Vesicles in biology are closed forms of membranes. The dimensions of vesicles can vary in terms of surface area and enclosed volume. Examples... Show moreVesicles in biology are closed forms of membranes. The dimensions of vesicles can vary in terms of surface area and enclosed volume. Examples range from small organelles to large cell bodies which all play a variety of resource transportation roles in biological systems. Research from the fields of chemistry and physics helps mathematical modeling by providing the mechanisms behind certain observed morphologies. Mathematical models and methods for simulating vesicle dynamics have produced accurate numerical solutions to verify experimental data and can be used to design new experiments that lead to more discoveries. The most researched case has been a single vesicle under shear flow. However, recent numerical and experimental results consider extensional flows on a single vesicle and hydrodynamic interactions among multiple vesicles. This thesis extends work on hydrodynamic interactions between vesicles in viscous fluid. We investigate numerically cases with multiple vesicles relaxing in asymmetrical configurations, time-dependent flow with more oscillation, and stochastic dynamics. Subjecting vesicles to these various cases reveals sensitivity to initial conditions such as distance and relative orientation. The effects from adding more vesicles are: increased time before equilibrium for the relaxation tests, and distributive wrinkling dynamics for the extensional flow tests. In stochastic cases, there are similar wrinkling distributions. However, initial conditions like distance and orientation have less important effects when competing with influence from thermal fluctuations. Additionally, in the presence of other vesicles under extensional flow, a vesicle may change the number and amplitude of wrinkles it would have experienced alone. M.S. in Applied Mathematics, July 2015 Show less
