Figure 2
From: Long range correlations and slow time scales in a boundary driven granular model
Sketch of the model and relation with higher dimensional systems. On the left we suggest a hypothetical 2D dense granular system where particles are roughly located on the vertices of a regular lattice. A possible mapping from the 2D to the 1D system involves replacing the mean horizontal velocity on the ith layer of the 2D system and replacing it with the \(v_i\) of the 1D system. The dynamics in the vertical direction is neglected, an approximation which is justified by the presence of the vertical confinement, while the periodic boundary conditions (indicated by the dotted lines) are representative of a ‘free’ direction in which the grains can flow without obstacles. This can be realized experimentally, for instance, in a 3D cylindrical geometry, where the velocity of grains in the tangential direction (with respect to the central axis of the cylinder) constitute the horizontal velocities in the putative 2D system sketched here, see for instance8,9. Red grains are in direct contact with the external source of energy coming from the boundaries (\(\gamma _b\), \(T_{1(L)}\)) while the green ones are in contact with the bulk bath, which is switched off in the NHHP.
