Physics Colloquium: "A Phase Diagram for Jammed Matter"

Wed., Sept. 10, 2008  Colloquium MR418N 4:00 pm  

Prof. Hernan Makse, CCNY Levich Institute and Physics Department

"A Phase Diagram for Jammed Matter"

Abstract: The problem of finding the most efficient way to pack
spheres (like oranges) has an illustrious history, dating back to the crystalline
arrays conjectured by Kepler in 1611 to the random geometries explored by
Bernal in the 60's. This problem is as much of interest to the mathematician's
pencil as it is to the granular processing industry all the way to the
fruit packing in every corner grocery.  There are presently numerous
experiments showing that the loosest way to pack spheres gives a
density of ~55% (named random loose packings, RLP) while filling all the
loose voids results in a maximum density of  63-64% (named random close
packings, RCP).  While those values seem robustly true, to this date there
is no physical interpretation nor theoretical predictions for them.

Here we show that random assemblies of  spheres in 3d cannot pack above
63.4%. The reason for this limit arises from a statistical picture of jammed
states in which the RCP can be interpreted as the ground state of the
ensemble of jammed matter. The results presented lead to a phase
diagram that provides a common view of the hard sphere packing problem
and further shedding light on a diverse spectrum of data including the
RLP state.