Thesis (Ed.D.) -- Central Connecticut State University, 2006. / Thesis advisor: Anthony Rigazio-Di-Gilio. "... in partial fulfillment of the requirements for the degree of Doctor of Education, Department of Educational Leadership." Includes bibliographical references (leaves 103-108) Also available via the World Wide Web.

Phase change in solidification and melting can be described with the aid of discontinuous functions. The aim of this project is to establish effective methodologies for the solution of discontinuous phase-change problems. The classic capacitance method, which distributes the effect of any discontinuity present over a finite region (typically an element), can suffer from inaccurate energy transport. Improvement is possible with the application of the classic non-physical enthalpy method. However, this approach is known to suffer with the imposition of material velocity, which gives rise to negative thermal capacitance providing a source of error and instability. In order to improve on the performance of the capacitance method and the classic non-physical enthalpy method, this research introduces a series of new non-physical variables. Firstly, a new non-physical enthalpy is defined via the weak form of the energy transport equation. The classical non-physical enthalpy was defined using a temporal integral term. In the new definition, the non-physical enthalpy involves both a temporal and an advection term, which is shown to avoid the generation of negative capacitance and improve the stability of advection heat transfer in numerical methods. Secondly, control volume analysis is performed on weighted and unweighted forms of the governing energy equation involving non-physical enthalpy. The analysis is shown to reveal non-physical source terms that facilitate the removal of phase-change discontinuities. Thirdly, it is demonstrated in the thesis how a non-physical heat source must be introduced into the governing non-physical transport equation to remove discontinuities arising from non-physical terms related to advection. To demonstrate the accuracy and stability of the new method, it is implemented in the finite element method for both one-dimensional linear rod elements and two dimensional triangular elements. Update techniques and root finding methods, such as the predictor-corrector method, the secant method and the homotopy method, are applied to solve the non-linear system of equations, which are constructed with the new theory. Results returned from the one-dimensional numerical experiments are compared with exact solutions, which show reasonable accuracy. Numerical experiments for isothermal solidification with advection-diffusion in both one and two dimensions demonstrate the feasibility of the new methodology.

This thesis starts by observing a change problem in a medical computer application. The change problem occurs when data and rules that make up the core of a computer application, degenerate. Sometimes the process is slow, but it is not unusual for the application to be out of date even before it has been put into use. The aim of this work is to develop a theoretical framework in which it is possible to formulate the change problem such that it becomes more accessible for conscious consideration and a base for design principles. Accordingly, the thesis follows a theoretical approach. In order to place the work in a historical perspective, some major lines of research in administrative data processing are outlined. The change problem has led the author to investigate the birth and change of facts. The result of this investigation is that two fundamental points of view can be identified. One is closely related to a view of knowledge that is characteristic of the age of enlightenment. The basic idea in this "depictive" view is that facts are more or less depictions of reality. The other point of view can be associated with philosophers such as Kant and Hegel. The fundamental idea in this "constructive" view is that facts are related to measuring systems that are created by man. The constructive view is developed to include computer applications, encompassing a concept with seven key elements. To demonstrate the usefulness of the concept, two case studies are discussed: a computer aided travel agency and the argumentation around a computer aided social research project. An attempt is then made to use the constructive view as an approach to the change problem. One important result of this work is that the change problem shifts into a problem of justice. The conclusion is that a depictive view of facts gives theoretical support for transforming every human activity into deterministic machinery. When this fails, we experience a change problem. A constructive view of facts gives theoretical support for participation in a redesigning process. When this fails we experience a problem of injustice among clients. Following that conclusion, one way to approach the injustice problem is to encourage clients to take part in a continuous reconstruction of the activity. This is the same thing as looking for solutions to the change problem. The focus of the thesis then turns to different strategies to encourage clients to participate in the reconstructive work, which is also knovyn as the question of implementation. The following complementary strategies for implementation are considered: The Metaphorical Strategy, the Heuristic Strategy, the Documentation Strategy, the Computer Application Strategy, the Education Strategy. These strategies are then applied to the first mentioned medical computer application. The thesis concludes with some outlines for further research and some fundamental questions conceiving constructive computer applications. These questions focused on the necessity for further work on ethical aspects of a constructive view. / digitalisering@umu