Thesis (Ph.D) - University of Queensland, 2006. / Includes bibliography.

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

Dynamical systems theory and bifurcation are used to analyze some simple models of nutrient limited phytoplankton growth. The models are restricted to batch culture type conditions allowing the use of a mass balance constraint. Two popular models from the literature, the Michaelis-Menton-Monod or M³ model, and the Droop internal nutrient model are analyzed and found to yield unreasonable predictions for certain ambient environmental conditions. The M³ model predicts that the population size becomes unbounded at equilibrium for certain values of the parameters. The Droop model predicts that the amount of nutrient left over during a nutrient uptake experiment would be very small, regardless of how large the initial external nutrient concentration is. Numerical comparisons of data with the predictions from both models demonstrate that the conditions for unreasonable behavior could occur both in cultures and in natural aquatic ecosystems. In the predicted nutrient concentration at uptake equilibrium is several orders of magnitude off. Two specific enzyme mechanisms for nutrient transport are proposed as alternatives to current models. The models differ in the assumptions made about how the backflow reaction with the enzymes responsible for transport proceeds. A nutrient uptake equation for each model is derived directly from the enzyme kinetics, while the equation for growth in population size is taken from the Droop model. The dynamics of both models are analyzed, treating the nutrient uptake equations with the singular perturbation assumption. The simple model predicts that the external nutrient concentration at uptake equilibrium should be a constant percentage of the internal concentration, while in the inhibition uptake model, the population size could exhibit relaxation type oscillations during the batch culture steady state. Qualitative evidence supporting both models is discussed. Applications of these models to water quality simulation and implications for theoretical ecology are discussed.

by Luk Wai Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 44-45). / ABSTRACT --- p.i / ACKNOWLEDGMENTS --- p.ii / Chapter CHAPTER 1. --- INTRODUCTION --- p.1 / Chapter CHAPTER 2. --- DRAWBACKS OF CLASSICAL THEORY --- p.4 / Chapter 2.1 --- Review of Sequential Iterative Methods --- p.4 / Chapter 2.2 --- Visualization Techniques --- p.8 / Chapter 2.3 --- Review of Deflation --- p.10 / Chapter CHAPTER 3. --- THE IMPROVEMENT OF THE ABERTH METHOD --- p.11 / Chapter 3.1 --- The Durand-Kerner method and the Aberth method --- p.11 / Chapter 3.2 --- The generalized Aberth method --- p.13 / Chapter 3.3 --- The modified Aberth Method for multiple-zero --- p.13 / Chapter 3.4 --- Choosing the initial approximations --- p.15 / Chapter 3.5 --- Multiplicity estimation --- p.16 / Chapter CHAPTER 4. --- THE HIGHER-ORDER ITERATIVE METHODS --- p.18 / Chapter 4.1 --- Introduction --- p.18 / Chapter 4.2 --- Convergence analysis --- p.20 / Chapter 4.3 --- Numerical Results --- p.28 / Chapter CHAPTER 5. --- PARALLEL DEFLATION --- p.32 / Chapter 5.1 --- The Algorithm --- p.32 / Chapter 5.2 --- The Problem of Zero Component --- p.34 / Chapter 5.3 --- The Problem of Round-off Error --- p.35 / Chapter CHAPTER 6. --- HOMOTOPY ALGORITHM --- p.36 / Chapter 6.1 --- Introduction --- p.36 / Chapter 6.2 --- Choosing Q(z) --- p.37 / Chapter 6.3 --- The arclength continuation method --- p.38 / Chapter 6.4 --- The bifurcation problem --- p.40 / Chapter 6.5 --- The suggested improvement --- p.41 / Chapter CHAPTER 7. --- CONCLUSION --- p.42 / REFERENCES --- p.44 / APPENDIX A. PROGRAM LISTING --- p.A-l / APPENDIX B. COLOR PLATES --- p.B-l

by Kwok, Wong-chuen Tony. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves [85-86]). / Acknowledgement / Abstract / Chapter I --- Laguerre's Method in Polynomial Zero-finding / Chapter 1 --- Background --- p.1 / Chapter 2 --- Introduction and Problems of Laguerre´ةs Method --- p.3 / Chapter 2.1 --- Laguerre´ةs Method in Symmetrie-Cluster Problem / Chapter 2.2 --- Cyclic Behaviour / Chapter 2.3 --- Supercluster Problem / Chapter 3 --- Proposed Enhancement to Laguerre 's Method --- p.9 / Chapter 3.1 --- Analysis of Adding a Zero or Pole / Chapter 3.2 --- Proposed Algorithm / Chapter 4 --- Conclusion --- p.17 / Chapter II --- Homotopy Methods applied to Polynomial Zero-finding / Chapter 1 --- Introduction --- p.18 / Chapter 2 --- Overcoming Bifurcation --- p.22 / Chapter 3 --- Comparison of Homotopy Algorithms --- p.27 / Chapter 4 --- Conclusion --- p.29 / Appendices / Chapter I --- Laguerre's Method in Polynomial Zero-finding / Chapter 0 --- Naming of Testing Polynomials / Chapter 1 --- Finding All Zeros using Proposed Laguerre's Method / Chapter 2 --- Experiments: Selected Pictures of Comparison of Proposed Strategy with Other Strategy / Chapter 3 --- Experiments: Tables of Comparison of Proposed Strategy with Other Strategy / Chapter 4 --- Distance Colorations and Target Colorations / Chapter II --- Homotopy Methods applied to Polynomial Zero-finding / Chapter 1 --- Comparison of Algorithms using Homotopy Method / Chapter 2 --- Experiments: Selected Pictorial Comparison / Chapter III --- An Example Demonstrating Effect of Round-off Errors References

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published_or_final_version / Civil and Structural Engineering / Doctoral / Doctor of Philosophy

Thesis (Ph.D.)--Tufts University, 1992. / Submitted to the Dept. of Mechanical Engineering. Adviser: Vincent P. Manno. Includes bibliographical references (leaves 183-193). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph. D.)--Missouri University of Science and Technology, 2008. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed August 21, 2008) Includes bibliographical references.