| This diploma thesis studies the application of computational mathematics to two different fields of research: tumor angiogenesis and Bose-Einstein condensates (BECs).;In Chapter 2, a minimal model for describing the effect of an angiogenic inhibitor upon tumor-induced angiogenesis is examined. Simulations of the model will make use of the Deterministic Cellular Automata technique developed by Dr. Sandy Anderson.;Chapter 3 examines steady states and their dynamics for four different scenarios related to Bose-Einstein condensates. The first two scenarios address the possibility of manipulating a condensate via the use of a laser in the form of either a localized inhomogeneity or optical lattice. A system of linearly coupled, discrete nonlinear Schrodinger equations is the subject of the third scenario, which can be used to describe the behavior of two different BECs contained within a strong optical lattice and subject to an external microwave or radio-frequency field. The final scenario expands upon previous research into radial BEC solutions by including numerical simulations achieved through the use of spectral methods.;Both of these problems provide interesting systems for study and draw upon different aspects of computational mathematics, along with other areas of analytical mathematics, including bifurcation and perturbation theory. |
