Premium
Waves around almost periodic arrangements of scatterers: Analysis of positional disorder
Author(s) -
Martin P. A.,
Maurel A.
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1333
Subject(s) - mathematics , scalar (mathematics) , realization (probability) , simple (philosophy) , extension (predicate logic) , mathematical analysis , statistical physics , geometry , physics , statistics , computer science , philosophy , epistemology , programming language
Much is known about the propagation of waves through periodic arrangements of identical scatterers, such as through a photonic crystal. Here, we consider a simple realization: scalar waves through a regular two‐dimensional array of identical small circles. We are interested in the effect of random disorder: the circles remain identical, but their centres are given small random displacements. We derive asymptotic approximations that can be used to quantify the effect of positional disorder. Extension to more complicated problems seems feasible and is expected. Copyright © 2010 John Wiley & Sons, Ltd.