Showing papers on "Mixture theory published in 2011"
TL;DR: In this article, a solution scheme for multiscale fluid transport equation of Singh et al. was developed, which could be easily implemented in a commercial finite elements package for solving swelling/shrinking problems.
32 citations
TL;DR: A constituent-based theoretical model of age-related changes in geometry and mechanical properties of conduit arteries was proposed based on the premise that given the time course of the load on an artery and the accumulation of advanced glycation end-products in the arterial tissue, the initial geometric dimensions and properties can be predicted by a solution of a boundary value problem.
Abstract: In the present report, a constituent-based theoretical model of age-related changes in geometry and mechanical properties of conduit arteries is proposed. The model was based on the premise that given the time course of the load on an artery and the accumulation of advanced glycation end-products in the arterial tissue, the initial geometric dimensions and properties of the arterial tissue can be predicted by a solution of a boundary value problem for the governing equations that follow from finite elasticity, structure-based constitutive modeling within the constrained mixture theory, continuum damage theory, and global growth approach for stress-induced structure-based remodeling. An illustrative example of the age-related changes in geometry, structure, composition, and mechanical properties of a human thoracic aorta is considered. Model predictions were in good qualitative agreement with available experimental data in the literature. Limitations and perspectives for refining the model are discussed.
28 citations
TL;DR: In this article, a Gaussian mixture of beamformers is used to extract a speech source from a known direction when there are fewer microphones than sources (the underdetermined case).
Abstract: This paper describes frequency-domain nonlinear mixture of beamformers that can extract a speech source from a known direction when there are fewer microphones than sources (the underdetermined case). Our approach models the data in each frequency bin via Gaussian mixture distributions, which can be learned using the expectation maximization algorithm. The model learning is performed using the observed mixture signals only, and no prior training is required. Nonlinear beamformers are then developed based on this model. The proposed estimators are a nonlinear weighted sum of linear minimum mean square error or minimum variance distortionless response beamformers. The resulting nonlinear beamformers do not need to know or estimate the number of sources, and can be applied to microphone arrays with two or more microphones. We test and evaluate the described methods on underdetermined speech mixtures.
22 citations
TL;DR: In this article, a nonlinear multi-field coupled model for multi-constituent three-phase soils is derived by using the hybrid mixture theory, and the balance equations with three levels (constituents, phases and the whole mixture soil) are set up under the assumption that soil is composed of multiscale elastic-plastic solid skeleton and viscous liquid and ideal gas.
Abstract: A nonlinear multi-field coupled model for multi-constituent three-phase soils is derived by using the hybrid mixture theory. The balance equations with three levels (constituents, phases and the whole mixture soil) are set up under the assumption that soil is composed of multi-constituent elastic-plastic solid skeleton (which is different from the linearization method) and viscous liquid and ideal gas. With reasonable constitutive assumptions in such restrictive conditions as the principles of determinism, equipresence, material frame-indifference and the compatible principle in continuum mechanics, a theoretical framework of constitutive relations modeling three-phase soil in both non-equilibrium and equilibrium states is established, thus the closed field equations are formed. In the theoretical framework, the concept of effective generalized thermodynamic forces is introduced, and the nonlinear coupling constitutive relations between generalized dissipation forces and generalized flows within the system at nonequilibrium state are also presented. On such a basis, four special coupling relations, i.e., solid thermal elastic-plastic constitutive relation, liquid visco-elastic-plastic constitutive relation, the generalized Fourier’s law, and the generalized Darcy’s law are put forward. The generalized or nonlinear results mentioned above can degenerate into the linear coupling results given by Bennethum and Singh. Based on a specific dissipation function, the concrete form of generalized Darcy’s law is deduced, which may degenerate into the traditional form of Darcy’s law by neglecting the influence of skeleton deformation and temperature. Without considering temperature and other coupling effects, the nonlinear coupled model in this paper can degenerate into a soil elastic-plastic constitutive model.
21 citations
DOI•
01 Jan 2011
TL;DR: In this paper, the authors used the smoothed particle hydrodynamics (SPH) method to simulate a dam break-like problem along a slope, where the two sets of equations related to the fluid and solid phases, as considered by the debris flow mixture theory, have been simplified in only one set of equations.
