Third-order Moments Research Articles

Color-deconvolution-based feature image extraction and application in water quality analysis.

We propose a feature color extraction method that improves the accuracy of water quality analysis using a digital image and eliminates the effect of interfering ions and chromogenic agents on the color after a color reaction. The proposed method is based on color deconvolution (CD) combined with machine learning for substance measurement in water. After an ordinary camera acquires the solution image after color reaction, the CD algorithm is applied to extract the feature image, calculate the first-order, second-order, and third-order color moments corresponding to RGB channels, and construct a gradient boosting regression tree prediction model based on color moment features to detect substances in water. In predicting ammonia, nitrite, and orthophosphate concentrations, the mean square error values were 0.01029, 0.00063, and 0.1361, and the mean absolute error values were 0.08103, 0.02231, and 0.32886, respectively. There was no significant difference in the results of the comparative spectrophotometric method on the actual water samples. The spiked recoveries of the samples ranged from 94% to 120%, confirming that the method can effectively measure the content of substances in water.

A Realizable Second-Order Advection Method with Variable Flux Limiters for Moment Transport Equations

A second-order total variation diminishing (TVD) method with variable flux limiters is proposed to overcome the non-realizability issue, which has been one of major obstacles in applying the conventional second-order TVD schemes to the moment transport equations. In the present method, a realizable moment set at a cell face is reconstructed by allowing the flexible selection of the flux limiter values within the second-order TVD region. Necessary conditions for the variable flux limiter scheme to simultaneously satisfy the realizability and the second-order TVD property for the third-order moment set are proposed. The strategy for satisfying the second-order TVD property is conditionally extended to the fourth- and fifth-order moments. The proposed method is verified and compared with other high-order realizable schemes in one- and two-dimensional configurations, and is found to preserve the realizability of moments while satisfying the high-order TVD property for the third-order moment set and conditionally for the fourth- and fifth-order moments.

Experimental Study on the Near-Bed Flow Characteristics of Alluvial Channel with Seepage

This paper aims to analyze the turbulent structure of flows over beds undergoing downward seepage under clear-water conditions. Laboratory experiments in this regard were carried out in a straight rectangular channel that was 17.20 m long and 1.00 m wide. A sandy bed with median grain size d50 = 0.50 mm and sediment gradation σg = 1.65 (i.e., slightly non-uniform sediment) was used for the channel bed. The 3D instantaneous velocities of water were measured with an Acoustic Doppler Velocimeter (ADV) at the working test section. In the vicinity of the bed surface with seepage, measurements revealed that the flow longitudinal velocities (i.e., velocities in x direction) were higher than those in the case of a bed without seepage. Moreover, the variations inthe Reynolds shear stresses increased for the bed with seepage, indicating a higher exchange of flow energy towards the boundary and vice versa. Therefore, it was found that seepage processes influence the turbulence intensity, with a prominent magnitude in the streamwise and vertical directions. The paper also focuses on the third-order moment (skewness) and the kurtosis of velocity fluctuations and the governance of sweep events within the near-bed flow in cases where seepage was observed.

Turbulent Cascade and Energy Transfer Rate in a Solar Coronal Mass Ejection

Abstract Turbulence properties are examined before, during, and after a coronal mass ejection (CME) detected by the Wind spacecraft in 2012 July. The power-law scaling of the structure functions, providing information on the power spectral density and flatness of the velocity, magnetic field, and density fluctuations, were examined. The third-order moment scaling law for incompressible, isotropic magnetohydrodynamic turbulence was observed in the preceding and trailing solar wind, as well as in the CME sheath and magnetic cloud. This suggests that the turbulence could develop sufficiently after the shock, or that turbulence in the sheath and cloud regions was robustly preserved even during the mixing with the solar wind plasma. The turbulent energy transfer rate was thus evaluated in each of the regions. The CME sheath shows an increase of energy transfer rate, as expected from the lower level of Alfvénic fluctuations and suggesting the role of the shock-wind interaction as an additional source of energy for the turbulent cascade.

Characterizing Brain Tumor Regions Using Texture Analysis in Magnetic Resonance Imaging.

