Abstract
Mixing due to cutting-and-shuffling is studied at a fundamental level using 2D mappings known as Piecewise Isometries (PWI) which can create beautiful mixing patterns. The PWI studied here splits a hemispherical shell (HS) into four curved triangular pieces that are rearranged to make a shuffled HS. Applying the PWI repeatedly (1, 20, and 20,000 times) to an initial condition (left) reveals circular regions devoid of mixing and regions that appear well-mixed (gray), the size of which determine how well the HS is mixed. PWI operations on initial conditions like those shown require highly parallel computation on a GPU to allow adequate repetition to resolve mixing patterns. The behavior of PWIs can be used to design efficient mixing systems. Funded by NSF CMMI 1435065.
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