Abstract
Critical infrastructures for transmitting materials, electricity and information between distant places, can be represented as spatial networks. The resilience of spatial networks usually shows unprecedented complexity, leading to the catastrophic cascading failures in the network under various local perturbations. From the viewpoint of physics, the cascading failure process of these networks can be considered as a phase transition, which is characterized by threshold and critical exponents. In this chapter, we first review our research on the definition and measurement of the dimension of these spatial networks, which is essential for determining the critical properties of the phase transition in the network failure process according to statistical physics. Secondly, we review our research on the dynamical organization of flow on these spatial networks, which can help to locate the relation between the flow and overload in the cascading failures. Thirdly, we review our research results on the failure propagation behaviors in the cascading failures, showing long-range decay of spatial correlation between component failures. Finally, we review our research on the modeling of self-healing against cascading failures and discuss the challenges in the reliability engineering for evaluating and improving the resilience of spatial networks.
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