Mixture theory

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

Modeling Approaches and Some Physical Considerations Concerning Thermodynamics and the Theory of Mixtures Applied to Time-Dependent Behaviors in Heterogeneous Materials

Abstract: Following a brief review of the theory of continuum mixtures, recent developments and applications emphasizing time-dependent behaviors of heterogeneous materials are described. Common approximations of mixture theory and related continuum homogenization schemes such as assigning material properties, boundary conditions and body forces are considered. Approaches to imposing restrictions due to the second law are discussed; traditional employment of the Clausius-Duhem inequality enforced for arbitrary processes is contrasted with maximization of the rate of entropy production applied to a functional space suitably restricted to conform with constitutive postulates. Remarks are made concerning related homogenization and thermodynamic developments, including poroelasticity, volume-averaging, local accompanying state, and linear irreversible thermodynamics. Applications to fibrous composite materials, and to additional classes of heterogeneous materials, are briefly discussed.

Mixture models for anomaly detection in hyperspectral imagery

Abstract: The majority of anomaly detection processes used for hyperspectral image data are based on pixel-by-pixel whitening and thresholding operations using local area statistics. This paper discusses an alternative approach to anomaly detection in which a mixture model is fitted to the whole of the image. This mixture model may be used to segment the image into component memberships and these may, in turn, be used for anomaly detection. In this study the mixture model is generated for the whole scene using the stochastic expectation maximization (SEM) algorithm. This is parameterized such that mixture components consisting of small numbers of pixels are eliminated. The maximum a-posteriori probability (MAP) mixture component for each pixel is then determined. The pixel may then be examined using a conventional statistical hypothesis test to see whether it is plausible that it was drawn from the distribution of the identified component, at a given significance level. This anomaly detection process has been examined using both synthetic and real hyperspectral imagery and results are presented here for real data containing no known military targets and for synthesized imagery which includes military target pixels. A range of results is presented for different parameterizations of the SEM algorithm and significance test. These results include the component map of the imagery and anomalous pixel maps at given significance levels.

Homogenization of pseudoparabolic reaction-diffusion-mechanics systems: multiscale modeling, well-posedness and convergence rates

Abstract: In this dissertation, parabolic-pseudoparabolic equations are proposed to couple chemical reactions, diffusion, flow and mechanics in heterogeneous materials using the framework of mixture theory. ...

Continuum modeling of electromagnetic waves in composite wave guides

Abstract: A continuum mixture theory with microstructure is developed for electromagnetic wave propagation in laminated waveguides. The theory leads to simple governing equations for the actual composite which retain the integrity of the propagation process in each constituent but allow them to coexist under derived interactions. The utility of the resulting equations is demonstrated by studying the response of the composite to harmonic excitations. In this case the dispersion relations are found to correlate well with some derived exact solutions.