Homogenization of Harmonic Maps and Superconducting Composites

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Some geometrical properties of the oscillator group

‎We consider the oscillator group equipped with‎ ‎a biinvariant Lorentzian metric‎. ‎Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional‎ ‎restricted to vector fields‎. ‎Left-invariant vector fields defining harmonic maps are...

Mean-field homogenization of multi-phase thermo-elastic composites: a general framework and its validation

This paper deals with mean-field Eshelby-based homogenization techniques for multi-phase composites and focuses on three subjects which in our opinion deserved more attention than they did in the existing literature. Firstly, for two-phase composites, that is when in a given representative volume element all the inclusions have the same material properties, aspect ratio and orientation, an inte...

Toughening by Crack Deflection in the Homogenization of Brittle Composites with Soft Inclusions

We present a simple example of toughening mechanism in the homogenization of composites with soft inclusions, produced by crack deflection at microscopic level. We show that the mechanism is connected to the irreversibility of the crack process. Because of that it cannot be detected through the standard homogenization tool of the Γ-convergence.

Quasi-Dynamic Homogenization of Geometrically Simple Dielectric Composites

The frequency dependence of the effective permittivities of simple dielectric composites is evaluated by different quasidynamic homogenization methods. Three retrieval approaches based on the scattering parameters are proposed for dielectric materials. A compensation method for the conventional Nicolson-Ross-Weir (NRW) retrieval is applied to eliminate the FabryPérot (FP) resonances and their d...