Intermittency Parameter Research Articles

Managing Inventory with Limited History of Intermittent Demand

We consider a single-product discrete-time inventory model with intermittent demand. In every period, either zero demand or a positive demand is observed with an unknown probability. The distribution of the positive demand is assumed to be from the location-scale family with unknown mean and variance. The functional form of the optimal inventory target is available but it is a function of the unknown intermittent demand parameters that must be estimated from a limited amount of historical demand data. We first quantify the expected cost associated with implementing the optimal inventory policy using the point estimates of the unknown parameters by ignoring the uncertainty around them. We then minimize this expected cost with respect to a threshold variable that factors the statistical estimation errors of the unknown parameters into the inventory decision. We find that the use of an optimized threshold leads to a significant reduction in the a priori expected cost of the decision maker.

Abstract 14869: Survivors of Adult Out-of-Hospital Cardiac Arrest Are Likely to be Neurologically Intact Despite Prolonged Prehospital Resuscitation

Introduction: Preliminary data suggest that adult out-of-hospital cardiac arrest (OHCA) patients may survive neurologically intact with duration of prehospital resuscitation (DOPR) exceeding previous guidelines. We assess how DOPR affects neurologically intact survival (NIS) from OHCA. Methods: We conducted an observational study of all OHCA patients in our urban/suburban advanced life support EMS system (pop 1,000,000) from 2005-2014. Excluded were resuscitations not attempted, age < 16, trauma patients, and EMS-witnessed arrests. DOPR was measured from time of dispatch to end of prehospital resuscitation, defined by first return of spontaneous circulation, en-route hospital, or death. Primary outcome was NIS, defined as cerebral performance category (CPC) 1 or 2. Multiple modelling approaches including decision trees and multivariate logistic regression were used to determine predictors of NIS. Results: Of 3814 eligible OHCA, patients were: mean age 64.3 years and 60.4% male, 38.2% bystander witnessed, and 43.3% bystander assisted. Median time to first arriving professional response unit was 4.6 min (IQR 3.4-6.0). We controlled for resuscitation protocol changes over time, with median CPR fraction of 96% (IQR 93-96) and median compression rate 114 (103-137) during the most recent phase. Overall, 467 survived (12.2%) and 392 had NIS (83.9% of survivors). The median DOPR for NIS was 18 min (12-25), and the 90th percentile for NIS was 35 min, with 39 patients surviving neurologically intact with DOPR > 35 min. The adjusted OR (95% CI) for the continuous variable DOPR was 0.99 (0.99-1.00) for NIS and 1.00 (0.99-1.00) for overall survival. The length of time that EMS was on scene also had an adjusted OR of 1.00 (1.00-1.00) for both survival and NIS. Significant predictors of NIS include age, initial rhythm, witnessed, basic airway, prehospital ROSC, and therapeutic hypothermia phase. Intermittent physiologic parameters such as End Tidal CO2 measured at 30 minutes after dispatch were not predictive. Limitations include the observational study design. CONCLUSIONS: In this retrospective analysis of OHCA, a majority of survivors were NIS regardless of DOPR. Further study should examine predictors of paramedics’ decision to extend resuscitation.

A framework for the reliability evaluation of grid-connected photovoltaic systems in the presence of intermittent faults

A framework for the reliability evaluation of grid-connected PV (photovoltaic) systems with intermittent faults is proposed using DBNs (dynamic Bayesian networks). A three-state Markov model is constructed to represent the state transition relationship of no faults, intermittent faults, and permanent faults for PV components. The model is subsequently fused into the DBNs. The reliability and availability of three simple PV systems with centralized, string, and multistring configurations, as well as a complex PV system, are analyzed through the proposed framework. The sequence of the degree of importance of PV components is investigated using mutual information. The effects of intermittent fault parameters, including the coefficients of intermittent fault, permanent fault, and intermittent repair, on the reliability and availability are explored. Results show that the reliability and availability of the PV system with centralized configuration rapidly decrease, compared with those of the PV systems with string and multistring configurations. The sequence of the degree of importance of PV components is DC/AC inverter, DC/DC converter, DC combiner, and PV module arranged from the largest to the smallest. The finding indicates that the DC/AC inverter should be given considerable attention to improve the reliability and availability and to prevent their possible failures.

