A simple dynamical model of two-dimensional vesicles

Two-dimensional vesicles are modelled as pressurized self-intersecting rings. The fluctuating motion of the bounding walls of the vesicle, when it is subjected to the random collisions of fluid molecules, is treated along the lines suggested by Rouse (1953) in his study of dilute polymer solutions. Within the model, exact solutions of the dynamical equation governing the probability distribution of shapes, when expressed in an appropriate set of normal coordinates, is obtained. Numerical simulations of the dynamical evolution of the distribution of the principal components of the square of the radius of gyration are also presented.