Universality of jamming of nonspherical particles

By Carolina Brito, Harukuni Ikeda, Pierfrancesco Urbani, Matthieu Wyart, Francesco Zamponi. 2018

58 citations recorded by the source corpus.

Significance The jamming transition is a key property of granular materials, including sand and dense suspensions. In the generic situation of nonspherical particles, its scaling properties are not completely understood. Previous empirical and theoretical work in ellipsoids and spherocylinders indicates that both structural and vibrational properties are fundamentally affected by shape. Here we explain these observations using a combination of marginal stability arguments and the replica method. We unravel a universality class for particles with internal degrees of freedom and derive how the structure of packings and their vibrations scale as the particles evolve toward spheres. Amorphous packings of nonspherical particles such as ellipsoids and spherocylinders are known to be hypostatic: The number of mechanical contacts between particles is smaller than the number of degrees of freedom, thus violating Maxwell’s mechanical stability criterion. In this work, we propose a general theory of hypostatic amorphous packings and the associated jamming transition. First, we show that many systems fall into a same universality class. As an example, we explicitly map ellipsoids into a system of “breathing” particles. We show by using a marginal stability argument that in both cases jammed packings are hypostatic and that the critical exponents related to the contact number and the vibrational density of states are the same. Furthermore, we introduce a generalized perceptron model which can be solved analytically by the replica method. The analytical solution predicts critical exponents in the same hypostatic jamming universality class. Our analysis further reveals that the force and gap distributions of hypostatic jamming do not show power-law behavior, in marked contrast to the isostatic jamming of spherical particles. Finally, we confirm our theoretical predictions by numerical simulations.

Subfields: Cognitive Neuroscience, Condensed Matter Physics, Materials Chemistry, AI for Physical Sciences