Showing papers on "Mixture theory published in 2002"

Mixture of experts classification using a hierarchical mixture model

Abstract: A three-level hierarchical mixture model for classification is presented that models the following data generation process: (1) the data are generated by a finite number of sources (clusters), and (2) the generation mechanism of each source assumes the existence of individual internal class-labeled sources (subclusters of the external cluster). The model estimates the posterior probability of class membership similar to a mixture of experts classifier. In order to learn the parameters of the model, we have developed a general training approach based on maximum likelihood that results in two efficient training algorithms. Compared to other classification mixture models, the proposed hierarchical model exhibits several advantages and provides improved classification performance as indicated by the experimental results.

On the local geometry of mixture models

Abstract: SUMMARY Despite the well-known difficulties of undertaking inference with mixture models, they are frequently used for modelling These inferential problems arise because the underlying geometry of a mixture family is very complicated This paper shows that by adding a simplifying assumption, which frequently is natural statistically, the geometric structure is reduced to a much more tractable form This enables standard inferential techniques to be applied successfully One result of studying the local geometry is that it unifies the convex and differential geometric theories of mixture models The techniques proposed are applied to prediction, random effects and measurement error models

How good is the equipartition assumption for the transport properties of a granular mixture

Abstract: Kinetic-theory, with the assumption of equipartition of granular energy, suggests that the pressure and viscosity of a granular mixture vary monotonically with the mass-ratio. Our simulation results show a non-monotonic behaviour that can be explained qualitatively by a simple model allowing for non-equipartition of granular energy between the species with different mass.

Parallel 3-d simulations for porous media models in soil mechanics

Abstract: Numerical simulations in 3-d for porous media models in soil mechanics are a difficult task for the engineering modelling as well as for the numerical realization. Here, we present a general numerical scheme for the simulation of two-phase models in combination with an abstract material model via the stress response with a specialized parallel saddle point solver. Therefore, we give a brief introduction into the theoretical background of the Theory of Porous Media and constitute a two-phase model consisting of a porous solid skeleton saturated by a viscous pore-fluid. The material behaviour of the skeleton is assumed to be elasto-viscoplastic. The governing equations are transfered to a weak formulation suitable for the application of the finite element method. Introducing an abstract formulation in terms of the stress response, we define a clear interface between the assembling process and the parallel solver modules. We demonstrate the efficiency of this approach by challenging numerical experiments realized on the Linux Cluster in Chemnitz.

Infiltration through Deformable Porous Media

Abstract: The equations driving the flow of an incompressible fluid through a porous deformable medium are derived in the framework of the mixture theory. This mechanical system is described as a binary saturated mixture of incompressible components. The mathematical problem is characterized by the presence of two moving boundaries, the material boundaries of the solid and the fluid, respectively. The boundary and interface conditions to be supplied to ensure the well-posedness of the initial boundary value problem are inspired by typical processes in the manufacturing of composite materials. They are discussed in their connections with the nature of the partial stress tensors. Then the equations are conveniently recast in a material frame of reference fixed on the solid skeleton. By a proper choice of the characteristic magnitudes of the problem at hand, the equations are rewritten in non-dimensional form and the conditions which enable neglecting the inertial terms are discussed. The second part of the paper is devoted to the study of one-dimensional infiltration by the inertia-neglected model. It is shown that when the flow is driven through an elastic matrix by a constant rate liquid inflow at the border some exact results can be obtained.

Modeling of the microwave drying process of aqueous dielectrics

Abstract: We propose a thermodynamic framework for describing the microwave drying process of aqueous dielectrics based on Maxwell-Lorentz field equations and mixture theory. Several issues are discussed such as the form of entropy equation; the constitutive relations for the macroscopic electric polarization vectors, Cauchy stresses, heat fluxes, internal momentum supplies, etc., for each component of the mixture: porous solid, water and gas in different regions; and the interfacial jump conditions between different regions in the mixture. A brief examination of the status of material frame indifference within the context of our framework is presented.

A mixture model for magneto-rheological materials

Abstract: To model the response of magnetorheological (MR) materials, a continuum theory for a mixture consisting of a fluid continuum and a solid one is developed. In this mixture theory, the structure composed of the magnetizable particles in MR fluids is treated as a solid continuum. The aim of this paper is two-fold. Firstly, we adopt the extended irreversible thermodynamics (EIT) approach as the thermodynamic framework to formulate the general dynamic equations of MR mixtures. Introducing the concept of plastic deformation of the solid continuum, the mechanisms of dissipation are discussed and the evolution equations for the fluxes are derived. Secondly, by virtue of this derivation we study the propagation of an acoustic wave through the MR fluids. This study shows that there exist two longitudinal acoustic waves propagating along the direction of an applied magnetic field.

