Bibliography: p. 196-200. / M.I.T. Project DSR 76094. Contract no. NOW-66-0178-d.

One important aspect of our present age of monolithic high speed computers is the computer's capability to solve complex problems hitherto impossible to tackle due to their complexity. This paper explains how to use a. digital computer to solve a specific type of problem; specifically, to find the inverse solution of a in the elliptical equation V2U(x,y) = g(a,U,x,y), with appropriate boundary conditions. This equation is very useful in the electronics field. The knowns are the complete set of boundary values of U(x,y) and a set of observations taken on internal points of U(x,y). Given this information, plus the specific form of the governing equation, we can solve for the unknown a. Once the computer program has been written using the technique of quasilinearization, Newton’S convergence method, discrete invariant imbedding, and the use of sensitivity functions, then we take data from the computer results and analyse it for proper convergence. This data shows that there are definite limits to the usefulness and capability of the technique. One of the results of this study is the observation that it is important to the proper functioning of this problem solving technique that the observations taken on U(x,y) are placed in the most efficient locations with the most efficient geometry in the region of largest effectiveness. Another result deals with the number of observation points used: too few gives insufficient information for proper program functioning, and too many tends to saturate the effectiveness of the observations. Thus this paper has two objectives. first to develop the technique and secondly to analyse the results from the realization of the technique through the use of a computer.

A modified source and dipole panel method to calculate the flow properties around an oscillating arbitrary body in the presence of a free surface is proposed. To demonstrate the feasibility of the method the problem of a pulsating line source submerged under a free surface is treated. The technique chosen is based on Green's identity whereby the boundary-value problem is expressed as a boundary integral equation which is solved numerically. The near field of the water surface is represented by singularity panels with constant strength. The work was motivated by the reported large computing times for existing programs using Green's functions satisfying the free surface boundary condition. The present approach uses free-space Green's function. The free surface boundary condition is applied to surface singularity panels using Green's theorem. Thus free surface effects are included in the solution while panel integrations are simplified considerably by the use of simpler Green's function. The matrix equations resulting from Green's identity were solved by using IMSL routines for Gaussian Elimination, and the behavior of the influence coefficient matrix was tested by using LINPACK routines. The depth of the submerged-source and wave number was kept constant while the length of near field and the number of panels per wavelength was varied systematically. A minimum of 10 panels per wavelength and paneled water surface length of 2 wavelengths gives good agreement with the known exact solution. Computing times were low, indicating the feasibility of the technique for application to unsteady ship problems. / Ph. D.

M. Tech. : Mathematical Technology. / Attempts will be made to extend the elementary quarter-mass models (for instance Gillepse, 1992, [5]; Kiecke & Nielsen, 2000, [6] and Singiresu, 2004, [7]) of a motor vehicle suspension system to include the radial vibrations of a rubber tyre in the model. Tangential vibrations of the tyre surface were investigated by Bekker (2009, [8]) and the possible incorporation of such vibrations into a suspension model invites the possibility of future study.

