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Showing papers on "Mixture theory published in 2003"


Journal ArticleDOI
TL;DR: In this paper, the authors compare the properties of Biot's theory and the theory of porous media (TPM) in terms of the second compressional wave in the Laplace domain.
Abstract: Wave propagation in porous media is an important topic for example in geomechanics or oil-industry. Especially due to the interplay of the solid skeleton with the fluid the so-called second compressional wave appears. The existence of this wave is reported in the literature not only for Biot's theory (BT) but also for theoretical approaches based on the Theory of Porous Media (TPM – mixture theory extended by the concept of volume fractions). Assuming a geometrically linear description (small displacements and small deformation gradients) and linear constitutive equations (Hooke's law) the governing equations are derived for both theories, BT and the TPM, respectively. In both cases, the solid displacements and the pore pressure are the primary unknowns. Note that this is only possible in the Laplace domain leading to the same structure of the coupled differential equations for both approaches. But the differential equations arising in BT and TPM possess different coefficients with different physical interpretations. Correlating these coefficients to each other leads to the well-known problem of Biot's “apparent mass density”. Furthermore, some inconsistencies are observed if Biot's stress coefficient is correlated to the structure arising in TPM. In addition to the comparison of the governing equations and the identification of the model parameters, the displacement and pressure solutions of both theories are presented for a one-dimensional column. The results show good agreement between both approaches in case of incompressible constituents whereas in case of compressible constituents large differences appear.

100 citations


Journal ArticleDOI
TL;DR: In this article, the authors give a brief review of the various relations proposed for the interaction force in multiphase (or multicomponent) mixtures and provide an alternative approach for finding the drag force on a particle in a particulate mixture.
Abstract: In the mechanics of multiphase (or multicomponent) mixtures, one of the outstanding issues is the formulation of constitutive relations for the interaction force. In this paper, we give a brief review of the various relations proposed for this interaction force. The review is tilted toward presenting the works of those who have used the mixture theory (or the theory of interacting continua) to derive or to propose a relationship for the interaction (or diffusive) force. We propose a constitutive relation which is general and frame-indifferent and thus suitable for use in many flow conditions. At the end, we provide an alternative approach for finding the drag force on a particle in a particulate mixture. This approach has been used in the non-Newtonian fluid mechanics to find the drag force on surfaces.

72 citations


Journal ArticleDOI
TL;DR: A review of GM based quantization and prediction using two previously presented algorithms of EM-type and a discussion on GM model optimization.
Abstract: Lately, Gaussian mixture (GM) models have found new applications in speech processing, and particularly in speech coding. This paper provides a review of GM based quantization and prediction. The main contribution is a discussion on GM model optimization. Two previously presented algorithms of EM-type are analyzed in some detail, and models are estimated and evaluated experimentally using theoretical measures as well as GM based speech spectrum coding and prediction. It has been argued that since many sources have a bounded support, this should be utilized in both the choice of model, and the optimization algorithm. By low-dimensional modeling examples, illustrating the behavior of the two algorithms graphically, and by full-scale evaluation of GM based systems, the advantages of a bounded support approach are quantified. For all evaluation techniques in the study, model accuracy is improved when the bounded support approach is adopted. The gains are typically largest for models with diagonal covariance matrices.

67 citations


Journal ArticleDOI
TL;DR: In this article, Galerkin and Orthogonal Collocation (OC) were used to solve the evolution of the spectral governing equations for quasi-steady vaporization and combustion of a spherically symmetrical droplet composed of a thermodynamically ideal mixture of mutually soluble fuels.

61 citations


Journal ArticleDOI
TL;DR: In this paper, the authors propose an Eshelbian approach to the nonlinear mechanics of a constrained solid-fluid mixture, made up of an inhomogeneous poroelastic solid and an inviscid compressible fluid.
Abstract: Looking at rational mixture theories within the context of a new perspective, this work aims to put forward a proposal for an Eshelbian approach to the nonlinear mechanics of a constrained solid-fluid mixture, made up of an inhomogeneous poroelastic solid and an inviscid compressible fluid, which do not undergo any chemical reaction.

