We study the statistics of the recurrence times between earthquakes above a certain magnitude M in California. We find that the distribution of the recurrence times strongly depends on the previous recurrence time τ0. As a consequence, the conditional mean recurrence time τ^(τ0) between two...

We study the daily river flow fluctuations of 30 international rivers. Using the detrended fluctuation analysis, we study the correlations in the magnitudes of river flow increments (volatilities), and find power-law correlations in volatilities for time scales less than 1 year; these...

Mixed β/β″-alumina crystals are two-dimensional ion conductors, whose conductivities vary dramatically upon mixing of two types of mobile ions. We summarize a theoretical model, which can explain these conductivity variations quantitatively. According to the model, percolation effects are...

The purpose of this talk is to describe some recent progress in applying scaling concepts to various systems in nature. We review several systems characterized by scaling laws such as DNA sequences, heartbeat rates and weather variations. We discuss the finding that the exponent α quantifying...

Structural disorder is an inherent property of solid materials, which can support a macroscopic ionic current. Many transport phenomena in these solid ionic conductors appear to be related to concepts from percolation theory. We demonstrate this for three classes of materials, namely (i)...

We review recent developments in the study of the multifractal properties of dynamical processes in disordered systems. In particular, we discuss the multifractality of the growth probabilities of DLA clusters and of the probability density for random walks on random fractals. The results for...

We investigate for the first time spin-lattice relaxation caused by particles diffusing in disordered environments. For noninteracting particles on a fractal substrate with fractal dimension df and diffusion exponent dw, we find that the NMR correlation functions G(q)(t) are asymptotically...

We briefly review some recent attempts to achieve some genuine understanding of diffusion-limited aggregation (DLA), the paradigm model for dynamical mechanisms of disorderly growth processes. We shall see that the seminal ideas of Professor Cyril Domb have influenced to a great degree many of...

General lower bounds for the time average CAA(∞)≡limT→∞(1T)∝T0 CAA(t) dt of the correlation CAA(t)≡〈A(t)A(0)〉−〈A〉2 of an arbitrary variable A are derived, which depend only on the temperature derivatives of the canonical averages of A and the Hamiltonian of the system. The...