Mixture theory

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

Two Further Gradient BYY Learning Rules for Gaussian Mixture with Automated Model Selection

Abstract: Under the Bayesian Ying-Yang (BYY) harmony learning theory, a harmony function has been developed for Gaussian mixture model with an important feature that, via its maximization through a gradient learning rule, model selection can be made automatically during parameter learning on a set of sample data from a Gaussian mixture. This paper proposes two further gradient learning rules, called conjugate and natural gradient learning rules, respectively, to efficiently implement the maximization of the harmony function on Gaussian mixture. It is demonstrated by simulation experiments that these two new gradient learning rules not only work well, but also converge more quickly than the general gradient ones.

Finite element simulation of deformation bands in saturated granular media with inhomogeneous porosities at the meso-scale

Abstract: The balance of mass and linear momentum of a solid-fluid mixture furnish a complete set of equations from which the displacements of the the solid matrix and the pore pressures can be resolved for the case of quasi-static loading, resulting in the so-called u — p Galerkin formulation. In this work, a recently proposed model for dense sands is utilized to model the effective stress response of the solid matrix appearing in the balance of linear momentum equation [1], [2], [3]. In contrast with other more traditional models, inherent inhomogeneities in the density field at the meso-scale can be easily incorporated and coupled with the macroscopic laws of mixture theory. The hydraulic conductivity is naturally treated as a function of the porosity in the solid matrix, hence allowing for a more realistic representation of the physical phenomenon. The aforementioned balance laws are cast into a fully nonlinear finite element program utilizing isoparametric elements satisfying the Babuska-Brezzi stability condition. Numerical simulations on dense sand specimens are performed to study the effects of inhomogeneities on the stability of saturated porous media at the structural level.

Oscillatory flow transition and thermocapillary convection during laser surface treatment

Abstract: A 2D laser surface remelting problem is numerically simulated. The mathematical formulation of this multiphase problem is obtained using a continuum model, constructed from classical mixture theory. This formulation permits to construct a set of continuum conservation equations for pure or binary, solid-liquid phase change systems. The numerical resolution of this set of coupled partial differential equations is performed using a finite volume method associated with a PISO algorithm. The numerical results show the modifications caused by an increase of the free surface shear stress (represented by the Reynolds number Re) upon the stability of the thermocapillary flow in the melting pool. The solutions exhibit a symmetry-- breaking flow transition, oscillatory behavior at higher values of Re. The spectral analysis of temperature and velocity signals for particular points situated in the melted pool, show that these oscillations are at first mono-periodic then new frequencies appear generating a quasi- periodic behavior. These oscillations of the flow in the melted pool could induced the deformation of the free surface which could explain the formation of surface ripples observed during laser surface treatments (surface remelting, cladding) or laser welding.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.