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Cassier M, DeGiovanni T, Guenneau S, Guevara Vasquez F. Active exterior cloaking for the two-dimensional Helmholtz equation with complex wavenumbers and application to thermal cloaking. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20220073. [PMID: 36209804 DOI: 10.1098/rsta.2022.0073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 05/09/2022] [Indexed: 06/16/2023]
Abstract
We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive wavenumbers, the sources are also determined by the Green identities. The novelty is that we prove that the same approach works for complex wavenumbers which makes it applicable to a variety of media, including media with dispersion, loss and gain. Furthermore, by deriving bounds on Graf's addition formulas with complex arguments, we obtain new estimates that allow to quantify the quality of the cloaking effect. We illustrate our results by applying them to achieve active exterior cloaking for the heat equation. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.
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Affiliation(s)
- Maxence Cassier
- Institut Fresnel, CNRS, Centrale Marseille, Aix Marseille University, Marseille, France
| | - Trent DeGiovanni
- Mathematics Department, University of Utah, Salt Lake City, UT 84112, USA
| | - Sébastien Guenneau
- UMI 2004 Abraham de Moivre-CNRS, Imperial College London, London SW7 2AZ, UK
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2
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Cassier M, DeGiovanni T, Guenneau S, Guevara Vasquez F. Active thermal cloaking and mimicking. Proc Math Phys Eng Sci 2021; 477:20200941. [PMID: 35153558 PMCID: PMC8300605 DOI: 10.1098/rspa.2020.0941] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Accepted: 04/13/2021] [Indexed: 12/04/2022] Open
Abstract
We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active, we mean that it relies on designing monopole and dipole heat source distributions on the boundary of the region to be cloaked. The same technique can be used to make a source or an object look like a different one to an observer outside the cloaked region, from the perspective of thermal measurements. Our results assume a homogeneous isotropic bulk medium and require knowledge of the source to cloak or mimic, but are in most cases independent of the object to cloak.
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Affiliation(s)
- Maxence Cassier
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
| | - Trent DeGiovanni
- University of Utah, Mathematics Department, Salt Lake City, UT 84112, USA
| | - Sébastien Guenneau
- UMI 2004 Abraham de Moivre-CNRS, Imperial College London, London, SW7 2AZ, UK
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He X, Yang T, Zhang X, Wu L, He XQ. Transient experimental demonstration of an elliptical thermal camouflage device. Sci Rep 2017; 7:16671. [PMID: 29192188 PMCID: PMC5709401 DOI: 10.1038/s41598-017-17016-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2017] [Accepted: 11/20/2017] [Indexed: 11/09/2022] Open
Abstract
The camouflage phenomenon (invisibility or illusion) of thermodynamics has attracted great attentions and many experimental demonstrations have been achieved by virtue of simplified approaches or the scattering cancellation. However, all of the experiments conducted are limited in the invisibility of spheres or two-dimensional (2D) cylinders. An ellipsoid camouflage device with a homogenous and isotropic shell is firstly reported based on the idea of the neutral inclusion and a 2D elliptical thermal camouflage device is realized by a thin-layer cloak of homogeneous isotropic material firstly. The robustness of this scheme is validated in both 2D and 3D configurations. The current work may provide a new avenue to the control of the thermal signatures and we believe this work will broaden the current research and pave a new path to the control of the path of the heat transfer.
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Affiliation(s)
- Xiao He
- Key Laboratory of Advanced Ship Materials and Mechanics, College of Aerospace and Civil Engineering, Harbin Engineering University Harbin, Harbin, 150001, PR China.,Department of Civil and Architectural Engineering, City University of Hong Kong, Tat Chee Avenue, Hong Kong
| | - Tianzhi Yang
- Faculty of Aerospace Engineering, Shenyang Aerospace University, Shenyang, 110136, PR China
| | - Xingwei Zhang
- Key Laboratory of Advanced Ship Materials and Mechanics, College of Aerospace and Civil Engineering, Harbin Engineering University Harbin, Harbin, 150001, PR China
| | - Linzhi Wu
- Key Laboratory of Advanced Ship Materials and Mechanics, College of Aerospace and Civil Engineering, Harbin Engineering University Harbin, Harbin, 150001, PR China.,Center for Composite Materials, Harbin Institute of Technology, Harbin, 150001, PR China
| | - Xiao Qiao He
- Department of Civil and Architectural Engineering, City University of Hong Kong, Tat Chee Avenue, Hong Kong.
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Alwakil A, Zerrad M, Bellieud M, Amra C. Inverse heat mimicking of given objects. Sci Rep 2017; 7:43288. [PMID: 28252031 PMCID: PMC5333104 DOI: 10.1038/srep43288] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2016] [Accepted: 01/03/2017] [Indexed: 11/10/2022] Open
Abstract
We address a general inverse mimicking problem in heat conduction. The objects to cloak and mimic are chosen beforehand; these objects identify a specific set of space transformations. The shapes that can be mimicked are derived from the conductivity matrices. Numerical calculation confirms all of the analytical predictions. The technique provides key advantages for applications and can be extended to the field of waves.
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Affiliation(s)
- Ahmed Alwakil
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
| | - Myriam Zerrad
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
| | | | - Claude Amra
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
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Amra C, Petiteau D, Zerrad M, Guenneau S, Soriano G, Gralak B, Bellieud M, Veynante D, Rolland N. Analogies between optical propagation and heat diffusion: applications to microcavities, gratings and cloaks. Proc Math Phys Eng Sci 2015; 471:20150143. [PMID: 26730214 PMCID: PMC4685876 DOI: 10.1098/rspa.2015.0143] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
A new analogy between optical propagation and heat diffusion in heterogeneous anisotropic media has been proposed recently by three of the present authors. A detailed derivation of this unconventional correspondence is presented and developed. In time harmonic regime, all thermal parameters are related to optical ones in artificial metallic media, thus making possible to use numerical codes developed for optics. Then, the optical admittance formalism is extended to heat conduction in multilayered structures. The concepts of planar microcavities, diffraction gratings and planar transformation optics for heat conduction are addressed. Results and limitations of the analogy are emphasized.
