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A generalized magnetically controlled ballistic rain-like deposition (MBD) model of granular piles has been numerically investigated in 2D. The grains are taken to be elongated disks whence characterized by a two-state scalar degree of freedom, called "nip", their interaction being described through a Hamiltonian. The results are discussed in order to search for the effect of nip flip (or grain rotation from vertical to horizontal and conversely) probability in building a granular pile. The characteristics of creation of + (or -) nip's clusters and clusters of holes (missing nips) are analyzed. Two different cluster-mass regimes have been identified, through the cluster-mass distribution function which can be exponential or have a power law form depending on whether the nip flip (or grain rotation) probability is large or small. Analytical forms of the exponent are empirically found in terms of the Hamiltonian parameters.

We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Our simulation results show that the (Abelian) BTW sandpile model, the (non-Abelian) Zhang model, and the ("Abelian") Manna model possesses different "weak chaos" exponents, so they may belong to different universality classes. Finally, we show that getting off the critical point destroys this behavior in these models.

We describe a lattice model for intermittent flow in granular materials. This model includes degrees of freedom, related to lattice grain orientations, that are additional to those associated with the coupled dynamics of columns of lattice grains. We have explored the development of granular structures in model piles and shown that the surface dynamics of lattice grains is strongly linked to relaxations of granular structures in the pile. The coupling is shown to lead to two distinct avalanche morphologies in model piles that have been disturbed from their steady state. The change of behaviour is explained in terms of the statistical properties of surface instabilities.