Research on interfacial phenomena has a long history, which has attracted tremendous interest in recent years. One of the most successful tools is the phase-field approach. As phase-field models usually involve very complex dynamics and it is nontrivial to obtain analytical solutions, numerical methods have played an important role in various simulations. This thesis is mainly devoted to developing accurate, efficient and robust numerical methods and the related numerical analysis for three representative phase-field models, namely the Allen-Cahn equation, the Cahn-Hilliard equation and the thin film models. The first part of this thesis is mainly concentrated on the stability analysis for these three models, with particular attention to the Allen-Chan equation. We have established three stability criterion, i.e., nonlinear energy stability, L∞-stability and L2-stability. As shared by most phase-field models, one of the intrinsic properties of the Allen- Cahn and the Cahn-Hilliard equations is that they satisfy a nonlinear stability re- lationship, usually expressed as a time-decreasing free energy functional. We have studied several stabilized temporal discretization for both the Allen-Cahn and the Cahn-Hilliard equations so that the relevant nonlinear energy stability can be pre- served. The corresponding temporal discretization schemes are linear and are of second-order accuracy. We also apply multi-step implicit-explicit methods to ap- proximate the Allen-Cahn equation. We demonstrate that by suitably choosing the parameters in multi-step implicit-explicit methods the nonlinear energy stability can be preserved. Apart from studying the energy stability for the Allen-Cahn equation, we also establish the numerical maximum principle for some fully discretized schemes. We further extend our analysis technique to the fractional-in-space Allen-Cahn equation. A more general Allen-Cahn-type equation with a nonlinear degenerate mobility and a logarithmic free energy is also considered. The third stability under investigation is the L2-stability. We prove that the con- tinuum Allen-Cahn equation satisfies a uniform Lp-stability. Furthermore, we show that both semi-discretized Fourier Galerkin and Fourier collocation methods can in- herit this stability for p = 2, i.e., L2-stability. Based on the established L2-stability, we accomplish the spectral convergence estimate for the Fourier Galerkin methods. We adopt the second-order Strang splitting schemes in the temporal direction with Fourier collocation methods to demonstrate the uniform L2-stability in the fully dis- cretized scheme. Another contribution of this thesis is to propose a p-adaptive spectral deferred correction methods for the long time simulations for all three models. We develop a high-order accurate and energy stable scheme to simulate the phase-field models by combining the semi-implicit spectral deferred correction method and first-order stabilized semi-implicit schemes. It is found that the accuracy improvement may affect the overall energy stability. To compromise the accuracy and stability, a local p- adaptive strategy is proposed to enhance the accuracy by sacrificing some local energy stability in an acceptable level. Numerical results demonstrate the high effectiveness of our proposed numerical strategy. Keywords: Phase-field models, Allen-Cahn equations, Cahn-Hilliard equations, thin film models, nonlinear energy stability, maximum principle, L2-stability, adaptive simulations, stabilized semi-implicit schemes, finite difference, Fourier spectral meth- ods, spectral deferred correction methods, convex splitting

We have a conjecture that “the precision of computed solutions for systems of linear equations is more closely related with componentwise condition number c(A) than normwise condition number κ(A). We conducted simulation experiments to verify this conjecture. A statistical tool, Hotelling-Williams T-Test is employed to check if difference between correlations is significant. Simulation results suggest that our conjecture is true for most of the well-known methods and matrix sizes. Keywords: condition numbers, simulation, correlation coefficients, Hotelling-Williams T-Test

A computer simulation program which models the operation of a British Columbia coast dimension sawmill has been developed in FORTRAN IV. The model represents the initial log breakdown by a double cut, multi-pass band headrig, cant breakdown by a bulledger and the further processing on two resaws, pony edger and the double end trimsaw. Simulation of the headrig and bulledger operation is event oriented, whereas the piece flow through the other processing units is updated with 1-minute intervals. Flowcharts describe the routines briefly. The principal types of data input are sawlog population characteristics, machine characteristics, buffer storage capacities, and product output constraints. Information about the model operation is collected during the simulation runs, and the printed output includes productivity in Mbfm per 8-hour shift, the time each saw was operating, idle, busy or blocked, the time the bulledger queue contained a given number of cants and histograms showing the queue length distribution in 10-piece classes for subsequent saws. Validation of the model plays an important part in system simulation. The approach has been to attempt a verification of the piece flow arriving at trimmer, #l and #2 resaw, ponyedger and greenchain. Although the productivity figures obtained from simulation correspond to those experienced by the mill, the piece flow could not be verified. Irregular log shape, not reflected in the sawlog population characteristics and leading to more manufacturing of slabs in the real system, is considered to be the principal factor contributing to this. Preferably, further modelling should lead to the development of one general assembly-system, which regards sawmills as a collection of interconnected components, with increased input and output flexibility. / Forestry, Faculty of / Graduate

An overview of the computer networks currently being developed is presented. Three types of network design are distinguished - packet switching, line switching and Newhall loops. Reference is made to several models developed during the design of these networks, but only those concerned with packet switching are described in detail. A gueueing model emerges as a feasible alternative to the more expensive simulation models. This model is developed to include the basic logic of the message switching centres (nodes) and used as the backbone to a heuristic procedure that considers limited capacity buffers and blocking at the nodes. Key words and phrases: Data transmission, computer nets, packet switching, switching centre, interactive computation, resource sharing, queueing network, Markovian queue, steady state. / Science, Faculty of / Computer Science, Department of / Graduate

