边缘刚性分形弹簧网络的粘弹性标度区
Viscoelastic scaling regimes for marginally-rigid fractal spring networks
摘要：
设计了一类具有分形结构的边缘刚性（均衡）弹簧网络，并计算了其粘弹性谱$G^{*}(ω)$。观察到两个非平凡的标度制度，（i）~ $G^{\prime}\approx G^{\prime\prime}\proptoω^Δ$在低频，与$Δ=1/2$一致;（ii）~ $G^{\prime}\propto G^{\prime\prime}\proptoω^{Δ^{\prime}}$的中频对应的分形结构，与理论预测$Δ^{\prime}=(\ln3-\ln2)/(\ln3+\ln2)$一致。这两个政权之间的交叉发生在较低的频率为较大的分形的方式，建议扩散式分散。通过引入内应力产生的固体凝胶在低频截止值以上表现出类似的行为，表明这些发现与现实应用的相关性。
英文摘要：
A family of marginally-rigid (isostatic) spring networks with fractal structure up to a controllable length was devised and the viscoelastic spectra $G^{*}(ω)$ calculated. Two non-trivial scaling regimes were observed, (i)~$G^{\prime}\approx G^{\prime\prime}\proptoω^Δ$ at low frequencies, consistent with $Δ=1/2$; (ii)~$G^{\prime}\propto G^{\prime\prime}\proptoω^{Δ^{\prime}}$ for intermediate frequencies corresponding to fractal structure, consistent with a theoretical prediction $Δ^{\prime}=(\ln3-\ln2)/(\ln3+\ln2)$. The cross-over between these two regimes occurred at lower frequencies for larger fractals in a manner suggesting diffusive-like dispersion. Solid gels generated by introducing internal stresses exhibited similar behaviour above a low-frequency cut-off, indicating the relevance of these findings to real-world applications.
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