配电网的伊辛模型
Ising model for distribution networks
摘要：
提出了一个基本的伊辛自旋模型演示级联故障（故障，停电，崩溃，雪崩，.）这可能发生在现实网络中，由供应商分发和交付给消费者。具有淬灭随机场的铁磁哈密顿量是由最大化需求和交付之间的差距的策略产生的。这种政策可能出现在竞争性市场中，企业人为地创造新的需求，也可能出现在团结一致的环境中，过高的需求无法得到合理的满足。当一个最初活跃的状态变成亚稳态并衰减到一个稳定的非活跃状态时，在团结政策的背景下，网络故障是可能的。我们探讨的需求和交付的特点，以及拓扑属性，这使得配电网络容易发生故障。定义了一个有效温度，它决定了可能引起崩溃的活动波动的强度。数值结果，通过蒙特卡罗模拟的模型（主要是）无标度网络，补充与分析平均场近似的几何随机场波动和热自旋波动。枢纽与连接不良的节点在启动网络活动的故障的作用进行了说明，并与模型参数。
英文摘要：
An elementary Ising spin model is proposed for demonstrating cascading failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidary environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of the model on (mainly) scale-free networks, are supplemented with analytic mean-field approximations to the geometrical random field fluctuations and the thermal spin fluctuations. The role of hubs versus poorly connected nodes in initiating the breakdown of network activity is illustrated and related to model parameters.
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