Self-structuring of granular media under internal avalanching

We study the phenomenon of internal avalanching within the context of recen tly proposed "Tetris" lattice models for granular media. We define a recycl ing dynamics under which the system reaches a steady state which is self-st ructured, i.e., it shows a complex interplay between textured internal stru ctures and critical avalanche behavior. Furthermore, we develop a general m ean-field theory for this class of systems and discuss possible scenarios f or the breakdown of universality.