Dispersion properties of electromagnetic crystals formed by small uniaxial resonant scatterers (magnetic or electric) are studied using the local field approach. The goal of the study is to determine the conditions under which the homogenization of such crystals is possible. Therefore the consideration is limited to the frequency region where the wavelength in the host medium is larger than the...

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We use the multiresolution homogenization theory to study the effective resonances representation of transient electromagnetic propagation in complex random multilayer ducts. The theory permits explicit choice of the smoothing (homogenization) scale, and can be applied to a wide range of micro-scale properties. The analytical study is based on a Wroskian equivalence result, which establishes th...

The role human activities play in reshaping biodiversity is increasingly apparent in terrestrial ecosystems. However, the responses of entire marine assemblages are not well-understood, in part, because few monitoring programs incorporate both spatial and temporal replication. Here, we analyse an exceptionally comprehensive 29-year time series of North Atlantic groundfish assemblages monitored ...

We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with constant impedance exhibit no effective dispersion. We show that a new kind of effective dispersion may arise in two dimensions, even in materials with const...

An analytical model and numerical approach to predict the effective mechanical properties of a composite conductor consisting of metallic core and insulation layers are presented in this paper. The analytical model was developed based on a two-step homogenizations and mechanics analysis for composite unit cell. The Step 1 homogenization derives the effective properties of the out-wrapped compos...

The series of lectures will overview some recent contributions on several theoretical aspects and numerical approaches in stochastic homogenization. After an introduction to the elementary aspects of stochastic homogenization, a variant of the classical theory will be presented. It has been introduced in [6], and further studied in [11, 16]. The relation between stochastic homogenization proble...

This contribution presents a novel homogenization technique for modeling heterogeneous materials with micro-inertia effects such as locally resonant acoustic metamaterials. Linear elastodynamics is used to model the micro and macro scale problems and an extended first order Computational Homogenization framework is used to establish the coupling. Craig Bampton Mode Synthesis is then applied to ...

The problem of homogenization, i.e. substantial reduction of the electrical size of the average lattice constant, of electromagnetic left-handed (LH), or more generally composite right/left-handed (CRLH) metamaterials (MTMs), is presented. The undesirable effects of an electrical very large structural unit cell are explained and illustrated by full-wave simulations and experiments with CRLH mus...

We show that artificial magnetism of periodic dielectric or metal/dielectric structures has limitations and is subject to at least two “uncertainty principles.” First, the stronger the magnetic response (the deviation of the effective permeability tensor from identity), the less accurate (“certain”) the predictions of any homogeneous model. Second, if the magnetic response is strong, then homog...