论文标题
相同分形维度等静态弹簧网络的独特粘弹性缩放
Distinct viscoelastic scaling for isostatic spring networks of the same fractal dimension
论文作者
论文摘要
分形结构从单体的化学交叉\链接到水凝胶中自发地出现，并且与凝胶过渡时的Power Law Visco \ - 弹性直接相关，正如最近证明的基于Sierpinski Triangle的等值静力（margin-rigid）弹簧网络。在这里，我们概括了Sierpinski三角生成规则，以产生4个分形，所有分形成$ d _ {\ rm f} = \ log 3/\ log 2 $，sierpinski Triangle是一种情况。我们表明，从这些分形得出的春季网络都是等静力的，但展示了其功率法粘弹性的两个不同指数之一。我们得出的结论是，即使对于具有固定连接性的网络，Power-Law粘弹性通常也不能单独是分形维度的函数。
Fractal structure emerges spontaneously from the chemical cross\-linking of monomers into hydrogels, and has been directly linked to power law visco\-elasticity at the gel transition, as recently demonstrated for isostatic (marginally--rigid) spring networks based on the Sierpinski triangle. Here we generalize the Sierpinski triangle generation rules to produce 4 fractals, all with the same dimension $d_{\rm f}=\log 3/\log 2$, with the Sierpinski triangle being one case. We show that spring networks derived from these fractals are all isostatic, but exhibit one of two distinct exponents for their power--law viscoelasticity. We conclude that, even for networks with fixed connectivity, power--law viscoelasticity cannot generally be a function of the fractal dimension alone.
