title: Advective-diffusive motion on large scales from small-scale dynamics with an internal symmetry.
abstract: We consider coupled diffusions in n-dimensional space and on a compact manifold and the resulting effective advective-diffusive motion on large scales in space. The effective drift (advection) and effective diffusion are determined as a solvability conditions in a multiscale analysis. As an example, we consider coupled diffusions in three-dimensional space and on the group manifold SO(3) of proper rotations, generalizing results obtained by H. Brenner [J. Colloid Interface Sci. 80, 548 (1981)JCISA50021-979710.1016/0021-9797(81)90214-9]. We show in detail how the analysis can be conveniently carried out using local charts and invariance arguments. As a further example, we consider coupled diffusions in two-dimensional complex space and on the group manifold SU(2). We show that although the local operators may be the same as for SO(3), due to the global nature of the solvability conditions the resulting diffusion will differ and generally be more isotropic.
authors.affiliation: NORDITA, Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden.
authors.forename: Raffaele
authors.initials: R
authors.lastname: Marino
authors.affiliation: Department of Computational Biology and Center for Quantum Materials, KTH-Royal Institute of Technology, AlbaNova University Center, SE-106 91 Stockholm, Sweden.
authors.forename: Erik
authors.initials: E
authors.lastname: Aurell