Characteristics of the turbulent/nonturbulent interface in boundary layers, jets and shear-free turbulence

The characteristics of turbulent/nonturbulent interfaces (TNTI) from boundary layers, jets and shear-free turbulence are compared using direct numerical simulations. The TNTI location is detected by assessing the volume of turbulent flow as function of the vorticity magnitude and is shown to be equivalent to other procedures using a scalar field. Vorticity maps show that the boundary layer contains a larger range of scales at the interface than in jets and shear-free turbulence where the change in vorticity characteristics across the TNTI is much more dramatic. The intermittency parameter shows that the extent of the intermittency region for jets and boundary layers is similar and is much bigger than in shear-free turbulence, and can be used to compute the vorticity threshold defining the TNTI location. The statistics of the vorticity jump across the TNTI exhibit the imprint of a large range of scales, from the Kolmogorov micro-scale to scales much bigger than the Taylor scale. Finally, it is shown that contrary to the classical view, the low-vorticity spots inside the jet are statistically similar to isotropic turbulence, suggesting that engulfing pockets simply do not exist in jets.

Detrended structure-function in fully developed turbulence

The classical structure-function (SF) method in fully developed turbulence or for scaling processes in general is influenced by large-scale energetic structures, known as the infrared effect. Therefore, the extracted scaling exponents ζ(n) might be biased due to this effect. In this paper, a detrended structure-function (DSF) method is proposed to extract scaling exponents by constraining the influence of large-scale structures. This is accomplished by removing a first-order polynomial fitting within a window size ℓ before calculating the velocity increment. By doing so, the scales larger than ℓ, i.e. r ≥ ℓ, are expected to be removed or constrained. The detrending process is equivalent to a high-pass filter in a physical domain. Meanwhile, the intermittency nature is retained. We first validate the DSF method by using a synthesised fractional Brownian motion for mono-fractal processes and a lognormal process for multifractal random walk processes. The numerical results show comparable scaling exponents ζ(n) and singularity spectra D(h) for the original SFs and DSFs. When applying the DSF to a turbulent velocity obtained from a high Reynolds number wind tunnel experiment with Reλ ≃ 720, the third-order DSF demonstrates a clear inertial range with on the range 10 < ℓ/η < 1000, corresponding to a wavenumber range 0.001 < kη < 0.1. This inertial range is consistent with the one predicted by the Fourier power spectrum. The directly measured scaling exponents ζ(n) (respectively, singularity spectrum D(h)) agree very well with a lognormal model with an intermittent parameter μ = 0.33. Due to large-scale effects, the results provided by the SFs are biased. The method proposed here is general and can be applied to different dynamics systems in which the concepts of multiscaling and multifractal are relevant.

Hilbert–Huang Transform based multifractal analysis of China stock market

In this paper, we employ the Hilbert–Huang Transform to investigate the multifractal character of Chinese stock market based on CSI 300 index. The measured Hilbert moment Lq(ω) shows a power-law behavior on the range 0.01<ω<0.1min−1, equivalent to a time scale range 10<τ<100min. The measured scaling exponents ζ(q) is convex with q and deviates from the value q/2, implying that the property of self-similarity is broken. Moreover, ζ(q) and the corresponding singularity spectrum D(h) can be described by a lognormal model with a Hurst number H=0.50 and an intermittency parameter μ=0.12. Our results suggest that the Chinese stock fluctuation might be captured well by a multifractal random walk model with a proper intermittency parameter.

Effects of Intermittent Faults on the Reliability of a Reduced Instruction Set Computing (RISC) Microprocessor

With the scaling of complementary metal-oxide-semiconductor (CMOS) technology to the submicron range, designers have to deal with a growing number and variety of fault types. In this way, intermittent faults are gaining importance in modern very large scale integration (VLSI) circuits. The presence of these faults is increasing due to the complexity of manufacturing processes (which produce residues and parameter variations), together with special aging mechanisms. This work presents a case study of the impact of intermittent faults on the behavior of a reduced instruction set computing (RISC) microprocessor. We have carried out an exhaustive reliability assessment by using very-high-speed-integrated-circuit hardware description language (VHDL)-based fault injection. In this way, we have been able to modify different intermittent fault parameters, to select various targets, and even, to compare the impact of intermittent faults with those induced by transient and permanent faults.

