Modified Mixture Model Research Articles

Effect of Copper Powder Addition on Microscopic Deformation Behavior of Al2O3/Cu‐Dispersion‐Strengthened Copper‐Sintered Billet

In this work, it is aimed to improve the deformation ability of the Al2O3 dispersion strengthened copper sintered billet by building heterogeneous structure with addition of different sizes of particle. Using the modified mixture model and equal work law, the stress distribution model of heterogeneous materials is derived. In the results, it is shown that higher deformation temperature and lower strain rate are conducive to steady deformation. Under the conditions of 950 °C and 0.01 s−1, the stress distribution coefficients from low to high are 10, 25, and 5 μm, respectively, when the strain is 0.1. The strain contribution rates of softness of the sintered billet are 45.5%, 62.1%, and 42.6%, respectively. The addition of 10 μm particle size copper powder can significantly improve the deformation capacity of the sintered billet. It is found that with the increase of the particle size of copper powder, the density of the microgeometrically necessary dislocation of the hot extrusion dispersed copper is lower. The reason is that the different particle size of copper powder leads to the different distribution in powder stacking, which affects the difficulty of harmonizing the deformation of soft and hard and the number of dislocation in the hot‐extrusion process of sintered billet.

PARAMETRIC STUDY AND DEVELOPMENT OF A CORRELATION FOR NUSSELT NUMBER IN NANOFLUID JET IMPINGEMENT

Numerical simulations for nanofluid ( water with Al<sub>2</sub>O<sub>3</sub> nanoparticles) jet impinging perpendicularly on a flat circular heated p late have been performed. A heated p late is subjected to constant heat flux boundary condition. A two-phase modified mixture mo del was used for the prediction of heat transfer coefficient, and comparisons are made with standard mixture model. Present results for average Nusselt number are validated with experimental data available in the literature. Though a standard mixture model predicted heat transfer with accepted accuracy, it was found that accuracy of modified mixture model is better (around 5% improvement) compared to standard mixture model. Thereafter, parametric study was performed considering nozzle exit Reynolds number (Re), spacing ratio (<i>H/D</i>), nanoparticle volume fraction (φ), and nanoparticle diameter (dp) on heat transfer prediction. The results reveal that particle diameter in the range 10-100 nm has no effect on the Nusselt number, Furthermore, heat transfer increased with increasing Reynolds number and volume fraction. However, spacing ratio shows first increasing and then, decreasing trend (similar to a log-normal distribution curve) in the prediction of heat transfer. Finally, a new correlation was developed for Nusselt number using nonlinear regression analysis. In the correlation, a two-phase multiplier was used, which is the ratio between two-phase Nusselt number (Nu<sub>nf</sub> ) and single-phase Nusselt number (Nu<sub>sp</sub>). The simplified correlation is found to predict data with maximum error of 8.9%, average error of 2.74% and <i>R</i><sup>2</sup> = 0.955.

The dynamic behaviour of a large‐scale 250‐mm hydrocyclone: A CFD study

AbstractThe fluctuating feed solid contents usually cause instationarities in industrial hydrocyclone separation. This demands a controlling mechanism for stabilizing the separation effect. Understanding the transitional/dynamic behaviour is necessary to design such control mechanisms. In this context, the present paper is aimed to understand the dynamic behaviour of a large‐scale 250‐mm hydrocyclone in terms of air core development and solid concentration distributions using the modified mixture model coupled with large eddy simulation turbulence model. Numerically predicted two‐phase flow field data is validated against laser Doppler velocimetry data at two axial positions. A close agreement is found between the modified mixture model predicted particle classification curve and experimental data. Longer residence time is observed with near cut size particle compared to the and fine size particles. Further, the analysis of the equilibrium radius of different solid particles inside the cyclone in the presence of turbulence is compared with the classical Kelsall experiments and observed that the classification of particles influenced by both the turbulent dispersion and the centrifugal force. Finally, the effect of feed solids concentration (10–50 wt%) on the hydrocyclone performance and particle segregation is also undertaken in this study.