56 citations


Journal ArticleDOI
TL;DR: A new method for estimation of internal link delay distributions using the end- to-end packet pair delay statistics gathered by back-to-back packet-pair unicast probes, based on a variant of the penalized maximum likelihood expectation-maximization (PML-EM) algorithm applied to an additive finite mixture model for the link delay probability density functions.
Abstract: Providers of high quality-of-service over telecommunication networks require accurate methods for remote measurement of link-level performance Recent research in network tomography has demonstrated that it is possible to estimate internal link characteristics, eg, link delays and packet losses, using unicast probing schemes in which probes are exchanged between several pairs of sites in the network We present a new method for estimation of internal link delay distributions using the end-to-end packet pair delay statistics gathered by back-to-back packet-pair unicast probes Our method is based on a variant of the penalized maximum likelihood expectation-maximization (PML-EM) algorithm applied to an additive finite mixture model for the link delay probability density functions The mixture model incorporates a combination of discrete and continuous components, and we use a minimum message length (MML) penalty for selection of model order We present results of Matlab and ns-2 simulations to illustrate the promise of our network tomography algorithm for light cross-traffic scenarios

52 citations


Journal ArticleDOI
TL;DR: In this article, a continuum theory for a mixture of a micropolar elastic solid and a micro-viscous viscous fluid was developed, allowing the rotational degrees of freedom that give rise to a nonsymmetric stress tensor and couple stresses.
Abstract: A continuum theory is developed for a mixture of a micropolar elastic solid and a micropolar viscous fluid. Soil with grains and tortuous rock formations containing dirty fluids may be modeled with this theory. The micropolar model allows the rotational degrees of freedom that give rise to a nonsymmetric stress tensor and couple stresses. Balance laws are given. The second law of thermodynamics is used to develop constitutive equations. Linear constitutive equations are constructed for a heat conducting mixture. Field equations are obtained, boundary and initial conditions presented. As a special case, the field equations of a mixture of an elastic solid and a Newtonian fluid are obtained, by dropping the micropolar effects.

44 citations


Journal ArticleDOI
TL;DR: A theory that can describe the mechanical aspects of cartilage growth is presented, based on a general thermomechanical theory for a mixture of an arbitrary number of growing elastic constituents and an inviscid fluid.
Abstract: The proteoglycan and collagen constituents of cartilage serve distinct mechanical roles. Changes to the mechanical loading conditions during cartilage growth lead to changes in the concentrations of these molecules and, consequently, the mechanical properties. The main aim of this paper is to present a theory that can describe the mechanical aspects of cartilage growth. The model for cartilage growth is based on a general thermomechanical theory for a mixture of an arbitrary number of growing elastic constituents and an inviscid fluid. Our development of a growth mixture theory is accomplished in two steps. First, the thermodynamics of growing elastic materials are considered. The resulting theory of growing thermoelastic materials is extended to continuum mixture theory. Using this general growth mixture theory, we then propose a cartilage growth model that includes two special types of internal constraints that are relevant to cartilage.

38 citations


Journal ArticleDOI
TL;DR: In this paper, a four-component mixture theory is used to model the swimming and shrinking of cartilaginous tissues, which results in a set of coupled non-linear partial differential equations for the electrochemical potentials and the displacement.

35 citations


Journal ArticleDOI
TL;DR: In this article, exact continuum forms of balance (for mass, linear momentum, and tensor-valued moment of momentum) are established as relations between weighted spatial averages of corpuscular quantities computed at any supra-molecular length scale.
Abstract: Exact continuum forms of balance (for mass, linear momentum, and tensor-valued moment of momentum) are established as relations between weighted spatial averages of corpuscular quantities computed at any supra-molecular length scale. Explicit expressions for stress and generalised couple stress in terms of particle interactions are obtained using a theorem due to Noll, and their physical interpretation is discussed for a specific choice of weighting function. Remarks are made on other choices of weighting function, the interpretation of partial stress in mixture theory, a link between couple stress and inhomogeneity, and other forms of moment of momentum balance. Comparison is made with the statistical mechanical viewpoint pioneered by Irving and Kirkwood.

33 citations


Book ChapterDOI
03 Dec 2003
TL;DR: This paper proposes a more general type of MML mixture modelling which allows the variables within a component to be correlated and shows that the proposed MML method performs better than both these criteria.
Abstract: Mixture modelling or unsupervised classification is the problem of identifying and modelling components (or clusters, or classes) in a body of data. We consider here the application of the Minimum Message Length (MML) principle to a mixture modelling problem of multivariate Gaussian distributions. Earlier work in MML mixture modelling includes the multinomial, Gaussian, Poisson, von Mises circular, and Student t distributions and in these applications all variables in a component are assumed to be uncorrelated with each other. In this paper, we propose a more general type of MML mixture modelling which allows the variables within a component to be correlated. Two MML approximations are used. These are the Wallace and Freeman (1987) approximation and Dowe’s MMLD approximation (2002). The former is used for calculating the relative abundances (mixing proportions) of each component and the latter is used for estimating the distribution parameters involved in the components of the mixture model. The proposed method is applied to the analysis of two real-world datasets – the well-known (Fisher) Iris and diabetes datasets. The modelling results are then compared with those obtained using two other modelling criteria, AIC and BIC (which is identical to Rissanen’s 1978 MDL), in terms of their probability bit-costings, and show that the proposed MML method performs better than both these criteria. Furthermore, the MML method also infers more closely the three underlying Iris species than both AIC and BIC.

