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Conventional generators in power grids are steadily substituted with new renewable sources of electric power. The latter are connected to the grid via inverters and as such have little, if any rotational inertia. The resulting reduction of total inertia raises important issues of power grid stability, especially over short-time scales. With the motivation in mind to investigate how inertia reduction influences the transient dynamics following a fault in a large-scale electric power grid, we have constructed a model of the high voltage synchronous grid of continental Europe. To assess grid stability and resilience against disturbance, we numerically investigate frequency deviations as well as rates of change of frequency (RoCoF) following abrupt power losses. The magnitude of RoCoF's and frequency deviations strongly depend on the fault location, and we find the largest effects for faults located on the support of the slowest mode-the Fiedler mode-of the network Laplacian matrix. This mode essentially vanishes over Belgium, Eastern France, Western Germany, northern Italy and Switzerland. Buses inside these regions are only weakly affected by faults occuring outside. Conversely, faults inside these regions have only a local effect and disturb only weakly outside buses. Following this observation, we reduce rotational inertia through three different procedures by either (i) reducing inertia on the Fiedler mode, (ii) reducing inertia homogeneously and (iii) reducing inertia outside the Fiedler mode. We find that procedure (iii) has little effect on disturbance propagation, while procedure (i) leads to the strongest increase of RoCoF and frequency deviations. This shows that, beyond absorbing frequency disturbances following nearby faults, inertia also mitigates frequency disturbances from distant power losses, provided both the fault and the inertia are located on the support of the slowest modes of the grid Laplacian. These results for our model of the European transmission grid are corroborated by numerical investigations on the ERCOT transmission grid.

Understanding random lasing is a formidable theoretical challenge. Unlike conventional lasers, random lasers have no resonator to trap light, they are highly multimode with potentially strong modal interactions, and they are based on disordered gain media, where photons undergo random multiple scattering. Interference effects notoriously modify the propagation of waves in such random media, but their fate in the presence of nonlinearity and interactions is poorly understood. Here, we present a semiclassical theory for multimode random lasing in the strongly scattering regime. We show that Anderson localization, a wave interference effect, is not affected by the presence of nonlinearities. To the contrary, its presence suppresses interactions between simultaneously lasing modes. Consequently, each lasing mode in a strongly scattering random laser is given by a single long-lived, Anderson localized mode of the passive cavity, the frequency and wave profile of which do not vary with pumping, even in the multimode regime when modes spatially overlap. Random lasing in the presence of nonlinearities and disordered gain media is still poorly understood. Researchers now present a semiclassical theory for multimode random lasing in the strongly scattering regime. They show that Anderson localization — a wave-interference effect — is not affected by the presence of nonlinearities, but instead suppresses interactions between simultaneously lasing modes.

With the ongoing energy transition, power grids are evolving fast. They operate more and more often close to their technical limit, under more and more volatile conditions. Fast, essentially real-time computational approaches to evaluate their operational safety, stability and reliability are therefore highly desirable. Machine Learning methods have been advocated to solve this challenge, however they are heavy consumers of training and testing data, while historical operational data for real-world power grids are hard if not impossible to access. This manuscript presents a large synthetic dataset of power injections in an electric transmission grid model of continental Europe, and describes the algorithm developed for its generation. The method allows one to generate arbitrarily large time series from the knowledge of the grid – the admittance of its lines as well as the location, type and capacity of its power generators – and aggregated power consumption data, such as the national load data given by ENTSO-E. The obtained datasets are statistically validated against real-world data.

There is growing evidence of systematic attempts to influence democratic elections by controlled and digitally organized dissemination of fake news. This raises the question of the intrinsic robustness of democratic electoral processes against external influences. Particularly interesting is to identify the social characteristics of a voter population that renders it more resilient against opinion manipulation. Equally important is to determine which of the existing democratic electoral systems is more robust to external influences. Here we construct a mathematical electoral model to address these two questions. We find that, not unexpectedly, biased electorates with clear-cut elections are overall quite resilient against opinion manipulations, because inverting the election outcome requires to change the opinion of many voters. More interesting are unbiased or weakly biased electorates with close elections. We find that such populations are more resilient against opinion manipulations (i) if they are less polarized and (ii) when voters interact more with each other, regardless of their opinion differences, and that (iii) electoral systems based on proportional representation are generally the most robust. Our model qualitatively captures the volatility of the US House of Representatives elections. We take this as a solid validation of our approach.

Decarbonization in the energy sector has been accompanied by an increased penetration of new renewable energy sources in electric power systems. Such sources differ from traditional productions in that, first, they induce larger, undispatchable fluctuations in power generation and second, they lack inertia. Recent measurements have indeed reported long, non-Gaussian tails in the distribution of local voltage frequency data. Large frequency deviations may induce grid instabilities, leading in worst-case scenarios to cascading failures and large-scale blackouts. In this article, we investigate how correlated noise disturbances, characterized by the cumulants of their distribution, propagate through meshed, high-voltage power grids. For a single source of fluctuations, we show that long noise correlation times boost non-Gaussian voltage angle fluctuations so that they propagate similarly to Gaussian fluctuations over the entire network. However, they vanish faster, over short distances if the noise fluctuates rapidly. We furthermore demonstrate that a Berry–Esseen theorem leads to the vanishing of non-Gaussianities as the number of uncorrelated noise sources increases. Our predictions are corroborated by numerical simulations on realistic models of power grids.

