WorkshopsMathematical analysis of the anomalous localized resonance
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The aim of this work is to give a mathematical justification of the anomalous localized resonance(ALR). We consider the conductivity problem with a source term in a structure with a layer of metamaterial. Using layer potentials and symmetrization techniques, we give a necessary and sufficient condition on the source term for the ALR to take place. This condition is written in terms of the Newton potential of the source term. In the case of concentric disks, we obtain such a condition even more explicitly. Using the condition, we are able to show that for any source supported outside the anomalous resonance region the ALR does not take place, and for the dipole or quadrapole sources inside the anomalous resonance region the ALR take place as the loss parameter of the metamaterial structure goes to zero. Moreover, we provide a weak condition for general source terms under which the ALR takes place.
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Hyundae Lee
2012-02-16
14:00:00 - 14:40:00
R101 , Astronomy and Mathematics Building
The aim of this work is to give a mathematical justification of the anomalous localized resonance(ALR). We consider the conductivity problem with a source term in a structure with a layer of metamaterial. Using layer potentials and symmetrization techniques, we give a necessary and sufficient condition on the source term for the ALR to take place. This condition is written in terms of the Newton potential of the source term. In the case of concentric disks, we obtain such a condition even more explicitly. Using the condition, we are able to show that for any source supported outside the anomalous resonance region the ALR does not take place, and for the dipole or quadrapole sources inside the anomalous resonance region the ALR take place as the loss parameter of the metamaterial structure goes to zero. Moreover, we provide a weak condition for general source terms under which the ALR takes place.
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