Scaling Theory for the Frictionless Unjamming Transition.
Scaling Theory for the Frictionless Unjamming Transition.
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无摩擦畅通过渡的缩放理论。
DOI：
10.1103/physrevlett.118.138001
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发表时间：
2016
影响因子：
8.6
通讯作者：
B. Chakraborty
中科院分区：
文献类型：
--
作者：
K. Ramola;B. Chakraborty
通过定义可唯一分配给每个接触点的局部区域，建立了二维软无摩擦盘无干扰过渡的标度理论。这些参数用于定义局部有序参数，随着解干扰过渡的逼近，其分布呈现发散性。我们从将局部区域视为非相互作用实体的平均场方法中推导出这些散度的标度形式，并证明这些结果与数值模拟非常吻合。我们发现，标度函数的渐近行为源于填料的几何结构，而整体标度随压缩能的变化取决于力律。我们使用分布的标度形式来确定总颗粒面积A_{G}和总接触数N_{C}的标度。
We develop a scaling theory of the unjamming transition of soft frictionless disks in two dimensions by defining local areas, which can be uniquely assigned to each contact. These serve to define local order parameters, whose distribution exhibits divergences as the unjamming transition is approached. We derive scaling forms for these divergences from a mean-field approach that treats the local areas as noninteracting entities, and demonstrate that these results agree remarkably well with numerical simulations. We find that the asymptotic behavior of the scaling functions arises from the geometrical structure of the packing while the overall scaling with the compression energy depends on the force law. We use the scaling forms of the distributions to determine the scaling of the total grain area A_{G} and the total number of contacts N_{C}.