Using boron nitride as a substrate for graphene has been suggested as a promising way to reduce the disorder in graphene caused by space fluctuations. It is now shown by scanning tunnelling microscopy that graphene conforms perfectly to boron nitride and the charge fluctuations are minimal compared with the conventionally used substrate, silica. Boron nitride could really be the natural graphene substrate. Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy–momentum dispersion relations which cross at the Dirac point 1 , 2 . However, accessing the physics of the low-density region at the Dirac point has been difficult because of disorder that leaves the graphene with local microscopic electron and hole puddles 3 , 4 , 5 . Efforts have been made to reduce the disorder by suspending graphene, leading to fabrication challenges and delicate devices which make local spectroscopic measurements difficult 6 , 7 . Recently, it has been shown that placing graphene on hexagonal boron nitride (hBN) yields improved device performance 8 . Here we use scanning tunnelling microscopy to show that graphene conforms to hBN, as evidenced by the presence of Moiré patterns. However, contrary to predictions 9 , 10 , this conformation does not lead to a sizeable band gap because of the misalignment of the lattices. Moreover, local spectroscopy measurements demonstrate that the electron–hole charge fluctuations are reduced by two orders of magnitude as compared with those on silicon oxide. This leads to charge fluctuations that are as small as in suspended graphene 6 , opening up Dirac point physics to more diverse experiments.

It is well known that graphene deposited on hexagonal boron nitride produces moiré patterns in scanning tunnelling microscopy images. The interaction that produces this pattern also produces a commensurate periodic potential that generates a set of Dirac points that are different from those of the graphene lattice itself. The Schrödinger equation dictates that the propagation of nearly free electrons through a weak periodic potential results in the opening of bandgaps near points of the reciprocal lattice known as Brillouin zone boundaries 1 . However, in the case of massless Dirac fermions, it has been predicted that the chirality of the charge carriers prevents the opening of a bandgap and instead new Dirac points appear in the electronic structure of the material 2 , 3 . Graphene on hexagonal boron nitride exhibits a rotation-dependent moiré pattern 4 , 5 . Here, we show experimentally and theoretically that this moiré pattern acts as a weak periodic potential and thereby leads to the emergence of a new set of Dirac points at an energy determined by its wavelength. The new massless Dirac fermions generated at these superlattice Dirac points are characterized by a significantly reduced Fermi velocity. Furthermore, the local density of states near these Dirac cones exhibits hexagonal modulation due to the influence of the periodic potential.

Trilayer graphene can be realized in two different stacking configurations, known as rhombohedral and Bernal stackings, which display different electronic characteristics. It is now shown that an applied perpendicular electric field can be used to switch between these two configurations. The crystal structure of a material plays an important role in determining its electronic properties. Changing from one crystal structure to another involves a phase transition that is usually controlled by a state variable such as temperature or pressure. In the case of trilayer graphene, there are two common stacking configurations (Bernal and rhombohedral) that exhibit very different electronic properties 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 . In graphene flakes with both stacking configurations, the region between them consists of a localized strain soliton where the carbon atoms of one graphene layer shift by the carbon–carbon bond distance 12 , 13 , 14 , 15 , 16 , 17 , 18 . Here we show the ability to move this strain soliton with a perpendicular electric field and hence control the stacking configuration of trilayer graphene with only an external voltage. Moreover, we find that the free-energy difference between the two stacking configurations scales quadratically with electric field, and thus rhombohedral stacking is favoured as the electric field increases. This ability to control the stacking order in graphene opens the way to new devices that combine structural and electrical properties.

We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in natural or lab-controlled ecosystems and in mathematical models. Here we emphasize the emergence of limit cycles following Hopf bifurcations tuned by the variability of interspecies interaction. As this variability increases, and owing to the large dimensionality of the system, limit cycles typically acquire a growing spectrum of frequencies. This often leads to the appearance of strange attractors, with a chaotic dynamics of species abundances characterized by a positive Lyapunov exponent. We observe that limit cycles and strange attractors preserve biodiversity to some extent, as they maintain dynamical stability without species extinction. We give numerical evidences that this route to chaos dominates in ecosystems with strong enough interactions and where predator-prey behavior dominates over competition and mutualism. Based on arguments from random matrix theory, we further conjecture that this scenario is generic in ecosystems with large number of species, and identify the key parameters driving it. Overall, we show that the model we consider provides a unifying framework, where a wide range of population dynamics emerge from a simple few-parameter model.

Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and what triggers species extinctions is a key, outstanding problem in theoretical ecology. Using standard methods of random matrix theory, I show that distributions of species abundances are Gaussian at equilibrium, in the weakly interacting regime. One consequence is that feasibility is generically broken before stability, for large enough number of species. I further derive an analytical expression for the probability that \\(n=0,1,2,...\\) species go extinct and conjecture that a single-parameter scaling law governs species extinctions. These results are corroborated by numerical simulations in a wide range of system parameters.