  Many real-world multilayer systems such as critical infrastructure are
interdependent and embedded in space with links of a characteristic length.
They are also vulnerable to localized attacks or failures, such as terrorist
attacks or natural catastrophes, which affect all nodes within a given radius.
Here we study the effects of localized attacks on spatial multiplex networks of
two layers. We find a metastable region where a localized attack larger than a
critical size induces a nucleation transition as a cascade of failures spreads
throughout the system, leading to its collapse. We develop a theory to predict
the critical attack size and find that it exhibits novel scaling behavior. We
further find that localized attacks in these multiplex systems can induce a
previously unobserved combination of random and spatial cascades. Our results
demonstrate important vulnerabilities in real-world interdependent networks and
show new theoretical features of spatial networks.