Lagrangian cascade in three-dimensional homogeneous and isotropic turbulence

AbstractIn this work, the scaling statistics of the dissipation along Lagrangian trajectories are investigated by using fluid tracer particles obtained from a high-resolution direct numerical simulation with $\mathit{Re}_{\lambda }=400$. Both the energy dissipation rate $\epsilon $ and the local time-averaged $\epsilon _{\tau }$ agree rather well with the lognormal distribution hypothesis. Several statistics are then examined. It is found that the autocorrelation function $\rho (\tau )$ of $\ln (\epsilon (t))$ and variance $\sigma ^2(\tau )$ of $\ln (\epsilon _{\tau }(t))$ obey a log-law with scaling exponent $\beta '=\beta =0.30$ compatible with the intermittency parameter $\mu =0.30$. The $q{\rm th}$-order moment of $\epsilon _{\tau }$ has a clear power law on the inertial range $10&lt;\tau /\tau _{\eta }&lt;100$. The measured scaling exponent $K_L(q)$ agrees remarkably with $q-\zeta _L(2q)$ where $\zeta _L(2q)$ is the scaling exponent estimated using the Hilbert methodology. All of these results suggest that the dissipation along Lagrangian trajectories could be modelled by a multiplicative cascade.

Non-stationary multifractality in stock returns

We perform an extensive empirical analysis of scaling properties of equity returns, suggesting that financial data show time varying multifractal properties. This is obtained by comparing empirical observations of the weighted generalised Hurst exponent (wGHE) with time series simulated via Multifractal Random Walk (MRW) by Bacry et al. [E. Bacry, J. Delour, J.-F. Muzy, Multifractal random walk, Physical Review E 64 (2) (2001) 026103]. While dynamical wGHE computed on synthetic MRW series is consistent with a scenario where multifractality is constant over time, fluctuations in the dynamical wGHE observed in empirical data are not in agreement with a MRW with constant intermittency parameter. We test these hypotheses of constant multifractality considering different specifications of MRW model with fatter tails: in all cases considered, although the thickness of the tails accounts for most of the anomalous fluctuations of multifractality, it still cannot fully explain the observed fluctuations.

Assessing market uncertainty by means of a time-varying intermittency parameter for asset price fluctuations

Maximum likelihood estimation techniques for multifractal processes are applied to high-frequency data in order to quantify intermittency in the fluctuations of asset prices. From time records as short as one month these methods permit extraction of a meaningful intermittency parameter λ characterising the degree of volatility clustering. We can therefore study the time evolution of volatility clustering and test the statistical significance of this variability. By analysing data from the Oslo Stock Exchange, and comparing the results with the investment grade spread, we find that the estimates of λ are lower at times of high market uncertainty.

Multifractal analysis of vertical total electron content (VTEC) at equatorial region and low latitude, during low solar activity

Abstract. This paper analyses the multifractal aspects of the GPS data (measured during a period of low solar activity) obtained from two Brazilian stations: Belém (01.3° S, 48.3° W) and São José dos Campos (SJC) (23.2° S, 45.9° W). The results show that the respective geographic sites show important scaling differences as well as similarities when their multifractal signatures for vertical total electron content (VTEC) are compared. The f(α) spectra have a narrow shape for great scales, which indicates the predominance of deterministic phenomena, such as solar rotation (27 days) over intermittent phenomena. Furthermore, the f(α) spectra for both sites have a strong multifractality degree at small scales. This strong multifractality degree observed at small scales (1 to 12 h) at both sites is because the ionosphere over Brazil is a non-equilibrium system. The differences found were that Belém presented a stronger multifractality at small scales (1 h to 12 h) compared with SJC, particularly in 2006. The reason for this behaviour may be associated with the location of Belém, near the geomagnetic equator, where at this location the actions of X-rays, ultraviolet, and another wavelength from the Sun are more direct, strong, and constant throughout the whole year. Although the SJC site is near ionospheric equatorial anomaly (IEA) peaks, this interpretation could explain the higher values found for the intermittent parameter μ for Belém compared with SJC. Belém also showed the presence of one or two flattening regions for f(α) spectra at the same scales mentioned before. These differences and similarities also were interpreted in terms of the IEA content, where this phenomenon is an important source of intermittence due the presence of the VTEC peaks at ±20° geomagnetic latitudes.

