Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and malicious outages is analyzed in the framework of complex network theory. In particular, the quantity known as efficiency is modified by introducing a new concept of distance between nodes. As a result, a new parameter called net-ability is proposed to evaluate the performance of power grids. A comparison between efficiency and net-ability is provided by estimating the vulnerability of sample networks, in terms of both the metrics.

Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals. We systematically study the performance of different variants of the DMA method when applied to artificially generated long-range power-law correlated signals with an a priori known scaling exponent ${\alpha }_0$ and compare them with the DFA method. We find that the scaling results obtained from different variants of the DMA method strongly depend on the type of the moving average filter. Further, we investigate the optimal scaling regime where the DFA and DMA methods accurately quantify the scaling exponent ${\alpha }_0$, and how this regime depends on the correlations in the signal. Finally, we develop a three-dimensional representation to determine how the stability of the scaling curves obtained from the DFA and DMA methods depends on the scale of analysis, the order of detrending, and the order of the moving average we use, as well as on the type of correlations in the signal.

Low-frequency current fluctuations are investigated over a bias range covering Ohmic, trap-filling, and space-charge-limited current regimes in polycrystalline polyacenes. The relative current noise power spectral density $\mathcal{S}(f)$ is constant in the Ohmic region, steeply increases at the trap-filling transition region, and decreases in the space-charge-limited-current region. The noise peak at the trap-filling transition is accounted for within a continuum percolation model. As the quasi-Fermi level crosses the trap level, intricate insulating paths nucleate within the Ohmic matrix, determining the onset of nonequilibrium conditions at the interface between the insulating and conducting phase. The noise peak is written in terms of the free and trapped charge carrier densities.

We analyze the stochastic function $C_n\mathrm{}\left(i\right)\mathrm{}\equiv y\left(i\right)\mathrm{}-y_n\mathrm{}\left(i\right),$ where $y\left(i\right)\mathrm{}$ is a long-range correlated time series of length $N_{\max }$ and $y_n\mathrm{}\left(i\right)\mathrm{}\equiv \mathrm{}(1/n)\mathrm{}{\sum }_{k=0\mathrm{}}^{n-1}y\left(i-k\right)$ is the moving average with window n. We argue that $C_n\mathrm{}\left(i\right)\mathrm{}$ generates a stationary sequence of self-affine clusters $\mathcal{C}$ with length $\mathcal{l},$ lifetime $\tau ,$ and area s. The length and the area are related to the lifetime by the relationships $\mathcal{l}\sim {\tau }^{{\psi }_{\mathcal{l}}}$ and $s\sim {\tau }^{{\psi }_s},$ where ${\psi }_{\mathcal{l}}=1\mathrm{}$ and ${\psi }_s=1+H.\mathrm{}$ We also find that $\mathcal{l},$ $\tau ,$ and s are power law distributed with exponents depending on H: $P\left(\mathcal{l}\right)\sim {\mathcal{l}}^{-\alpha },$ $P\left(\tau \right)\sim {\tau }^{-\beta },$ and $P\left(s\right)\mathrm{}\sim s^{-\gamma },$ with $\alpha =\beta =2\mathrm{}-H$ and $\gamma =2/(1+H).$ These predictions are tested by extensive simulations on series generated by the midpoint displacement algorithm of assigned Hurst exponent H (ranging from 0.05 to 0.95) of length up to $N_{\max }{=2\mathrm{}}^{21}$ and n up to $2^{13}.$