BibTex format

author = {Makwana, M and Antonakakis, T and Maling, B and Guenneau, S and Craster, RV},
doi = {10.1137/15M1020976},
journal = {SIAM Journal on Applied Mathematics},
pages = {1--26},
title = {Wave mechanics in media pinned at bravais lattice points},
url = {},
volume = {76},
year = {2016}

RIS format (EndNote, RefMan)

AB - The propagation of waves through microstructured media with periodically arrangedinclusions has applications in many areas of physics and engineering, stretching from photonic crystalsthrough to seismic metamaterials. In the high-frequency regime, modeling such behavior iscomplicated by multiple scattering of the resulting short waves between the inclusions. Our aimis to develop an asymptotic theory for modeling systems with arbitrarily shaped inclusions locatedon general Bravais lattices. We then consider the limit of pointlike inclusions, the advantage beingthat exact solutions can be obtained using Fourier methods, and go on to derive effective mediumequations using asymptotic analysis. This approach allows us to explore the underlying reasons fordynamic anisotropy, localization of waves, and other properties typical of such systems, and in particulartheir dependence upon geometry. Solutions of the effective medium equations are comparedwith the exact solutions, shedding further light on the underlying physics. We focus on examplesthat exhibit dynamic anisotropy as these demonstrate the capability of the asymptotic theory to pickup detailed qualitative and quantitative features.
AU - Makwana,M
AU - Antonakakis,T
AU - Maling,B
AU - Guenneau,S
AU - Craster,RV
DO - 10.1137/15M1020976
EP - 26
PY - 2016///
SN - 1095-712X
SP - 1
TI - Wave mechanics in media pinned at bravais lattice points
T2 - SIAM Journal on Applied Mathematics
UR -
UR -
UR -
VL - 76
ER -