New Insights on Quasistatic and Acoustic Cloaking
Meklachi, Taoufik 1978-
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In the first four chapters 1-4, we study, in the quasistatic regime, the behavior of the dissipated power inside the boundary layers of a two dimensional metamaterial slab of negative permittivity . We consider a compactly supported charge distribution at the right-hand side of the slab in a medium of permittivity 1. The medium to the left of the slab has a positive permittivity with loss dependent of a parameter beta. The blow up of the dissipated power as the loss in the slab aproaches 0, when the charge density is close enough to the slab, is strongly dependent on beta in (0,1). The key motivation for this research work is that the divergence of the dissipated power (caused by anomalous localized resonance at these layers) is crucial to cloaking and superlensing phenomena. Levels of blow-up magnitudes and regions where the charge distribution should be placed to excite the phenomena are estimated in terms of the loss. In chapter 5, in an effort to understand active and passive SONAR acoustic cloaking, we study the vibration suppression questions in the context of a 1D coupled spring-mass system. The longitudinal motion of the latter is considered to be a discretization of acoustic systems, where the stiffness of the springs represents the compressibility and the masses represent the density of the medium. We study systems, with and without damping, of an arbitrary number of masses N. We propose discrete models for Active as well as Passive SONAR and describe explicitly the necessary controls for the desired cloaking effects.