Distribution Functions Of Mixtures Research Articles

Deviation from the prediction of the Maier-Saupe theory of mixtures of charged discotic Gay-Berne and Lennard-Jones particles

ABSTRACT We report an analysis of the orientational order and orientational distribution functions of mixtures of discotic charged Gay-Berne (GB) and Lennard-Jones (LJ) particles as models of ionic liquid crystals and colloidal suspensions. We have studied three different stoichiometries (GB:LJ of 1:2, 1:1 and 2:1), with the opposite charges on the two particles selected to guarantee electroneutrality. We have found that for relatively low values of the scaled charge the dependence of the fourth-rank orientational order parameter, <P 4>, on the second-rank orientational order parameter, <P 2>, is in very good agreement with the prediction of the Maier-Saupe theory. In contrast, for relatively high values of the charge a deviation is observed which is in opposite directions for mixtures with an excess for GB particles and mixtures with an excess of LJ particles.

Assessing testicular germ cell DNA damage in the comet assay; introduction of a proof-of-concept.

The in vivo comet assay is widely used to measure genotoxicity; however, the current OECD test guideline (TG 489) does not recommend using the assay to assess testicular germ cells, due to the presence of testicular somatic cells. An adapted approach to specifically assess testicular germ cells within the comet assay is certainly warranted, considering regulatory needs for germ cell-specific genotoxicity data in relation to the increasing global production of and exposure to potentially hazardous chemicals. Here, we provide a proof-of-concept to selectively analyze round spermatids and primary spermatocytes, distinguishing them from other cells of the testicle. Utilizing the comet assay recordings of DNA content (total fluorescence intensity) and DNA damage (% tail intensity) of individual comets, we developed a framework to distinguish testicular cell populations based on differences in DNA content/ploidy and appearance. Haploid round spermatid comets are identified through (1) visual inspection of DNA content distributions, (2) setting DNA content thresholds, and (3) modeling DNA content distributions using a normal mixture distribution function. We also describe an approach to distinguish primary spermatocytes during comet scoring, based on their high DNA content and large physical size. Our concept allows both somatic and germ cells to be analyzed in the same animal, adding a versatile, sensitive, rapid, and resource-efficient assay to the limited genotoxicity assessment toolbox for germ cells. An adaptation of TG 489 facilitates accumulation of valuable information regarding distribution of substances to germ cells and their potential for inducing germ cell gene mutations and structural chromosomal aberrations.

Planning of a Group of Dynamic Systems Operation Program Based on the Failure Time Prediction

The article is devoted to the justification of group of dynamic systems (DS) operation program based on the failure time prediction. The following assumptions are made: the group includes DS operating under the same conditions, but having different service life; the composition of the DS includes a number of potentially faulty elements with similar values of reliability indicators; for each element a number of parameters are measured and the failure of the DS occurs when at least one of the controlled parameters leaves the tolerance range. The use of a piecewise linear regression model of parameter drift corresponding to the life cycle of DS is justified. The rule of correction of the linear model is formed based on the results of last measurements of the controlled parameters. A unified algorithm for calculating the reliability characteristics in a group of DS based on the drift of controlled parameters is proposed. At the first step, the probability of failure-free operation for a given time and a gamma-percent resource is calculated for one controlled parameter. At the second step, the time moment of a DS failure (which is assumed to happen when at least one controlled parameter leaves the tolerance range) is calculated. At the third step, the reliability characteristics of a group of DS are predicted using a mixture of distributions. The realization of a random variable corresponding to a random mixture is modeled as follows: first, DS is selected at random, then a random variable is modeled in accordance with its distribution function. The mixture distribution function is expressed as a weighted sum of the component distribution functions. Model examples allowing to rank the considered DS according to the predicted failure time with subsequent adjustment of the operation program are considered.

Development of an assessment framework for the proposed Multi-Scalar Seasonally Amalgamated Regional Standardized Precipitation Evapotranspiration Index (MSARSPEI) for regional drought classifications in global warming context

Drought hazard is one of the main consequences of global warming and climate change. Unlike other natural disasters, drought has complex climatic features. Therefore, accurate drought monitoring is a challenging task. This paper proposes a framework for assessing drought classifications at the regional level. The proposed framework provides a new drought monitoring indicator called Multi-Scalar Seasonally Amalgamated Regional Standardized Precipitation Evapotranspiration Index (MSARSPEI). MSARSPEI is an amalgam of the Standardized Precipitation Evapotranspiration (SPEI) (Vicente-Serrano et al., 2010) and Regionally Improved Weighted Standardized Drought Index (RIWSDI) (Jiang et al., 2020). In the proposed framework, the Boruta algorithm of feature selection is configured to ensemble monthly time series data of evaporation in various meteorological stations located in specific regions. Further, the framework suggests the standardization of the Cumulative Distribution Function (CDF) of K-Component Gaussian (K-CG) mixture distribution function for obtaining MSARSPEI data. The application of the proposed framework is based on seven different regions of Pakistan. For comparative analysis, this paper compared the performance of MSARSPE with SPEI using Pearson correlation. Outcomes associated with this research show that the proposed regional drought index has a strong correlation with the competing indicator in various time scales. In addition, the study assessed the spatial extent of various drought classifications under MSARSPEI. In summation, this research concludes that the choice of the MSARSPEI is rationally valid and more appropriate for the regional assessment of drought under the global warming scenario.