Numerical simulation of near-gravity coal particle behavior in a dense medium cyclone using a mixture model coupled with a discrete phase model

ABSTRACT In general, the washing of coal is greatly influenced by the amount of near-gravity material (NGM) present at the desired cut density. It is observed that the presence of a high percentage of NGM coal results in significant misplacement of particles to wrong products and reduces the separation efficiency of dense medium cyclone (DMC). In this work, an attempt is made to study the behavior of different sizes of NGM coal particles at three feed relative densities inside 350 mm DMC using a discrete phase model (DPM) superimposed on the magnetite medium segregation simulated by modified mixture model. The Reynolds stress model (RSM) is used to resolve turbulence. The DPM is adopted to track different sizes and densities of coal particles, and then a partition curve is constructed to calculate the Ecart probable (Ep) error, percent misplacement, and imperfection. The results show that the lighter and heavier density coal particles away from the separation cut density exhibit very short residence times. Fine-sized coal particles close to the cut density have a significant misplacement compared to the coarse-sized particles having the same density. It is also observed that NGM coal particles show very long residence times irrespective of size.

Flexible clustering via extended mixtures of common t-factor analyzers

Mixtures of t-factor analyzers have been broadly used for model-based density estimation and clustering of high-dimensional data from a heterogeneous population with longer-than-normal tails or atypical observations. To reduce the number of parameters in the component covariance matrices, the mixtures of common t-factor analyzers (MCtFA) have been recently proposed by assuming a common factor loading across different components. In this paper, we present an extended version of MCtFA using distinct covariance matrices for component errors. The modified mixture model offers a more appropriate way to represent the data in a graphical fashion. Two flexible EM-type algorithms are developed for iteratively computing maximum likelihood estimates of parameters. Practical considerations for the specification of starting values, model-based clustering, classification of new subject and identification of potential outliers are also provided. We demonstrate the superiority of the proposed methodology by analyzing the Italian wine data and a simulation study.

Rheology‐Based Computational Fluid Dynamics Modeling for De‐oiling Hydrocyclone Efficiency

AbstractThe de‐oiling hydrocyclone belongs to the most effective devices to recover oil from oily wastewater. An improved multiphase computational fluid dynamics (CFD) model is developed for simulating oil‐water separation in a de‐oiling hydrocyclone. This model approach uses the Reynolds stress model to resolve the turbulent and the modified mixture model with a new viscosity correlation of oil‐in‐water (O/W) emulsions. This modified model of emulsion viscosity based on the power law equation and experimental data of three types of crude oil is introduced to predict the viscosity of O/W emulsions. A comparison between experimental and predicted values of separation efficiency demonstrates that multiphase simulations with the modified model of viscosity provide a better accuracy than CFD models associated with original rheological models. This improved CFD model can be further applied in developing new designs in the future.

Rheology-based CFD modeling of magnetite medium segregation in a dense medium cyclone

In this work, an improved multiphase computational fluid dynamics (CFD) model is developed for simulating medium segregation in a dense medium cyclone. This model approach uses the modified mixture model with the granular option and Reynolds stress model (RSM) to resolve the turbulent mixing of the particles. Rheological behavior of the medium is considered through various forms of viscosity models such as granular viscosity, Newtonian and non-Newtonian model corrected with particle loading and fraction of ultra-fines. Multiphase simulations using the granular viscosity option although predict the overall slurry volume split, product medium densities better than Newtonian models, but the mixture viscosity values are restricted to substantially lower values close to water viscosity levels. Simulations using the Newtonian viscosity model corrected with particle loading and fine fraction below 53μm size are predicted the overall medium viscosity levels well above water viscosity levels but underpredicted the cyclone underflow medium density to the experimental data. Multiphase simulations with the non-Newtonian Herschel–Bulkley viscosity model are able to predict the medium segregation close to the gamma ray tomography data, and the predicted medium viscosity levels are increased up to 18 cp. Overall predicted product medium densities, underflow volume split and radial medium segregation levels are compared to the experimental data. Lagrangian particle tracking (LPT) is super imposed on converged medium simulations used for coal partitioning predictions. This model can be further used in developing new designs in the future.

