Algebras and their bimodules form a 2-category in which 2-morphisms are certain zero-th Hochschild cohomology groups. When we derive this structure (i.e., use Hochschild cochains instead of HH^0 for 2-morphisms), we find that algebras form a category in dg cocategories. The Hochschild-Kostant-Rosenberg theorem and non-commutative calculus give a rich algebraic...
Mixing of granular materials is an important engineering process, and a very complex problem. In this thesis, I use granular mixing in a half-full biaxial spherical tumbler (BST), a spherical container that rotates sequentially about two orthogonal axes, to motivate the study of mixing with piecewise isometries (PWIs), a rich...