临界光纤网络中的有限尺寸效应
Finite size effects in critical fiber networks
摘要：
纤维网络如胶原蛋白在生理系统中是常见的。这些网络的一个重要功能是为细胞和组织提供机械稳定性。在生理水平的连通性，这样的网络将是机械不稳定的，只有中心力的相互作用。虽然网络可以通过弯曲相互作用来稳定，但也已经表明，它们表现出从松弛到刚性的临界转变作为施加应变的函数。超过一定的应变阈值，据预测，欠约束网络与只有中心力的相互作用表现出剪切模量的不连续性。我们研究了这种转变的有限尺寸标度行为，并确定了热力学极限中的力学不连续性和临界指数。我们发现非平均场行为和证据的超标度关系的临界指数，网络刚度是类似的热相变的热容量。这一点的进一步证据也可以在纤维网络的自平均特性中找到。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
