论文标题

在局部最佳路径上缩放裂纹

Scaling in Local Optimal Paths Cracks

论文作者

de Noronha, Aurelio W. T., Leite, Levi R.

论文摘要

当地的裂缝如何为全球裂缝构成构成,是几个科学主题的目标,例如,瓶颈如何影响到城市的交通稳健性?在一个方向上,使用Andrade等人提出的修改最佳路径裂缝(OPC)模型生成了从级联故障到网络中的裂纹。在此模型中,我们从具有线性尺寸$ l $的网络中的两个网站(欧几里得)距离之间的最佳路径链接了最大能量的链接。该网络的每个链接都有一个能量值,该能量可以用幂律来控制疾病$β$的参数。使用有限尺寸的缩放和渗透理论的指数,我们发现,局部最佳路径上的破裂链接的质量与powerlaw $ l^{0.4} $作为与$ l $的可分离方程式,并且可以独立于疾病参数。

How local cracks can contribute to the global cracks landscape is a goal of several scientific topics, for example, how bottlenecks can impact the robustness of traffic into a city? In one direction, cracks from cascading failures into networks were generated using a modified Optimal Path-Cracking (OPC) model proposed by Andrade et al \cite{Andrade2009}. In this model, we broke links of maximum energies from optimal paths between two sites with internal (euclidean) distances $l$ in networks with linear size $L$. Each link of this network has an energy value that scales with a power-law that can be controlled using a parameter of the disorder $β$. Using finite-size scaling and the exponents from percolation theory we found that the mass of the cracked links on local optimal paths scales with a power-law $l^{0.4}$ as a separable equation from $L$ and that can be independent of the disorder parameter.

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