CSpace  > 计算数学与科学工程计算研究所
On isotropic cloaking and interior transmission eigenvalue problems
Ji, Xia1; Liu, Hongyu2,3
AbstractThis paper is concerned with the invisibility cloaking in acoustic wave scattering from a new perspective. We are especially interested in achieving the invisibility cloaking by completely regular and isotropic mediums. It is shown that an interior transmission eigenvalue problem arises in our study, which is the one considered theoretically in Cakoni et al. (Transmission eigenvalues for inhomogeneous media containing obstacles, Inverse Problems and Imaging, 6 (2012), 373-398). Based on such an observation, we propose a cloaking scheme that takes a three-layer structure including a cloaked region, a lossy layer and a cloaking shell. The target medium in the cloaked region can be arbitrary but regular, whereas the mediums in the lossy layer and the cloaking shell are both regular and isotropic. We establish that if a certain non-transparency condition is satisfied, then there exists an infinite set of incident waves such that the cloaking device is nearly invisible under the corresponding wave interrogation. The set of waves is generated from the Herglotz approximation of the associated interior transmission eigenfunctions. We provide both theoretical and numerical justifications.
KeywordAcoustic wave scattering invisibility cloaking isotropic and regular interior transmission eigenvalues
Funding ProjectFRG grants from Hong Kong Baptist University, Hong Kong RGC General Research Fund[12302415] ; NSFC[11371115] ; National Natural Science Foundation of China[11271018] ; National Natural Science Foundation of China[91230203] ; Special Funds for National Basic Research Program of China, 973 Program[2012CB025904]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000426855300003
Citation statistics
Document Type期刊论文
Corresponding AuthorJi, Xia
Affiliation1.Chinese Acad Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
2.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China
3.Virtual Univ Pk, HKBU Inst Res & Continuing Educ, Shenzhen, Peoples R China
Recommended Citation
GB/T 7714
Ji, Xia,Liu, Hongyu. On isotropic cloaking and interior transmission eigenvalue problems[J]. EUROPEAN JOURNAL OF APPLIED MATHEMATICS,2018,29(2):253-280.
APA Ji, Xia,&Liu, Hongyu.(2018).On isotropic cloaking and interior transmission eigenvalue problems.EUROPEAN JOURNAL OF APPLIED MATHEMATICS,29(2),253-280.
MLA Ji, Xia,et al."On isotropic cloaking and interior transmission eigenvalue problems".EUROPEAN JOURNAL OF APPLIED MATHEMATICS 29.2(2018):253-280.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Ji, Xia]'s Articles
[Liu, Hongyu]'s Articles
Baidu academic
Similar articles in Baidu academic
[Ji, Xia]'s Articles
[Liu, Hongyu]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Ji, Xia]'s Articles
[Liu, Hongyu]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.