Mixing with piecewise isometries on a hemispherical shell

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


We introduce mixing with piecewise isometries (PWIs) on a hemispherical shell, which mimics features of mixing by cutting and shuffling in spherical shells half-filled with granular media. For each PWI, there is an inherent structure on the hemispherical shell known as the exceptional set E, and a particular subset of E, E+, provides insight into how the structure affects mixing. Computer simulations of PWIs are used to visualize mixing and approximations of E+ to demonstrate their connection. While initial conditions of unmixed materials add a layer of complexity, the inherent structure of E+ defines fundamental aspects of mixing by cutting and shuffling.

Original languageEnglish (US)
Article number073115
Issue number7
StatePublished - Jul 1 2016

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • Mathematical Physics


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