Sharp bounds on distribution functions and expectations of mixtures of ordered families of distributions

We compare two mixtures of arbitrary collection of stochastically ordered distribution functions with respect to fixed mixing distributions. Under the assumption that the first mixture distribution is known, we establish optimal lower and upper bounds on the latter mixture distribution function and present single families of ordered distributions which attain the bounds uniformly at all real arguments. Furthermore, we determine sharp upper and lower bounds on the differences between the expectations of the mixtures expressed in various scale units. General results are illustrated by several examples.

A mortality model based on a mixture distribution function

A new mortality model based on a mixture distribution function is proposed. We mix a half-normal distribution with a generalization of the skew-normal distribution. As a result, we get a six-parameter distribution function that has a good fit with a wide variety of mortality patterns. This mixture model is fitted to several mortality data schedules and compared with the Siler (five-parameter) and Heligman–Pollard (eight-parameter) models. Our proposal serves as a convenient compromise between the Heligman–Pollard model (which ensures a good fit with data but is often overparameterized) and the Siler model (which is more compact but fails to capture ‘accident humps’).

Clustering gene expression data analysis using an improved EM algorithm based on multivariate elliptical contoured mixture models

Clustering gene expression data is an important research topic in bioinformatics because knowing which genes act similarly can lead to the discovery of important biological information. Many clustering algorithms have been used in the field of gene clustering. The multivariate Gaussian mixture distribution function was frequently used as the component of the finite mixture model for clustering, however the clustering cannot be restricted to the normal distribution in the real dataset. In order to make the cluster algorithm strong adaptability, this paper proposes a new scheme for clustering gene expression data based on the multivariate elliptical contoured mixture models (MECMMs). To solve the problem of over-reliance on the initialization, we propose an improved expectation maximization (EM) algorithm by adding and deleting initial value for the classical EM algorithm, and the number of clusters can be treated as a known parameter and inferred with the QAIC criterion. The improved EM algorithm based on the MECMMs is tested and compared with some other clustering algorithms, the performance of our clustering algorithm has been extensively compared over several simulated and real gene expression datasets. Our results indicated that improved EM clustering algorithm is superior to the classical EM algorithm and the support vector machines (SVMs) algorithm, and can be widely used for gene clustering.

A framework for medical image retrieval using merging-based classification with dependency probability-based relevance feedback

Content-based image retrieval (CBIR) systems are used to retrieve relevant images from large-scale databases. In this paper, a framework for the image retrieval of a large-scale database of medical X-ray images is presented. This framework is designed based on query image classification into several prespecified homogeneous classes. Using a merging scheme and an iterative classification, the homogeneous classes are formed from overlapping classes in the database. For this purpose, the shape and texture features, selected using the forward selection algorithm, are optimized by a novel genetic algorithm-based feature reduction and optimization algorithm in the feature space. In this algorithm, using a new fitness function, we try to locate similar images in the database together in the feature space. Using the merging-based classification, the m-nearest classes to the query image are selected as a filtered search space. To increase the retrieval efficiency, we integrate a novel dependency probability-based relevance feedback (RF) approach with the proposed CBIR framework. The proposed RF uses a synthetic distance measure based on the weighted Euclidean distance measure and Gaussian mixture model-based dependency probability similarity measure of the database images to the Gaussian mixture distribution function of the positive images. The experimental results are reported based on a database consisting of 10,000 medical X-ray images of 57 classes (ImageCLEF 2005 database). The provided results show the effectiveness of the proposed framework compared to the approaches presented in the literature.

A mixed Weibull model for size reduction of particulate and fibrous materials

This paper describes a simple alternative to the classical population balance breakage model, which characterizes and controls the size distribution of particles submitted to a reduction process. The new approach is based on cumulative distribution functions of mixed random variables. Results indicate that a Weibull mixture distribution function adequately models the size of particles submitted to various breakage processes. The model was further applied to experimental reduction processes with apparently random breakage probability and yielded good estimates of the unbroken particle and fragment distributions. Use of these results for direct and indirect prediction of the size alteration under dimensional reduction processes is discussed.

