Mixture theory

About: Mixture theory is a research topic. Over the lifetime, 616 publications have been published within this topic receiving 19350 citations.

A Multiphase Mixture Theory for Fluid-Particle Flows

Abstract: Publisher Summary This chapter presents a theory for suspension of particles in fluids based on the continuum theory of multiphase mixtures and it describes the application of the continuum mixture theory to the description of fluid–particle flows. The maximum concentration of particles can occur off the axis of symmetry because of a balance between lift forces and dynamic pressure forces. This provides a possible explanation of the Segre–Silberberg effect in the context of mixture theory. The classical theory of translational Brownian motion is concerned with the random migration of isolated colloidal particles in a suspending fluid. This random motion is a result of the collisions between the particles and the molecules of the fluid, which are undergoing thermal fluctuations. For neutrally buoyant particles, the particle flux, because of the fluctuating velocity field, is the same as that which can be produced by thermodynamic force acting on each particle. This thermodynamic force is equal to the gradient of the chemical potential of the particles.

A numerical method for the evaluation of non-linear transient moisture flow in cellulosic materials

Abstract: A numerical method for the transient moisture flow in porous cellulosic materials like paper and wood is presented. The derivation of the model is based on mass conservation for a mixture containing a vapour phase and an adsorbed water phase embedded in a porous solid material. The principle of virtual moisture concentrations in conjunction with a consistent linearization procedure is used to produce the iterative finite element equations. A monolithic solution strategy is chosen in order to solve the coupled non-symmetric equation system. A model for the development of higher order sorption hysteresis is also developed. The model is capable of describing cyclic hardening as well as cyclic softening of the equilibrium water concentration. The model is verified by comparison with the measured response to natural variations in temperature and humidity. A close agreement of the simulated results to measured data is found. Copyright (c) 2005 John Wiley & Sons, Ltd. (Less)

Learning Gaussian Mixture Models With Entropy-Based Criteria

Abstract: In this paper, we address the problem of estimating the parameters of Gaussian mixture models. Although the expectation-maximization (EM) algorithm yields the maximum-likelihood (ML) solution, its sensitivity to the selection of the starting parameters is well-known and it may converge to the boundary of the parameter space. Furthermore, the resulting mixture depends on the number of selected components, but the optimal number of kernels may be unknown beforehand. We introduce the use of the entropy of the probability density function (pdf) associated to each kernel to measure the quality of a given mixture model with a fixed number of kernels. We propose two methods to approximate the entropy of each kernel and a modification of the classical EM algorithm in order to find the optimum number of components of the mixture. Moreover, we use two stopping criteria: a novel global mixture entropy-based criterion called Gaussianity deficiency (GD) and a minimum description length (MDL) principle-based one. Our algorithm, called entropy-based EM (EBEM), starts with a unique kernel and performs only splitting by selecting the worst kernel attending to GD. We have successfully tested it in probability density estimation, pattern classification, and color image segmentation. Experimental results improve the ones of other state-of-the-art model order selection methods.

Resistivity coefficients for body composition analysis using bioimpedance spectroscopy: effects of body dominance and mixture theory algorithm.

Abstract: Body composition is commonly predicted from bioelectrical impedance spectroscopy using mixture theory algorithms. Mixture theory algorithms require the input of values for the resistivities of intra-and extracellular water of body tissues. Various derivations of these algorithms have been published, individually requiring resistivity values specific for each algorithm. This study determined apparent resistivity values in 85 healthy males and 66 healthy females for each of the four published mixture theory algorithms. The resistivity coefficients determined here are compared to published values and the inter-individual (biological) variation discussed with particular reference to consequential error in prediction of body fluid volumes. In addition, the relationships between the four algorithmic approaches are derived and methods for the inter-conversion of coefficients between algorithms presented.