Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Sensitivity of anomalous localized resonance phenomena with respect to dissipation


Authors: Taoufik Meklachi, Graeme W. Milton, Daniel Onofrei, Andrew E. Thaler and Gregory Funchess
Journal: Quart. Appl. Math. 74 (2016), 201-234
MSC (2010): Primary 35Q60
DOI: https://doi.org/10.1090/qam/1408
Published electronically: March 16, 2016
MathSciNet review: 3505601
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Abstract: We analyze cloaking due to anomalous localized resonance in the quasistatic regime in the case when a general charge density distribution is brought near a slab superlens. If the charge density distribution is within a critical distance of the slab, then the power dissipation within the slab blows up as certain electrical dissipation parameters go to zero. The potential remains bounded far away from the slab in this limit, which leads to cloaking due to anomalous localized resonance. On the other hand, if the charge density distribution is farther than this critical distance from the slab, then the power dissipation within the slab remains bounded and cloaking due to anomalous localized resonance does not occur. The critical distance is shown to strongly depend on the rate at which the dissipation outside the slab goes to zero.


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Additional Information

Taoufik Meklachi
Affiliation: Department of Mathematics, Drexel University, 15 South 33rd Street, Room 206, Philadelphia, PA 19104
Email: tmeklachi@gmail.com

Graeme W. Milton
Affiliation: Department of Mathematics, University of Utah, 155 South 1400 East, Room 233, Salt Lake City, Utah 84112-0090
Email: milton@math.utah.edu

Daniel Onofrei
Affiliation: Department of Mathematics, University of Houston, 651 PGH, Houston, Texas 77204-3008
Email: onofrei@math.uh.edu

Andrew E. Thaler
Affiliation: Institute for Mathematics and its Applications, 207 Church Street SE, Minneapolis, MN 55455
Email: andythaler05@gmail.com

Gregory Funchess
Affiliation: Department of Mathematics, University of Houston, 651 PGH, Houston, Texas 77204-3008
Email: gfunchess@gmail.com

DOI: https://doi.org/10.1090/qam/1408
Received by editor(s): June 19, 2014
Published electronically: March 16, 2016
Additional Notes: The work of the first author was supported by the Air Force through grant AFOSR YIP Early Career Award FA9550-13-1-0078
The work of the second author was supported by the National Science Foundation through grant DMS-1211359.
The work of the third author was supported under the Simons Collaborative Grant and the Air Force through grant AFOSR YIP Early Career Award FA9550-13-1-0078
The work of the fourth author was supported by the National Science Foundation through grant DMS-1211359.
The work of the fifth author was supported by the Air Force through grant AFOSR YIP Early Career Award FA9550-13-1-0078
Article copyright: © Copyright 2016 Brown University

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