While some attempts have been made to model the behaviour of the grand piano action (the mechanism that translates a key press into a hammer striking a string), most researchers have reduced the system to a simple model with little relation to the components of a real action. While such models are useful for certain applications, they are not appropriate as design tools for piano makers, since the model parameters have little physical meaning and must be calibrated from the behaviour of a real action. A new model for a piano action is proposed in this thesis. The model treats each of the five main action components (key, whippen, jack, repetition lever, and hammer) as a rigid body. The action model also incorporates a contact model to determine the normal and friction forces at 13 locations between each of the contacting bodies. All parameters in the model are directly measured from the physical properties of individual action components, allowing the model to be used as a prototyping tool for actions that have not yet been built. To test whether the model can accurately predict the behaviour of a piano action, an experimental apparatus was built. Based around a keyboard from a Boston grand piano, the apparatus uses an electric motor to actuate the key, a load cell to measure applied force, and optical encoders and a high speed video camera to measure the positions of the bodies. The apparatus was found to produce highly repeatable, reliable measurements of the action. The behaviour of the action model was compared to the measurements from the experimental apparatus for several types of key blows from a pianist. A qualitative comparison showed that the model could very accurately reproduce the behaviour of a real action for high force blows. When the forces were lower, the behaviour of the action model was still reasonable, but some discrepancy from the experimental results could be seen. In order to reduce the discrepancy, it was recommended that certain improvements could be made to the action model. Rigid bodies, most importantly the key and hammer, should be replaced with flexible bodies. The normal contact model should be modified to account for the speed-independent behaviour of felt compression. Felt bushings that are modelled as perfect revolute joints should instead be modelled as flexible contact surfaces.

While some attempts have been made to model the behaviour of the grand piano action (the mechanism that translates a key press into a hammer striking a string), most researchers have reduced the system to a simple model with little relation to the components of a real action. While such models are useful for certain applications, they are not appropriate as design tools for piano makers, since the model parameters have little physical meaning and must be calibrated from the behaviour of a real action. A new model for a piano action is proposed in this thesis. The model treats each of the five main action components (key, whippen, jack, repetition lever, and hammer) as a rigid body. The action model also incorporates a contact model to determine the normal and friction forces at 13 locations between each of the contacting bodies. All parameters in the model are directly measured from the physical properties of individual action components, allowing the model to be used as a prototyping tool for actions that have not yet been built. To test whether the model can accurately predict the behaviour of a piano action, an experimental apparatus was built. Based around a keyboard from a Boston grand piano, the apparatus uses an electric motor to actuate the key, a load cell to measure applied force, and optical encoders and a high speed video camera to measure the positions of the bodies. The apparatus was found to produce highly repeatable, reliable measurements of the action. The behaviour of the action model was compared to the measurements from the experimental apparatus for several types of key blows from a pianist. A qualitative comparison showed that the model could very accurately reproduce the behaviour of a real action for high force blows. When the forces were lower, the behaviour of the action model was still reasonable, but some discrepancy from the experimental results could be seen. In order to reduce the discrepancy, it was recommended that certain improvements could be made to the action model. Rigid bodies, most importantly the key and hammer, should be replaced with flexible bodies. The normal contact model should be modified to account for the speed-independent behaviour of felt compression. Felt bushings that are modelled as perfect revolute joints should instead be modelled as flexible contact surfaces.

The study of cardiac action potentials has many medical applications. Dr. Dennis Noble first used mathematical models to study cardiac action potentials in the 1960s. We begin our study of cardiac action potentials with one form of the Fitzhugh-Nagumo partial differential equation. We use the non-classical method to produce a closed form solution for the decoupled Fitzhugh Nagumo equation. Using voltage recording data of action potentials in a cardiac myocyte and in purkinje fibers, we estimate parameter values for the closed form solution with standard linear and non-linear regression methods. Results are limited, thus leading us to perturb the solution to obtain a better fit. We turn to singular perturbation theory to justify our pole-based approach. Finally, we test our model on independent action potential data sets to evaluate our model and to draw conclusions on how our model can be applied.

