# 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.