A calculadora gráfica na promoção da escrita matemática na aprendizagem de modelos contínuos não lineares: um estudo com alunos do 11.º ano de Matemática B

Relatório de estágio de mestrado em Ensino de Matemática no 3.º Ciclo do Ensino Básico e no Ensino Secundário

Specification and testing of multiplicative time-varying GARCH models with applications

In this article, we develop a specification technique for building multiplicative time-varying GARCH models of Amado and Teräsvirta (2008, 2013). The variance is decomposed into an unconditional and a conditional component such that the unconditional variance component is allowed to evolve smoothly over time. This nonstationary component is defined as a linear combination of logistic transition functions with time as the transition variable. The appropriate number of transition functions is determined by a sequence of specification tests. For that purpose, a coherent modelling strategy based on statistical inference is presented. It is heavily dependent on Lagrange multiplier type misspecification tests. The tests are easily implemented as they are entirely based on auxiliary regressions. Finite-sample properties of the strategy and tests are examined by simulation. The modelling strategy is illustrated in practice with two real examples: an empirical application to daily exchange rate returns and another one to daily coffee futures returns.

Pure elastic contact force models

"Series: Solid mechanics and its applications, vol. 226"

Dissipative contact force models

"Series: Solid mechanics and its applications, vol. 226"

Contact force models for multibody dynamics

"Series: Solid mechanics and its applications, vol. 226"

Acellular Gellan-gum based bilayered structures for the regeneration of osteochondral defects: a preclinical study

 In orthopaedics, the management and treatment of osteochondral (OC) defects remains an ongoing clinical challenge. Autologous osteochondral mosaicplasty has been used as a valid option for OC treatments although donor site morbidity remains a source of concern [1]. Engineering a whole structure capable of mimicking different tissues (cartilage and subchondral bone) in an integrated manner could be a possible approach to regenerate OC defects. In our group we have been proposing the use of bilayered structures to regenerate osteochondral defects [2,3]. The present study aims to investigate the pre-clinical performance of bilayered hydrogels and spongy-like hydrogels in in vivo  models (mice and rabbit, respectively), in both subcutaneous and orthotopic models. The bilayered structures were produced from Low Acyl Gellan Gum (LAGG) from Sigma-Aldrich, USA. Cartilage-like layers were obtained from a 2wt% LAGG solution. The bone-like layers were made of 2wt% LAGG with incorporation of hydroxyapatite at 20% and 30% (w/v). Hydrogels and spongy-like were subcutaneouly implanted in mice to evaluate the inflammatory response. Then, OC defects were induced in rabbit knee to create a critical size defect (4 mm diameter and 5 mm depth), and then hydrogels and sponges implanted. Both structures followed different processing methods. The hydrogels were injected allowing in situ  crosslinking. Unlike, the spongy-like were pre-formed by freeze-drying. The studies concerning subcutaneous implantation and critical size OC defect were performed for 2 and 4 weeks time, respectively. Cellular behavior and inflammatory responses were assessed by means of histology staining and biochemical function and matrix deposition by immunohistochemistry. Additionally, both OC structures stability and new cartilage and bone formation were evaluated by using vivo- computed tomography (Scanco 80). The results showed no acute inflammatory response for both approaches. New tissue formation and integration in the adjacent tissues were also observed, which present different characteristic behaviors when comparing hydrogels and sponges response. As future insights, a novel strategy for regeneration of OC defects can be designed encompassing both, hydrogels and spongy-like structures and cellular approaches. References: 1. Espregueira-Mendes J. et al. Osteochondral transplantation using autografts from the upper tibio-fibular joint for the treatment of knee cartilage lesions. Knee Surgery, Sports Traumatology, Arthroscopy 20,1136, 2012. 2. Oliveira JM. et al, Novel hydroxyapatite/chitosan bilayered scaffold for osteochondral tissue-engineering applications: Scaffold design and its performance when seeded with goat bone marrow stromal cells. Biomaterials 27, 6123, 2006. 3. Pereira D R. et al. Gellan Gum-Based Hydrogel Bilayered Scaffolds for Osteochondral Tissue Engineering. Key Engineering Materials 587, 255, 2013.

