Predicting mixing via resonances: Application to spherical piecewise isometries

Lachlan D. Smith*, Paul P. Park, Paul B. Umbanhowar, Julio M. Ottino, Richard M. Lueptow

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We present an analytic method to find the areas of nonmixing regions in orientation-preserving spherical piecewise isometries (PWIs), and apply it to determine the mixing efficacy of a class of spherical PWIs derived from granular flow in a biaxial tumbler. We show that mixing efficacy has a complex distribution across the protocol space, with local minima in mixing efficacy, termed resonances, that can be determined analytically. These resonances are caused by the interaction of two mode-locking-like phenomena.

Original languageEnglish (US)
Article number062210
JournalPhysical Review E
Issue number6
StatePublished - Jun 13 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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