| Modeling vesicle dynamics involves a complicated moving boundary problem where fluids, thermal fluctuations, and vesicle morphology are intimately coupled. In this thesis, we study the dynamics of a two-dimensional membrane in linear viscous flows. 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 flows. 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 effects of thermal fluctuations in vesicle dynamics. Comparing with the deterministic results, thermal fluctuation 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 find that for an elongated vesicle with large excess arc length, the inhomogeneous bending introduces nontrivial asymmetric wrinkling and buckling dynamics. |
