We study the temporal correlations in the atmospheric variability by 14 meteorological stations around the globe, the variations of the daily maximum temperatures from their average values. We apply several methods that can systematically overcome possible nonstationarities in the data. We find that the persistence, characterized by the correlation C(s) of temperature variations separated by s days, approximately decays $C\left(s\right)\sim s^{-\gamma }$, with roughly the same exponent $\gamma \cong 0.7$ for all stations considered. The range of this universal persistence law seems to exceed one decade, and is possibly even larger than the range of the temperature series considered.

We perform Monte Carlo simulations for diffusion of charged particles in structurally disorderd lattices. As a consequence of the Coulomb interaction, pronounced backward correlations occur which lead to power-law behavior of the relevant transport quantities at intermediate time and frequency scales. Both the exponents and the size of the dispersive regime depend on temperature. Our simulations suggest that the combined effect of disorder and Coulomb interaction provides a new mechanism for understanding non-Debye relaxation, which is experimentally known for a wide class of materials.

The conductivity of ionic conductors containing a dispersed insulating second phase is investigated from the point of view of percolation theory. Using Monte Carlo simulations, we study a resistor model in two and three dimensions, which emphasizes the role of an enhanced interface conductivity. The existence of two critical concentrations $p_c^{\mathcal{’}}$ and $p_c^{2\mathrm{sprime}}$ of an insulating phase leads to a characteristic dependence of the overall conductivity on composition which is in remarkable agreement with experiment. Detailed calculations near the two thresholds $p_c^{\mathcal{’}}$ and $p_c^{2\mathrm{sprime}}$ yield critical properties in accord with random superconducting and random resistor networks. The question of a possible experimental verification of those critical properties is also discussed.