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Topic

Mathematical modeling and numerical methods in three types of physical systems

Department of Physics and Astronomy

Date & location

• Tuesday, July 29, 2025
• 10:00 A.M.
• Virtual Defence

Examining Committee

Supervisory Committee

• Dr. Thomas Baker, Department of Physics and Astronomy, ßÉßɱ¬ÁÏ (Supervisor)
• Dr. Kristan Jensen, Department of Physics and Astronomy, UVic (Member)
• Dr. Lucinda Leonard, School of Earth and Ocean Sciences, UVic (Outside Member)

External Examiner

• Dr. Rachel Wortis, Department of Physics and Astronomy, Trent University

Chair of Oral Examination

• Dr. Sudhakar Ganti, Department of Computer Science, UVic

Abstract

Through this thesis three physical systems are explored through a variety of methods. First, the ice thickness of Comox and Kokanee glaciers are modeled via relative gravity measurements. Efficacy of the modeling method is contrasted to more direct techniques, showing it to be largely viable. A first ever average ice thickness is therefore provided for Comox glacier at 42 ± 4 m. At the opposite scale, a 1D quantum system is constructed and explored through random matrices. The 1 dimensional Anderson model is considered here, exploring the effects of correlated disorder on localization, scaling, and the overall behavior in contrast to similar systems with uniform disorder. While some differences are seen in scaling and some questions remain unanswered, the behavior largely coincides with expectations. Finally, numerical methods are explored for 2 dimensional classical spin systems via tensor network renormalization algorithms. With the goal of eventually contrasting all known algorithms to date, how tensor networks are constructed, how they are represented, and a summary of the algorithms coded to date are provided. This thesis therefore provides not only new results across several areas of physics, but also serves as a set of short introductions into a variety of different topics.