PurposeTo extract texture features from magnetic resonance imaging (MRI) scans of patients with brain tumors and use them to train a classification model for supporting an early diagnosis.MethodsTwo groups of regions (control and tumor) were selected from MRI scans of 40 patients with meningioma or glioma. These regions were analyzed to obtain texture features. Statistical analysis was conducted using SPSS (version 20.0), including the Shapiro–Wilk test and Wilcoxon signed-rank test, which were used to test significant differences in each feature between the tumor and healthy regions. T-distributed stochastic neighbor embedding (t-SNE) was used to visualize the data distribution so as to avoid tumor selection bias. The Gini impurity index in random forests (RFs) was used to select the top five out of all features. Based on the five features, three classification models were built respectively with three machine learning classifiers: RF, support vector machine (SVM), and back propagation (BP) neural network.ResultsSixteen of the 25 features were significantly different between the tumor and healthy areas. Through the Gini impurity index in RFs, standard deviation, first-order moment, variance, third-order absolute moment, and third-order central moment were selected to build the classification model. The classification model trained using the SVM classifier achieved the best performance, with sensitivity, specificity, and area under the curve of 94.04%, 92.3%, and 0.932, respectively.ConclusionTexture analysis with an SVM classifier can help differentiate between brain tumor and healthy areas with high speed and accuracy, which would facilitate its clinical application.

Higher-Order Turbulence Around Different Circular Cylinders Using Particle Image Velocimetry

Abstract Wakes and higher-order turbulence around circular cylinders of different diameters are investigated using particle image velocimetry measurements. The cylinder Reynolds number (Red) is defined by the depth-averaged velocity, cylinder diameter, and kinematic viscosity. The influence of Red on third-order moment of velocity fluctuations, turbulent kinetic energy (TKE) flux, TKE budget, and turbulent length scales are presented. The intermittency factor (IF) and quadrant analysis around the cylinders are discussed for Red values ranging from 12,600 to 21,000. The energy budget mostly near free surface upstream and near-bed downstream is changed due to Red. Stream-wise and transverse TKE fluxes decreased significantly with Red, but not the vertical flux. Stream-wise skewness changed sign from positive to negative at a certain critical distance downstream, while vertical skewness showed reversed effect with Red. Negative stream-wise skewness and positive vertical skewness indicate the occurrence of ejection events. On the downstream, the production and dissipation rates increased with Red, whereas an opposite trend was observed for dissipation only on the upstream. Increase of Red led to an increase in the Kolmogorov length-scale much higher on the upstream than the downstream, whereas it showed depleting effect on Taylor's length-scale on the upstream and an increasing effect on the downstream. Ejection and sweep events were more prominent in the downstream near the cylinder than upstream with higher values of shear stress on the downstream. The sum of the shear stress contributions of all quadrant events increased consistently with an increase in Red near the cylinder.

Self-exciting jumps in the oil market: Bayesian estimation and dynamic hedging

In this paper we propose a novel self-exciting jump-diffusion model for oil price dynamics based on a Hawkes-type process. In particular, the jump intensity is stochastic and path dependent, implying that the occurrence of a jump will increase the probability of observing a new jump and this feature of the model aims at explaining the jumps clustering effect. Moreover, volatility is described by a stochastic process, which can jump simultaneously with prices. The model specification is completed by a stochastic convenience yield. In order to estimate the model we apply the two-stage Sequential Monte Carlo (SMC) sampler (Fulop and Li, 2019) to both spot and futures quotations. From the estimation results we find evidence of self-excitation in the oil market, which leads to an improved fit and a better out of sample futures forecasting performance with respect to jump-diffusion models with constant intensity. Furthermore, we compute and discuss two optimal hedging strategies based on futures trading. The optimality of the first hedging strategy proposed is based on the variance minimization, while the second strategy takes into account also the third-order moment contribution in considering the investors attitudes. A comparison between the two strategies in terms of hedging effectiveness is provided.

Asymptotically Exact Constants in Natural Convergence Rate Estimates in the Lindeberg Theorem

Following (Shevtsova, 2013) we introduce detailed classification of the asymptotically exact constants in natural estimates of the rate of convergence in the Lindeberg central limit theorem, namely in Esseen’s, Rozovskii’s, and Wang–Ahmad’s inequalities and their structural improvements obtained in our previous works. The above inequalities involve algebraic truncated third-order moments and the classical Lindeberg fraction and assume finiteness only the second-order moments of random summands. We present lower bounds for the introduced asymptotically exact constants as well as for the universal and for the most optimistic constants which turn to be not far from the upper ones.

