The rapid increase in renewable energy production facilities, domestic installations injecting back onto the grid, and surge electric vehicle adoption associated high voltage charging stations are all placing unprecedented demands on power grid. This article summarizes physics that can inform design operation principles for future compliant grids. authors show mathematically modeling grids as coupled nonlinear dynamical systems networks, utilizing concepts from statistical graph theory...

Abstract The Texas power grid on the Gulf Coast of United States is frequently hit by tropical cyclones (TCs) causing widespread outages, a risk that expected to substantially increase under global warming. Here we introduce new approach combines probabilistic line failure model with network simulate spatio-temporal co-evolution wind-induced failures high-voltage transmission lines and resulting cascading outages from seven major historical TCs. allows reproducing observed supply failures....

The amplitude for the 4-simplex in a spin foam model quantum gravity is defined using graphical calculus unitary representations of Lorentz group.The asymptotics this are studied limit when representation parameters large, various cases boundary data.It shown that data corresponding to Lorentzian simplex, asymptotic formula has two terms, with phase plus or minus signature Regge action geometry, multiplied by an Immirzi parameter.Other also considered, including surprising contribution from...

The semiclassical limit of a four-simplex amplitude for spin foam quantum gravity model with an Immirzi parameter is studied. If the boundary state represents nondegenerate geometry, asymptotic formula contains Regge action general relativity. A canonical choice phase introduced and shown to be necessary obtain results.

Abstract The stability of synchronised networked systems is a multi-faceted challenge for many natural and technological fields, from cardiac neuronal tissue pacemakers to power grids. For these, the ongoing transition distributed renewable energy sources leads proliferation dynamical actors. desynchronisation few or even one those would likely result in substantial blackout. Thus synchronous state has become leading topic grid research. Here we uncover that, when taking into account...

Abstract The notion of a part phase space containing desired (or allowed) states dynamical system is important in wide range complex systems research. It has been called the safe operating space, viability kernel or sunny region. In this paper we define survivability: Given random initial condition, what likelihood that transient behaviour deterministic does not leave region desirable states. We demonstrate utility novel stability measure by considering models from climate science, neuronal...

We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current foam models to be defined on arbitrary 2-complexes as well generalize arbitrary, in particular, finite groups. The similarity with standard theories us apply coarse graining methods, groups can now easily considered numerically. will summarize other and network formulations foams group field explain how different representations arise through variable...

The goal of this paper is to introduce a systematic approach spin foams.We define operator foams, that foams labelled by group representations and operators, as our main tool.A set moves we in the allows (among other operations) split faces edges assign each foam contracted operator, using contractions at vertices suitably adjusted face amplitudes.The emergence amplitudes consequence assuming invariance with respect moves.Next, models consider class assumed be symmetric have introduced,...

The asymptotics of the SU(2) 15j-symbol are obtained using coherent states for boundary data. geometry all nonsuppressed data is given. For some data, resulting formula interpreted in terms Regge action a 4-simplex four-dimensional Euclidean space. This asymptotic can be used to derive and extend spin foam amplitudes quantum gravity models. relation Ooguri model these models their continuum Lagrangians discussed.

Abstract The prediction of dynamical stability power grids becomes more important and challenging with increasing shares renewable energy sources due to their decentralized structure, reduced inertia volatility. We investigate the feasibility applying graph neural networks (GNN) predict dynamic synchronisation in complex using single-node basin (SNBS) as a measure. To do so, we generate two synthetic datasets for 20 100 nodes respectively estimate SNBS Monte-Carlo sampling. Those are used...

90% of all Renewable Energy Power in Germany is installed tree-like distribution grids. Intermittent power fluctuations from such sources introduce new dynamics into the lower grid layers. At same time, distributed resources will have to contribute stabilize against these future. In this paper, we model a system as oscillators on tree-like, lossy and its ability withstand desynchronization localized intermittent renewable infeed. We find remarkable interplay network structure position node...

Coupled oscillator networks show a complex interrelations between topological characteristics of the network and nonlinear stability single nodes with respect to large but realistic perturbations. We extend previous results on these relations by incorporating sampling-based measures transient behaviour system, its survivability, as well asymptotic behaviour, basin stability. By combining survivability we uncover novel, previously unknown states solitary, desynchronized oscillators which are...

We study two generalizations of the basin attraction a stable state, to case stochastic dynamics, arbitrary regions, and finite-time horizons. This is done by introducing generalized committor functions studying soujourn times. show that volume basin, stability, can be efficiently estimated using Monte Carlo-like techniques, making this concept amenable high-dimension systems. Finally, we illustrate in set examples basins capture realm metastable sets, which parts phase space go into long...

Using the coherent state techniques developed for analysis of EPRL model we give asymptotic formula Ponzano–Regge amplitude non-tardis triangulations handlebodies in limit large boundary spins. The produces a sum over all possible immersions triangulation and its value is given by cosine Regge action evaluated on these. Furthermore scaling registers existence flexible immersions. We verify numerically that this approximates 6j-symbol

To mitigate climate change, the share of renewable energies in power production needs to be increased. Renewables introduce new challenges grids regarding dynamic stability due decentralization, reduced inertia, and volatility production. Since simulations are intractable exceedingly expensive for large grids, graph neural networks (GNNs) a promising method reduce computational effort analyzing grids. As testbed GNN models, we generate new, datasets synthetic provide them as an open-source...

The energy transition introduces new classes of dynamical actors into the power grid. There is, in particular, a growing need for so-called grid-forming inverters (GFIs) that can contribute to dynamic grid stability as share synchronous generators decreases. Understanding collective behavior and future grids, featuring heterogeneous mix dynamics, remains an urgent challenging task. Two recent advances describing such modern dynamics have made this problem more tractable. First, normal form...

We review the basic steps in building asymptotic analysis of Euclidean sector new spin foam models using coherent states, for Immirzi parameter less than one. focus on conceptual issues and by so doing omit peripheral proofs original discussion structures.

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PowerDynamics.jl is a Julia package for time-domain modeling of power grids that specifically designed the stability analysis systems with high shares renewable energies. It makes use Julia's state-of-the-art differential equation solvers and highly performant even large number components. Further, it compatible machine learning libraries allows utilization these methods dynamical optimization parameter fitting. The comes predefined models synchronous machines, transmission lines inverter...

Future power grids will be operating a large number of heterogeneous dynamical actors. Many these contribute to the fundamental stability system, and play central role in establishing self-organized synchronous state that underlies energy transport through grid. We derive normal form for grid-forming components grids. This allows analyzing grids’ systemic properties technology neutral manner, without detailed component models. Our approach is based on physics flow grid one hand, common...

We discuss the definition of quantum probability in context ``timeless'' general-relativistic mechanics. In particular, we study sequences events, or multievent probability. conventional mechanics this can be obtained by means ``wave function collapse'' algorithm. first point out certain difficulties some natural definitions probability, including conditional widely considered literature. then observe that reduced to single-event taking into account nature measuring apparatus. fact,...

We discuss the expansions used in spin foam cosmology. point out that already at one-vertex level, arbitrarily complicated amplitudes contribute and geometric asymptotics of five simplest ones. what type consistency conditions would be required to control expansion. show factorization amplitude originally considered is best interpreted topological terms. then consider next-higher term graph demonstrate tension between truncation small graphs going homogeneous sector conclude it necessary...