Granular systems display a fascinating range of properties and behaviors, some of which are reminiscent of flow phenomena well-known from fluid dynamics, while others are unique to matter in particulate form. This investigation has focused on two such attributes, one from each category: first, the tendency for confined granular materials to develop internal, circulatory flows when shaken, motions that bear a strong resemblance to laminar convection in a liquid heated from below; and second, the tendency for confined granular materials to spatially separate according to size when shaken (the BNE), rather than mix as in the case of ordinary fluids. The principal conclusions of this investigation are: