Electric Field Multifractal Features in the High-Latitude Ionosphere: CSES-01 Observations

In the polar ionosphere, the electric field is characterized by broadband and power law spectral densities at small/short spatio-temporal scales, which support a possible turbulent nature of the electric field fluctuations. Here, we investigate the multifractal character of the full three-dimensional electric field in the polar ionosphere as recorded on board the first Chinese Seismo-Electromagnetic Satellite (CSES-01). The results of our analysis prove a clear different degree of multifractality of the electric field fluctuations approaching either the polar cap trailing edge or the auroral region. The observed differences in the multifractal character are interpreted in terms of the different natures of the particle precipitation in the polar cap and in the auroral region. A possible link between the multifractal nature of electric field fluctuations, parallel to the geomagnetic field, and filamentation of field aligned currents (FACs) is established.

Intermittency Study of Charged Particles Generated in Pb-Pb Collisions at sNN=2.76 TeV Using EPOS3

Charged particle multiplicity fluctuations in Pb-Pb collisions are studied for the central events generated using EPOS3 (hydro and hydro+cascade) at sNN=2.76 TeV. Intermittency analysis is performed in the midrapidity region in two-dimensional (η, ϕ) phase space within the narrow transverse momentum (pT) bins in the low pT region (pT≤1.0 GeV/c). Power-law scaling of the normalized factorial moments with the number of bins is not observed to be significant in any of the pT bins. Scaling exponent ν, deduced for a few pT bins, is greater than that of the value 1.304, predicted for the second-order phase transition by the Ginzburg-Landau theory. The link in the notions of fractality is also studied. Generalized fractal dimensions, Dq, are observed to decrease with the order of the moment q suggesting the multifractal nature of the particle generation in EPOS3.

Multifractal Nature of Diesel Engine Rattle Noise in Vehicle

The investigation results of the emission of noises accompanying the diesel engine powertrain running in unloaded condition at low or idle speed, are presented in the hereby paper. The multifractal nature of the tested signals was confirmed by means of two groups of parameters. The proposed local parameters are based on the distribution of the probability density of measures, segregated into subsets according to pointwise Holder exponents. The obtained spectra constitute a set of multifractal measures related to singularities representing the local scaling of measures in various points of the time series. Global parameters were defined on the basis of multifractal measures of the parametrised Renyi’s entropy. These are properties treating summarily the whole spectrum of the emitted noise and reflecting changes of the vibroacoustic energy levels generated by noise sources. The tests encompassing simultaneous application of both groups of parameters confirmed their efficiency in the comparative analysis as well as in the subjective assessment of the noise level generated in the drive system of vehicles with diesel engines. This opens new possibilities within the simulation range of vehicle noises, for the needs of constructing the passive and active reduction systems of the effects of the vibroacoustic energy propagation.

ABOUT THE MULTIFRACTAL NATURE OF CANTOR’S BIJECTION: BOUNDS FOR THE HÖLDER EXPONENT AT ALMOST EVERY IRRATIONAL POINT

In this note, we investigate the regularity of Cantor’s one-to-one mapping between the irrational numbers of the unit interval and the irrational numbers of the unit square. In particular, we explore the fractal nature of this map by showing that its Hölder regularity lies between 0.35 and 0.72 almost everywhere (with respect to the Lebesgue measure).

The Analysis of Eigenstates of a Few Generalized Quantum Baker’s Maps Using Hadamard and Related Transforms

Application of the Hadamard and related transforms on a few generalized quantum baker’s maps have been studied. Effectiveness of the Hadamard transform and a new transform which combines the Fourier and the Hadamard transforms, for simplifying the eigenstates or resonances of the quantization of a few generalized baker’s map namely tetradic baker and lazy baker’s map when the Hilbert space dimension is power of [Formula: see text] has been done by comparing the participation ratios in the transformed basis with respect to the position basis. Several special family of states based on their maximal compression in either Hadamard transform or the new transform are identified and they are related to the ubiquitous Thue–Morse and allied sequences. Evidence is provided that these special family of states as well as average over all eigenstates exhibits multifractal nature.