Journal ArticleDOI
TL;DR: In this article, a micro-structured model for describing global deformations of heterogeneous mixtures is presented, where the solid volume fraction is regarded as a microstructural parameter so as to enlarge the space of admissible deformations.
Abstract: In this paper, we present a micro-structured model for describing global deformations of heterogeneous mixtures. In particular, for a saturated solid-fluid mixture, we regard the solid volume fraction as a microstructural parameter so as to enlarge the space of admissible deformations with respect to the classical theory of mixtures. According to the variational approach, the governing equations are obtained as the stationarity of a suitable action functional. The micro-structured model is then forced to establish a second-gradient mixture theory, by introducing among the considered state parameters a suitable internal constraint. Finally, we determine under which (integrability) conditions the additional balance laws, typically employed to close the theory of porous media endowed with the volume fraction, can fit the variational framework.

Book ChapterDOI
26 Nov 2003
TL;DR: A criterion based on the entropy of the pdf (probability density function) associated to each kernel is proposed to measure the quality of a given mixture model, and a modification of the classical EM algorithm to find the optimal number of kernels in the mixture is proposed.
Abstract: In this paper we address the problem of estimating the parameters of a Gaussian mixture model. Although the EM (Expectation-Maximization) algorithm yields the maximum-likelihood solution it has many problems: (i) it requires a careful initialization of the parameters; (ii) the optimal number of kernels in the mixture may be unknown before-hand. We propose a criterion based on the entropy of the pdf (probability density function) associated to each kernel to measure the quality of a given mixture model, and a modification of the classical EM algorithm to find the optimal number of kernels in the mixture. We test this method with synthetic and real data and compare the results with those obtained with the classical EM with a fixed number of kernels.

Journal ArticleDOI
TL;DR: In this article, a novel averaging process for modeling the mechanical behavior of heterogeneous fine grained or nanostructured materials is presented, and the results of the analysis of a groove created in a scratch test can be used to determine the material parameters in the constitutive equations of gradient dependent elasticity.

01 Jan 2003
TL;DR: In this paper, the governing equations for two poroelastic theories, Biot's theory (BT) and the Theory of Porous Media (TPM), are derived for a one-dimensional column.
Abstract: Assuming a geometrically linear description (small displacements and small deformation gradients) and linear constitutive equations (Hooke’s law) the governing equations are derived for two poroelastic theories, Biot’s theory (BT) and the Theory of Porous Media (TPM ‐ mixture theory extended by the concept of volume fractions). In both cases, the solid displacements and the pore pressure are the primary unknowns. Note that this is only possible in the Laplace domain leading to the same structure of the coupled differential equations for both approaches. But the differential equations arising in BT and TPM possess different coefficients with different physical interpretations. Correlating these coefficients to each other leads to the well-known problem of Biot’s ‘apparent mass density’. Furthermore, some inconsistencies are observed if Biot’s stress coefficient is correlated to the structure arising in TPM. In addition to the comparison of the governing equations and the identification of the model parameters, the displacement and pressure solutions of both theories are presented for a one-dimensional column. The results show good agreement between both approaches in case of incompressible constituents whereas in case of compressible constituents large differences appear.

Book ChapterDOI
26 Jun 2003
TL;DR: A hierarchical mixture of autoregressive (AR) models is proposed for the analysis of nonlinear time-series and an illustration of the flexibility and robustness of the models generated by these mixtures is presented.
Abstract: A hierarchical mixture of autoregressive (AR) models is proposed for the analysis of nonlinear time-series. The model is a decision tree with soft sigmoidal splits at the inner nodes and linear autoregressive models at the leaves. The global prediction of the mixture is a weighted average of the partial predictions from each of the AR models. The weights in this average are computed by the application of the hierarchy of soft splits at the inner nodes of the tree on the input, which consists in the vector of the delayed values of the time series. The weights can be interpreted as a priori probabilities that an example is generated by the AR model at that leaf. As an illustration of the flexibility and robustness of the models generated by these mixtures, an application to the analysis of a financial time-series is presented.

Journal ArticleDOI
TL;DR: The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory in this article, where the soils were treated as the mixture composed of three constituents.
Abstract: The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.