Micropolar mixture models on the basis of the Theory of Porous Media

Abstract: The behaviour of porous media can be described in a continuum mechanical setting by the Theory of Porous Media, i. e. by a mixture theory extended by the concept of volume fractions. In addition to the volume fractions, micropolarity is taken into account to model the internal structure of porous media on the macroscopic scale. After a microscopic motivation of the approach, which shows that it is physically motivated to deal with micropolar mixture models, the kinematics, the balance relations, and the constitutive framing of such a theory are discussed. A set of model equations is formulated within the presented frame and applied to some boundary value problems showing the evidence of the theoretical approach.

Material Identification of Nonlinear Solids Infused with a Fluid

Abstract: It is common in the theory of mixtures to prescribe a constitutive relation for the homogenized mixture rather than for each of the individual constituents. Such a relation should describe well the behavior of the mixture, that is experimental data. In this paper, we offer a theoretical framework to guide the performance and interpretation of biaxial tests on solid-fluid mixtures and, in particular, to identify forms of the response functions directly from the data. Moreover, in contrast to prior work, we include the effects of the inertia of the fluid constituent. The potential importance of the latter is illustrated via solutions for an assumed form of the Helmholtz potential for the mixture.

A New Explicit Algorithm for Bi-Phasic Mixture Flow in MIM

Abstract: Metal injection moulding (MIM) is a new technology to manufacture small intricate parts in large quantity. Numerical simulation plays an important role in its development. To predict the specific segregation effect in MIM injection, mixture theory is adopted to model the injection flow by a bi-phasic model. This model conducts to the solution of two-coupled Stokes equations. It is an extremely computational consuming solution in the scope of the traditional algorithms, which induce a serious challenge to cost-effectivity of the MIM simulation. Referred to some methods proposed by Lewis in mono-phasic simulation and the implicit algorithms in MIM simulation, a new explicit algorithm is proposed and realized to perform efficiently this type of bi-phasic flow. Numerically this algorithm is devised to perform the simulation in a fully uncoupled manner except for a global solution of the pressure field in each time step. The physical coupling is taken into account in a sequential pattern by fractional steps. This special algorithm does not need any iteration, so it is straightforward and robust, suitable for MIM simulation and other sorts of simulations for multi-phasic flow.

Structure Mixture Response Of Buildings Due To Simulated Earthquake Loading

Abstract: This paper presents two case studies to evaluate the performance of the structure mixture theory in the earthquake response analysis of buildings. In the first case study, the actual earthquake responses of the two-story reinforced concrete building, which was tested at the University of California at Berkeley, were compared to those obtained using the structure mixture theory. In the second case study, the seven-story reinforced concrete building, which was tested as a part of the US-Japan Cooperative Earthquake Program, was considered. Both case studies showed that the structure mixture theory results were very close to experimental results. The mean differences between the maximum roof displacements obtained experimentally in the first and second case studies and those obtained using the structure mixture theory were found to be equal to 3.5% and 3.2%, respectively.

Effects of volume fraction condition on thermodynamic restrictions in mixture theory

Abstract: Volume fraction condition is a true constraint that must be taken into consideration in deducing the thermodynamic restrictions of mixture theory applying the axiom of dissipation. For a process to be admissible, the constraints imposed by the volume fraction condition include not only the equation obtained by taking its material derivative with respect to the motion of a given phase, but also those by taking its spatial gradient. The thermodynamic restrictions are deduced under the complete constraints, the results obtained are consistent for the mixtures with or without a compressible phase, and in which the free energy of each phase depends on the densities of all phases.

Population Coding of Multiple Edge Orientation

Abstract: We present a probabilistic population coding model of Gabor filter responses. Based on the analytically derived orientation tuning function and a von Mises mixture model of the filter responses, a probability density function of the local orientation in a given point can be extracted through a parameter estimation procedure. The probability density captures angular information at edges, corners or T-junctions and also yields a contrast invariant description of the certainty of each orientation estimate, which can be characterized in terms of the entropy of the corresponding mixture component.