Integration of geometric consistency contributory factors in three-leg junctions collision prediction models of Portuguese two-lane national highways

This paper aims at developing a collision prediction model for three-leg junctions located in national roads (NR) in Northern Portugal. The focus is to identify factors that contribute for collision type crashes in those locations, mainly factors related to road geometric consistency, since literature is scarce on those, and to research the impact of three modeling methods: generalized estimating equations, random-effects negative binomial models and random-parameters negative binomial models, on the factors of those models. The database used included data published between 2008 and 2010 of 177 three-leg junctions. It was split in three groups of contributing factors which were tested sequentially for each of the adopted models: at first only traffic, then, traffic and the geometric characteristics of the junctions within their area of influence; and, lastly, factors which show the difference between the geometric characteristics of the segments boarding the junctionsâ area of influence and the segment included in that area were added. The choice of the best modeling technique was supported by the result of a cross validation made to ascertain the best model for the three sets of researched contributing factors. The models fitted with random-parameters negative binomial models had the best performance in the process. In the best models obtained for every modeling technique, the characteristics of the road environment, including proxy measures for the geometric consistency, along with traffic volume, contribute significantly to the number of collisions. Both the variables concerning junctions and the various national highway segments in their area of influence, as well as variations from those characteristics concerning roadway segments which border the already mentioned area of influence have proven their relevance and, therefore, there is a rightful need to incorporate the effect of geometric consistency in the three-leg junctions safety studies.

The potential field method and the nonlinear attractor dynamics approach: what are the differences?

One of the most popular approaches to path planning and control is the potential field method. This method is particularly attractive because it is suitable for on-line feedback control. In this approach the gradient of a potential field is used to generate the robot's trajectory. Thus, the path is generated by the transient solutions of a dynamical system. On the other hand, in the nonlinear attractor dynamic approach the path is generated by a sequence of attractor solutions. This way the transient solutions of the potential field method are replaced by a sequence of attractor solutions (i.e., asymptotically stable states) of a dynamical system. We discuss at a theoretical level some of the main differences of these two approaches.

Numerical Assessment of the out-of-plane response of a brick masonry structure without box behaviour

This paper presents the assessment of the out-of-plane response due to seismic loading of a masonry structure without rigid diaphragm. This structure corresponds to real scale brick masonry specimen with a main façade connected to two return walls. Two modelling approaches were defined for this evaluation. The first one consisted on macro modelling, whereas the second one on simplified micro modelling. As a first step of this study, static nonlinear analyses were conducted to the macro model aiming at evaluating the out-of-plane response and failure mechanism of the masonry structure. A sensibility analyses was performed in order to assess the mesh size and material model dependency. In addition, the macro models were subjected to dynamic nonlinear analyses with time integration in order to assess the collapse mechanism. Finally, these analyses were also applied to a simplified micro model of the masonry structure. Furthermore, these results were compared to experimental response from shaking table tests. It was observed that these numerical techniques simulate correctly the in-plane behaviour of masonry structures. However, the

Seismic vulnerability of existing masonry buildings: Nonlinear parametric analysis

Existing masonry structures are usually associated to a high seismic vulnerability, mainly due to the properties of the materials, weak connections between floors and load-bearing walls, high mass of the masonry walls and flexibility of the floors. For these reasons, the seismic performance of existing masonry structures has received much attention in the last decades. This study presents the parametric analysis taking into account the deviations on features of the gaioleiro buildings - Portuguese building typology. The main objective of the parametric analysis is to compare the seismic performance of the structure as a function of the variations of its properties with respect to the response of a reference model. The parametric analysis was carried out for two types of structural analysis, namely for the non-linear dynamic analysis with time integration and for the pushover analysis with distribution of forces proportional to the inertial forces of the structure. The Young's modulus of the masonry walls, Young's modulus of the timber floors, the compressive and tensile non-linear properties (strength and fracture energy) were the properties considered in both type of analysis. Additionally, in the dynamic analysis, the influences of the vis-cous damping and of the vertical component of the earthquake were evaluated. A pushover analysis proportional to the modal displacement of the first mode in each direction was also carried out. The results shows that the Young's modulus of the masonry walls, the Young's modulus of the timber floors and the compressive non-linear properties are the pa-rameters that most influence the seismic performance of this type of tall and weak existing masonry structures. Furthermore, it is concluded that that the stiffness of the floors influences significantly the strength capacity and the collapse mecha-nism of the numerical model. Thus, a study on the strengthening of the floors was also carried out. The increase of the thickness of the timber floors was the strengthening technique that presented the best seismic performance, in which the reduction of the out-of-plane displacements of the masonry walls is highlighted.

