Counting and Characterizing the Catchment Regions of Jammed Packings

The potential energy landscapes of granular and amorphous systems are complex, high dimensional, and vast. A direct characterization of these complex energy landscapes would reveal the configurational entropy as well as provide an understanding for the origin of the commonalities that link all amorphous configurations. Because the landscape is far too large to exhaustively sample we instead characterize it by a direct measurement of the catchment regions found within randomly chosen small volumes of the landscape. By exhaustively searching these volumes, we are able to report on the size, shape, and structure of the catchment regions contained therein. From these measurements we estimate the configurational entropy (and the statistical complexity) of the energy minima and discuss its relation to the Edward's conjecture.