Tetris Model

Under this denomination falls a new class of lattice models whose basic ingredient is the geometrical frustration. The models are defined on a lattice with particles of randomly chosen shapes and sizes. The only constraint in the system is that particles cannot overlap. The interactions are hence not spatially quenched  but determined in a self-consistent way by local particle configurations.
Despite their seeming simplicity, these systems present a very rich response to perturbations: slow-relaxations, time-scale separations, spatial structures, memory, etc..

Some nice animations:

(Note that the time grows exponentially in during the animations: (simulated time) ~ exp(animation time))

Compaction: In this animation you see the dynamical evolution of the Tetris model. Each time step is the results of a tapping dynamics.

Coarsening: In this animation you see the dynamical evolution of the same system resolved now in the two possible type of domains.

Persistence: In this animation you see the persistent sites, i.e. the particles that neved moved during the dynamics up to the current time (in red) and the voids never occupied by a particle up to the current time (in black).

Compaction and Clusters syncronized
 

Compaction, Clusters and Persistent sites syncronized
 

Here there is a huge simulation (60k particles) with the corresponding domain resolved image

References

E. Caglioti, V. Loreto, H.J. Herrmann, and M. Nicodemi
A ''Tetris-like'' Model for the Compaction of Dry Granular Media,
Phys. Rev. Lett. 79, 1575 (1997).
 

E. Caglioti, A. Coniglio, H.J. Herrmann, V. Loreto, and M. Nicodemi
Cooperative Length Approach for Granular Media,
Physica A 265, 311 (1999).
 

E. Caglioti, A. Coniglio, H.J. Herrmann, V. Loreto, and M. Nicodemi
Segregation of granular mixtures in presence of compaction,
Europhys. Lett. 43, 591 (1998).
 

S. Khrishnamurthy, V. Loreto, H.J. Herrmann and M. Nicodemi
Internal avalanches in granular packings,
Fractals 7, No. 1 p.51-58 (1999).

S. Khrishnamurthy, V. Loreto, H.J. Herrmann, S.S. Manna and S. Roux
Self-Structuring of Granular Media under Internal Avalanches,
Phys. Rev. Lett. 83, 304 (1999).

S. Khrishnamurthy, V. Loreto and S. Roux
Bubbling and large-scale structures in avalanche dynamics,
Phys. Rev. Lett. 84, 1039 (2000).

M. Piccioni, V. Loreto and Stéphane Roux
Criticality of the ``critical state'' of granular media: Dilatancy angle in the Tetris model,
Phys. Rev. E 61, 2813 (2000).

A. Barrat and V. Loreto
Response properties in a model for granular matter,
J. Phys. A: Math. and Gen. 33, 4401-4426 (2000).

A. Baldassarri, S. Krishnamurthy, V. Loreto and S. Roux
Coarsening and Slow-Dynamics in Granular Compaction,
Phys. Rev. Lett.(2001).

A. Barrat, J. Kurchan, V. Loreto and M. Sellitto
Edwards Ensembles for Powders and Glasses,
Phys. Rev. Lett. 85, 5034 (2000).

A. Barrat, J. Kurchan, V. Loreto and M. Sellitto
Edwards' measures: a thermodynamic construction for dense granular media and glasses,
Phys. Rev. E 63, 051301-1 (2001).

A. Barrat and V. Loreto
Memory in aged granular media,
Europhys. Letters. 53, 297 (2001).