The multifractal formalism is applied for investigating probability measures of energy levels of an Ising model with four-spin interactions on finite-size hexagonal lattices. The Hölder exponent characterizing singularities of these measures is determined as a function of the temperature...

In this short paper we describe the essential ideas behind a new consistent closure procedure for the calculation of the scaling exponents ζn of the nth order correlation functions in fully developed hydrodynamic turbulence, starting from first principles. The closure procedure is constructed...

A 3D copepod trajectory is recorded in the laboratory, using two digital cameras. The copepod undergoes a very structured type of trajectory, with successive moves displaying intermittent amplitudes. We perform a statistical analysis of this 3D trajectory using statistical tools developed in the...

An intensity–duration–area–frequency (IDAF) function is derived for the small-scale, large-intensity limit of multifractal fields. A parameterization of the function from tropical rainfall, filmed with a digital camera in Mexico City, is being attempted. Implications of the formulae are...

We analyze the spatial and the luminosity properties of the Perseus-Pisces redshift survey. We find that the two point correlation function (CF) Γ(r) is a power law up to the sample effective depth (∼ 30 h−1 Mpc), showing the fractal nature of the galaxy distribution in this catalog. The...

We investigate the multifractal properties for the spectra of plasmon–polaritons and light waves in multiple layers arranged in a quasiperiodic fashion. The profiles of the plasmon polariton bandwidths and the light transmission spectra are analyzed and the f(α) functions are calculated for...

The multifractal properties of spin wave bandwidths in quasiperiodic magnetic multilayers are studied. The profiles of the bandwidths are analyzed and the f(α) function is calculated for different values of the dimensionless in-plane wave vector kxa and for four different sequences: Fibonacci,...

We investigate the probability of observing a given pattern of n rises and falls in a random stationary data series. The data are modeled as a sequence of n+1 independent and identically distributed random numbers. This probabilistic approach has a combinatorial equivalent, where the data are...

Strongly inhomogeneous multifractal measures involving extremely diverse local probability scales and exhibiting left-sided multifractal spectra are considered. The standard multifractal formalism is extended to such drastically inhomogeneous multifractal measures by introducing additional...