Simulations of Flexible Manifolds

Monte Carlo simulations of flexible two-dimensional model membranes embedded in three space dimensions are reported. We explain in detail the techniques how to simulate fluid open membranes and fluid closed membranes (vesicles). It is shown that polymerized open membranes are rough and flat. Accordingly, the two larger components of the inertia tensor are proportional to the number of monomers of the surface, λ3 ≈ λ2 ∼ N, whereas the smallest λ1 ∼ N 0.65. Polymerized vesicles are isotropic and their mean square radius of gyration is R 2 ∼ λ k ∼ N. In contrast, fluid membranes and vesicles exhibit crumpled shapes with λ k ∼ N 0.8 for k = 1,2,3. A monomer on a fluid surface exhibits a time-dependent mean squared displacement of r 2 (t) ∼ t 0.8.