Comparing turbulence in a Kelvin–Helmholtz instability region across the terrestrial magnetopause

ABSTRACTThe properties of turbulence observed within the plasma originating from the magnetosheath and the magnetospheric boundary layer, which have been entrained within vortices driven by the Kelvin–Helmholtz Instability (KHI), are compared. The goal of such a study is to determine similarities and differences between the two different regions. In particular, we study spectra, intermittency and the third-order moment scaling, as well as the distribution of a local energy transfer rate proxy. The analysis is performed using the Magnetospheric Multiscale data from a single satellite that crosses longitudinally the KHI. Two sets of regions, one set containing predominantly magnetosheath plasma and the other containing predominantly magnetospheric plasma, are analysed separately, thus allowing us to explore turbulence properties in two portions of very different plasma samples. Results show that the dynamics in the two regions is different, with the boundary layer plasma presenting a shallower spectra and larger energy transfer rate, indicating an early stage of turbulence. In both regions, the effect of the KHI is evidenced.

EXPERIMENT OF UNIQUE COMBINATION NUMBER DUE TO THE THIRD-ORDER NEUTRON-CORRELATION

From zero-power reactor noise measurement, the second- and third-order neutron correlation factors Y and y3 can be evaluated by analyzing mean, variance, the third-order central moment of neutron count data. Theoretically, it is expected that the neutron-correlation ratio y3/Y2 converges to the unique combination number “3” at a near-critical state in an arbitrary system without depending on the fissile material and the neutron-energy spectrum of core, as the neutron counting gate width T increases sufficiently. Thus, the information about the difference between y3/Y2 and “3” has the potential to judge whether a target unknown system is critical or not and to roughly guess the absolute value of subcriticality. In this study, the detector dead-time effect on y3/Y2 is theoretically investigated based on the heuristic method using the single-, pair-, and trio-detection probabilities with the fundamental mode approximation. As a result, it is clarified that the saturation value of y3/Y2 converges to “3” independent of the dead time, when a target system is a critical state. For validation, actual experimental results are presented for a non-multiplication system driven by 252Cf spontaneous source, and shallow and deep subcritical systems at Japanese experimental facilities (UTR-KINKI and KUCA) under the shutdown state. Consequently, it is demonstrated that y3/Y2 shows a significant difference from “3” in the non-multiplication system. In the case of subcritical systems driven by inherent neutron sources, it is confirmed that the ratios y3/Y2 are close to the unique combination number “3,” and the slight difference from “3” is measurable by the long-time reactor noise measurement for the deep subcritical system.

Gas mixture flow, diffusion, and heat transfer in a long tube at moderately small Knudsen numbers

The binary gas mixture flow, diffusion, and heat transfer through a long tube in the near-continuum regime (moderately small Knudsen numbers) are analyzed. The system of linearized third-order moment equations, obtained by Grad’s method, is used. An expression for the total mass flux of a binary gas mixture is deduced by using the extension of the procedure, proposed in the work by Zhdanov [“Slip and barodiffusion phenomena in slow flows of a gas mixture,” Phys. Rev. E 95, 033106 (2017)] for the study of slip phenomena in slow flows of a gas mixture. Relations for diffusion and heat fluxes are determined from the initial system of moment equations, averaged over the channel cross section, and supplied with several moments of the distribution function at the channel wall found with the modified Maxwell method. Analytical formulas for kinetic coefficients of the Onsager matrix, which connect averaged fluxes and gradients of the corresponding thermodynamic quantities, are obtained. It is shown that the employed approach automatically ensures the validity of the reciprocal relations for the cross terms in the Onsager matrix. The results of calculations of the derived kinetic coefficients for several binary mixtures of noble gases (He–Ar, Ne–Ar, and He–Xe) are presented and compared with numerical data found by the discrete velocity method on the basis of the linearized Boltzmann equation with the McCormack model.

Color representation model for pre-colored fiber blends based on local-to-global features fusion

This paper proposes a color representation model of pre-colored fiber blends that combines global and local features, and the main purpose of this model is to establish scientific and effective evaluation standards for the colorimetry index of colored spun fabric, which can be used to solve the difficulty faced by people to accurately describe the overall coloration characteristics of dyed fibers in colored spinning process. Firstly, the third-order color moment features and three structure descriptor features are extracted, and decision level image fusion of feature is performed to represent the color of the samples. Secondly, the normalized difference of the fusing features between different samples are obtained, and it makes a correlation analysis of the difference of the mass ratio of dyed fiber. The experimental results show that the color representation model can effectively represent the change of the mass ratio of dyed fibers, and meanwhile it is more practical compared with the traditional spectrophotometry.

