1202.0259 (Matthieu Wyart)

Stability at Random Close Packing    [PDF]

Matthieu Wyart

The constraint that packings of hard spheres are stable with respect to
rearrangements of the contacts between particles is investigated. This
constraint is shown to lead to a bound between the distribution of contact
forces P(f) and the pair distribution function g(r). This bound plays a role
similar to those found in some glassy materials with long-range interactions,
such as the Coulomb gap in Anderson insulators or the distribution of local
fields in mean-field spin glasses. If P(f) \sim f^(theta) and g(r) \sim
(r-sigma)^(-gamma), where sigma is the particle diameter, one finds that gamma
\geq 1/(2+theta). Experimental observations indicate that this bound is
saturated.

View original: http://arxiv.org/abs/1202.0259