Approach to equilibrium of particles diffusing on curved surfaces

We present a simple numerical analysis of the diffusion on a curved surface given by the equation φ(r)=0 in a finite domain D R3. The first non-vanishing eigenvalue of the Beltrami–Laplace operator with the reflecting boundary conditions is determined in our simulations for the P, D, G, S, S1 and I-WP, nodal periodic surfaces, where D is their respective cubic unit cell. We observe that the first eigenvalue for the surfaces of simple topology (P,D,G,I-WP) is smaller than for the surfaces of complex topology (S,S1).