标题： 关于高斯尺度无标度聚合物网络的形状 显示英文标题

标题： On the shape of Gaussian scale-free polymer networks

摘要： 我们考虑基于无标度图形成的复杂超支化聚合物结构模型，其中节点的功能性（度数）$k$遵循幂律衰减概率$p(k)\sim{k^{-\alpha}}$。 这种聚合物拓扑结构可以看作是具有固定功能性的规则分层树状大分子结构的推广。 通过应用魏的方法得到这类聚合物网络的构象尺寸和形状特征，如平均非球性$\langle A_3 \rangle$和尺寸比$g$，该方法通过相应基尔霍夫矩阵的特征值谱来定义任何复杂高斯网络的构型。 我们的定量结果表明，随着参数$\alpha$的减少，网络结构的紧密性和对称性增加。 显示英文摘要

摘要： We consider the model of complex hyperbranched polymer structures formed on the basis of scale-free graphs, where functionalities (degrees) $k$ of nodes obey a power law decaying probability $p(k)\sim{k^{-\alpha}}$. Such polymer topologies can be considered as generalization of regular hierarchical dendrimer structures with fixed functionalities. The conformational size and shape characteristics, such as averaged asphericity $\langle A_3 \rangle$ and size ratio $g$ of such polymer networks are obtained numerically by application of Wei's method, which defines the configurations of any complex Gaussian network in terms of eigenvalue spectra of corresponding Kirchhoff matrix. Our quantitative results indicate, in particular, an increase of compactness and symmetry of network structures with the decrease of parameter $\alpha$.