title: Mixing with piecewise isometries on a hemispherical shell.
abstract: 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.
authors.affiliation: Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
authors.forename: Paul P
authors.initials: PP
authors.lastname: Park
authors.affiliation: Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA.
authors.forename: Paul B
authors.initials: PB
authors.lastname: Umbanhowar
authors.affiliation: Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA.
authors.forename: Julio M
authors.initials: JM
authors.lastname: Ottino
authors.affiliation: Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA.
authors.forename: Richard M
authors.initials: RM
authors.lastname: Lueptow