Topic
Mixture theory
About: Mixture theory is a research topic. Over the lifetime, 616 publications have been published within this topic receiving 19350 citations.
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TL;DR: In this article, a minimal set of field equations, constitutive relations, and material parameters suitable for the solutions of meaningful diffusion problems was derived for a single solid and two fluids, and they may be extended to any number of fluids.
Abstract: In this paper, I begin with the general formulation of mixture theory by Bowen and present the derivation of a minimal set of field equations, constitutive relations, and material parameters suitable for the solutions of meaningful diffusion problems. The specific results are for a single solid and two fluids, and they may be extended to any number of fluids. I allude to the results of three problems, viz. (1) the injection of a fluid into a geological formation saturated with another fluid, (2) the drainage of two dissimilar fluids from a geological formation due to in-situ fluid pore pressures, and (3) the process of squeezing a sponge dry, in order to illustrate the general applicability of the derived theory.
3 citations
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3 citations
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26 Jun 2003TL;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.
3 citations
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TL;DR: The one-temperature field thermo-mechanical theory of a fluid-filled porous material with a linearly elastic solid and a Newtonian viscous fluid is established in this paper.
Abstract: The one-temperature field thermo-mechanical theory of a fluid-filled porous material with a linearly elastic solid and a Newtonian viscous fluid is established. The author's previous work, phenomenological constitutive theory for fluid-filled porous materials with solid/fluid outer boundaries, is introduced into a conventional mixture theory. Kinetical and kinematical quantities defined for a sample with a solid/fluid outer boundary, including interaction terms, correspond to those in the mixture theory directly from their definitions. The approximations involved in one to one correspondence between the constitutive equations in the mixture theory and those in the phenomenological theory are made clear.
3 citations
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TL;DR: In this paper , a variational energy-based continuum mechanics framework is proposed to model large deformation poroelasticity in a porous medium, which is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on.
Abstract: The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance, that include fracturing or damage of the solid phase, require a nonlinear description of the large deformations that can occur. This paper presents a variational energy-based continuum mechanics framework to model large-deformation poroelasticity. The approach begins from the total free energy density that is additively composed of the free energy of the components. A variational procedure then provides the balance of momentum, fluid transport balance, and pressure relations. A numerical approach based on finite elements is applied to analyze the behavior of saturated and unsaturated porous media using a nonlinear constitutive model for the solid skeleton. Examples studied include the Terzaghi and Mandel problems; a gas-liquid phase-changing fluid; multiple immiscible gases; and unsaturated systems where we model injection of fluid into soil. The proposed variational approach can potentially have advantages for numerical methods as well as for combining with data-driven models in a Bayesian framework.
3 citations