Anisotropic Analysis of Some Gaussian Models

Although the classical Fractional Brownian Motion is often used to describe porosity, it is not adapted to anisotropic situations. In the present work, we study a class of Gaussian fields with stationary increments and spectral density. They present asymptotic self-similarity properties and are good candidates to model a homogeneous anisotropic material, or its radiographic images. Unfortunately, the paths of all Gaussian fields with stationary increments have the same apparent regularity in all directions (except at most one). Hence we propose here a procedure to recover anisotropy from one realization: computing averages over all the hyperplanes which are orthogonal to a fixed direction, we get a process whose Hölder regularity depends explicitly on the asymptotic behavior of the spectral density in this direction.     

Sur les valeurs propres d'un oscillateur harmonique perturbé

Sans résumé Dedicated to Professor Shmuel Agmon     

Implementation of the Laser Diffraction Technique for Acoustic Cavitation Bubble Investigations

Knowledge of the acoustic cavitation cloud would be useful for improving ultrasound reactor design. Among the characterisation techniques, few are adapted to bubble investigations in an intense ultrasound field. Some problems raised by these measurements result from interactions between the acoustic pressure wave and the measuring light wave. This paper reports the implementation of the laser diffraction technique to determine the size and volume concentration of bubbles generated by a dipping horn operating at 20 kHz. Measurements were performed with a Malvern 2600 instrument. The size distribution, deduced from the diffraction pattern scattered by the bubble cloud crossed by a laser beam, is disturbed by the acoustic pressure wave involving deviation of a light beam at low diffusion angles (acousto‐optic effect). A bubble size correction procedure based on the subtraction of the light energy due to the ultrasound wave is described. The size measurements, and thus the correction procedure, were validated by a second laser technique based on a different measuring principle: phase Doppler interferometry. The measurement reliability was further confirmed by an original application of laser diffraction based on measurements performed just after sonication. These three methods lead to a mean bubble size (Sauter mean diameter) of about 10 μm at a high ultrasound power input. Concerning the void fraction, only measurements achieved after sonication and by laser diffraction predict a correct estimation of this parameter.     

Fundamental processes in long air gap discharges

The development of atmospheric lightning is initiated and sustained by the formation in virgin air of ‘streamer corona’ and ‘leader’ discharges, very similar to those observed in laboratory long sparks. Therefore, the experimental and theoretical investigations of these laboratory discharges have become of large interest to improve the physical knowledge of the lightning process and to develop self-consistent models that could be applied to new protection concepts.In the present paper the fundamental processes of the subsequent phases of long air gap discharges are analyzed, from the first corona inception and development to the leader channel formation and propagation. For all these processes simulations models are discussed that have been essentially derived and simplified by the authors, in order to develop sequential time-dependent simulation of the laboratory breakdown, with both positive and negative voltages. The possibility of extending these models to the case of natural lightning is discussed in the companion paper, presented in this same volume. To cite this article: I. Gallimberti et al., C. R. Physique 3 (2002) 1335–1359.     

Associations between Neurocardiovascular Signal Entropy and Physical Frailty

In this cross-sectional study, the relationship between noninvasively measured neurocardiovascular signal entropy and physical frailty was explored in a sample of community-dwelling older adults from The Irish Longitudinal Study on Ageing (TILDA). The hypothesis under investigation was that dysfunction in the neurovascular and cardiovascular systems, as quantified by short-length signal complexity during a lying-to-stand test (active stand), could provide a marker for frailty. Frailty status (i.e., “non-frail”, “pre-frail”, and “frail”) was based on Fried’s criteria (i.e., exhaustion, unexplained weight loss, weakness, slowness, and low physical activity). Approximate entropy (ApEn) and sample entropy (SampEn) were calculated during resting (lying down), active standing, and recovery phases. There was continuously measured blood pressure/heart rate data from 2645 individuals (53.0% female) and frontal lobe tissue oxygenation data from 2225 participants (52.3% female); both samples had a mean (SD) age of 64.3 (7.7) years. Results revealed statistically significant associations between neurocardiovascular signal entropy and frailty status. Entropy differences between non-frail and pre-frail/frail were greater during resting state compared with standing and recovery phases. Compared with ApEn, SampEn seemed to have better discriminating power between non-frail and pre-frail/frail individuals. The quantification of entropy in short length neurocardiovascular signals could provide a clinically useful marker of the multiple physiological dysregulations that underlie physical frailty.     

