Holistic projection of initial conditions onto a finite difference approximation

Modern dynamical systems theory has previously had little to say about finite difference and finite element approximations of partial differential equations (Archilla, 1998). However, recently I have shown one way that centre manifold theory may be used to create and support the spatial discretisation of \pde{}s such as Burgers' equation (Roberts, 1998a) and the Kuramoto-Sivashinsky equation (MacKenzie, 2000). In this paper the geometric view of a centre manifold is used to provide correct initial conditions for numerical discretisations (Roberts, 1997). The derived projection of initial conditions follows from the physical processes expressed in the PDEs and so is appropriately conservative. This rational approach increases the accuracy of forecasts made with finite difference models.Comment: 8 pages, LaTe

The inertial dynamics of thin film flow of non-Newtonian fluids

Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case of a viscosity that depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general nonlinear dependence. The modelling allows for large changes in film thickness provided the changes occur over a large enough lateral length scale. Modifying the surface boundary condition for tangential stress forms an accessible base for the analysis where flow with constant shear is a neutral critical mode, in addition to a mode representing conservation of fluid. Perturbatively removing the modification then constructs a model for the coupled dynamics of the fluid depth and the lateral momentum. For example, the results model the dynamics of gravity currents of non-Newtonian fluids even when the flow is not very slow

Initial Conditions for Models of Dynamical Systems

The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with appropriate initial conditions, so that it faithfully reproduces the long-term behaviour of the original high-dimensional dynamical system. Our method involves putting the dynamical system into normal form, which not only generates the low-dimensional model, but also provides the correct initial conditions for the model. We illustrate the method with several examples. Keywords: normal form, isochrons, initialisation, centre manifoldComment: 24 pages in standard LaTeX, 66K, no figure

Thermomechanical Behavior of Thermoelectric SMA Actuators

In this paper we analyse numerically thermomechanical behaviour of a sandwich-type actuator where a shape memory alloy layer is located between two oppositely doped semiconductors. The mathematical model for this analysis is based on a coupled system of partial differential equations with constitutive equations taken in the Falk form. The system is solved using an efficient differential-algebraic solver and computational results describing thermomechanical fields in such devices are presented

Novel expression of Haemonchus contortus vaccine candidate aminopeptidase H11 using the free-living nematode Caenorhabditis elegans

With the problem of parasitic nematode drug resistance increasing, vaccine development offers an alternative sustainable control approach. For some parasitic nematodes, native extracts enriched for specific proteins are highly protective. However, recombinant forms of these proteins have failed to replicate this protection. This is thought to be due to differences in glycosylation and/or conformation between native and recombinant proteins. We have exploited the free-living nematode Caenorhabditis elegans to examine its suitability as an alternative system for recombinant expression of parasitic nematode vaccine candidates. We focussed on Haemonchus contortus aminopeptidase H11 glycoprotein, which is enriched in a gut membrane fraction capable of inducing significant protection against this important ovine gastrointestinal nematode. We show that H. contortus H11 expressed in C. elegans is enzymatically active and MALDI mass spectrometry identifies similar di- and tri-fucosylated structures to those on native H11, with fucose at the 3- and/or 6-positions of the proximal GlcNAc. Some glycan structural differences were observed, such as lack of LDNF. Serum antibody to native H11 binds to C. elegans recombinant H11 and most of the antibody to rH11 or native H11 is directed to glycan moieties. Despite these similarities, no reduction in worm burden or faecal egg count was observed following immunisation of sheep with C. elegans-expressed recombinant H11 protein. The findings suggest that the di- and tri-fucosylated N-glycans expressed on rH11 do not contribute to the protective effect of H11 and that additional components present in native H11-enriched extract are likely required for enhancing the antibody response necessary for protection

Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling

Equation-free macroscale modelling is a systematic and rigorous computational methodology for efficiently predicting the dynamics of a microscale system at a desired macroscale system level. In this scheme, the given microscale model is computed in small patches spread across the space-time domain, with patch coupling conditions bridging the unsimulated space. For accurate simulations, care must be taken in designing the patch coupling conditions. Here we construct novel coupling conditions which preserve translational invariance, rotational invariance, and self-adjoint symmetry, thus guaranteeing that conservation laws associated with these symmetries are preserved in the macroscale simulation. Spectral and algebraic analyses of the proposed scheme in both one and two dimensions reveal mechanisms for further improving the accuracy of the simulations. Consistency of the patch scheme's macroscale dynamics with the original microscale model is proved. This new self-adjoint patch scheme provides an efficient, flexible, and accurate computational homogenisation in a wide range of multiscale scenarios of interest to scientists and engineers

Normal form transforms separate slow and fast modes in stochastic dynamical systems

Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate transforms of stochastic differential systems when the dynamics has both slow modes and quickly decaying modes. The thrust is to derive normal forms useful for macroscopic modelling of complex stochastic microscopic systems. Thus we not only must reduce the dimensionality of the dynamics, but also endeavour to separate all slow processes from all fast time processes, both deterministic and stochastic. Quadratic stochastic effects in the fast modes contribute to the drift of the important slow modes. The results will help us accurately model, interpret and simulate multiscale stochastic systems

Are pregnancy outcomes associated with risk factor reporting in routinely collected perinatal data?

Relatório de estágio do mestrado em Ensino da Educação Física dos Ensinos Básico e Secundário, apresentado à Faculdade de Ciências do Desporto e Educação Física da Universidade de CoimbraApresentado como um documento reflexivo e figurativo das experiências e vivências tidas durante o ano de Estágio Pedagógico em Ensino da Educação Física nos Ensinos Básico e Secundário, este relatório final foi desenvolvido com base no contexto da Turma do 11º PS da Escola Secundária de Avelar Brotero, contendo, assim, todas as expetativas, conceções, aprendizagens, dificuldades, estratégias, soluções e etapas superadas. Estruturado em cinco capítulos – Enquadramento pessoal onde consta as expetativas iniciais relativas ao Estágio Pedagógico; contextualização da prática desenvolvida, onde caracterizamos o contexto; realização da prática profissional, da qual consta uma reflexão sobre todo o processo de planeamento, realização e avaliação; reflexões acerca do processo pedagógico, onde expomos opiniões edificantes dos desafios e dilemas na condução do processo de ensino-aprendizagem; e o aprofundamento do tema problema – foi evidenciado o caminho que fomos (re)construindo com identidade, partilha e reflexão, e a forma como encaramos o compromisso com as aprendizagens dos alunos. Fundamentado no paradigma construtivista, o desenvolvimento curricular foi neste relatório assumido como um processo que deverá centrar-se no aluno, aludindo ao conjunto de estratégias, métodos e procedimentos que permitem a concretização de um projeto de formação pessoal e social que a prática desportiva pode potenciar. Tendo em atenção os contextos e cenários de aprendizagem, os papéis e responsabilidades de quem ensina e de quem aprende, fomos delegando ao aluno autonomia, iniciativa, criatividade, capacidade de cooperação e entreajuda, capacidade de decidir, vontade de aprender e de praticar. O Modelo de Educação Desportiva, enquanto modelo de ensino, foi um marco neste processo, pelo que foi objeto de um estudo mais aprofundado. This document was presented as a reflective essay on the experiences lived during the year of Practicum in Teaching of Physical Education on learning stages of Elementary School and High School. This final report was based on the class of 11º PS of Avelar Brotero’s High School, and represents all the expectations, conceptions, learning skills, difficulties found in the process, strategies adopted, solutions found and overcome barriers. It was structured in five chapters: initial expectations relating to the Practicum; characterization of the context; professional practice, in which lies was a reflexion about all the process of planning, making and evaluation; problems and challenges occurred during the process of teaching and learning; and finally deep reflection about he main theme - was then noted the way in which we had been (re)building our study with identity, sharing and reflexion and the way we faced the commitment with the students own learning skills and paths. Under the influence of the constructivist paradigm, curriculum development was seen as a process that will focus on the student, alluding to the set of strategies, methods and procedures that allow the making of a project of personal and social development that the sports practice may enhance, delegating the student autonomy, responsibility, initiative, creativity, ability to cooperate and assist others, and ability to learn and share. The Sport Education Model while teaching model it was a milestone in this process, whereat it was object of further study