Transformation twinning to create isospectral cavities

Simon V. Lenz; Sébastien Guenneau; Bruce W. Drinkwater; Richard V. Craster; Marc W. Holderied

doi:10.1103/PhysRevB.108.064209

Transformation twinning to create isospectral cavities

Simon V. Lenz^*, Sébastien Guenneau, Bruce W. Drinkwater, Richard V. Craster, Marc W. Holderied

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

Abstract

Bounded domains have discrete eigenfrequencies/spectra, and cavities with different boundaries and areas have different spectra. A general methodology for isospectral twinning, whereby the spectra of different cavities are made to coincide, is created by combining ideas from across physics including transformation optics, inverse problems, and metamaterial cloaking. We twin a hexagonal drum with a deformed hexagonal drum using a nonsingular coordinate transform that adjusts the deformed shape by mapping a near boundary domain to a zone of heterogeneous anisotropic medium. Splines define the mapping zone for twinning these two drums and we verify isospectrality by a finite-element analysis.

Original language	English
Article number	064209
Number of pages	6
Journal	Physical Review B
Volume	108
Issue number	6
DOIs	https://doi.org/10.1103/PhysRevB.108.064209
Publication status	Published - 23 Aug 2023

Bibliographical note

Funding Information:
The authors are funded by the U.K. Engineering and Physical Sciences Research Council (EP/T002654/1) and R.V.C. was additionally funded by the H2020 FETOpen project BOHEME under Grant Agreement No. 863179. This work was supported by the Biotechnology and Biological Sciences Research Council-funded South West Biosciences Doctoral Training Partnership (BB/M009122/1).

Publisher Copyright:
© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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@article{c290139832c24afe8607152c84b5d1e5,

title = "Transformation twinning to create isospectral cavities",

abstract = "Bounded domains have discrete eigenfrequencies/spectra, and cavities with different boundaries and areas have different spectra. A general methodology for isospectral twinning, whereby the spectra of different cavities are made to coincide, is created by combining ideas from across physics including transformation optics, inverse problems, and metamaterial cloaking. We twin a hexagonal drum with a deformed hexagonal drum using a nonsingular coordinate transform that adjusts the deformed shape by mapping a near boundary domain to a zone of heterogeneous anisotropic medium. Splines define the mapping zone for twinning these two drums and we verify isospectrality by a finite-element analysis.",

author = "Lenz, \{Simon V.\} and S{\'e}bastien Guenneau and Drinkwater, \{Bruce W.\} and Craster, \{Richard V.\} and Holderied, \{Marc W.\}",

note = "Funding Information: The authors are funded by the U.K. Engineering and Physical Sciences Research Council (EP/T002654/1) and R.V.C. was additionally funded by the H2020 FETOpen project BOHEME under Grant Agreement No. 863179. This work was supported by the Biotechnology and Biological Sciences Research Council-funded South West Biosciences Doctoral Training Partnership (BB/M009122/1). Publisher Copyright: {\textcopyright} 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the {"}https://creativecommons.org/licenses/by/4.0/{"}Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.",

year = "2023",

month = aug,

day = "23",

doi = "10.1103/PhysRevB.108.064209",

language = "English",

volume = "108",

journal = "Physical Review B",

issn = "2469-9950",

publisher = "American Physical Society (APS)",

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TY - JOUR

T1 - Transformation twinning to create isospectral cavities

AU - Lenz, Simon V.

AU - Guenneau, Sébastien

AU - Drinkwater, Bruce W.

AU - Craster, Richard V.

AU - Holderied, Marc W.

N1 - Funding Information: The authors are funded by the U.K. Engineering and Physical Sciences Research Council (EP/T002654/1) and R.V.C. was additionally funded by the H2020 FETOpen project BOHEME under Grant Agreement No. 863179. This work was supported by the Biotechnology and Biological Sciences Research Council-funded South West Biosciences Doctoral Training Partnership (BB/M009122/1). Publisher Copyright: © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

PY - 2023/8/23

Y1 - 2023/8/23

N2 - Bounded domains have discrete eigenfrequencies/spectra, and cavities with different boundaries and areas have different spectra. A general methodology for isospectral twinning, whereby the spectra of different cavities are made to coincide, is created by combining ideas from across physics including transformation optics, inverse problems, and metamaterial cloaking. We twin a hexagonal drum with a deformed hexagonal drum using a nonsingular coordinate transform that adjusts the deformed shape by mapping a near boundary domain to a zone of heterogeneous anisotropic medium. Splines define the mapping zone for twinning these two drums and we verify isospectrality by a finite-element analysis.

AB - Bounded domains have discrete eigenfrequencies/spectra, and cavities with different boundaries and areas have different spectra. A general methodology for isospectral twinning, whereby the spectra of different cavities are made to coincide, is created by combining ideas from across physics including transformation optics, inverse problems, and metamaterial cloaking. We twin a hexagonal drum with a deformed hexagonal drum using a nonsingular coordinate transform that adjusts the deformed shape by mapping a near boundary domain to a zone of heterogeneous anisotropic medium. Splines define the mapping zone for twinning these two drums and we verify isospectrality by a finite-element analysis.

UR - https://www.scopus.com/pages/publications/85169290169

U2 - 10.1103/PhysRevB.108.064209

DO - 10.1103/PhysRevB.108.064209

M3 - Article (Academic Journal)

AN - SCOPUS:85169290169

SN - 2469-9950

VL - 108

JO - Physical Review B

JF - Physical Review B

IS - 6

M1 - 064209

ER -

Transformation twinning to create isospectral cavities

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Transformation twinning to create isospectral cavities

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