Abstract: D muddy debris flow has been simulated accord - ing to a dam break like problem along a slope. The two sets of equations related to the fluid and solid phases, as considered by the debris flow mixture theory, have been simplified in only one set of equations, consider - ing just one equivalent material. Then the Herschel- Bulkley fluid constitutive equations have been select - ed. The correct parameters of the HeRsCHel-bulkley model have been chosen in order to correctly simulate the behaviour of mudflows. The final mathematical model, has been solved numerically with the smoothed particle hydrodynamics (SPH) method. SPH is a par- ticle mesh-free Lagrangian method, well suitable for computing highly transitory free surface flows of com - plex fluids in complex geometries. Finally a laboratory experimental test has been selected for comparison. Satisfactory results have been achieved. Nevertheless, further parametric analyses will be carried out and fur- ther considerations about both constitutive equations and numerical improvements will be employed and discussed in future papers.
20 citations
TL;DR: In this article, a phase field model is developed for the saturated porous medium undergoing phase transition, and the constitutive representations for the stresses, entropies, heat fluxes, drag force and the evolution equations for the order parameter and porosity are derived by exploitation of the entropy inequality.
19 citations
TL;DR: This paper extends the GMM clustering method to calculate a local weight vector as well as a local variance within each cluster, and uses the weight and variance values to capture main properties that discriminate different clusters, including subsets of relevant dimensions and shape volumes.
17 citations
TL;DR: SedMix3D as discussed by the authors is a 3D bottom boundary layer model developed from mixture theory to simulate the complex coupled interactions between fluid and sandy sediment on the seafloor.
Abstract: The complex coupled interactions between fluid and sandy sediment on the seafloor are simulated with a three-dimensional bottom boundary layer model (SedMix3D) developed from mixture theory. SedMix3D solves the unfiltered Navier-Stokes equations for a fluid-sediment mixture treated as a single continuum with effective properties that parameterize the fluid-sediment and sediment-sediment interactions including a variable mixture viscosity, a bulk hindered settling velocity, and a shear-induced, empirically calibrated, mixture diffusion term. A sediment flux equation models the concentration of sediment by describing the balance of sediment flux by advection, gravity, and shear-induced diffusion. The grid spacing is on the order of a sediment grain diameter, and simulated flows had maximum free-stream velocities between 20 and 120 cm/s and periods between 2 and 4 s. Modeled ripple geometries ranged from a single ripple to multiple ripples with varying heights, lengths, and steepness. Only noncohesive sedim...
14 citations
TL;DR: By analyzing both volumetric and surface dissolutions, the two fundamental modes of growth are investigated within the unified framework of mixture theory.
Abstract: Growth mechanics problems require the solution of mass balance equations that include supply terms and account for mass exchanges among constituents of a mixture. Though growth may often be accompanied by a variety of concomitant phenomena that increase modeling complexity, such as solid matrix deformation, evolving traction-free configurations, cell division, and active cell contraction, it is important to distinguish these accompanying phenomena from the fundamental growth process that consists of deposition or removal of mass from the solid matrix. Therefore, the objective of this study is to present a canonical problem of growth, namely, dissolution of a rigid solid matrix in a solvent. This problem illustrates a case of negative growth (loss of mass) of the solid in a mixture framework that includes three species, a solid, a solvent, and a solute, where the solute is the product of the solid dissolution. By analyzing both volumetric and surface dissolutions, the two fundamental modes of growth are investigated within the unified framework of mixture theory.
13 citations
TL;DR: In this paper, the authors investigate the asymptotic behavior of solutions to the initial boundary value prob- lem for the interaction between the temperature field and the porosity fields in a homogeneous and isotropic mixture from the linear theory of porous Kelvin-Voigt materials.
Abstract: In this paper, we investigate the asymptotic behavior of solutions to the initial boundary value prob- lem for the interaction between the temperature field and the porosity fields in a homogeneous and isotropic mixture from the linear theory of porous Kelvin-Voigt materials. Our main result is to establish conditions which insure the analyticity and the exponential stability of the corresponding semigroup. We show that under certain conditions for the coefficients we obtain a lack of exponential stability. A numerical scheme is given.
10 citations
TL;DR: Using the proposed model, one can find a theoretical explanation for some clinically observed behavior of bone, for instance for the greater rate of bone resorption in cortical than cancellous bone, using the conservation equations and/or consistency requirements of continuum mixture theory.