The purpose of this study was to test the effects of teacher-made and pupil-made simulation games on student attitudes toward social studies. A sample of seventy grades four and five students was randomly assigned to a control group, a teacher-made-simulation treatment group or a pupil-made-simulation treatment group. The control treatment group was instructed through the analytic approach while the teacher-made-simulation treatment group was instructed through the use of simulation games developed by the researcher. In the pupil-made-simulation treatment, the students developed and played simulation games within the classroom. The same objectives and instructional data were employed in each treatment. The researcher developed this unit following the procedures utilized in recent curriculum development practice. The inquiry processes incorporated in this unit were adapted from the analytic and integrative modes of inquiry. The control treatment utilized primarily the analytic mode while the teacher-made and pupil-made-simulation treatments employed primarily the integrative mode. The researcher administered the three treatments consecutively with each treatment consisting of fourteen instructional periods. Student attitudes toward social studies were evaluated by means of a paired-comparison rating scale. A pre-test was administered five months prior to the study and a post-test was administered one week after the administration of each treatment. A modified paired comparison rating scale was given as a delayed post-test to the control and teacher-made-simulation treatment groups on the same day that the pupil-made-simulation treatment received its first post-test. The post-test mean scores for the three treatments were adjusted by an analysis of covariance in comparing group performance. Duncan's Multiple Range Test was used to determine the significance and order of differences between treatment group mean scores. The study revealed that students in the teacher-made and pupil-made-simulation treatments had significantly more favorable attitudes toward social studies than did the children in the control treatment. The teacher-made and pupi1-made- simulation treatments were found to be equally effective in influencing favorable student attitudes toward social studies. Conclusions and implications were drawn relevant to classroom practice and curriculum development. / Education, Faculty of / Graduate

Gaming-simulations (G-S) are those in which participants play roles, make decisions and receive feedback while interacting with a simulation model. This study used attitude change to measure of G-S effectiveness in exploring questions relating simulation design and effectiveness. To define participant attitudes and the content for a simulation, the organizational culture of a software engineering firm was studied using an ethnographic approach. Inconsistencies between the existing culture and expressed ideals were measured using an 40 item attitude questionnaire drawn from statements made during interviews. Simulation structure and participant cognitive style were factors hypothesized to influence identification with a simulation role. Role identification was hypothesized to influence attitude change. Two versions of the simulation were designed to produce differential role identification. Role identification was measured by having the simulation software ask players questions near the end of the eight hour simulation class. The Davis (1980) Empathy scale was used to measure cognitive style. The WINNING AT DESIGN AUTOMATION gaming-simulation was created to induce attitude change toward the ideals. The simulation is written in HyperCard. Each participant managed a department, allocating their time to tasks that earned points as they competed in teams. A control group of 42 employees and 97 of the 122 who played the simulation completed pre- and post-simulation questionnaires. There was significant attitude change for all treatment groups. The different versions of the simulation did generate stronger and weaker role identification as predicted. The Empathy scale did predict role identification. The treatment group with highest role identification did not have the greatest attitude change. Other factors influencing the linkage of role identification to attitude change are discussed.

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The competitive strategy used by a new firm may be the most important strategy it ever employs (Covin & Slevin, 1989; Ferrier, 2001). A well-chosen and executed firm strategy is essential for a firm to realize its potential competitive advantage (Porter, 1981). A firm‘s strategic intent and resulting competitive actions are especially important when firms are new and vulnerable as they strive to learn which strategic actions help them adapt to their rivals actions and to their environment (Stinchcombe, 1965). Further, the competitive actions that new firms choose to take with rival firms affects the overall competitive dynamics of their industry (Smith, Ferrier, and Ndofor, 2001). One way to explore how the competitive actions of new firms affect their future is to capture and examine their individual competitive moves and countermoves over time (Smith, Grimm, Gannon, & Chen, 1991). Red Queen competition is a particular form of competitive dynamics that is well-suited to explore these issues of new rival firms (Barnett, 2008). Barnett and Sorenson (2002) suggested that competition and learning reinforce one another as organizations develop, and this is what van Valen (1973) referred to as the ‗Red Queen.‘ This definition of the Red Queen led to the development of the concept of Red Queen competition and the Red Queen effect. The competitive strategies these new firms use to obtain resources as they adapt, in particular how these firms compete and or cooperate, are key competitive strategies that remain understudied to-date (Amit, Glosten, and Muller, 1990). I explore Red Queen competition, and the ensuing Red Queen Effect, in a complex environmental setting that represents a high technology ecosystem (Arned, 1996, 2010; Iansiti & Levien, 2004a, 2004b; Moore, 1993; Pierce, 2009). New firms in such an ecosystem represent a particularly salient combination of type of firm, firm lifecycle period, and firm environment to iii examine strategic actions since these firms comprise a significant portion of the high-growth and future of our global economy (Stangler, 2010). Further, due to their need to rapidly adapt in a complex ecosystem, these firms rely heavily on short-lived information resources for competitive advantage (Barney, 1991; Nelson and Winter, 1982; Omerzel, 2008). To place this research in context, I consider the moderating effects of key environmental ecosystem resource conditions (Dess & Beard, 1984; Miller & Friesen, 1983; Sharfman & Dean, 1991). Empirical studies to-date have yielded mixed results and left unanswered questions about the basic components and the effects of Red Queen competition. To address these issues I explore this literature in chapter one of the dissertation, and in chapter two I develop a theoretical model of Red Queen competition that draws on the available empirical and theoretical literature to-date. Due to the mixed finding from the empirical results, I develop a precise agent-based simulation model of Red Queen competition in chapter three to facilitate data collection. Using this data I test a series of hypotheses designed to explore the fundamentals of Red Queen competition, specifically how escalating competitive activity for resources among new firms impacts their survival and performance. In addition, the moderating effect of environmental changes on Red Queen competition is also tested to explore the affect of context on Red Queen competition. Chapter four explains the findings from these hypotheses, future research directions, implications and limitations from the research, and my concluding thoughts