Dynamic programming for a Markov-switching jump–diffusion

We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.

Determinação da tenacidade à fratura em corte (GIIc) de adesivos estruturais pelo ensaio End-Notched Flexure (ENF)

Os adesivos têm sido alvo de estudo ao longo dos últimos anos para ligação de componentes a nível industrial. Devido à crescente utilização das juntas adesivas, torna-se necessária a existência de modelos de previsão de resistência que sejam fiáveis e robustos. Neste âmbito, a determinação das propriedades dos adesivos é fundamental para o projeto de ligações coladas. Uma abordagem recente consiste no uso de modelos de dano coesivo (MDC), que permitem simular o comportamento à fratura das juntas de forma bastante fiável. Esta técnica requer a definição das leis coesivas em tração e corte. Estas leis coesivas dependem essencialmente de 2 parâmetros: a tensão limite e a tenacidade no modo de solicitação respetivo. O ensaio End-Notched Flexure (ENF) é o mais utilizado para determinar a tenacidade em corte, porque é conhecido por ser o mais expedito e fiável para caraterizar este parâmetro. Neste ensaio, os provetes são sujeitos a flexão em 3 pontos, sendo apoiados nas extremidades e solicitados no ponto médio para promover a flexão entre substratos, o que se reflete numa solicitação de corte no adesivo. A partir deste ensaio, e após de definida a tenacidade em corte (GIIc), existem alguns métodos para estimativa da lei coesiva respetiva. Nesta dissertação são definidas as leis coesivas em corte de três adesivos estruturais através do ensaio ENF e um método inverso de ajuste dos dados experimentais. Para o efeito, foram realizados ensaios experimentais considerado um adesivo frágil, o Araldite® AV138, um adesivo moderadamente dúctil, o Araldite® 2015 e outro dúctil, o SikaForce® 7752. O trabalho experimental consistiu na realização dos ensaios ENF e respetivo tratamento dos dados para obtenção das curvas de resistência (curvas-R) através dos seguintes métodos: Compliance Calibration Method (CCM), Direct Beam Theory (DBT), Corrected Beam Theory (CBT) e Compliance-Based Beam Method (CBBM). Os ensaios foram simulados numericamente pelo código comercial ABAQUS®, recorrendo ao Métodos de Elementos Finitos (MEF) e um MDC triangular, com o intuito de estimar a lei coesiva de cada um dos adesivos em solicitação de corte. Após este estudo, foi feita uma análise de sensibilidade ao valor de GIIc e resistência coesiva ao corte (tS 0), para uma melhor compreensão do efeito destes parâmetros na curva P- do ensaio ENF. Com o objetivo de testar adequação dos 4 métodos de obtenção de GIIc usados neste trabalho, estes foram aplicados a curvas P- numéricas de cada um dos 3 adesivos, e os valores de GIIc previstos por estes métodos comparados com os respetivos valores introduzidos nos modelos numéricos. Como resultado do trabalho realizado, conseguiu-se obter uma lei coesiva única em corte para cada um dos 3 adesivos testados, que é capaz de reproduzir com precisão os resultados experimentais.

Electrochemical methods in pesticides control

The state of the art of voltammetric and amperometric methods used in the study and determination of pesticides in crops, food, phytopharmaceutical products, and environmental samples is reviewed. The main structural groups of pesticides, i.e., triazines, organophosphates, organochlorides, nitrocompounds, carbamates, thiocarbamates, sulfonylureas, and bipyridinium compounds are considered with some degradation products. The advantages, drawbacks, and trends in the development of voltammetric and amperometric methods for study and determination of pesticides in these samples are discussed.

Strength prediction of single- and double-lap joints by standard and extended finite element modelling

The structural integrity of multi-component structures is usually determined by the strength and durability of their unions. Adhesive bonding is often chosen over welding, riveting and bolting, due to the reduction of stress concentrations, reduced weight penalty and easy manufacturing, amongst other issues. In the past decades, the Finite Element Method (FEM) has been used for the simulation and strength prediction of bonded structures, by strength of materials or fracture mechanics-based criteria. Cohesive-zone models (CZMs) have already proved to be an effective tool in modelling damage growth, surpassing a few limitations of the aforementioned techniques. Despite this fact, they still suffer from the restriction of damage growth only at predefined growth paths. The eXtended Finite Element Method (XFEM) is a recent improvement of the FEM, developed to allow the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom with special displacement functions, thus overcoming the main restriction of CZMs. These two techniques were tested to simulate adhesively bonded single- and double-lap joints. The comparative evaluation of the two methods showed their capabilities and/or limitations for this specific purpose.

A New Approach in the Design of Air Stripping Columns for the Treatment of Groundwater Contaminated With Volatile Organic Compounds

Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for column design for any type of packing and contaminant which avoids the necessity of an arbitrary chosen diameter. It also avoids the employment of the usual graphical Eckert correlations for pressure drop. The hydraulic features are previously chosen as a project criterion. The design procedure was translated into a convenient algorithm in C++ language. A column was built in order to test the design, the theoretical steady-state and dynamic behaviour. The experiments were conducted using a solution of chloroform in distilled water. The results allowed for a correction in the theoretical global mass transfer coefficient previously estimated by the Onda correlations, which depend on several parameters that are not easy to control in experiments. For best describe the column behaviour in stationary and dynamic conditions, an original mathematical model was developed. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting ODE can be solved by analytical methods, and in dynamic state the discretization of the PDE by finite differences allows for the overcoming of this difficulty. To estimate the contaminant concentrations in both phases in the column, a numerical algorithm was used. The high number of resulting algebraic equations and the impossibility of generating a recursive procedure did not allow the construction of a generalized programme. But an iterative procedure developed in an electronic worksheet allowed for the simulation. The solution is stable only for similar discretizations values. If different values for time/space discretization parameters are used, the solution easily becomes unstable. The system dynamic behaviour was simulated for the common liquid phase perturbations: step, impulse, rectangular pulse and sinusoidal. The final results do not configure strange or non-predictable behaviours.