For simplicity, below we suppose the characteristic frequency, w , of external driving is fixed, and actually in typical experiments we are interested in, it plays a minor role with respect to G ex . Material parameters such as restitution, friction coefficients, presence of moisture, etc., are also to be usually considered, but they generally do not affect the overall behaviours. Furthermore, they are new important applications of the statistical mechanics to powders. The crucial ingredient of the models is the presence of geometric constraints on the motion of the grains, thus, they have been called Frustrated Lattice Gases. The models consist of a system of elongated grains which move on a lattice.
Grains are subject to gravity and, eventually, to shaking.
Two nearest neighbour sites can be both occupied only if the particles do not overlap. A real granular system may contain more disorder due to the presence of a wider grain shape distribution or to the absence of a regular underlying lattice. The phase diagram of the Tetris Hamiltonian corresponds to the usual antiferromagnetic Ising model with dilution. The Hamiltonian of the IFLG exhibits richer behaviours. This law has proved to be satisfied very well by relaxation data in the IFLG model, which can be excellently rescaled with experimental data.