Rigidity percolation by next-nearest-neighbor bonds on generic and regular isostatic lattices.
Rigidity percolation by next-nearest-neighbor bonds on generic and regular isostatic lattices.
复制标题
通用和规则等静压晶格上次最近邻键的刚性渗透。
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Xiaoming Mao
中科院分区：
文献类型：
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作者：
Leyou Zhang;D. Rocklin;B. Chen;Xiaoming Mao
我们研究了二维中心力均衡晶格中的刚性渗透转变，包括正方形和kagome晶格，因为下近邻键（“括号”）被随机添加到系统中。我们特别关注规则晶格（完全周期性）与具有相同键拓扑但其位置在空间中随机位置的一般晶格之间的差异。我们发现，当支撑数为~ LlnL时，正则方形和kagome晶格表现出刚性渗透转变，其中L是晶格的线性大小。这种跃迁具有一阶和二阶跃迁的特点：整个晶格在跃迁时变得刚性，并且存在发散的长度尺度。相反，我们发现当支撑的数量非常接近从麦克斯韦定律得到的软盘模态的数量时，一般晶格中的刚性渗透跃迁发生，即~ L。一般晶格中的跃迁是一种非常尖锐的一阶类跃迁，在这种跃迁中，添加一个支撑将晶格中所有小的刚性区域连接起来，只在边缘留下软盘模式。我们使用数值模拟来描述这些转变，并开发捕捉每个转变的分析理论。我们的结果涉及到其他有趣的问题，包括干扰和自举渗透。
We study rigidity percolation transitions in two-dimensional central-force isostatic lattices, including the square and the kagome lattices, as next-nearest-neighbor bonds ("braces") are randomly added to the system. In particular, we focus on the differences between regular lattices, which are perfectly periodic, and generic lattices with the same topology of bonds but whose sites are at random positions in space. We find that the regular square and kagome lattices exhibit a rigidity percolation transition when the number of braces is ∼LlnL, where L is the linear size of the lattice. This transition exhibits features of both first-order and second-order transitions: The whole lattice becomes rigid at the transition, and a diverging length scale also exists. In contrast, we find that the rigidity percolation transition in the generic lattices occur when the number of braces is very close to the number obtained from Maxwell's law for floppy modes, which is ∼L. The transition in generic lattices is a very sharp first-order-like transition, at which the addition of one brace connects all small rigid regions in the bulk of the lattice, leaving only floppy modes on the edge. We characterize these transitions using numerical simulations and develop analytic theories capturing each transition. Our results relate to other interesting problems, including jamming and bootstrap percolation.