Jamming of Ideal Spheres at Zero Temperature

Andrea Liu (U Penn)
Sid Nagel (U Chicago)

Most of my current research involves understanding the jamming transition for idealized soft spheres at zero temperature. Below is a brief description of a few select projects.

Length Scales

Packings of soft, ideal spheres at zero temperature are rigid, or jammed, when the density is above a critical density. When a large section is cut out of an infinite system, soft modes appear at the edge but the particles in the center remain rigid. In the movie to the right, the rigid cluster is indicated by the red particles. As the size of this cut section decreases, the size of this rigid cluster remains roughly the size of the cut section. However, when the size of the cut section gets too small, the rigid cluster disappears as soft modes penetrate the bulk. This transition is sudden and identifies a length scale, called l*. Originally proposed by Wyart et al. in 2005, this length scale diverges at the jamming transition and is the cornerstone of much of our theoretical understanding of jammed systems.

Finite-Size Effects

It has long been argued that jamming resembles a standard equilibrium phase transition because it displays 1) a finite jump in the number of contacts per particle, 2) power law scalings in the excess contact number and the shear modulus, and 3) diverging length scales. However, at the heart of the theory of phase transitions is the idea of scaling collapse, where measurements on finite systems can be collapsed onto a single curve by scaling variables by the size of the system. We have recently shown such effects to be present at the jamming transition, confirming that jamming is a phase transition.

The Jamming Phase Diagram