  Remarkably persistent mixing and non-mixing regions (islands) are observed to
coexist in a three-dimensional dynamical system where randomness is expected.
The track of an x-ray opaque particle in a spherical shell half-filled with dry
non-cohesive particles and periodically rotated about two axes reveals
interspersed structures that are spatially complex and vary non-trivially with
the rotation angles. The geometric skeleton of the structures forms from the
subtle interplay between fluid-like mixing by stretching-and-folding, and
solids mixing by cutting-and-shuffling, which is described by the mathematics
of piecewise isometries. In the physical system, larger islands predicted by
the cutting-and-shuffling model alone can persist despite the presence of
stretching-and-folding flows and particle-collision-driven diffusion, while
predicted smaller islands are not observed. By uncovering the synergy of
simultaneous fluid and solid mixing, we point the way to a more fundamental
understanding of advection driven mixing in materials with both solid and
flowing regions.