M3: an improved SNP calling algorithm for Illumina BeadArray data

Genotype calling from high-throughput platforms such as Illumina and Affymetrix is a critical step in data processing, so that accurate information on genetic variants can be obtained for phenotype-genotype association studies. A number of algorithms have been developed to infer genotypes from data generated through the Illumina BeadStation platform, including GenCall, GenoSNP, Illuminus and CRLMM. Most of these algorithms are built on population-based statistical models to genotype every SNP in turn, such as GenCall with the GenTrain clustering algorithm, and require a large reference population to perform well. These approaches may not work well for rare variants where only a small proportion of the individuals carry the variant. A fundamentally different approach, implemented in GenoSNP, adopts a single nucleotide polymorphism (SNP)-based model to infer genotypes of all the SNPs in one individual, making it an appealing alternative to call rare variants. However, compared to the population-based strategies, more SNPs in GenoSNP may fail the Hardy-Weinberg Equilibrium test. To take advantage of both strategies, we propose a two-stage SNP calling procedure, named the modified mixture model (M(3)), to improve call accuracy for both common and rare variants. The effectiveness of our approach is demonstrated through applications to genotype calling on a set of HapMap samples used for quality control purpose in a large case-control study of cocaine dependence. The increase in power with M(3) is greater for rare variants than for common variants depending on the model. M(3) algorithm: http://bioinformatics.med.yale.edu/group. name@bio.com; hongyu.zhao@yale.edu Supplementary data are available at Bioinformatics online.

Tensile properties and morphological evolution of polypropylene and poly(ethylene‐co‐1‐octene) blends

AbstractExtruded sheet of isotactic polypropylene and poly(ethylene‐co‐1‐octene) blends extruded from a counterrotating twin‐screw extruder were studied by scanning electron microscopy, tensile test, and small‐angle X‐ray scattering. The average characteristic length (Λm) determined by the statistical computing from the SEM images increases linearly with increasing of dispersed phase concentration. When POE content is 50 wt% (double continuous phase), Λm is two or three times as big as that of other blends ratio. The analyses of SAXS data confirm this result. Comparison has been made between experimental data of tensile test and those predicted from several meso‐mechanical models such as parallel model, series model, Halpin's model, Mori‐Tanaka's model, and modified mixture model. The modified mixture model is an effective method for predicting Young's modulus in comparison with other models. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers

A Review of CFD Modelling for Performance Predictions of Hydrocyclone

A critical assessment is presented for the existing numerical models used for the performance prediction of hydrocyclones. As the present discussion indicates, the flow inside a hydrocyclone is quite complex and there have been numerous numerical studies on the flows and the particle motions in hydrocyclone, with a wide range of turbulence and multiphase models tested. Two-equation k-ε and RNG k-ε models flow velocities with empirical modifications were led to poor results, especially the tangential components in comparison with experimental measurements. Most of the recent studies have utilized the Reynolds stress models (RSM) with different degrees of complexity in the pressure-strain correlation. These RSM studies showed good agreements with velocity measurements. Unfortunately, the velocity profiles were not validated in most of the RSM cases where multiphase particle tracking were applied. Finally, large eddy simulation (LES) is the most advanced turbulence model applied in recent hydrocyclone numeric studies. Besides the additional information on précising the air core correctly, LES provides an additional accuracy in predicting the velocity profiles or the grade efficiency in comparison to the RSM.The multiphase models have been successfully applied in a hydrocyclone to model the Lagrangian motions of spherical particles. Eulerian-Eulerian model have been used to account for the particles effect on the fluid viscosity. Simplified Eulerian model (mixture) model predictions for solid transportation in cyclone were well predicted. Further, the inclusion of modified slip velocity calculation in the Mixture model improves the efficiency predictions close to the experimental data at low feed solid loadings. In future studies, the focus should be to model the three-dimensional flow in a hydrocyclone using at least the Reynolds stress model/LES. The particle tracking should at least include the effects of the turbulence on the particles. All these developed models will only applicable to low feed solid concentration levels. Since most of these models neglect the particle-particle interactions, a more comprehensive numerical method of modified Mixture model is applied for simulating solids flow in hydrocyclones for high feed solids concentration. Explicit models for accounting hindered settling and turbulent diffusion investigated for high feed solid concentrations in industrial cyclones are encouraging.