Intermittency, Moments, and Friction Coefficient during the Subcritical Transition of Channel Flow.

The intermittent distribution of localized turbulent structures is a key feature of the subcritical transitions in channel flows, which are studied in this paper with a wind channel and theoretical modeling. Entrance disturbances are introduced by small beads, and localized turbulent patches can be triggered at low Reynolds numbers (Re). High turbulence intensity represents strong ability of perturbation spread, and a maximum turbulence intensity is found for every test case as Re ≥ 950, where the turbulence fraction increases abruptly with Re. Skewness can reflect the velocity defects of localized turbulent patches and is revealed to become negative when Re is as low as about 660. It is shown that the third-order moments of the midplane streamwise velocities have minima, while the corresponding forth-order moments have maxima during the transition. These kinematic extremes and different variation scenarios of the friction coefficient during the transition are explained with an intermittent structure model, where the robust localized turbulent structure is simplified as a turbulence unit, a structure whose statistical properties are only weak functions of the Reynolds number.

Non-equilibrium phenomena in gas mixture flow through a plane channel in near-continuum regime

Non-equilibrium phenomena in the flow of a binary gas mixture between two parallel plates, driven by gradients of the pressure, temperature and concentration, are studied. The phenomenological relationships that describe the energy and mass transfer in the flow of a gas mixture through a channel are analyzed by using methods of the non-equilibrium thermodynamics of discontinuous systems. The solution of the linearized moment equations in the 13-moments approximation of the Grad’s method and the relation for the slip velocity previously found in Zhdanov (Phys. Rev. E95 (2017), 033106) are applied to deduce the expression for the mass-average velocity of the mixture flowing in a plane channel in the near-continuum regime. Expressions for the diffusion and heat fluxes are determined from the initial third-order moment equations for the gas mixture, averaged over the channel cross-section, with the subsequent evaluation of several moments of the distribution function at the channel wall by using the modified Maxwell method. It is shown that the employed approach automatically ensures the validity of the reciprocal relations for the cross terms in the Onsager matrix. Analytical formulas for kinetic coefficients of the Onsager matrix, expressed in terms of known transport coefficients of the gas mixture and slip coefficients at the channel wall, are obtained. The results of calculations of the matrix coefficients for several binary mixtures of noble gases (Ne–Ar and He–Xe) and their comparison with the results of the numerical calculations on the basis of the linearized Boltzmann equation with the McCormack model are presented.

Turbulence anisotropy with higher-order moments in flow through passive grid under rigid boundary influence

The investigation presents the estimate of the degree of deviation from the isotropic turbulence in terms of Reynolds stress tensor for grid generated turbulence under the influence of bottom boundary. The turbulence triangle, Eigen values, and the invariant functions are presented at near and far field regions of the grids with different solidity ratio. In addition, the work also deals with the analysis based on third-order moments of the velocity fluctuations and the ratio of momentum flux to the turbulent kinetic energy in the frequency domain. The Reynolds stress anisotropy exposes that the anisotropic invariant maps possess a closed looping trend in the near field region and an open looping trend in the far-field region of the grid. Further, to describe the physical behaviour of the velocity time-series of random fluctuating components in the stream-wise directions, the probability distribution function are estimated and interpreted.

On Natural Convergence Rate Estimates in the Lindeberg Theorem

We prove two estimates of the rate of convergence in the Lindeberg theorem, involving algebraic truncated third-order moments and the classical Lindeberg fraction, which generalize a series of inequalities due to (Esseen, 1969), (Rozovskii, 1974), (Wang, Ahmad, 2016), some of our recent results in (Gabdullin, Makarenko, Shevtsova, 2018, 2019) and, up to constant factors, also (Katz, 1963), (Petrov, 1965), (Osipov, 1966). The technique used in the proof is completely different from that in (Wang, Ahmad, 2016) and is based on some extremal properties of introduced fractions which has not been noted in (Katz, 1963), (Petrov, 1965), (Wang, Ahmad, 2016).

Compressibility in lattice Boltzmann on standard stencils: effects of deviation from reference temperature.