Intermittency and local Reynolds number in Navier-Stokes turbulence: A cross-over scale in the Caffarelli-Kohn-Nirenberg integral

We study space-time integrals, which appear in the Caffarelli-Kohn-Nirenberg (CKN) theory for the Navier-Stokes equations analytically and numerically. The key quantity is written in standard notations \documentclass[12pt]{minimal}\begin{document}$\delta (r)=1/(\nu r)\int _{Q_r}\left|\nabla {\bm u}\right|^2\,d{{\bm x}} \,dt$\end{document}δ(r)=1/(νr)∫Qr∇u2dxdt, which can be regarded as a local Reynolds number over a parabolic cylinder Qr. First, by re-examining the CKN integral, we identify a cross-over scale \documentclass[12pt]{minimal}\begin{document}$r_* \propto L\left( \frac{ \overline{\Vert \nabla \bm {u} \Vert ^2_{L^2}} }{\Vert \nabla \bm {u} \Vert ^2_{L^\infty }} \right)^{1/3},$\end{document}r*∝L‖∇u‖L22¯‖∇u‖L∞21/3, at which the CKN Reynolds number δ(r) changes its scaling behavior. This reproduces a result on the minimum scale rmin in turbulence: \documentclass[12pt]{minimal}\begin{document}$r_{\rm min}^2 \Vert \nabla {\bm u}\Vert _\infty \propto \nu ,$\end{document}r min 2‖∇u‖∞∝ν, consistent with a result of Henshaw et al. [“On the smallest scale for the incompressible Navier-Stokes equations,” Theor. Comput. Fluid Dyn. 1, 65 (1989)10.1007/BF00272138]. For the energy spectrum E(k) ∝ k−q (1 &amp;lt; q &amp;lt; 3), we show that r* ∝ νa with \documentclass[12pt]{minimal}\begin{document}$a=\frac{4}{3(3-q)}-1$\end{document}a=43(3−q)−1. Parametric representations are then obtained as \documentclass[12pt]{minimal}\begin{document}$\Vert \nabla {\bm u}\Vert _\infty \propto \nu ^{-(1+3a)/2}$\end{document}‖∇u‖∞∝ν−(1+3a)/2 and rmin ∝ ν3(a+1)/4. By the assumptions of the regularity and finite energy dissipation rate in the inviscid limit, we derive \documentclass[12pt]{minimal}\begin{document}$\lim _{p \rightarrow \infty }\frac{\zeta _p}{p}=1 - \zeta _2$\end{document}limp→∞ζpp=1−ζ2 for any phenomenological models on intermittency, where ζp is the exponent of pth order (longitudinal) velocity structure function. It follows that ζp ⩽ (1 − ζ2)(p − 3) + 1 for any p ⩾ 3 without invoking fractal energy cascade. Second, we determine the scaling behavior of δ(r) in direct numerical simulations of the Navier-Stokes equations. In isotropic turbulence around Rλ ≈ 100 starting from random initial conditions, we have found that δ(r) ∝ r4throughout the inertial range. This can be explained by the smallness of a ≈ 0.26,with a result that r* is in the energy-containing range. If the β-model is perfectly correct, the intermittency parameter a must be related to the dissipation correlation exponent μ as \documentclass[12pt]{minimal}\begin{document}$\mu =\frac{4a}{1+a} \approx 0.8,$\end{document}μ=4a1+a≈0.8, which is larger than the observed μ ≈ 0.20. Furthermore, corresponding integrals are studied using the Burgers vortex and the Burgers equation. In those single-scale phenomena, the cross-over scale lies in the dissipative range. The scale r* offers a practical method of quantifying intermittency. This paper also sorts out a number of existing mathematical bounds and phenomenological models on the basis of the CKN Reynolds number.

Impact of temperature variation on energy consumption and productivity of the occupants in office buildings

Heating and cooling equipment in office buildings is usually controlled according to external air temperature. However, due to sudden outdoor air temperature variations, indoor climate may not always be adjusted to fit into the comfort range. Despite the modern facilities, occupants may be exposed to a temporary thermal discomfort that affects their performance. The aim of this study was to outline the influence of indoor air temperature variation on office work performance and energy consumption. During the experiment in the real office, indoor and outdoor climate parameters as well as energy consumption were observed. Employees were asked to fill questionnaires by indicating their thermal sensation, perception of air quality and humidity. The results of the study showed that indoor climate changes may cause dissatisfaction of participants, which could lead to their lower productivity. The effects of intermittent indoor climate parameters on energy consumption were outlined as well.