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Affiliation(s)
- C Amra
- Aix Marseille Université, Institut Fresnel, CNRS, Ecole Centrale Marseille, Faculté des Sciences et Techniques de St Jérôme , 13397 Marseille Cedex 20, France
| | - D Petiteau
- Aix Marseille Université, Institut Fresnel, CNRS, Ecole Centrale Marseille, Faculté des Sciences et Techniques de St Jérôme , 13397 Marseille Cedex 20, France
| | - M Zerrad
- Aix Marseille Université, Institut Fresnel, CNRS, Ecole Centrale Marseille, Faculté des Sciences et Techniques de St Jérôme , 13397 Marseille Cedex 20, France
| | - S Guenneau
- Aix Marseille Université, Institut Fresnel, CNRS, Ecole Centrale Marseille, Faculté des Sciences et Techniques de St Jérôme , 13397 Marseille Cedex 20, France
| | - G Soriano
- Aix Marseille Université, Institut Fresnel, CNRS, Ecole Centrale Marseille, Faculté des Sciences et Techniques de St Jérôme , 13397 Marseille Cedex 20, France
| | - B Gralak
- Aix Marseille Université, Institut Fresnel, CNRS, Ecole Centrale Marseille, Faculté des Sciences et Techniques de St Jérôme , 13397 Marseille Cedex 20, France
| | - M Bellieud
- Université Montpellier 2, CNRS, LMGC , Montpellier, France
| | - D Veynante
- Ecole Centrale Paris , CNRS, EM2C, Paris, France
| | - N Rolland
- Université de Lille 1 , CNRS, IEMN, Lille, France
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Lan C, Li B, Zhou J. Simultaneously concentrated electric and thermal fields using fan-shaped structure. OPTICS EXPRESS 2015; 23:24475-24483. [PMID: 26406652 DOI: 10.1364/oe.23.024475] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In recent years, considerable attention has been focused on transformation optics and metamaterial due to their fascinating properties and wide range of promising applications. Concentrator, one of the most well-known applications of transformation optics and metamaterial, is now limited only to a single physical domain. Here we propose and give the experimental demonstration of a bifunctional concentrator that can concentrate both electric and thermal fields to a given region simultaneously while keeping the external fields undistorted. Fan-shaped structure composed of alternating wedges made of two kinds of natural materials is proposed to achieve this goal. Numerical simulation and experimental results show good agreement, indicating the soundness and feasibility of our scheme.
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Xu J, Jiang X, Fang N, Georget E, Abdeddaim R, Geffrin JM, Farhat M, Sabouroux P, Enoch S, Guenneau S. Molding acoustic, electromagnetic and water waves with a single cloak. Sci Rep 2015; 5:10678. [PMID: 26057934 PMCID: PMC4460817 DOI: 10.1038/srep10678] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2014] [Accepted: 04/16/2015] [Indexed: 11/09/2022] Open
Abstract
We describe two experiments demonstrating that a cylindrical cloak formerly introduced for linear surface liquid waves works equally well for sound and electromagnetic waves. This structured cloak behaves like an acoustic cloak with an effective anisotropic density and an electromagnetic cloak with an effective anisotropic permittivity, respectively. Measured forward scattering for pressure and magnetic fields are in good agreement and provide first evidence of broadband cloaking. Microwave experiments and 3D electromagnetic wave simulations further confirm reduced forward and backscattering when a rectangular metallic obstacle is surrounded by the structured cloak for cloaking frequencies between 2.6 and 7.0 GHz. This suggests, as supported by 2D finite element simulations, sound waves are cloaked between 3 and 8 KHz and linear surface liquid waves between 5 and 16 Hz. Moreover, microwave experiments show the field is reduced by 10 to 30 dB inside the invisibility region, which suggests the multi-wave cloak could be used as a protection against water, sonic or microwaves.
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Affiliation(s)
- Jun Xu
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307
| | - Xu Jiang
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307
| | - Nicholas Fang
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307
| | - Elodie Georget
- Aix-Marseille Université, CNRS, Centrale Marseille- Institut Fresnel, Campus universitaire de Saint-Jérôme, 13013 Marseille, France
| | - Redha Abdeddaim
- Aix-Marseille Université, CNRS, Centrale Marseille- Institut Fresnel, Campus universitaire de Saint-Jérôme, 13013 Marseille, France
| | - Jean-Michel Geffrin
- Aix-Marseille Université, CNRS, Centrale Marseille- Institut Fresnel, Campus universitaire de Saint-Jérôme, 13013 Marseille, France
| | - Mohamed Farhat
- Division of Computer, Electrical, and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
| | - Pierre Sabouroux
- Aix-Marseille Université, CNRS, Centrale Marseille- Institut Fresnel, Campus universitaire de Saint-Jérôme, 13013 Marseille, France
| | - Stefan Enoch
- Aix-Marseille Université, CNRS, Centrale Marseille- Institut Fresnel, Campus universitaire de Saint-Jérôme, 13013 Marseille, France
| | - Sébastien Guenneau
- Aix-Marseille Université, CNRS, Centrale Marseille- Institut Fresnel, Campus universitaire de Saint-Jérôme, 13013 Marseille, France
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