Compaction

With Antonio Coniglio we established an analogy between glasses and granular packings at different densities as described in a paper in Physica A Vol.225, p.1-6 (1995). Then we studied a "frustrated percolation" model with Mario Nicodemi as published in Phys.Rev.E., Vol. 55, p.3962-3969 (1997) which reproduces the slow compaction dynamics under gravity measured in the Chicago experiments. This model also allowed to calculate the density profile and the force distribution inside the packing as published in Physica A, Vol.240, p.405-418 (1997) and the density fluctuations, its power-spectrum and its correlations as published in Phys.Rev.E, Vol.59, p.6830 (1999) also in agreement with experiments. The relation to magnetic systems is worked out in a paper in J. Phys. A, Vol.30, p.L379 (1997).

The figure shows a 2d system of particles compactified on the under vibrations. The colors distiguish local stresses when the packing is submitted to gravity. For more detail see our paper printed in the proceedings of the Enrico Fermi School CXXXIV (1996)

More adapted to packings is the model Tetris which we (Emanuele Cagliotti, Vittorio Loreto and Mario Nicodemi) introduced in a paper published in Phys.Rev.Lett. 79 ,1575-1578 (1997). This model also reproduces size segregation under vibration as seen in the paper published in Europhys. Lett. Vol. 43, 591-597 (1998). It is also particularly rewarding to study the internal avalanches of a packing when a particle at the bottom is removed using Tetris as done with Suprija Krishnamurty in the paper published in Phys. Rev. Lett., Vol.83, p.304-307 (1999). More details about the statistics of these avalanches are given in the paper published in Fractals, Vol. 7, p.51-58 (1999).

In the same collaboration with we also studied the concept of the cooperative length that determines the relaxation of glasses for the case of granular packings as discussed in our article in Physica A, Vol.265, p.311-318 (1999) and worked out the concept of geometric frustration as elucidated in the paper published in Physica A, Vol.257, p.419-423 (1998).

With Martin Wackenhut we are studying the compaction of polydisperse systems, in particular if the size distribution follows a power law. We defined a parking lot model suited to polydispersity and calculated its properties as published in an article in Phys. Rev. E Vol.68, 041303 (2003). The order by which the particles of different size are initially put into the system has enormous influence on the outcome. We also developped a generalization of the linked cell algorithm to improve the numerical algorithm. Here one has cells of different size according to the particles that must be covered and the search is performed using a quad-tree. An example can be seen for two dimensions in the figure at right.

Below we see a packing in three dimensions.