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## Statistical mechanics of static granular media |

The large number of particles in granular systems
makes a statistical treatment very tempting. Classical statistical mechanics is
based on the existence of a distribution that is left invariant by the dynamics
(e.g., the microcanonical ensemble), and then assume
that this distribution will be reached by the system, under suitable conditions
of ‘‘ergodicity.’’ Unfortunately,
because energy of granular systems is lost through internal friction and
through dissipative collisions, and eventually gained by a nonthermal
forcing such as tapping or shearing, the dynamical equations do not leave the microcanonical or any other known ensemble invariant. Can
one construct another statistical theory for compact, slowly moving powders and
grains? Almost 20 years ago, Edwards and coworkers
proposed a possible step in this direction, raising the fascinating perspective
that such systems have a statistical mechanics of their own, different from
that of Maxwell, Boltzmann, and Gibbs, allowing us to have some information
while still neglecting dynamic details. The focus of the theory is on granular
systems in static (jammed) configurations. The aim of this workshop was to explore the prospects
and boundaries of a statistical mechanics approach to granular media in the
spirit first laid down by Edwards and coworkers in
their seminal papers from 1989. This was also a unique occasion to celebrate
the 20
The workshop had a high attendance. There were 59
registered participants, and most of them were present the whole week. Nearly
all the prominent scientists in the field had agreed to participate, with a
surprising low number of cancellations – only 1 invited speaker finally in the
end could not come, which is a good measure of the perceived importance of the
workshop in the community. During the workshop, talks and discussions have been
organized around four themes: •
Force space Configurational
space Exploring the phase space, ergodicity What physics do granular temperatures describe? The level and intensity of scientific discussion was
extremely high while remaining very collegial and accessible to PhD students
and Postdocs. This was made possible by the presence
of world-leading experts in all the fields covered by the workshop, some well
known for their clarity and deepness of thoughts. Following a
format common in the economic community, and experimented with success last
year by the “Dynamical heterogeneities in glasses, colloids
and granular media”
workshop (Lorentzcenter, Leiden, NL, august 25 –
September 5, 2009), the workshop has been organized with long talks (40mn),
followed by a commentary of a “discussant” (20mn) and by an open discussion
(20mn). The goal of the discussant was that of putting the previous talk in a
general perspective, commenting on relations with other works, open questions, weak points. We selected the speaker-discussant combinations
well before the beginning of the workshop, and asked each speaker to provide
relevant papers and a preliminary presentation to his discussant. This format most frequently led to rich discussions
and animated debates, lasting the whole allocated time. It was indubitably a
success. The format could be possibly improved by reducing to 35mn the length
of the invited talks. Particular care should be used when selecting the
speaker-discussant combinations, in order to promote an interesting discussion
and not one which is too technical. All the participants had the possibility to present
their ideas and results during two poster sessions and a poster announcement
session. Following requests from most of the audience, we also organized two
unplanned topical seminars, one led by Prof. H. Makse,
and one led by Prof. B. Chakraborty.
Among the
outcomes of the workshop, there is the identification of emerging areas of
investigation. Among the others, we mention the following: 1) The density of state of granular packing: from very
loose packings to the ideal glass Particular attention has been given to the theoretical/experimental
measure of the “granular entropy”. How it is possible to determine the number
of jammed states at any given value of the density? What is the relation
between the granular entropy and special values of the density such as
random loose and random close packings? 2) What can we
learn and measure from fluctuations? The relation between the fluctuations (mostly volume fluctuations) and
thermodynamic parameters introduced in the statistical mechanics of granular
system has been discussed. Particularly, the measure of the fluctuations could
provide a way to understand whether there is a kind of zeroth
law of the thermodynamics for granular systems. 3) Characterisation of the structure: towards the
determination of the volume function The determination of the volume function emerged as debated and open
question in the development of the statistical mechanics of powders. At the
hearth of this problem there the fundamental issue of the identification of the
degree of freedom of the system. Possibilities include degrees of freedom
determined geometrically, such as Voronoi cells, or
relying on the structure and intensity of the contact forces between grains. A important open question regards the real independence of
the proposed degrees of freedom. The organizers also plan to organize another workshop
on the same subject in 2011 or 2012. Overall, the workshop surely stimulated new ideas and
collaborations among the participants, especially among the youngest ones.
We would like
to thanks the Lorentz Center for providing excellent
facilities and support, and the extremely helpful support of Mrs. Corrie Kuster. Besides grant from the workshop budget of the
Lorentz Center, the workshop was generously supported
by the Max Planck Institute, the Lorentz Fund and the European Physical
Society. Massimo Pica Ciamarra (Napoli, Italy)
Patrick Richard (Rennes, France) Matthias Schröter (Goettingen, Germany) Brian Tighe (Leiden,
Netherlands) [Back] |