La démarche scientifique (ou expérimentale) en milieu scolaire nécessite des savoir-faire expérimentaux qui ne s’acquièrent habituellement qu’en présentiel, c’est-à-dire en laboratoire institutionnel où l’enseignant ou le technicien sont présents et peuvent, à tout moment, assister pleinement l’apprenant dans sa démarche d’investigation scientifique et technologique. Ils peuvent l’orienter, le diriger, susciter sa réflexion, faire des démonstrations réelles ou contrôler son expérimentation en lui montrant comment paramétrer les outils d’expérimentation assistée par ordinateur (ExAO). Pour répondre aux besoins de la formation à distance, cette recherche de développement en didactique des sciences et de la technologie propose de mettre à la disposition des apprenants et des enseignants un environnement de laboratoire informatisé, contrôlé et assisté à distance. Cet environnement, axé sur un microlaboratoire d’ExAO (MicrolabExAO), que nous avons nommé Ex@O pour le distinguer, a été testé de manière fonctionnelle, puis évalué en situation réelle par des étudiants-maîtres et des élèves de l’éducation des adultes qui ont pratiqué et expérimenté la démarche scientifique, en situation de laboratoire réel, mais à distance. Pour ce faire, nous avons couplé le logiciel MicrolabExAO à un logiciel de prise en main à distance avec outils audio et vidéo (Teamviewer). De plus, nous avons créé et inséré, dans le logiciel MicrolabExAO, une aide en ligne pour télécharger et faciliter la prise en main à distance. Puisque cet environnement Ex@O permet de multiplier les contacts des apprenants avec une expérimentation concrète, ce prototype répond bien à l’un des objectifs du Programme de formation de l’école québécoise (PFEQ) qui est de rendre l’apprenant plus actif dans ses apprentissages. Et parce que ce premier prototype d’environnement Ex@O permet d’effectuer des activités en laboratoire à distance, nous avons pu vérifier qu’il met aussi l’accent, non seulement sur les savoirs, mais également sur les savoir-faire expérimentaux en sciences et technologie, traditionnellement développés dans les locaux des laboratoires institutionnels. Notons ici que la démarche expérimentale s’acquiert très majoritairement en laboratoire en pratiquant, souvent et régulièrement, le processus inductif et déductif propre à cette démarche. Cette pratique de la démarche expérimentale, à distance, avec la technologie Ex@O qui l’accompagne, nous a permis de vérifier que celle-ci était possible, voire comparable à la réalisation, pas-à-pas, d’un protocole expérimental effectué dans un laboratoire institutionnel. / In the school environment, the scientific (or experimental) approach requires experimental «savoir-faire» which is usually acquired in presential, that is to say in an institutional laboratory where the teacher or technician are present and may, at any time, fully assist the learner in his inquiry-based scientific and technological approach. The teacher or technician can direct, guide and stimulate the learner’s thinking, to do live demonstrations and control experiment by showing the learner how to configures the computer assisted experimentation (expérimentation assistée par ordinateur or ExAO) tools. To meet the needs of distance learning, the R&D in science and technology education, provides learners and teachers with a computer laboratory environment, controlled and attended to from a distance. In order to distinguish between the remote computer lab environment and the ExAO microlaboratory, we named our environment Ex@O. It was first tested in order to werify its functionality and it was then evaluated in classroom situations by student teachers and students of adult education who practiced and experienced the scientific approach. This was done with a computer laboratory environment, but from a distance. To achieve this, we combine the MicrolabExAO software with a grip remote, and audio and video tools (Teamviewer). In addition, we have create and included in the MicrolabExAO software, online help in order to facilitate the download and the grip remote laboratory. Because of Ex@O, the learner benefits from increased contacts with concrete experiments. In doing so, the Ex@O prototype meets the objectives of the « Programme de formation de l’école québécoise » (PFEQ), which is to increase the learner’s active participation in his learnings. With the first version of Ex@O prototype, where the learner can perform activities in remote laboratory, we were able to verify that it also focuses not only on knowledge, but also the experimental science and technology « savoir-faire », traditionally developed in institutional laboratories. Note here that the experimental approach is acquired almost exclusively in the laboratory practicing, often and on a regular basis, both inductive and deductive processes which are specific to this approach. The practice of the experimental approach from a distance with the Ex@O technology, has enabled us to verify that it was possible, even comparable to a real, step-by-step, experimental protocol traditionally conducted in an institutional laboratory.

The Model Driven Architecture (MDA) allows moving the software development from the time consuming and error-prone level of writing program code to the next higher level of modeling. In order to gain benefit from this innovative technology, it is necessary to satisfy two requirements. These are first, the creation of compact, complete and correct platform independent models (PIM) and second, the development of a flexible and extensible model transformation framework taking into account frequent changes of the target platform. In this thesis a platform-based methodology is developed to create PIM by abstracting common modeling elements into a platform independent modeling library called Design Platform Model (DPM). The DPM contains OCL-based types for modeling primitive and collection types, a platform independent GUI toolkit as well as other common modeling elements, such as those for IO-operations. Furthermore, a DPM profile containing diverse domain specific and design pattern-based stereotypes is also developed to create PIM with high-level semantics. The behavior in PIM is specified using an OCL-like action language called eXecutable OCL (XOCL), which is also developed in this thesis. For model transformation, the model compiler MOCCA is developed based on a flexible and extensible architecture. The model mapper components in the current version of MOCCA are able to map desktop applications onto JSE platform; the both business object layer and persistence layer of a three-layered enterprise applications onto JEE platform and SAP ABAP platform. The entire model transformation process is finished with complete code generation.