2018/07/31 by Carolina Brito, Harukuni Ikeda, Pierfrancesco Urbani +2 · 1 citation
Chemistry · Materials Science · Neuroscience · Physics and Astronomy · #Amorphous solid #Chemistry #Classical mechanics #Condensed matter physics #Critical exponent #Crystallography #Ellipsoid #Jamming #Material Dynamics and Properties #Neural dynamics and brain function #Phase transition #Physics #Statistical physics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1073/pnas.1812457115
published as PNAS 115, 11736-11741 (2018) · 6 pages, 5 figures
openalex publication_date 2018/10/31 · arxiv created 2018/11/03 · arxiv updated 2018/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.