Active matter on Riemannian manifolds. Issue 48 (29th November 2018) - Apaza, Leonardo; Sandoval, Mario
Abstract : Diffusion of active Brownian particles moving on any Riemannian 2-manifold is analytically characterized at both long and short times. Abstract : We formulate the dynamics of overdamped Brownian active particles (swimmers) moving on any Riemannian 2-manifold. To characterize such dynamics at short times, an analytical expression for the variance of swimmers diffusing on any Riemmanian 2-manifold is derived. To show the generality of the present work, we apply the latter dynamics to swimmers moving on the surface of a spheroid and a torus, and offer analytical expressions for both their long-time variances and steady angular marginal probability density functions. Finally, Brownian dynamics simulations are used to validate our theoretical findings.