Parameter Analysis of Multiscale Two-Dimensional Fuzzy and Dispersion Entropy Measures Using Machine Learning Classification

Two-dimensional fuzzy entropy, dispersion entropy, and their multiscale extensions (MFuzzyEn2D and MDispEn2D, respectively) have shown promising results for image classifications. However, these results rely on the selection of key parameters that may largely influence the entropy values obtained. Yet, the optimal choice for these parameters has not been studied thoroughly. We propose a study on the impact of these parameters in image classification. For this purpose, the entropy-based algorithms are applied to a variety of images from different datasets, each containing multiple image classes. Several parameter combinations are used to obtain the entropy values. These entropy values are then applied to a range of machine learning classifiers and the algorithm parameters are analyzed based on the classification results. By using specific parameters, we show that both MFuzzyEn2D and MDispEn2D approach state-of-the-art in terms of image classification for multiple image types. They lead to an average maximum accuracy of more than 95% for all the datasets tested. Moreover, MFuzzyEn2D results in a better classification performance than that extracted by MDispEn2D as a majority. Furthermore, the choice of classifier does not have a significant impact on the classification of the extracted features by both entropy algorithms. The results open new perspectives for these entropy-based measures in textural analysis.     

Estimation of lake water—groundwater interactions in meromictic mining lakes by modelling isotope signatures of lake water

Abstract

A method is presented to assess lake water–groundwater interactions by modelling isotope signatures of lake water using meteorological parameters and field data. The modelling of δ¹⁸O and δD variations offers information about the groundwater influx into a meromictic Lusatian mining lake. Therefore, a water balance model is combined with an isotope water balance model to estimate analogies between simulated and measured isotope signatures within the lake water body. The model is operated with different evaporation rates to predict δ¹⁸O and δD values in a lake that is only controlled by weather conditions with neither groundwater inflow nor outflow. Comparisons between modelled and measured isotope values show whether the lake is fed by the groundwater or not. Furthermore, our investigations show that an adaptation of the Craig and Gordon model [H. Craig, L.I. Gordon. Deuterium and oxygen-18 variations in the ocean and the marine atmosphere. In Stable Isotopes in Oceanographic Studies and Paleotemperature, Spoleto, E. Tongiorgi (Ed.), pp. 9–130, Consiglio Nazionale delle Ricerche, Laboratorio di Geologia Nucleare, Pisa (1965).] to specific conditions in temperate regions seems necessary.     

Dating problems with selected mining lakes and the adjacent groundwater body in Lusatia,Germany

This study presents selected results, applying environmental tracers to investigate lake water–groundwater interactions at two study sites located in Lusatia, Germany. The focus of the investigations were two meromictic pit lakes and their adjacent aquifers. In order to follow hydrodynamic processes between lake and groundwater, mixing patterns within the lakes as well as ages of lake and groundwater, water samples of ground- and lake water were collected at three occasions, representing summer and winter conditions in the aquatic systems. The water samples were analysed for stable isotopes (deuterium, oxygen-18) and tritium and sulphurhexafluoride (SF₆ concentration). Lake water profiles of conductivity and ¹⁸O could validate the permanent stratification pattern of both the lakes. Groundwater data sets showed a heterogeneous local distribution in stable isotope values between rain and lake water. A two-component mixing model had been adopted only from ¹⁸O data to determine lake water proportions in the surrounding groundwater wells in order to correct measured tritium and SF₆ concentrations in groundwater samples. This procedure had been hampered by upstream-located wells indicating strong ¹⁸O enrichment in groundwater samples. However, rough groundwater ages were estimated. For both study sites, Piston flow ages between 12.9 and 27.7 years were calculated. The investigations showed the good agreement between two different environmental dating tools, considering the marginal data sets.     

Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators

A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.     

Green ultrasound-assisted extraction of carotenoids based on the bio-refinery concept using sunflower oil as an alternative solvent

A green, inexpensive and easy-to-use method for carotenoids extraction from fresh carrots assisted by ultrasound was designed in this work. Sunflower oil was applied as a substitute to organic solvents in this green ultrasound-assisted extraction (UAE): a process which is in line with green extraction and bio-refinery concepts. The processing procedure of this original UAE was first compared with conventional solvent extraction (CSE) using hexane as solvent. Moreover, the UAE optimal conditions for the subsequent comparison were optimized using response surface methodology (RSM) and ultra performance liquid chromatography – diode array detector – mass spectroscopy (UPLC–DAD–MS). The results showed that the UAE using sunflower as solvent has obtained its highest β-carotene yield (334.75 mg/l) in 20 min only, while CSE using hexane as solvent obtained a similar yield (321.35 mg/l) in 60 min. The green UAE performed under optimal extraction conditions (carrot to oil ratio of 2:10, ultrasonic intensity of 22.5 W cm^?2, temperature of 40 °C and sonication time of 20 min) gave the best yield of β-carotene.