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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 original theory and its following developments have introduced “thermodynamic” parameters, such as compactivity and angoricity, which play the same role that usual thermodynamic parameters such as temperature and pressure play in classical statistical mechanics.
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 20th birthday of this pioneer work.
Highlights of the workshop
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
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 “” 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)