La mise à l’échelle (scaling up) est un processus qui vise à accroitre l’impact et la pérennité des effets d’innovations jugées prometteuses. Les publications à ce sujet sont en progression importante dans le domaine de la santé depuis une vingtaine d’années. Toutefois, ces processus ont été étudiés de manière essentiellement technique malgré l’importance soulignée dans la littérature d’y prendre en compte des questions évolutives de sens et de valeurs. Ceci est particulièrement significatif pour les innovations de promotion de la santé, construites sur les capacités et collaborations de différents acteurs qui y partagent et négocient diverses vues sur les problèmes, les actions à entreprendre et leur but. Les contenus de ces innovations sont susceptibles d’évoluer de manière significative dans la mise à l’échelle, et d’affecter la fonction d’impact et pérennité du processus. Peu d’études, cependant, mobilisent des théories et méthodologies explicites à cet égard. Cette thèse s’inscrit dans une vision sociale de la mise à l’échelle et propose d’ajouter le concept de cadre interprétatif, ou « frame », à son outillage conceptuel ; elle vise à explorer l’utilité de cette notion au regard de la dynamique sociale de la mise à l’échelle d’innovations complexes de promotion de la santé. La thèse poursuit deux objectifs : 1) développer une articulation théorique de nature sociale pour la mise à l’échelle intégrant la notion de frame ; et 2) explorer l’utilité des frames comme ‘représentations’ pour documenter l’évolution du contenu des innovations au cours de leur mise à l’échelle. La réponse au premier objectif s’appuie sur une perspective de complexité des interventions en tant que réseaux dynamiques d’acteurs pour conceptualiser la mise à l’échelle comme une expansion de réseaux où le framing des questions de santé évolue au travers des relations entre acteurs. L’articulation théorique développée combine la sociologie de l’innovation - théorie de l’acteur-réseau - et les perspectives des frames pour envisager ceux-ci en tant que ‘représentations’ ou ‘interactions’. En réponse au second objectif, l’approche ‘représentationnelle’ aux frames est appliquée à l’étude d’un cas de mise à l’échelle d’innovation éducative à caractère intersectoriel concernant le développement de jeunes enfants socialement désavantagés. Sur la base de documents cadres qui balisent les phases ‘pilote’ et ‘programme à l’échelle’ de l'innovation, une analyse critique de frames est pratiquée au regard de la capacité du programme à grande échelle à supporter l’action sur les inégalités sociales de développement des enfants et l’équité. Les résultats illustrent des différences significatives de définitions du ‘problème’ du DJE et de la solution préconisée pour le programme à grande échelle, qui constituent des améliorations, mais aussi certaines ‘détériorations’ au regard des inégalités et de l’équité. En tant que constructions réalisées à partir des ‘produits’ du processus social qui s’opère dans le réseau intersectoriel des acteurs, les frames comme ‘représentations’ analysés de manière critique sont utiles pour expliciter et caractériser l’évolution des contenus des innovations et leurs conséquences pour la mise à l’échelle. Mobilisés dans un échange constructif avec les acteurs concernés, les frames pourraient constituer un outil intéressant pour favoriser la réflexivité à l’égard de ces processus et de l’impact et de la durabilité des effets des innovations portées à grande échelle. Cette thèse contribue de manière théorique à la littérature de santé publique en clarifiant l’utilité des frames et la manière dont ce concept peut être mobilisé pour documenter la dynamique de la mise à l’échelle d’innovations complexes de promotion de la santé. / Scaling up is a process that aims to increase the impact and sustainability of the effects of innovations deemed promising. Publications on this subject have markedly increased in the field of health over the past twenty years. However, these processes have essentially been studied in a technical way, despite the importance underlined in the literature to take into account their evolving meanings and values. This is particularly significant for health promotion innovations, built on the capacities and collaborations of different actors who share and negotiate various views on the problems, the actions to be taken and their goal. The contents of these innovations are likely to evolve significantly during scaling up, affecting impact and sustainability goals of the process. Few studies, however, mobilize explicit theories and methodologies in this respect. This thesis is part of a social vision of scaling up, and proposes to add the concept of ‘frame’ to its conceptual tools; it aims to explore the usefulness of this notion with regard to the social dynamics of scaling up health promotion innovations. The thesis pursues two objectives: 1) to develop a theoretical articulation of a social nature for scaling up, integrating the notion of frame; and 2) to explore the usefulness of frames as ‘representations’ to document the evolution of the content of innovations during their scaling up. The response to the first objective is based on a complexity perspective of interventions as dynamic networks of actors to conceptualize scaling up as an expansion of networks where the framing of health issues evolves through the relationships between the actors. The theoretical articulation developed combines the sociology of innovation - actor-network theory - and the perspectives of frames to consider them as 'representations' or 'interactions'. In response to the second objective, the 'representational' approach to frames is applied to the study of a scaling up case concerning an intersectoral educational innovation for the development of socially disadvantaged young children. On the basis of framework documents which mark out the 'pilot' and 'at scale program' phases of the innovation, a critical analysis of frames is carried out with regard to the capacity of the large-scale program to support action on the social inequalities in child development and equity. The results illustrate significant differences in definitions of the ECD ‘problem’ and of the recommended ‘solution’ for the at scale program, which constitute improvements, but also some ‘deteriorations’ with regard to inequalities and equity. As constructions made from the 'products' of the social process that takes place in the intersectoral network of actors, the frames as 'representations' critically analyzed are useful for explaining and characterizing the evolution of the contents of innovations and their consequences for scaling up. Mobilized in a constructive exchange with the actors concerned, the frames could constitute an interesting tool to promote reflexivity with regard to these processes and to the impact and sustainability of the effects of innovations carried out on a large scale. This thesis contributes theoretically to the public health literature by clarifying the usefulness of frames and the way in which this concept can be mobilized to document the dynamics of the scaling up of complex health promotion innovations.