Evaluation of seismic vulnerability assessment parameters for portuguese vernacular constructions with nonlinear numerical analysis

Considering that vernacular architecture may bear important lessons on hazard mitigation and that well-constructed examples showing traditional seismic resistant features can present far less vulnerability than expected, this study aims at understanding the resisting mechanisms and seismic behavior of vernacular buildings through detailed finite element modeling and nonlinear static (pushover) analysis. This paper focuses specifically on a type of vernacular rammed earth constructions found in the Portuguese region of Alentejo. Several rammed earth constructions found in the region were selected and studied in terms of dimensions, architectural layout, structural solutions, construction materials and detailing and, as a result, a reference model was built, which intends to be a simplified representative example of these constructions, gathering the most common characteristics. Different parameters that may affect the seismic response of this type of vernacular constructions have been identified and a numerical parametric study was defined aiming at evaluating and quantifying their influence in the seismic behavior of this type of vernacular buildings. This paper is part of an ongoing research which includes the development of a simplified methodology for assessing the seismic vulnerability of vernacular buildings, based on vulnerability index evaluation methods.

Conceptual-physical bridging – From BPMN models to physical implementations on kettle

Developing and implementing data-oriented workflows for data migration processes are complex tasks involving several problems related to the integration of data coming from different schemas. Usually, they involve very specific requirements - every process is almost unique. Having a way to abstract their representation will help us to better understand and validate them with business users, which is a crucial step for requirements validation. In this demo we present an approach that provides a way to enrich incrementally conceptual models in order to support an automatic way for producing their correspondent physical implementation. In this demo we will show how B2K (Business to Kettle) system works transforming BPMN 2.0 conceptual models into Kettle data-integration executable processes, approaching the most relevant aspects related to model design and enrichment, model to system transformation, and system execution.

Automatic generation of ETL physical systems from BPMN conceptual models

ETL conceptual modeling is a very important activity in any data warehousing system project implementation. Owning a high-level system representation allowing for a clear identification of the main parts of a data warehousing system is clearly a great advantage, especially in early stages of design and development. However, the effort to model conceptually an ETL system rarely is properly rewarded. Translating ETL conceptual models directly into something that saves work and time on the concrete implementation of the system process it would be, in fact, a great help. In this paper we present and discuss a hybrid approach to this problem, combining the simplicity of interpretation and power of expression of BPMN on ETL systems conceptualization with the use of ETL patterns to produce automatically an ETL skeleton, a first prototype system, which has the ability to be executed in a commercial ETL tool like Kettle.

Implementation of a lean six sigma project in a production line

Companies from the motorcycles components branch are dealing with a dynamic environment, resulting from the introduction of new products and the increase of market demand. This dynamic environment requires frequent changes in production lines and requires flexibility in the processes, which can cause reductions in the level of quality and productivity. This paper presents a Lean Six Sigma improvement project performed in a production line of the company's machining sector, in order to eliminate losses that cause low productivity, affecting the fulfillment of the production plan and customer satisfaction. The use of Lean methodology following the DMAIC stages allowed analyzing the factors that influence the line productivity loss. The major problems and causes that contribute to a reduction on productivity and that were identified in this study are the lack of standardization in the setup activities and the excessive stoppages for adjustment of the processes that caused an increase of defects. Control charts, Pareto analysis and cause-and-effect diagrams were used to analyze the problem. On the improvement stage, the changes were based on the reconfiguration of the line layout as well as the modernization of the process. Overall, the project justified an investment in new equipment, the defective product units were reduced by 84% and an increase of 29% of line capacity was noticed.

Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem