. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

We generalize the classical Legendre-Hadamard conditions by using quadratic extensions of the energy around a set of two configurations and obtain new algebraic necessary conditions for nonsmooth strong local minimizers. The implied bounds of stability are easily accessible as we illustrate on a nontrivial example where quasiconvexification is unknown.

In this paper we determine, in dimension three, the effective conductivities of non periodic high-contrast two-phase cylindrical composites, placed in a constant magnetic field, without any assumption on the geometry of their cross sections. Our method, in the spirit of the H-convergence of Murat-Tartar, is based on a compactness result and the cylindrical nature of the microstructure. The homo...

Here we shall introduce the concept of harmonic balls in subdomains of Rn, through a mean value property for a sub-class of harmonic functions on such domains. In the complex plane, and for analytic functions, a similar concept fails to exist due to the fact that analytic functions can not have prescribed data on the boundary. Nevertheless, a two-phase version of the problem does exists, and gi...

The field distribution, dielectric constant, and loss in a two-phase composite, in which phase A is distributed inside a square matrix of phase B, have been calculated using the finite-element method ~FEM!. The calculation was carried out by taking into account different shapes for phase A, such as circles, triangles, and rings with different sizes. The modeling by FEM in the dielectric composi...

in this paper, the problem of turbulent forced convection flow of water- alumina nanofluid in a uniformly heated pipe has been thoroughly investigated. in numerical study, single and two-phase models have been used. in single-phase modeling of nanofluid, thermal and flow properties of nanofluid have been considered to be dependent on temperature and volume fraction. effects of volume fraction a...

The spatial averaging theorem is applied to rigorously derive continuum-scale equations of radiative transfer in two-phase media consisting of either two semi-transparent or one semitransparent and one opaque homogeneous phases in the limit of geometric optics. The derivations are based on the equations of radiative transfer and the corresponding boundary conditions applied at the discrete-scal...

In this chapter we shall introduce a new and practical method for two-phase flow rate measurement, which is known as flow division and separation method. As its name suggested, a two-phase flow is measured by diverting a small fraction of the total stream to a division loop and metering it with the separation means. This method has been developed in Xi’an jiaotong university since the end of la...

We consider a kinetic-fluid model with random initial inputs which describes disperse two-phase flows. In the light particle regime, using energy estimates, we prove the uniform regularity in the random space of the model for random initial data near the global equilibrium in some suitable Sobolev spaces, with the randomness in the initial particle distribution and fluid velocity. By hypocoerci...