%0 Book Section %1 statphys23_0965 %A Schwarz, J.M. %A Silbert, L.E. %A O'hern, C.S. %A Xu, N. %A Chayes, L. %A Liu, A.J. %A Nagel, S.R. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K bootstrap glass granular materials mixed packings percolation phase random statphys23 topic-2 transition %T The mixed nature of the jamming transition of frictionless granular packings %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=965 %X I will present numerical and theoretical results that suggest that the physics of the glass transition, the physics of granular materials, and the mathematics of sphere packings are related near the density commonly called random close-packing. We have studied zero-temperature packings of soft repulsive, frictionless spheres, and find evidence of a transition from an unjammed state to a jammed one (i.e. a state with a nonzero shear modulus) with increasing particle density. Our results suggest that this point has characteristics of both first and second-order phase transitions: there is a discontinuity in the number of interacting neighbors at the transition, but there is also a diverging length scale. I will suggest that aspects of this transition can be understood by analogy to a correlated percolation model, namely k-core or bootstrap percolation, that can be solved exactly in the mean-field limit. The exponents and discontinuity that we find at the jamming transition are very close to those for the mean-field k-core percolation transition. Moreover, several models that have been proposed for the glass transition also exhibit the same exponents and a discontinuity in the mean-field approximation. This is the first quantitative hint that the jamming of granular materials may be related to the glass transition.

@incollection{statphys23_0965, abstract = {I will present numerical and theoretical results that suggest that the physics of the glass transition, the physics of granular materials, and the mathematics of sphere packings are related near the density commonly called random close-packing. We have studied zero-temperature packings of soft repulsive, frictionless spheres, and find evidence of a transition from an unjammed state to a jammed one (i.e. a state with a nonzero shear modulus) with increasing particle density. Our results suggest that this point has characteristics of both first and second-order phase transitions: there is a discontinuity in the number of interacting neighbors at the transition, but there is also a diverging length scale. I will suggest that aspects of this transition can be understood by analogy to a correlated percolation model, namely k-core or bootstrap percolation, that can be solved exactly in the mean-field limit. The exponents and discontinuity that we find at the jamming transition are very close to those for the mean-field k-core percolation transition. Moreover, several models that have been proposed for the glass transition also exhibit the same exponents and a discontinuity in the mean-field approximation. This is the first quantitative hint that the jamming of granular materials may be related to the glass transition.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Schwarz, J.M. and Silbert, L.E. and O'hern, C.S. and Xu, N. and Chayes, L. and Liu, A.J. and Nagel, S.R.}, biburl = {https://www.bibsonomy.org/bibtex/2d8da5d5c25b966ca80d921b6c67de755/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {7f7a99099abea3bc84d1a92c8a1e3366}, intrahash = {d8da5d5c25b966ca80d921b6c67de755}, keywords = {bootstrap glass granular materials mixed packings percolation phase random statphys23 topic-2 transition}, month = {9-13 July}, timestamp = {2007-06-20T10:16:35.000+0200}, title = {The mixed nature of the jamming transition of frictionless granular packings}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=965}, year = 2007 }