting of the mentioned strategies. Conducting a useful and realistic backtesting is by no means a trivial exercise since the \laws" that govern financial markets are constantly evolving in time. This is the reason because we make emphasis in the calibration process of the strategies' parameters to adapt the given market conditions. We find out that the parameters from technical models are more volatile than their counterpart form market neutral strategies and calibration must be done in a high-frequency sampling manner to constantly track the currently market situation. As a whole, the goal of this project is to provide an overview of a quantitative approach to investment reviewing basic strategies and illustrating them by means of a back-testing with real financial market data. The sources of the data used in this project are Bloomberg for intraday time series and Yahoo! for daily prices. All numeric computations and graphics used and shown in this project were implemented in MATLAB^R scratch from scratch as a part of this thesis. No other mathematical or statistical software was used.