Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be mechanically unstable with only central-force interactions. While networks can be stabilized by bending interactions, it has also been shown that they exhibit a critical transition from floppy to rigid as a function of applied strain. Beyond a certain strain threshold, it is predicted that underconstrained networks with only central-force interactions exhibit a discontinuity in the shear modulus. We study the finite-size scaling behavior of this transition and identify both the mechanical discontinuity and critical exponents in the thermodynamic limit. We find both non-mean-field behavior and evidence for a hyperscaling relation for the critical exponents, for which the network stiffness is analogous to the heat capacity for thermal phase transitions. Further evidence for this is also found in the self-averaging properties of fiber networks.

中文翻译：

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关键光纤网络中的有限尺寸效应。

诸如胶原蛋白的纤维网络在生理系统中是常见的。这些网络的一项重要功能是为细胞和组织提供机械稳定性。在连通性的生理水平上，仅通过中心力相互作用，此类网络在机械上将不稳定。虽然可以通过弯曲相互作用来稳定网络，但也已显示出它们根据所施加的应变而呈现出从软盘到刚性的临界转变。超过某个应变阈值，可以预测只有中心力相互作用的欠约束网络在剪切模量上会出现不连续性。我们研究了这种转变的有限尺度缩放行为，并确定了热力学极限中的机械不连续性和临界指数。我们发现非平均场行为和关键指数超比例关系的证据，为此，网络刚度类似于热相转变的热容。在光纤网络的自平均特性中也找到了进一步的证据。