论文标题
边缘分形弹簧网络的粘弹性缩放制度
Viscoelastic scaling regimes for marginally-rigid fractal spring networks
论文作者
论文摘要
设计了一个边缘 - 刚性（等距）弹簧网络，其分形结构达到了可控长度，并计算出粘弹性光谱$ g^{*}（ω）$。观察到两个非平凡的缩放制度，（i）〜$ g^{\ prime} \大约g^{\ prime \ prime} \ propto \ propto \proptoΩupopoω^δ$在低频下，与$Δ= 1/2 $一致； （ii）〜$ g^{\ prime} \ propto g^{\ prime \ prime} \proptoΩ^{δ^{Δ^{\ prime}} $，用于与分形结构相对应的中间频率，与理论预测$δ^{\ prime} =（\ prime} =（\ ln3- \ ln2）/（+ln2）/（这两个方案之间的交叉发生在较大分形的较低频率上，表明散射样分散体。通过引入内部应力产生的固体凝胶在低频切断之上表现出相似的行为，表明这些发现与现实世界应用的相关性。
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.
