Robust synchronization (phase locking) of power plants and consumers centrally underlies the stable operation of electric power grids. Despite current attempts to control large-scale networks, even their uncontrolled collective dynamics is not fully understood. Here we analyze conditions enabling self-organized synchronization in oscillator networks that serve as coarse-scale models for power grids, focusing on decentralizing power sources. Intriguingly, we find that whereas more decentralized grids become more sensitive to dynamical perturbations, they simultaneously become more robust to topological failures. Decentralizing power sources may thus facilitate the onset of synchronization in modern power grids.

Paramagnetic correlations in the magnetic material Yb2Ti2O7 have been investigated via neutron scattering, revealing a [111] rod of scattering intensity. Assuming interactions between the Yb 3+ ions composed of all symmetry-allowed nearest neighbor exchange interactions and long-range dipolar interactions, we construct a model Hamiltonian that allows for an excellent description of the neutron scattering data. Our results provide compelling evidence for significant anisotropic exchange interactions in an insulating magnetic pyrochlore oxide. We also compute the real space correlations leading to the [111] rod of scattering.In geometrically frustrated magnetic materials there exists no configuration of magnetic moments that simultaneously satisfies all the pairwise magnetic interactions. Experimental and theoretical research over the past twenty years has shown that frustrated magnetic systems are prone to exhibit novel and intriguing collective thermodynamic phenomena [1].Among frustrated three dimensional systems, the A 2 B 2 O 7 pyrochlores have attracted much attention [2]. In these compounds, A is a trivalent rare earth ion (Ho, Dy, Tb, Gd, Yb) or yttrium (Y) and B is a tetravalent transition metal ion (Ti, Sn, Mo, Mn). Both A and B reside on two distinct lattices of corner-sharing tetrahedra. Theory predicts that classical [3] and quantum [4] Heisenberg spins on a pyrochlore lattice interacting via an isotropic antiferromagnetic nearest neighbor exchange Hamiltonian, H H , fail to develop conventional LRO down to zero temperature. In real pyrochlore compounds, however, there generally exists some combination of other perturbing magnetic interactions (e.g. single ion anisotropy, dipolar interactions, etc) beyond H H . Since H H alone does not produce LRO, the low temperature magnetic correlations of these materials are strongly influenced by the competition between materialspecific perturbations. This is the origin of the richness of phenomena observed in the A 2 B 2 O 7 pyrochlores [2] including spin liquid [5], spin glass [6], spin ice [7], and LRO with persistent low-temperature spin dynamics [8,9]. In this article, we consider the Yb 2 Ti 2 O 7 pyrochlore which does not apparently exhibit any of the aforementioned phenomena and has some unique and unusual features of its own which have heretofore remained unexplained.Yb 2 Ti 2 O 7 has a ferromagnetic character with a Curie-Weiss temperature, θ CW = +0.65 ± 0.15 K [10,11]. The Yb 3+ ∼ 3 µ B magnetic moments predominantly lie perpendicular to the local [111] cubic unit cell diagonals, making this system the only known local [111] XY pyrochlore with a ferromagnetic θ CW [2]. Magnetic specific heat (C m ) measurements reveal a sharp first order transition at T c ≈ 240 mK [12], suggesting the onset of LRO. While a single crystal elastic neutron scattering (NS) study suggested ferromagnetic order below T c [13], a subsequent polarized NS study [14] did not confirm such ordering. Furthermore, powder NS shows no LRO down to 110 mK [15] and very recent NS on a si...

Replacing conventional power sources by renewable sources in current power grids drastically alters their structure and functionality. In particular, power generation in the resulting grid will be far more decentralized, with a distinctly different topology. Here, we analyze the impact of grid topologies on spontaneous synchronization, considering regular, random, and small-world topologies and focusing on the influence of decentralization. We model the consumers and sources of the power grid as second order oscillators. First, we analyze the global dynamics of the simplest non-trivial (two-node) network that exhibit a synchronous (normal operation) state, a limit cycle (power outage), and coexistence of both. Second, we estimate stability thresholds for the collective dynamics of small network motifs, in particular, star-like networks and regular grid motifs. For larger networks, we numerically investigate decentralization scenarios finding that decentralization itself may support power grids in exhibiting a stable state for lower transmission line capacities. Decentralization may thus be beneficial for power grids, regardless of the details of their resulting topology. Regular grids show a specific sharper transition not found for random or small-world grids.

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