The superconducting-insulator transition is simulated in disordered networks of Josephson junctions with thermally activated Arrhenius-like resistive shunt. By solving the conductance matrix of the network, the transition is reproduced in different e
xperimental conditions by tuning thickness, charge density and disorder degree. In particular, on increasing fluctuations of the parameters entering the Josephson coupling and the Coulomb energy of the junctions, the transition occurs for decreasing values of the critical temperature Tc and increasing values of the activation temperature To. The results of the simulation compare well with recent experiments where the mesoscopic fluctuations of the phase have been suggested as the mechanism underlying the phenomenon of emergent granularity in otherwise homogeneous films. The proposed approach is compared with the results obtained on TiN films and nanopatterned arrays of weak-links, where the superconductor-insulator transition is directly stimulated.
A method for estimating the cross-correlation $C_{xy}(tau)$ of long-range correlated series $x(t)$ and $y(t)$, at varying lags $tau$ and scales $n$, is proposed. For fractional Brownian motions with Hurst exponents $H_1$ and $H_2$, the asymptotic exp
ression of $C_{xy}(tau)$ depends only on the lag $tau$ (wide-sense stationarity) and scales as a power of $n$ with exponent ${H_1+H_2}$ for $tauto 0$. The method is illustrated on (i) financial series, to show the leverage effect; (ii) genomic sequences, to estimate the correlations between structural parameters along the chromosomes.
We propose an algorithm to estimate the Hurst exponent of high-dimensional fractals, based on a generalized high-dimensional variance around a moving average low-pass filter. As working examples, we consider rough surfaces generated by the Random Mid
point Displacement and by the Cholesky-Levinson Factorization algorithms. The surrogate surfaces have Hurst exponents ranging from 0.1 to 0.9 with step 0.1, and different sizes. The computational efficiency and the accuracy of the algorithm are also discussed.
