Infinitesimal asphericity changes the universality of the jamming transition

Abstract

The jamming transition of non-spherical particles is fundamentally different from the spherical case. Non-spherical particles are hypostatic at their jamming points, while isostaticity is ensured in the case of the jamming of spherical particles. This structural difference implies that the presence of asphericity affects the critical exponents related to the contact number and the vibrational density of states. Moreover, while the force and gap distributions of isostatic jamming present power-law behaviors, even an infinitesimal asphericity is enough to smooth out these singularities. In a recent work [PNAS 115(46), 11736], we have used a combination of marginal stability arguments and the replica method to explain these observations. We argued that systems with internal degrees of freedom, like the rotations in ellipsoids, or the variation of the radii in the case of the \textit{breathing} particles fall in the same universality class. In this paper, we review comprehensively the results about the jamming with internal degrees of freedom in addition to the translational degrees of freedom. We use a variational argument to derive the critical exponents of the contact number, shear modulus, and the characteristic frequencies of the density of states. Moreover, we present additional numerical data supporting the theoretical results, which were not shown in the previous work.

17 pages, 7 figures

References in corpus (8)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Fractal free energy landscapes in structural glasses
• Universal microstructure and mechanical stability of jammed packings
• Jamming Criticality Revealed by Removing Localized Buckling Excitations
• Hypostatic jammed packings of frictionless nonspherical particles
• Universality of jamming of non-spherical particles
• Theory for Swap Acceleration near the Glass and Jamming Transitions
• Mean field theory of jamming of nonspherical particles

Cited by in corpus (6)

• Free-then-freeze: transient learning degrees of freedom for introducing function in materials
• Jamming with tunable roughness
• Finite size effects in the microscopic critical properties of jammed configurations: A comprehensive study of the effects of different types of disorder
• Jamming below upper critical dimension
• Force balance controls the relaxation time of the gradient descent algorithm in the satisfiable phase
• Testing mean-field theory for jamming of non-spherical particles: Contact number, gap distribution, and vibrational density of states