Molecular dynamics results for the radial distribution functions of highly asymmetric hard sphere mixtures

Molecular dynamics (MD) results for the radial distribution functions of mixtures of large and small hard spheres are reported for size ratios whose (large/small) values are 1, 2.5, 5, 7.5, and 10 in the region where the concentration of the large spheres is very small. The MD contact values of these functions are compared with formulae due to Boublik, Mansoori, Carnahan, Starling, Leland, Grundke, and Henderson, Viduna and Smith, Henderson, Trokhymchuk, Woodcock, and Chan, as well as new formulae that are considered here. The new formulae give good agreement for the large–small contact values and reasonably good agreement for the large–large contact values. The Viduna–Smith formula is satisfactory for the small–small contact value and quite reasonable for the small–large contact value. Undoubtedly, further improvements are possible. These results give insight into what may be called the colloidal limit, where the size ratio is exceedingly large while the concentration of the large spheres is exceedingly small, and into the passage to this limit.

Viscosity of Alternative Refrigerants R407C and R407E in the Vapor Phase from 298.15 to 423.15 K

This paper presents new measurements of the viscosity of gaseous R407C (23 mass% HFC-32, 25 mass% HFC-125, 52 mass% HFC-143a) and R407E (25 mass% HFC-32, 15 mass% HFC-125, 60 mass% HFC-143a). The measurements were carried out with an oscillating-disk viscometer of the Maxwell type at temperatures from 298.15 to 423.15 K. The densities of these two fluid mixtures were calculated with the equation-of-state model in REFPROP. The viscosity at normal pressures was analyzed with the extended law of corresponding states developed by Kestin et al., and the scaling parameters needed in the analysis were obtained from our previous studies for the viscosity of the binary mixtures consisting of HFC-32, HFC-125, and HFC-134a. The modified Enskog theory developed by Vesovic and Wakeham (V-W method) was applied to predict the viscosity for the ternary gaseous HFC mixtures under pressure. As for the calculation of pseudo-radial distribution functions in mixtures, a method based on the equation of state for hard-sphere fluid mixtures proposed by Carnahan-Starling was applied. It was found that the V-W method can predict the viscosity of R407C and R407E without any additional parameters for the ternary mixture.

Viscosity of Gaseous Mixtures of HFC-134a (1,1,1,2-Tetrafluoroethane)+HFC-32 (Difluoromethane)

This paper reports experimental results for the viscosity of gaseous mixtures of HFC-134a (1,1,1,2-tetrafluoroethane)+HFC-32 (difluoromethane). The measurements were carried out with an oscillating-disk viscometer of the Maxwell type at temperatures from 298.15 to 423.15 K. The viscosity was measured for three mixtures containing 25.00, 52.40, and 74.98 mole% HFC-134a in HFC-32. Experimental results for the viscosity at normal pressures show a minimum as plotted against mole fraction in the higher temperature region, which may be the first experimental observation of the minima for dilute binary gaseous mixtures of HFCs. The viscosity at normal pressures was analyzed with the extended law of corresponding states developed by Kestin et al., and the scaling parameters were obtained for unlike-pair interactions between HFC-32 and HFC-134a. The modified Enskog theory developed by Vesovic and Wakeham was applied to predict the viscosity for the binary gaseous mixtures under pressure. As for the calculation of pseudo-radial distribution functions in mixtures, a method based on the equation of state for hard-sphere fluid mixtures proposed by Carnahan–Starling was applied.

Analytical representations for the radial distribution functions of mixtures of adhesive spheres

A study has been made of the pole topology of the Laplace transforms of the pair distribution functions (PDFs) of a binary mixture of adhesive hard spheres (AHS) both for the Percus-Yevick equation and the mean spherical model (MSM). Expressions are given that describe how the distribution of the poles in the left half of the complex plane varies with the system parameters for the special case of the MSM for symmetric binary AHS mixtures. The locations of the poles closest to the imaginary axis are known to determine the asymptotic form of the PDFs, i.e. either exponentially monotonic or exponentially oscillatory decaying. As a byproduct of this inquiry analytical r space representations of the PDFs are derived that allow their accurate and efficient determination over the entire r range.

Deriving integral equations for radial distribution functions of multicomponent mixtures on the basis of scale transformations in the phase space

It is shown that scale transformations of the coordinate part of the phase space for one of the mixture components correspond to virtual variations in the local density for the same component in a thermodynamic system. The investigation results are used to construct different variants of a generating functional with the goal of deriving a system of integral equations for the radial distribution functions of mixtures. An equation of state, which is a modification of the Tate equation, is obtained. Systems of integral equations that imply, in the limit, the Perkus-Yevick equations and systems of equations for hypernetted chains are derived for radial distribution functions.

