We determine the geometrical properties of the most probable paths at finite temperatures T, between two points separated by a distance r, in one-dimensional lattices with positive energies of interaction εi associated with bond i. The most probable path-length tmp in a homogeneous medium...

We study numerically and by scaling arguments the probability P(M)dM that a given dangling end of the incipient percolation cluster has a mass between M and M+dM. We find by scaling arguments that P(M) decays with a power law, P(M)∼M−(1+κ), with an exponent κ=dfB/df, where df and dfB are...

There has been growing interest in the study of Lévy flights observed in the movements of biological organisms performing random walks while searching for other organisms. Here, we approach the problem of what is the best statistical strategy for optimizing the encounter rate between...

Generic three-dimensional (3D) exact relations were found recently (Phys. Rev. B (2002) 184416) between macroscopic or bulk effective moduli of composite systems with related microstructures which are, in general, different. As an example of possible application of these relations, a new...

We use the generating function formalism to calculate the fractal dimensions for the percolating cluster at criticality in Erdős–Rényi (ER) and random scale free (SF) networks, with degree distribution P(k)=ck−λ. We show that the chemical dimension is dl=2 for ER and SF networks with...

We analyze transport properties of a random walk on a comb structure, which serves as a model for a random walk on the backbone of a percolation cluster. It is shown that the random walk along the x axis, which is the analog of the backbone, exhibits anomalous diffusion in that 〈x2(n)〉 ∼...

It is well known that while daily price returns of financial markets are uncorrelated, their absolute values (‘volatility’) are long-term correlated. Here we provide evidence that certain subsequences of the returns themselves also exhibit long-term memory. These subsequences consist of...

We investigate the local cumulative phases at single sites of the lattice for time-dependent wave functions in the Anderson model in d=2 and 3. In addition to a local linear trend, the phases exhibit some fluctuations. We study the time correlations of these fluctuations using detrended...

Using detrended fluctuation analysis, we study the scaling properties of the volatility time series Vi=|Ti+1−Ti| of daily temperatures Ti for 10 chosen sites around the globe. We find that the volatility is long-range power-law correlated with an exponent γ close to 0.8 for all sites...

We study the Zipf plots describing the occurrence of different elements in a given group as a function of their rank. We define a “distance” between two Zipf plots characterizing the differences between the two groups. We apply the distance concept on groups of words contained in books. Our...