Journal ArticleDOI
TL;DR: In this paper, a boundary element numerical scheme for a flowing mixture of solid particles and a fluid is developed within the context of mixture theory, which is typically employed theories called the averaging approach and mixture theory.
Abstract: A boundary element numerical scheme for a flowing mixture of solid particles and a fluid is developed within the context of mixture theory. Major differences between the two in literature on the subject are studied, these are typically employed theories called the averaging approach and mixture theory. A numerical technique applied is the boundary element method based on velocityvorticity formulation of general equations describing the flow of a twocomponent mixture of a Newtonian fluid and a granular solid. Integral representations for conservation and field functions, based on parabolic diffusion fundamental solution, are presented. Special attention is focused on the mechanical interaction between the mixture components.

Book ChapterDOI
21 Mar 2003
TL;DR: In this article, the authors proposed the principal component analysis (PCA) fuzzy mixture model for speaker identification, which is derived from the combination of the PCA and the fuzzy version of mixture model with diagonal covariance matrices.
Abstract: In this paper, we proposed the principal component analysis (PCA) fuzzy mixture model for speaker identification. A PCA fuzzy mixture model is derived from the combination of the PCA and the fuzzy version of mixture model with diagonal covariance matrices. In this method, the feature vectors are first transformed by each speaker’s PCA transformation matrix to reduce the correlation among the elements. Then, the fuzzy mixture model for speaker is obtained from these transformed feature vectors with reduced dimensions. The orthogonal Gaussian Mixture Model (GMM) can be derived as a special case of PCA fuzzy mixture model. In our experiments, with having the number of mixtures equal, the proposed method requires less training time and less storage as well as shows better speaker identification rate compared to the conventional GMM. Also, the proposed one shows equal or better identification performance than the orthogonal GMM does.

Book ChapterDOI
04 Jun 2003
TL;DR: A robust learning estimator is proposed by means of the generalization of the maximum likelihood estimator called M-estimator, where the robust estimator presents a better performance than the maximumlihood estimator (MLE).
Abstract: The Mixture of Experts model (ME) is a type of modular artificial neural network (MANN) whose architecture is composed by different kinds of networks who compete to learn different aspects of the problem. This model is used when the searching space is stratified. The learning algorithm of the ME model consists in estimating the network parameters to achieve a desired performance. To estimate the parameters, some distributional assumptions are made, so the learning algorithm and, consequently, the parameters obtained depends on the distribution. But when the data is exposed to outliers the assumption is not longer valid, the model is affected and is very sensible to the data as it is showed in this work. We propose a robust learning estimator by means of the generalization of the maximum likelihood estimator called M-estimator. Finally a simulation study is shown, where the robust estimator presents a better performance than the maximum likelihood estimator (MLE).

Journal ArticleDOI
TL;DR: In this article, the authors derived an evolution equation for the field here denoted by @Dn, which represents the difference between the porosity in an arbitrary state of a deformable porous medium and its equilibrium value.


01 Jan 2003
TL;DR: The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory in this paper, where the soils were treated as the mixture composed of three constituents.
Abstract: The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory.The soils were treated as the mixture composed of three constituents.First ,from the researches of soil mechanics,some basic assumptions about the unsaturated soil mixture were mode,and the entropy inequality unsaturated soil mixture was derived.Then,with the common method usually used to deal with the constitutive problems in mixture theory,the nonlinear constitutive equations were obtained.Finally,putting the constiutive equtions of constituents into the balance equations of momentum,the nonlinear field equations of constitutents into the balance equations of momentum,the nonliear field equations of constitutents were set up.The balance equation of energy of unsaturated soil was also given,and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.

Proceedings ArticleDOI
16 Jun 2003
TL;DR: An image denoising method by using mixture modelling of wavelet coefficients to design Wiener filter to reduce noise and also develop the method of selecting windows of different sizes around the coefficient.
Abstract: A wavelet coefficient is generally classified into two categories: significant (large) and insignificant (small). Therefore, each wavelet coefficient is efficiently modelled as a random variable of a Gaussian mixture distribution with unknown parameters. In this paper, we propose an image denoising method by using mixture modelling of wavelet coefficients. The coefficient is classified as either noisy or clean by using proper threshold [2]. Based on this classification, binary mask value that takes an important role to suppress noise is produced. The probability of being clean signal is estimated by a set of mask values. Then we apply this probability to design Wiener filter to reduce noise and also develop the method of selecting windows of different sizes around the coefficient. Despite the simplicity of our method, experimental results show that our method outperforms other critically sampled wavelet denoising schemes.