期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 115, 期 46, 页码 11736-11741出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1812457115
关键词
jamming; glass; marginal stability; nonspherical particles
资金
- European Research Council under the European Union [723955]
- Simons Foundation [689 454953, 454955]
- Laboratoire d'Excellence Physics Atoms Light Mater (LabEx PALM) by the French National Research Agency (ANR) [ANR-10-LABX-0039-PALM]
- European Research Council (ERC) [723955] Funding Source: European Research Council (ERC)
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.
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