Tryfon Antonakakis, Department of Mathematics, Imperial College London
Abstract :
We present an accurate methodology for representing the physics of waves,
for periodic structures, through effective properties for a replacement bulk medium : This is valid even for media with zero
frequency stop-bands and where high frequency phenomena dominate. Since
the work of Lord Rayleigh in 1892, low frequency (or quasi-static) behaviour has been neatly encapsulated in effective anisotropic media.
However such classical homogenization theories break down in the high-frequency or stop band regime. Higher frequency phenomena are of significant importance in photonics (transverse magnetic waves propagating in infinite conducting parallel
fibers), phononics (anti-plane shear waves propagating in isotropic elastic
materials with inclusions), and platonics (flexural waves propagating in thin-elastic plates with holes). Fortunately, the recently proposed high-frequency homogenization (HFH) theory is only constrained by the knowledge of standing waves in order to asymptotically reconstruct dispersion curves and associated
Floquet-Bloch eigenfields : It is capable of accurately representing zero-frequency
stop band structures. The homogenized equations are partial differential equations with a dispersive anisotropic homogenized tensor that characterizes the effective medium.
We apply HFH to metamaterials and gratings, exploiting the subtle features of Bloch dispersion curves such as zero and negative group velocity near stop bands in order to achieve exciting physical phenomena such as localization and dynamic anisotropy. Guiding and lensing effects are simulated numerically using finite
elements and compared to predictions from HFH. Some extensions of the theory to fully coupled elastic waves are also discussed.
Biography : Tryfon Antonakakis is currently a researcher in a London-Based Hedge Fund (80cap LLP- 4 days per week) as well as a postdoctoral researcher at the Department of Mathematics of Imperial College London (ICL- 1 day per week).
He is developing a new theory of homogenization with Prof. Richard Craster (ICL) for periodic and stochastic wave problems which may also find interesting applications in trading activities. Dr. Antonakakis graduated with a PhD from ICL in 2013. He has worked as a research assistant at EPF Lausanne (2005-2006) and CERN (2010-2013) on diffusion and stochastic problems.
Contact : tryfon.antonakakis09@imperial.ac.uk
Invitation : Sébastien Guenneau, Boris Gralak & Claude Amra - Équipe CONCEPT
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