Multifractal analysis of selected rare-earth elements

Abstract

The multifractal formalism is applied to the energy eigenvalues of Ce I, Ce II, Nd II, Sm I, Sm II, and Tb I. The Rényi dimensions D q , mass exponents τ (q) and f (α) spectra are calculated and used to characterize the eigenvalue spectra. It is found that these elements show multi-scaling behaviour that can be accurately modelled by simple multifractal recursive Cantor sets. The effect of unfolding the spectra is also investigated.

Signatures of quantum chaos in rare-earth elements: II. Characterization of the energy eigenvalues and dipole moments of CeIand PrI

“…This has perhaps relevance to [30], where these elements apparently give rise to f (α) spectra. However, it should be stressed that relatively few energy eigenvalues were used in the f (α) analysis and the levels were not sorted according to parity or J value.…”

Spectral fluctuation characterization of random matrix ensembles through wavelets

“…Study of multi-fractal behaviour has been carried out earlier in the context of various atoms and ions. Methods like, box-counting [20] and correlation sum have been employed [21,22]. Keeping in mind the possible non-stationary nature of the data, as well as efficacy of the wavelet based approach for extracting fluctuations, we have used the same here for studying the self-similar nature of the fluctuations.…”

Multifractal Analysis of Charged Particle Multiplicity Distribution in the Framework of Renyi Entropy

“…Multifractal theory is essentially rooted in probability theory, though draws on complex ideas from each of physics, mathematics, probability theory and statistics [6]. Apart from multiparticle production in high energy physics, multifractal analysis has proved to be a valuable method of capturing the underlying scaling structure present in many types of systems including diffusion limited aggregation [8][9][10], fluid flow through random porous media [11], atomic spectra of rare-earth elements [12], cluster-cluster aggregation [13] and turbulent flow [14]. In physiology, multifractal structures have been found in heart rate variability [15] and brain dynamics [16].…”