Using the linearized DC power flow model, we study cascading failures and their spatial and temporal properties in the US Western Interconnect (USWI) power grid. We also introduce the preferential Degree And Distance Attachment (DADA) model, with similar degree distributions, resistances, and currents to the USWI. We investigate the behavior of both grids resulting from the failure of a single line. We find that the DADA model and the USWI model react very similarly to that failure, and that their blackout characteristics resemble each other. In many cases, the failure of a single line can cause cascading failures, which impact the entire grid. We characterize the resilience of the grid by three parameters, the most important of which is tolerance α, which is the ratio of the maximal load a line can carry to its initial load. We characterize a blackout by its yield, which we define as the ratio of the final to the initial consumed currents. We find that if α ≥ 2, the probability of a large blackout occurring is very small. By contrast, in a broad range of 1 < α < 2, the initial failure of a single line can result, with a high probability, in cascading failures leading to a massive blackout with final yield less than 80%. The yield has a bimodal distribution typical of a first-order transition, i.e., the failure of a randomly selected line leads either to an insignificant current reduction or to a major blackout. We find that there is a latent period in the development of major blackouts during which few lines are overloaded, and the yield remains high.The duration of this latent period is proportional to the tolerance. The existence of the latent period suggests that intervention during early time steps of a cascade can significantly reduce the risk of a major blackout.

We model an isothermal aggregation process of particles/atoms interacting according to the Lennard-Jones pair potential by mapping the energy landscapes of each cluster size N onto stochastic networks, computing transition probabilities from the network for an N -particle cluster to the one for N + 1, and connecting these networks into a single joint network. The attachment rate is a control parameter. The resulting network representing the aggregation of up to 14 particles contains 6427 vertices. It is not only time-irreversible but also reducible. To analyze its transient dynamics, we introduce the sequence of the expected initial and preattachment distributions and compute them for a wide range of attachment rates and three values of temperature. As a result, we find the configurations most likely to be observed in the process of aggregation for each cluster size. We examine the attachment process and conduct a structural analysis of the sets of local energy minima for every cluster size. We show that both processes taking place in the network, attachment and relaxation, lead to the dominance of icosahedral packing in small (up to 14 atom) clusters. 1 arXiv:1612.09599v2 [cond-mat.stat-mech] 11 Apr 2017 102, 103, and 104, the energy-minimizing configurations are non-icosahedral [37]. Some of them are highly symmetric. For example, the global minimum for N = 38, a truncated octahedron with FCC atomic packing, has the point group O h of order 48, i.e., there are 48 orthogonal transformations mapping the cluster onto itself. The global minimum for N = 75, a Marks decahedron, has point group D 5h of order 20. Remarkably, the mass spectra graphs in [15,20] do not have prominent peaks at N = 38 and N = 75. On the other hand, the mass spectra in [15,16,17,20,21] consistently exhibit peaks corresponding to the clusters of the so-called magic numbers of atoms N admitting complete icosahedra. These numbers are: N = 13, 55, 147, 309, 561, etc. The point group order of an icosahedron is 120. Evidently, atoms tend to self-assemble into highly symmetric complete icosahedra in experimental settings, while they seem to miss highly symmetric low-energy configurations based on other kinds of packing, at least for small numbers of atoms. Choosing a model and an approachIntrigued by these facts, we undertook an attempt to understand the self-assembly of free Lennard-Jones particles (atoms) into clusters on the quantitative level by means of combined analytical and computational methods. Most previous theoretical studies of Lennard-Jones clusters dealt with those of fixed numbers of atoms, i.e., atoms were allowed neither to fly away nor to join the cluster. These works can be divided into two groups, full phase-space-based (e.g. [29,34]) and network-based. The latter approach was pioneered by Wales and collaborators [31,37,11,40,41]. Their powerful computational tools for mapping energy landscapes onto networks are based on the basin-hopping method [37] and discrete path sampling [38]. Numerous networks representing energy landsca...