Parameter estimation and forecasting for multiplicative log-normal cascades

We study the well-known multiplicative log-normal cascade process in which the multiplication of Gaussian and log normally distributed random variables yields time series with intermittent bursts of activity. Due to the nonstationarity of this process and the combinatorial nature of such a formalism, its parameters have been estimated mostly by fitting the numerical approximation of the associated non-Gaussian probability density function to empirical data, cf. Castaing et al. [Physica D 46, 177 (1990)]. More recently, alternative estimators based upon various moments have been proposed by Beck [Physica D 193, 195 (2004)] and Kiyono et al. [Phys. Rev. E 76, 041113 (2007)]. In this paper, we pursue this moment-based approach further and develop a more rigorous generalized method of moments (GMM) estimation procedure to cope with the documented difficulties of previous methodologies. We show that even under uncertainty about the actual number of cascade steps, our methodology yields very reliable results for the estimated intermittency parameter. Employing the Levinson-Durbin algorithm for best linear forecasts, we also show that estimated parameters can be used for forecasting the evolution of the turbulent flow. We compare forecasting results from the GMM and Kiyono et al.'s procedure via Monte Carlo simulations. We finally test the applicability of our approach by estimating the intermittency parameter and forecasting of volatility for a sample of financial data from stock and foreign exchange markets.

Influence of Obstructive Sleep Apnea on Fatty Liver Disease: Role of Chronic Intermittent Hypoxia

Currently the common pathogenetic mechanisms in nonalcoholic fatty liver disease (NAFLD) and obstructive sleep apnea (OSA) are gaining increased attention. The aim of this study is to find out the influence of chronic intermittent hypoxemia and OSA related parameters to the severity of NAFLD. We examined the liver functions tests and ultrasonographic data of liver as well as markers of OSA severity (apnea-hypopnea index [AHI], oxygen desaturation index, minimum oxygen saturation, percentage of time spent with S(pO(2)) < 90%) of 106 subjects. Fatty liver disease was diagnosed in 71 subjects (group 1), and the remaining 35 subjects were taken as controls (group 2). The prevalence of OSA was 71.2% versus 35.7% for group 1 and 2, respectively (P < .001). As NAFLD severity increased from mild to severe form, mean AHI and oxygen desaturation index values also increased significantly. Our multivariate analysis showed that AHI, oxygen desaturation index, lowest desaturation values, and percentage of sleep duration with S(pO(2)) < 90% were independent predictors of NAFLD after adjustment for BMI, weight, and insulin resistance. Furthermore, the most correlated parameter for the severity of NAFLD was found as the duration of hypoxia during sleep. The prevalence of NAFLD was higher in patients with severe OSA, suggesting a role for nocturnal hypoxemia in the pathogenesis of fatty liver disease.

Parameter motivated mutual correlation analysis: Application to the study of currency exchange rates based on intermittency parameter and Hurst exponent

We present a novel method for the parameter oriented analysis of mutual correlation between independent time series or between equivalent structures such as ordered data sets. The proposed method is based on the sliding window technique, defines a new type of correlation measure and can be applied to time series from all domains of science and technology, experimental or simulated. A specific parameter that can characterize the time series is computed for each window and a cross correlation analysis is carried out on the set of values obtained for the time series under investigation. We apply this method to the study of some currency daily exchange rates from the point of view of the Hurst exponent and the intermittency parameter. Interesting correlation relationships are revealed and a tentative crisis prediction is presented.

Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: Comparison study with detrended fluctuation analysis and wavelet leaders

In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first show numerically that due to a nonlinear distortion, traditional methods require high-order harmonic components to represent nonlinear processes, except for the Hilbert-based method. This will lead to an artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus the power law, if it exists, is contaminated. We then compare the Hilbert method with structure functions (SF), detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing fractional Brownian motion and synthesized multifractal time series. For the former simulation, we find that all methods provide comparable results. For the latter simulation, we perform simulations with an intermittent parameter μ=0.15. We find that the SF underestimates scaling exponent when q>3. The Hilbert method provides a slight underestimation when q>5. However, both DFA and WL overestimate the scaling exponents when q>5. It seems that Hilbert and DFA methods provide better singularity spectra than SF and WL. We finally apply all methods to a passive scalar (temperature) data obtained from a jet experiment with a Taylor's microscale Reynolds number Re(λ)≃250. Due to the presence of strong ramp-cliff structures, the SF fails to detect the power law behavior. For the traditional method, the ramp-cliff structure causes a serious artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus DFA and WL underestimate the scaling exponents. However, the Hilbert method provides scaling exponents ξ(θ)(q) quite close to the one for longitudinal velocity, indicating a less intermittent passive scalar field than what was believed before.