Abstract: In this paper, for the first time, a tri-phasic model of bone resorption using a mixture with chemical reactions is proposed. Three constituents (matrix, fluid, and cells) are considered. Conservation equations and entropy inequality are provided. The dependent variables in the constitutive equations, such as the rate of resorption, are assumed to be a function of temperature, deformation gradient, and the extent of the chemical reactions. Using constitutive equations in the second law of thermodynamics, a criterion for the thermodynamic equilibrium state is obtained which contains a bio-chemo-mechanical affinity. Using the proposed model, one can find a theoretical explanation for some clinically observed behavior of bone, for instance for the greater rate of bone resorption in cortical than cancellous bone, using the conservation equations and/or consistency requirements of continuum mixture theory. This work can be seen as a first step towards establishing a new theoretical framework which could be developed in the future by collaborative work, and with the hope of shedding some light on the multidisciplinary and complex process of bone resorption.
TL;DR: This work introduces flexible practical quantizers based on possibly non-Gaussian models in both the constrained resolution (CR) and the constrained entropy cases and derives model estimation criteria optimizing asymptotic quantizer performance.
Abstract: Using high-rate theory approximations we introduce flexible practical quantizers based on possibly non-Gaussian models in both the constrained resolution (CR) and the constrained entropy cases. We derive model estimation criteria optimizing asymptotic (with increasing rate) quantizer performance. We show that in the CR case the optimal criterion is different from the maximum likelihood criterion commonly used for that purpose and introduce a new criterion that we call constrained resolution minimum description length (CR-MDL). We apply these principles to the generalized Gaussian scaled mixture model, which is accurate for many real-world signals. We provide an explanation of the reason why the CR-MDL improves quantization performance in the CR case and show that CR-MDL can compensate for a possible mismatch between model and data distribution. Thus, this criterion is of a great interest for practical applications. Our experiments apply the new quantization method to controllable artificial data and to the commonly used modulated lapped transform representation of audio signals. We show that both the CR-MDL criterion and a non-Gaussian modeling have significant advantages.
TL;DR: In this paper, a parallel hybrid method using Lattice Boltzmann Method (LBM) for fluid phase and Finite Element Method (FEM) for solid phase is used for direct numerical simulation of saturated deformable porous media.
Abstract: Numerical techniques for modeling saturated deformable porous media have mainly been based on mixture theory or homogenization techniques. However, these techniques rely on phenomenological relationships for the constitutive equations along with assumptions of homogeneous and isotopic material properties to obtain closure. Direct numerical simulations of the multiphasic problem for flow in deformable porous media avoid such assumptions and thus can provide significantly accurate understanding of the physics involved. They serve as a tool to investigate the constitutive relationships in complex geometries. They also allow the validation of the existing mixture theory models and determine their limitations. In this work, a parallel hybrid method using Lattice Boltzmann Method (LBM) for fluid phase and Finite Element Method (FEM) for solid phase is used for direct numerical simulation of saturated deformable porous media. The method provides a number of unique features including scalability on distributed computing necessary for such a problem. The method has been validated for modeling fluid―structure interactions in complex geometries against a number of experimental and analytical solutions. Further some challenging problems has been chosen to show the capability of the method.
TL;DR: A novel method for estimating multimodal data distribution based on the Gaussian mixture model is proposed and is applied to a character recognition problem that requires high-dimensional feature vectors.
Abstract: Precise estimation of data distribution with a small number of sample patterns is an important and challenging problem in the field of statistical pattern recognition. In this paper, we propose a novel method for estimating multimodal data distribution based on the Gaussian mixture model. In the proposed method, multiple random vectors are generated after classifying the elements of the feature vector into subsets so that there is no correlation between any pair of subsets. The Gaussian mixture model for each subset is then constructed independently. As a result, the constructed model is represented as the product of the Gaussian mixture models of marginal distributions. To make the classification of the elements effective, a graph cut technique is used for rearranging the elements of the feature vectors to gather elements with a high correlation into the same subset. The proposed method is applied to a character recognition problem that requires high-dimensional feature vectors. Experiments with a public handwritten digit database show that the proposed method improves the accuracy of classification. In addition, the effect of classifying the elements of the feature vectors is shown by visualizing the distribution.
