Universality of jamming of nonspherical particles
Universality of jamming of nonspherical particles
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DOI：
10.1073/pnas.1812457115
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发表时间：
2018-11-13
影响因子：
11.1
通讯作者：
Zamponi, Francesco
中科院分区：
文献类型：
--
作者：
Brito, Carolina;Ikeda, Harukuni;Zamponi, Francesco
椭球体、球柱体等非球形粒子的非晶态填料被认为是实体的：粒子之间的机械接触数小于自由度数，因此违反了麦克斯韦的机械稳定性准则。在这项工作中，我们提出了一个一般理论的实体非晶填料和相关的干扰转变。首先，我们证明了许多系统属于同一个普适性类。作为一个例子，我们明确地将椭球体映射到“呼吸”粒子的系统中。我们通过使用边际稳定性论证表明，在这两种情况下，堵塞填料都是实体的，并且与接触数和状态的振动密度相关的临界指数是相同的。此外，我们还引入了一个广义感知器模型，该模型可以用复制方法解析求解。解析解预测了同一实体干扰普适性类的临界指数。我们的分析进一步表明，实体干扰的力和间隙分布不表现幂律行为，与球形颗粒的等静力干扰形成鲜明对比。最后，通过数值模拟验证了我们的理论预测。
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.