. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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...

Lee-Yang zeros are points on the complex plane of physical parameters where the partition function of a system vanishes and hence the free energy diverges. Lee-Yang zeros are ubiquitous in many-body systems and fully characterize their thermodynamics. Notwithstanding their fundamental importance, Lee-Yang zeros have never been observed in experiments, due to the intrinsic difficulty that they w...

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...