# Density waves and sand swimmers

##
Spontaneously unbounded fluctuations in the density or the forces
against the wall can appear when a granular medium flows
through pipes or
hoppers.

##
With Gongwen Peng we formulated a cellular automaton which
predicted density waves in pipe flow and a background
power spectrum following a power-law with exponent 4/3. The first
paper was published in Phys. Rev. E. 49 (1994) R1796.
A longer paper showing that the power law spectrum is always
present with periodic boundary conditions but only appears at a
certain flux in the open pipe was
published in Phys. Rev. E 51 (1995)
1745-1756. A clear experimental verifications came several years later
by the group of Matsushita ().

Simulations of outflowing hoppers as performed with Gerald Ristow
show that the fluctuations in density have a power spectrum of
1/f noise (see paper in Phys. Rev. 50, R5 (1994)).
The forces acting against the walls also follow
a power law in their spectrum if the opening angle is not too large
(see
paper in Physica A 213, 474-481 (1995)). You can also see how
the pipe in the figure
clogs .

## A particularly interesting type of waves are those of small
amplitude namely
sound waves.

## In a collaboration with the group of
Jean Pierre Hulin at the FAST in
Orsay we studied density waves of glass beads flowing through
a vertical pipe. With Tareck Raafat we analyzed the time series
for different humidities and fluxes and found various phases as
described in a
paper
published in Phys. Rev. E, Vol. 53, 4345-4350 (1996).
Pressure measurements are reported in the
paper
published in J. Fluid Mech. Vol. 458, 317-345 (2002).

A technical implementation of the above phenomenon is realized in
pneumatic transport. In a DFG joint collaboration with Prof. Karl Sommer
of the chemical engineering department at the Technical University of Munich
we studied with
Martin Strauss in detail plug motion for
vertical pipes as seen in this
movie
and as discussed in a
preprint
and compared it to the results from experiments by Gerhard Niederreiter
in a
proceedings for PARTEC 2004. We also studied horizontal pipe flow
as seen in this
movie
and presented in our recent
preprint .

## With Takashi Shimada, Troy Shinbrot and Dirk Kadau we investigated
swimming inside sand as it is realized for instance buy the sand skink.
We introduced a push-me-pull-you mechanism of two disks connected by
a spring and calculated its velocity and energy consumption as function
of its geometry and frequency as
published in Phys.Rev.E Vol. 80, p.020301 (2009) and commented in
News and Views of Nature Physics
Vol.5, p.709 (2009).