摘要翻译：
本文是从统计物理学的角度对网络中电流流动的一个小综述。我们简要地讨论了求解任意电阻网络电导的解析方法。然后我们转向与渗流有关的基本结果：即，一个大的随机电阻网络的导电性质随电阻的分数变化。我们的重点是当从上方接近渗流阈值时，这种网络的电导是如何消失的。我们还讨论了一个大网络中每个电阻内更微观的电流分布。在渗流阈值处，这种分布是多重分形的，因为这种分布的所有矩都具有独立的标度性质。我们将讨论多重分形尺度的含义及其对网络中电流流动的影响，特别是网络中最大电流的影响。最后，我们讨论了电阻网络与随机游动之间的关系，并说明了随机游动的经典递归和瞬态现象是如何简单地与相应电网络的电导有关的。
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英文标题：
《Fractal and Multifractal Scaling of Electrical Conduction in Random
  Resistor Networks》
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作者：
S. Redner
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics        物理学
二级分类：Classical Physics        经典物理学
分类描述：Newtonian and relativistic dynamics; many particle systems; planetary motions; chaos in classical dynamics. Maxwell's  equations and  dynamics of charged systems and  electromagnetic forces in materials. Vibrating systems such as membranes and cantilevers; optomechanics. Classical waves, including acoustics and elasticity; physics of music and musical instruments. Classical thermodynamics and  heat flow problems.
牛顿和相对论动力学；许多粒子系统；行星运动；经典动力学中的混沌。材料中带电系统和电磁力的麦克斯韦方程组和动力学。振动系统，如薄膜和悬臂；光学力学。经典波，包括声学和弹性；音乐和乐器物理学。经典热力学和热流问题。
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英文摘要：
  This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic results related to percolation: namely, the conduction properties of a large random resistor network as the fraction of resistors is varied. We focus on how the conductance of such a network vanishes as the percolation threshold is approached from above. We also discuss the more microscopic current distribution within each resistor of a large network. At the percolation threshold, this distribution is multifractal in that all moments of this distribution have independent scaling properties. We will discuss the meaning of multifractal scaling and its implications for current flows in networks, especially the largest current in the network. Finally, we discuss the relation between resistor networks and random walks and show how the classic phenomena of recurrence and transience of random walks are simply related to the conductance of a corresponding electrical network.
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PDF链接：
https://arxiv.org/pdf/710.1105