Comparison of various statistical methods for identifying differential gene expression in replicated microarray data

DNA microarray is a new tool in biotechnology, which allows the simultaneous monitoring of thousands of gene expression in cells. The goal of differential gene expression analysis is to identify those genes whose expression levels change significantly by the experimental conditions. Although various statistical methods have been suggested to confirm differential gene expression, only a few studies compared the performance of the statistical tests. In our study, we extensively compared three types of parametric methods such as T-test, B-statistic and Bayes T-test and three types of non-parametric methods such as samroc, significance analysis of microarray and a modified mixture model using both the simulated datasets and the three real microarray experiments.

MECHANICAL PROPERTIES AND MORPHOLOGY OF POLYPROPYLENE/POLYSTYRENE BLENDS1*

In this article the relation between the morphology and macroscopic mechanical properties, i.e., stiffness and strength, of blends of polypropylene (PP) and polystyrene (PS) within the framework of micromechanics of composite materials was studied. Test results on tensile properties of immiscible PP/PS blends showed that the micromechanical models were valid for the prediction of elastic moduli. The Mori–Tanaka model would be a more effective method for designing materials in comparison with the Halpin–Tsai model and the modified mixture model because there is no restriction on the experimental parameters. The ultimate strengths were predicted in terms of pure component strength and composition. On the basis of the assumption that the ultimate strength will be controlled by the dispersed phase when the blend has more than the minimum fraction, the minimum fraction of dispersed phase calculated was found close to the phase inversion region determined by observing the blend morphologies. It is confirmed that the blends have a stationary mechanical property at the phase inversion region. Because the poor interface was not taken into account and an assumption was made for the failure of the entire dispersed phase, the model gave an overestimate for strength. *Contract grant sponsor: National Natural Science Foundation, China (Grant No. 59733070).

A Bayesian analysis of stock return volatility and trading volume

The relationship between stock return volatility and trading volume is analysed by using the modified mixture model (MMM) framework proposed by Andersen (1996). This theory postulates that price changes and volumes are driven by a common latent information process, which is commonly interpreted as the volatility. Using GMM estimation Andersen finds that the persistence in this latent process falls when a bivariate model of returns and volume, i.e. the MMM, is estimated instead of a univariate model for returns. This empirical finding is inconsistent with the MMM. As opposed to Andersen's study we apply recently developed simulation techniques based on Markov Chain Monte Carlo (MCMC). A clear advantage of MCMC methods is that estimates of volatility are readily available for use in, for example, dynamic portfolio allocation and option pricing applications. Using Andersen's data for IBM we find that the persistence of volatility remains high in the bivariate case. This suggests that the choice of the estima...

Mixture composition determination from measurements of the acoustic nonlinearity parameter

An important inverse problem in biomedical acoustics is the determination of the composition of a tissue based upon measurements of its acoustic properties. Under many circumstances, the tissue can be modeled as an ideal mixture of components, each with known or assumed properties. The measured properties of the mixture as a whole are then related to those of the components through a set of mixture laws. Once formulated, the problem can be inverted to yield the volume or mass fractions of the components present in the tissue. In this laboratory, the use of the acoustic nonlinearity parameter B/A to help infer the composition of mixtures of bioligical materials has been studied. Various mixture models have been investigated, and a modified version of Apfel's model [J. Acoust. Soc. Am. 79, 148–152 (1986)] has yielded the most useful results. This modified mixture model will be presented, along with precise data that have been obtained on biological mixtures using a novel acoustic interferometry technique reported earlier [J. Acoust. Soc. Am. Suppl. 1 80, S4 (1986)]. [Work supported by the U. S. National Institutes of Health through Grant R004GM300 19].