  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.
