# Mean field theory of jamming of nonspherical particles

## TL;DR

This paper extends mean field theory to analyze the jamming transition of nonspherical particles, revealing different scaling behaviors and providing detailed insights into the full scaling behavior near the jamming point.

## Contribution

It develops a mean field model incorporating rotational degrees of freedom to better understand the jamming of nonspherical particles, expanding on previous work.

## Key findings

- Different contact number and shear modulus scaling near jamming for nonspherical particles.
- Detailed analysis of the model's scaling behavior in convex and non-convex phases.
- Extension of perceptron-based models to include rotational degrees of freedom.

## Abstract

Recent computer simulations have uncovered the striking difference between the jamming transition of spherical and non-spherical particles. While systems of spherical particles are isostatic at the jamming point, systems of nonspherical particles are not: the contact number and shear modulus of the former exhibit a square root singularity near jamming, while those of the latter are linearly proportional to the distance from jamming. Furthermore, while our theoretical understanding of jamming of spherical particles is well developed, the same is not true for nonspherical particles. To understand jamming of non-spherical particles, in the previous work [Brito, PNAS 115(46), 111736], we extended the perceptron model, whose SAT/UNSAT transition belongs to the same universality class of jamming of spherical particles, to include additional variables accounting for the rotational degrees of freedom of nonspherical particles. In this paper, we give more detailed investigations of the full scaling behavior of the model near the jamming transition point in both convex and non-convex phases.