Scaling electrical percolation networks based on renormalization group theory
Scaling electrical percolation networks based on renormalization group theory
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DOI：
10.1007/s00339-022-05817-1
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Weijian Li;Yan He;Kaiyuan Yang;G. Naik
中科院分区：
文献类型：
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作者：
Weijian Li;Yan He;Kaiyuan Yang;G. Naik
许多自然界的无序系统，如渗滤金属膜，都可以近似为分形。探测它们的性质可能很困难，这取决于所涉及的长度尺度。通常，优选以方便的长度尺度表征系统并构建用于将测量数据外推到其他长度尺度的模型。在这种情况下，需要一种通用算法来缩放模型网络，同时保持其统计等效性。在这里，我们提供了一个算法，从重正化群理论的启发缩放无序分形网络。该算法包括三个步骤：扩展，映射和降低分辨率，其中映射是唯一的计算昂贵的步骤。我们描述了一种方法来最大限度地减少计算负担，并准确地缩放模型网络。我们实验验证了该算法在一个超薄的金膜形成的电网络的玻璃基板。通过测量由给定长度分开的多对焊盘之间的电阻，我们准确地预测了在由原始距离的两倍分开的焊盘上测量的电阻分布的平均值和标准差。本文提出的算法是通用的，可应用于任何无序分形系统。
Many natural disordered systems such as percolation metal films may be approximated as fractals. Probing their properties can be difficult depending on the length scale involved. Often, characterizing the system at a convenient length scale and building models for extrapolating the measured data to other length scales is preferred. In such situations, a general algorithm for scaling the model network while preserving its statistical equivalence is required. Here, we provide an algorithm that draws inspiration from renormalization group theory for scaling disordered fractal networks. This algorithm includes three steps: expand, map, and reduce resolution, where the mapping is the only computationally expensive step. We describe a way to minimize the computational burden and accurately scale the model network. We experimentally validate the algorithm in a percolating electrical network formed by an ultra-thin gold film on a glass substrate. By measuring the resistance between many pairs of pads separated by a given length, we accurately predict the mean and standard deviation of the resistance distribution measured across pads separated by twice the original distance. The algorithm presented here is general and may be applied to any disordered fractal system.