Intermittency of near‐bottom turbulence in tidal flow on a shallow shelf

The higher‐order structure functions of vertical velocity fluctuations (transverse structure functions (TSF)) were employed to study the characteristics of turbulence intermittency in a reversing tidal flow on a 19 m deep shallow shelf of the East China Sea. Measurements from a downward‐looking, bottom‐mounted Acoustic Doppler Velocimeter, positioned 0.45 m above the seafloor, which spanned two semidiurnal tidal cycles, were analyzed. A classical lognormal single‐parameter (μ) model for intermittency and the universal multifractal approach (specifically, the two‐parameter (C1 and α) log‐Levy model) were employed to analyze the TSF exponent ξ(q) in tidally driven turbulent boundary layer and to estimate μ, C1, and α. During the energetic flooding tidal phases, the parameters of intermittency models approached the mean values of ≈ 0.24, 1 ≈ 0.15, and ≈ 1.5, which are accepted as the universal values for fully developed turbulence at high Reynolds numbers. With the decrease of advection velocity, μ and C1 increased up to μ ≈ 0.5–0.6 and C1 ≈ 0.25–0.35, but α decreased to about 1.4. The results explain the reported disparities between the smaller “universal” values of intermittency parameters μ and C1 (mostly measured in laboratory and atmospheric high Reynolds number flows) and those (μ = 0.4–0.5) reported for oceanic stratified turbulence in the pycnocline, which is associated with relatively low local Reynolds numbers Rλw. The scaling exponents ξ(2) of the second‐order TSF, relative to the third‐order structure function, was also found to be a decreasing function of Rλw, approaching the classical value of 2/3 only at very high Rλw. A larger departure from the universal turbulent regime at lower Reynolds numbers could be attributed to the higher anisotropy and associated intermittency of underdeveloped turbulence.

TURBULENCE IN A THREE-DIMENSIONAL DEFLAGRATION MODEL FOR TYPE Ia SUPERNOVAE. II. INTERMITTENCY AND THE DEFLAGRATION-TO-DETONATION TRANSITION PROBABILITY

The delayed detonation model describes the observational properties of the majority of type Ia supernovae very well. Using numerical data from a three-dimensional deflagration model for type Ia supernovae, the intermittency of the turbulent velocity field and its implications on the probability of a deflagration-to-detonation (DDT) transition are investigated. From structure functions of the turbulent velocity fluctuations, we determine intermittency parameters based on the log-normal and the log-Poisson models. On the other hand, the analysis of the turbulent velocity fluctuations in the vicinity of the flame front by Roepke suggests a much higher probability of large velocity fluctuations on the grid scale in comparison to the log-normal intermittency model. Following Pan et al., we computed probability density functions for a DDT for the different distributions. Assuming that a DDT can occur in the stirred flame regime, as proposed by Woosley et al., the log-normal model would imply a delayed detonation between 0.7 and 0.8 seconds after the beginning of the deflagration phase for the multi-spot ignition scenario used in the simulation. However, the probability drops to virtually zero if a DDT is further constrained by the requirement that the turbulent velocity fluctuations reach about 500 km/s. Under this condition, delayed detonations are only possible if the distribution of the velocity fluctuations is not log-normal. From our calculations follows that the distribution obtained by Roepke allow for multiple DDTs around 0.8 seconds after ignition at a transition density close to 1x10^7 g/cm^3.

Scaling analyses of high-resolution dye tracer experiments / Analyses scalaires d'expériences de traçage coloré à haute résolution

Four unsaturated solute transport experiments with different water fluxes were conducted in a Hele-Shaw cell filled with uniform sand. The transport of the dye tracer used was recorded with a camera and the dye concentration was calculated using image analysis. The concentrations fields were analysed in terms of time moments and converted into vertical solute transport velocity V. Both mean value and standard deviation of V increased with water flux. The autocorrelation function exhibited a linear decrease for short lags. The pronounced variability of V suggested a description in terms of scaling properties, and a scaling regime was indeed found from the resolution 1.8 mm up to almost 0.1 m. The upper limit corresponds roughly to a characteristic scale of fingering structures seen in the dye concentration images. Indications of a second scaling regime at larger scales were found. In the small-scale scaling regime, the power spectrum exponent β was generally slightly below 1 and the intermittency parameter C 1 was on average 0.00025. The moment scaling K q functions were convex, implying a multiscaling process.