Characterization of Nanofluids Using Multifractal Analysis of a Liquid Droplet Trace

This paper presents a novel approach to the analysis of nanofluids by using a nonlinear multifractal algorithm. Multifractal analysis allows to present detailed local descriptions of complex scaling behavior using a spectrum of singularity exponents. Nanoliquids prepared from nanoparticles of SiO2 (~0,01g) suspended in 100 ml of demineralized water and in 100 ml of 99,5% isopropanol were subjected to classical methods of analysis: determination of the contact angle, determination of the zeta potential, pH, and examination with a particle size analyzer. The obtained results show that the obtained nanofluid is stable and well prepared, while further nonlinear analyzes show that the usage of multifractal analysis for nanofluids can significantly improve both the process of analyzing this issue as well as its preparation, based on the multifractional spectrum.

On the connection between intermittency and dissipation in ocean turbulence: a multifractal approach

The multifractal theory of turbulence is used to investigate the energy cascade in the Northwestern Atlantic ocean. The statistics of singularity exponents of horizontal velocity gradients computed from in situ measurements at 2 km resolution are used to characterize the anomalous scaling of the velocity structure functions at depths between 50 ad 500 m. Here, we show that the degree of anomalous scaling can be quantified using singularity exponents. Observations reveal, on one side, that the anomalous scaling has a linear dependence on the exponent characterizing the strongest velocity gradient and, on the other side, that the slope of this linear dependence decreases with depth. Since the observed distribution of exponents is asymmetric about the mode at all depths, we use an infinitely divisible asymmetric model of the energy cascade, the log-Poisson model, to derive the functional dependence of the anomalous scaling with the exponent of the strongest velocity gradient, as well as the dependence with dissipation. Using this model we can interpret the vertical change of the linear slope between the anomalous scaling and the exponents of the strongest velocity gradients as a change in the energy cascade. This interpretation assumes the validity of the multifractal theory of turbulence, which has been assessed in previous studies.

Restriction formula and subadditivity property related to multiplier ideal sheaves

We give a restriction formula on jumping numbers which is a reformulation of Demailly–Ein–Lazarsfeld’s important restriction formula for multiplier ideal sheaves and a generalization of Demailly–Kollár’s important restriction formula on complex singularity exponents, and then we establish necessary conditions for the extremal case in the reformulated formula; we pose the subadditivity property on the complex singularity exponents of plurisubharmonic functions which is a generalization of Demailly–Kollár’s fundamental subadditivity property, and then we establish necessary conditions for the extremal case in the generalization. We also obtain two sharp relations on jumping numbers, introduce a new invariant of plurisubharmonic singularities and get its decreasing property for consecutive differences.

Multifractal analysis of uterine electromyography signals to differentiate term and preterm conditions

In this study, an attempt has been made to identify the origin of multifractality in uterine electromyography signals and to differentiate term (gestational age > 37 weeks) and preterm (gestational age ≤ 37 weeks) conditions by multifractal detrended moving average technique. The signals obtained from a publicly available database, recorded from the abdominal surface during the second trimester, are used in this study. The signals are preprocessed and converted to shuffle and surrogate series to examine the source of multifractality. Multifractal detrended moving average algorithm is applied on all the signals. The presence of multifractality is verified using scaling exponents, and multifractal spectral features are extracted from the spectrum. The variation of multifractal features in term and preterm conditions is analyzed statistically using Student’s t-test. The results of scaling exponents show that the uterine electromyography or electrohysterography signals reveal multifractal characteristics in term and preterm conditions. Further investigation indicates the existence of long-range correlation as the primary source of multifractality. Among all extracted features, strength of multifractality, exponent index, and maximum and peak singularity exponents are statistically significant ( p < 0.05) in differentiating term and preterm conditions. The coefficient of variation is found to be lower for strength of multifractality and peak singularity exponent, which reveal that these features exhibit less inter-subject variance. Hence, it appears that multifractal analysis can aid in the diagnosis of preterm or term delivery of pregnant women.

MULTIFRACTAL FORMALISM OF OSCILLATING SINGULARITIES FOR RANDOM WAVELET SERIES

The oscillating multifractal formalism is a formula conjectured by Jaffard expected to yield the spectrum d(h, β) of oscillating singularity exponents from a scaling function ζ(p, s'), for p > 0 and s' ∈ ℝ, based on wavelet leaders of fractional primitives f-s' of f. In this paper, using some results from Jaffard et al., we first show that ζ(p, s') can be extended on p ∈ ℝ to a function that is concave with respect to p ∈ ℝ and independent on orthonormal wavelet bases in the Schwartz class. We also establish its concavity with respect to s' when p > 0. Then, we prove that, under some assumptions, the extended scaling function ζ(p, s') is the Legendre transform of the wavelet leaders density of f-s'. Finally, as an application, we study the validity of the extended oscillating multifractal formalism for random wavelet series (under the assumption of independence and laws depending only on the scale).