With growing interest in the simulation of compressible flows using the lattice Boltzmann (LB) method, a number of different approaches have been developed. These methods can be classified as pertaining to one of two major categories: (i) solvers relying on high-order stencils recovering the Navier-Stokes-Fourier equations, and (ii) approaches relying on classical first-neighbour stencils for the compressible Navier-Stokes equations coupled to an additional (LB-based or classical) solver for the energy balance equation. In most cases, the latter relies on a thermal Hermite expansion of the continuous equilibrium distribution function (EDF) to allow for compressibility. Even though recovering the correct equation of state at the Euler level, it has been observed that deviations of local flow temperature from the reference can result in instabilities and/or over-dissipation. The aim of the present study is to evaluate the stability domain of different EDFs, different collision models, with and without the correction terms for the third-order moments. The study is first based on a linear von Neumann analysis. The correction term for the space- and time-discretized equations is derived via a Chapman-Enskog analysis and further corroborated through spectral dispersion-dissipation curves. Finally, a number of numerical simulations are performed to illustrate the proposed theoretical study. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Theoretical and numerical analysis of key sub-grid quantities' effect on filtered Eulerian drag force

An expression of the filtered Eulerian drag force is proposed based on the second order Taylor polynomial approximation of a microscopic drag coefficient. Theoretical computations of the expression at low particle Reynolds numbers show that four sub-grid quantities, the gas drift velocity, the solid drift velocity, the scalar variance of solid volume fraction and a third-order moment, are significant for an accurate estimation of the filtered drag force. Various drag models with different combinations of the four sub-grid quantities are proposed and their coefficients are optimized based on fine-grid two fluid model results. The gas drift velocity is demonstrated to be the most important marker in predicting the filtered drag force. The model with the solid drift velocity and the scalar variance of the solid volume fraction is found to be promising in computational fluid dynamic-discrete element model simulations due to the ready availability of the two sub-grid quantities.

Effects of aspect ratio on higher-order moments, conditional statistics, TKE budget and anisotropy in narrow open channel flow

The purpose of the present study is to investigate the influence of aspect ratio on the higher- order statistics of velocity fluctuations, conditional statistics, turbulent kinetic energy (TKE) fluxes, TKE budget, and Reynolds stress anisotropy in hydraulically rough narrow open channel flow (OCF). In the experiments, the aspect ratios were maintained low and varied between 2.5 and 4. The velocities were measured with an acoustic Doppler velocimeter (ADV). The higher-order moments, quadrant analysis, and TKE budget from the present experiments were compared with available literature data in wide and narrow OCFs to elucidate the effect of the aspect ratio. In this analysis, the third-order moments of velocity fluctuations were found to be sensitive to the aspect ratio in the outer region. The fractional contributions of all quadrant events are approximately equal in magnitude in lower aspect ratio flows, whereas ejections and sweeps are the dominant events as the aspect ratio increases. The upward transfer of TKE flux increases in the outer layer with increase in aspect ratio. In the inner layer, the TKE production and rate of dissipation are found to be increasing with decreasing aspect ratio. Therefore, the production and dissipation of TKE are dependent on the aspect ratio of the flow. The analysis of Reynolds stress AIM reveals that for low aspect ratio flows turbulence tends to attain rod-like axisymmetric turbulence only in the intermediate layer whereas for higher aspect ratio, turbulence attains rod-like axisymmetric turbulence throughout the depth.

Upward Overshooting in Turbulent Compressible Convection. III. Calibrate Parameters for One-dimensional Reynolds Stress Model

Abstract In this paper, we calibrate the coefficients for the one-dimensional Reynolds stress model (RSM) with the data generated from the three-dimensional (3D) numerical simulations of upward overshooting in turbulent compressible convection. It has been found that the calibrated convective and isotropic coefficients are almost the same as those calibrated in the pure convection zone. However, the calibrated diffusive coefficients differ significantly from those calibrated in the pure convection zone. We suspect that the diffusive effect induced by the boundary is stronger than by the adjacent stable zone. We have checked the validity of the downgradient approximation (DGA). We find that the prediction of the DGA on the third-order moments (TOMs) is unsatisfactory. However, the prediction on their derivatives is much better. It explains why the performance of the RSM is reasonable in application to the real stars. With the calibrated coefficients, we have solved the full set of nonlocal turbulent equations on RSM. We find that the RSM has successfully produced the thermal adjustment layer and turbulent dissipation layer, which were identified in the 3D numerical simulations. We suggest to use the inflection point of the auto-correlation of temperature perturbation and the Péclet number as the indicators on measuring the extents of the thermal adjustment layer and turbulent dissipation layer, respectively. This result may offer a practical guidance on the application of the RSM in 1D stellar structure and evolution models.