01 Jan 2011
TL;DR: In this paper, a general model for the analysis of concrete as multiphase porous material, obtained from microscopic scale by applying the so-called Hybrid Mixture Theory, is presented The final formulation of the governing equations at macro-level is obtained by upscaling their local form from the micro-scale.
Abstract: In this paper a general model for the analysis of concrete as multiphase porous material, obtained from microscopic scale by applying the so-called Hybrid Mixture Theory, is presented The final formulation of the governing equations at macro-level is obtained by upscaling their local form from the micro-scale This procedure allows for taking into account both bulk phases and interfaces of the multiphase system, to define several quantities used in the model and to obtain some thermodynamic restrictions imposed on the evolution equations describing the material deterioration Two specific forms of the general model adapted to the case of concrete structures under fire and to the case of concrete degradation due to the leaching process are shown Some numerical simulations aimed at proving the validity of the approach adopted, are also presented and discussed
TL;DR: In this article, the authors consider a class of processes in which the flow of an incompressible fluid through a porous matrix is accompanied by a mass exchange between the constituents, and derive a macroscopic law for the flow, starting from the analysis of the phenomena at the pore scale.
Abstract: We consider a class of processes in which the flow of an incompressible fluid through a porous matrix is accompanied by a mass exchange between the constituents. This paper is in two parts. In the first part we use an upscaling procedure to derive a macroscopic law for the flow, starting from the analysis of the phenomena at the pore scale. To this end we utilize a simplified geometry of the solid matrix. The resulting governing equation is of Darcy type, as expected, but, owing to mass exchange, it contains a complicated nonlocal dependence on the hydraulic conductivity. In the second part we look directly for the formulation of a macroscopic model in the framework of mixture theory. We emphasize the basic role of energy dissipation: the two methods lead to the same conclusions, provided that the same dissipation rates are postulated.
TL;DR: In this paper, the generalized micropolar mixture theory for porous media is generalized in the context of generalized L-S theory and classical C-T theory of thermoelasticity.
Abstract: In this article, the micropolar mixture theory for porous media is generalized in the context of generalized L-S theory and classical C-T theory of thermoelasticity. The thermoelastic problem for a micropolar mixture of porous media is investigated in the context of the generalized micropolar mixture theory for porous media. The surface of a semi-infinite porous media is subjected to a zonal time-dependent thermal shock. The problem is solved by using the finite element method. The results, including the temperature, stresses, displacements, and microrotation are presented graphically. Comparisons are made between the results obtained by using two theories. The fluid constituting the mixture has a significant influence on the microrotation but a very slight influence on other responses.
01 Jan 2011
TL;DR: SedMix3D as mentioned in this paper is a high-resolution model based on mixture theory that accurately models the evolution of seabed roughness for sandy substrates, which has significant implications for naval operations (e.g., mine hunting missions, littoral navigation).
Abstract: Introduction: Our lack of understanding of the evolution of seabed roughness (e.g., sand ripples) in sandy coastal regions inhibits our ability to accurately forecast waves and currents and ultimately large-scale morphodynamics. Most wave and circulation models input a constant bottom roughness value (i.e., friction factor) or fixed bed profile that parameterizes the effects of seabed roughness, ignoring any temporal or spatial response of the bed to changing wave and sediment conditions. However, seabed roughness length scales may span three orders of magnitude (e.g., from grain-scale variations to sand ripples), causing significant differences in boundary layer turbulence, wave energy dissipation, coastal circulation, and sediment transport. The constant evolution of the seabed also has significant implications for naval operations (e.g., ocean acoustics, mine hunting missions, littoral navigation). All bathymetric change ultimately results from sediment entrainment and deposition occurring at the fluid-sediment interface inside the wave bottom boundary layer (WBBL). Despite the apparent accessibility of the phenomena, highly turbulent, sedimentladen flow remains poorly understood and difficult to quantify mainly because of our failure to understand the fundamental interaction forces driving sediment transport. However, with recent advances in high performance computing, it is now possible to perform highly resolved simulations of fluid-sediment dynamics in the WBBL that accurately model the evolution of seabed roughness for sandy substrates. The highresolution model described here (SedMix3D) is based on mixture theory. Although the approach is well known and understood for industrial and biological applications, it has never before been applied to coastal sediment dynamics.