Advective-diffusive motion on large scales from small-scale dynamics with an internal symmetry

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Research units

  • Stockholm University
  • Royal Institute of Technology


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). 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.


Original languageEnglish
Article number062147
Pages (from-to)1-15
JournalPhysical Review E
Issue number6
Publication statusPublished - 30 Jun 2016
MoE publication typeA1 Journal article-refereed

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