Mixture theory

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

General coupling of porous flows and hyperelastic formulations -- From thermodynamics principles to energy balance and compatible time schemes

Abstract: We formulate a general poromechanics model -- within the framework of a two-phase mixture theory -- compatible with large strains and without any simplification in the momentum expressions, in particular concerning the fluid flows. The only specific assumptions made are fluid incompressibility and isothermal conditions. Our formulation is based on fundamental physical principles -- namely, essential conservation and thermodynamics laws -- and we thus obtain a Clausius-Duhem inequality which is crucial for devising compatible constitutive laws. We then propose to model the solid behavior based on a generalized hyperelastic free energy potential -- with additional viscous effects -- which allows to represent a wide range of mechanical behaviors. The resulting formulation takes the form of a coupled system similar to a fluid-structure interaction problem written in an Arbitrary Lagrangian-Eulerian formalism, with additional volume-distributed interaction forces. We achieve another important objective by identifying the essential energy balance prevailing in the model, and this paves the way for further works on mathematical analyses, and time and space discretizations of the formulation.

Blind Separation of Superimposed Shifted Images Using Parameterized Joint Diagonalization

Abstract: We consider the blind separation of source images from linear mixtures thereof, involving different relative spatial shifts of the sources in each mixture. Such mixtures can be caused, e.g., by the presence of a semi-reflective medium (such as a window glass) across a photographed scene, due to slight movements of the medium (or of the sources) between snapshots. Classical separation approaches assume either a static mixture model or a fully convolutive mixture model, which are, respectively, either under-or over-parameterized for this problem. In this paper, we develop a specially parameterized scheme for approximate joint diagonalization of estimated spectrum matrices, aimed at estimating the succinct set of mixture parameters: the static (gain) coefficients and the shift values. The estimated parameters are, in turn, used for convenient frequency-domain separation. As we demonstrate using both synthetic mixtures and real-life photographs, the advantage of the ability to incorporate spatial shifts is twofold: Not only does it enable separation when such shifts are present, but it also warrants deliberate introduction of such shifts as a simple source of added diversity whenever the static mixing coefficients form a singular matrix - thereby enabling separation in otherwise inseparable scenes.

An Eshelbian approach to the nonlinear mechanics of constrained solid-fluid mixtures

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.