Modeling vesicle dynamics involves a complicated moving boundary problem where uids, thermal uctuations, and vesicle morphology are intimately... Show moreModeling vesicle dynamics involves a complicated moving boundary problem where uids, thermal uctuations, and vesicle morphology are intimately coupled. In this thesis, we study the dynamics of a two-dimensional membrane in linear viscous ows. In the asymptotic analysis section, we derive deterministic and stochastic equations describing the motion of a slightly perturbed membrane interface. Using a 2nd order Runge-Kutta method, we solve these equations numerically, and explain the formation and development of wrinkling patterns. We then develop a boundary integral method and an immersed boundary method for simulating the nonlinear wrinkling dynamics of a homogenous vesicle in viscous ows. The nonlinear results agree with the asymptotic theory for a nearly circular vesicle, and also agree with experimental results for an elongated vesicle. Using a stochastic immersed boundary method, we investigate the e ects of thermal uctuations in vesicle dynamics. Comparing with the deterministic results, thermal uctuation can lead to the development of odd modes and asymmetric wrinkles. Finally, we investigate the nonlinear wrinkling dynamics of a multi-component vesicle. The model includes a 4th order Cahn-Hilliard type equation describing the phase transitions on the vesicle surface. We nd that for an elongated vesicle with large excess arc length, the inhomogeneous bending introduces nontrivial asymmetric wrinkling and buckling dynamics. Ph.D. in Applied Mathematics, December 2014 Show less
