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Register a new userEvolving Powergrids in Self-Organized Criticality: An analogy with Sandpile and Earthquakes
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The stability of powergrid is crucial since its disruption affects systems ranging from street lightings to hospital life-support systems. Nevertheless, large blackouts are inevitable if powergrids are in the state of self-organized criticality (SOC). In this paper, we introduce a simple model of evolving powergrid and establish its connection with the sandpile model, i.e. a prototype of SOC, and earthquakes, i.e. a system considered to be in SOC. Various aspects are examined, including the power-law distribution of blackout magnitudes, their inter-event waiting time, the predictability of large blackouts, as well as the spatial-temporal rescaling of blackout data. We verified our observations on simulated networks as well as the IEEE 118-bus system, and show that both simulated and empirical blackout waiting times can be rescaled in space and time similarly to those observed between earthquakes. Finally, we suggested proactive maintenance strategies to drive the powergrids away from SOC to suppress large blackouts.
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A self-organization of efficient and robust networks is important for a future design of communication or transportation systems, however both characteristics are incompatible in many real networks. Recently, it has been found that the robustness of onion-like structure with positive degree-degree correlations is optimal against intentional attacks. We show that, by biologically inspired copying, an onion-like network emerges in the incremental growth with functions of proxy access and reinforced connectivity on a space. The proposed network consists of the backbone of tree-like structure by copyings and the periphery by adding shortcut links between low degree nodes to enhance the connectivity. It has the fine properties of the statistically self-averaging unlike the conventional duplication-divergence model, exponential-like degree distribution without overloaded hubs, strong robustness against both malicious attacks and random failures, and the efficiency with short paths counted by the number of hops as mediators and by the Euclidean distances. The adaptivity to heal over and to recover the performance of networking is also discussed for a change of environment in such disasters or battlefields on a geographical map. These properties will be useful for a resilient and scalable infrastructure of network systems even in emergent situations or poor environments.
We argue that atmospheric cascades can be regarded as example of the self-organized criticality and studied by using Levy flights and nonextensive approach. It allows us to understand the scale-invariant energy fluctuations inside cascades in a natural way.
The robustness of connectivity and the efficiency of paths are incompatible in many real networks. We propose a self-organization mechanism for incrementally generating onion-like networks with positive degree-degree correlations whose robustness is nearly optimal. As a spatial extension of the generation model based on cooperative copying and adding shortcut, we show that the growing networks become more robust and efficient through enhancing the onion-like topological structure on a space. The reasonable constraint for locating nodes on the perimeter in typical surface growth as a self-propagation does not affect these properties of the tolerance and the path length. Moreover, the robustness can be recovered in the random growth damaged by insistent sequential attacks even without any remedial measures.
In this work we present a general mechanism by which simple dynamics running on networks become self-organized critical for scale free topologies. We illustrate this mechanism with a simple arithmetic model of division between integers, the division model. This is the simplest self-organized critical model advanced so far, and in this sense it may help to elucidate the mechanism of self-organization to criticality. Its simplicity allows analytical tractability, characterizing several scaling relations. Furthermore, its mathematical nature brings about interesting connections between statistical physics and number theoretical concepts. We show how this model can be understood as a self-organized stochastic process embedded on a network, where the onset of criticality is induced by the topology.
From the starting point of the well known Reynolds number of fluid turbulence we propose a control parameter $R$ for a wider class of systems including avalanche models that show Self Organized Criticality (SOC) and ecosystems. $R$ is related to the driving and dissipation rates and from similarity analysis we obtain a relationship $Rsim N^{beta_N}$ where $N$ is the number of degrees of freedom. The value of the exponent $beta_N$ is determined by detailed phenomenology but its sign follows from our similarity analysis. For SOC, $R=h/epsilon$ and we show that $beta_N<0$ hence we show independent of the details that the transition to SOC is when $R to 0$, in contrast to fluid turbulence, formalizing the relationship between turbulence (since $beta_N >0$, $R to infty$) and SOC ($R=h/epsilonto 0$). A corollary is that SOC phenomenology, that is, power law scaling of avalanches, can persist for finite $R$ with unchanged exponent if the system supports a sufficiently large range of lengthscales; necessary for SOC to be a candidate for physical systems. We propose a conceptual model ecosystem where $R$ is an observable parameter which depends on the rate of throughput of biomass or energy; we show this has $beta_N>0$, so that increasing $R$ increases the abundance of species, pointing to a critical value for species explosion.
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