A study of the Buckingham exponential-six fluid mixtures

Extensive Monte Carlo computer simulation results for the configurational energy, compressibility and the radial distribution functions of mixtures of exponential-six molecules at 352 state points and presented. These data are used to test mixture models that have been proposed, and to develop a model which describes the exp-6 fluid quite well. Using this model, explicit expressions are obtained for the partition function for pure fluids and mixtures of exp-6 molecules.It is also shown how, by redefinition of the free volume and mean potential terms, simple models can be used to describe the behavior of exp-6 fluids and that with this definition the behavior of the exp-6 and square-well fluids are very similar.

Chemical potential prediction in realistic fluid models with scaled particle theory

A procedure frequently proposed in the literature for calculating chemical potentials relies on the Kirkwood charging process. Numerical problems associated with coupling large repulsive forces can be avoided by estimating the contribution to the chemical potential due to these forces with scaled particle theory. The contribution due to soft repulsive forces and attractive forces can be calculated with the Kirkwood charging process using distribution functions for a test particle obtained from integral equation theories. We have used the accurate HMSA theory of Zerah and Hansen to provide distribution functions in mixtures of Lennard-Jones molecules, and we have used the PYP theory of Lee to scale the distribution functions over the charging process. The theory provides accurate estimates of chemical potentials over a range of densities from gas-like to liquid-like when the reduced temperature kT/ɛ is greater than 2. Accurate results for excess free energy changes of mixing are also obtained at these conditions. At lower temperatures accurate results are obtained for low to moderate reduced densities (ρσ 3⩽0.5).

Mean density approximation and hard sphere expansion theory: A review

This review surveys research dealing with the Mean Density Approximation (MDA) and the Hard Sphere Expansion (HSE) theory developed by Leland and coworkers. MDA and its modifications provide a simple way to predict radial distribution functions of mixtures from the pure fluid information. Comparisons with computer simulation data show the MDA to be superior to the van der Waals approximation for mixture radial distribution functions. Derivations of the HSE theory and the HSE Conformal Solution Theory (HSE-CST) are also described. For Lennard-Jones mixtures, the HSE theory is proven to be superior to the van der Waals theory by using a proper method to determine the hard-sphere diameter. The major problem associated with the development of a consistent method to determine the hard-sphere diameter of the HSE-CST and the requirements regarding the extension of the HSE-CST to polar mixtures are discussed. It is concluded that the HSE-CST is capable of predicting, satisfactorily, the vapor-liquid equilibrium properties of mixtures containing hydrocarbons and/or slightly quadrupolar or polar compounds such as CO 2 and H 2S.

Monte carlo simulation and thermodynamic perturbation theory for mixtures of diatomic molecules

The thermodynamic properties and site—site distribution functions of mixtures of non-spherical molecules are obtained by Monte Carlo simulation. A non-spherical reference-system perturbation theory based on the RISM equation is developed to predict these results. The agreement between theory and simulation for the thermodynamic properties is encouraging. Important differences in the relative peak heights of the site—site distribution functions from theory and simulation are attributed to the role of attractive forces in determining local structure in the fluid mixtures, where the volumes of the components are similar but the well depths differ.

Fluids of hard spheres with nonadditive diameters

Monte Carlo results are reported for the equation of state and radial distribution functions of mixtures of hard spheres with nonadditive diameters. Comparison is made with the predictions of perturbation theories of various types and methods based on a one-component reference fluid are found to give the most satisfactory results.

Correlation functions of classical fluids. I. The radial distribution functions of mixtures of Kihara molecules in the Percus-Yevick approximation and their thermodynamic functions

The Percus-Yevick integral equation is solved for systems of molecules interacting with the Kihara potential. Radial distribution functions for the pure fluid systems of argon, krypton, and xenon, and for the binary mixture argon-nitrogen are obtained. For the one-component system, the use of the Kihara potential yields equivalent results in comparison with previous theoretical and experimental studies. For the case of argon, a numerical potential proposed by Dymond and Alder is also employed and the results show superior agreement with the x-ray diffraction data. The solutions of the two-component case cover a wide range of temperatures, densities, and compositions, including those of the liquid state. The variations of the radial distribution functions with density, temperature, and composition are ascertained. It is found that the main features of the radial distribution functions, such as the peak heights, their relative magnitudes, and the zeros of the total correlation functions, vary under quite complex rules, yet in most part are verifiable by experiments. The macroscopic properties of Ar–N2 mixtures, such as the internal energy and the Helmholtz free energy, are also calculated. Hiroike's formula for the calculation of the free energy is adopted which avoids the usual procedure of integrating a pressure term that has two values, one from the virial theorem and the other from the fluctuation-compressibility derivation. Agreements with values derived from the Strobridge equation of state are close for the internal energy and less satisfactory for the Helmholtz free energy. Their variations with temperature, density, and composition are also demonstrated.