Localized Sensitivity Analysis at High-Curvature Boundary Points of Reconstructing Inclusions in Transmission Problems
@article{Ammari2022LocalizedSA, title={Localized Sensitivity Analysis at High-Curvature Boundary Points of Reconstructing Inclusions in Transmission Problems}, author={Habib M. Ammari and Yat Tin Chow and Hongyu Liu}, journal={SIAM Journal on Mathematical Analysis}, year={2022} }
In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the local shape around a boundary point with a high magnitude of mean curvature can be reconstructed more easily and stably. In proving this, we develop a novel mathematical scheme by analyzing the generalized polarisation tensors (GPTs) and the scattering…
6 Citations
Quantum integrable systems and concentration of plasmon resonance
- Mathematics
- 2021
We are concerned with the quantitative mathematical understanding of surface plasmon resonance (SPR). SPR is the resonant oscillation of conducting electrons at the interface between negative and…
Shape reconstructions by using plasmon resonances
- MathematicsESAIM: Mathematical Modelling and Numerical Analysis
- 2022
It is shown that when plasmon resonance occurs, the sensitivity functional blows up and hence ensures a more robust and effective construction of the reconstruction, which is proposed by incorporating Drude’s model of the permittivity parameter.
On Calderón’s inverse inclusion problem with smooth shapes by a single partial boundary measurement
- MathematicsInverse Problems
- 2021
We consider Calderón’s inverse inclusion problem of recovering the shape of an anomalous inhomogeneity embedded in a homogeneous conductivity by the associated electric boundary measurements. It is a…
Surface concentration of transmission eigenfunctions
- Mathematics, Physics
- 2021
The transmission eigenvalue problem is a type of non-elliptic and non-selfadjoint spectral problem that arises in the wave scattering theory when invisibility/transparency occurs. The transmission…
On local and global structures of transmission eigenfunctions and beyond
- MathematicsJournal of Inverse and Ill-posed Problems
- 2020
Abstract The (interior) transmission eigenvalue problems are a type of non-elliptic, non-selfadjoint and nonlinear spectral problems that arise in the theory of wave scattering. They connect to the…
Quantum ergodicity and localization of plasmon resonances
- Mathematics
- 2020
We are concerned with the geometric properties of the surface plasmon resonance (SPR). SPR is a non-radiative electromagnetic surface wave that propagates in a direction parallel to the negative…
References
SHOWING 1-10 OF 96 REFERENCES
Weyl's law for the eigenvalues of the Neumann--Poincaré operators in three dimensions: Willmore energy and surface geometry
- Mathematics
- 2018
We deduce eigenvalue asymptotics of the Neumann--Poincar\'e operators in three dimensions. The region $\Omega$ is $C^{2, \alpha}$ ($\alpha>0$) bounded in ${\mathbf R}^3$ and the Neumann--Poincar\'e…
The Foundations Of Differential Geometry
- Education
- 2016
The the foundations of differential geometry is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Characterization of Non-Smooth Pseudodifferential Operators
- Mathematics
- 2015
Smooth pseudodifferential operators on $$\mathbb {R}^{n}$$Rn can be characterized by their mapping properties between $$L^p-$$Lp-Sobolev spaces due to Beals and Ueberberg. In applications such a…
Riemannian geometry and geometric analysis
- Mathematics
- 1995
* Established textbook
* Continues to lead its readers to some of the hottest topics of contemporary mathematical research
This established reference work continues to lead its readers to some of…
Pseudodifferential Operators and Nonlinear PDE
- Mathematics
- 1991
The theory of pseudodifferential operators has played an important role in many investigations into linear PDE. This book is devoted to a summary and reconsideration of some uses of…
Spectral approximation for compact operators
- Mathematics
- 1975
In this paper a general spectral approximation theory is developed for compact operators on a Banach space. Results are obtained on the approximation of eigenvalues and generalized eigenvectors.…
"J."
- Philosophy
- 1890
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)…
Quantum ergodicity and localization of plasmon resonances
- Mathematics
- 2020
We are concerned with the geometric properties of the surface plasmon resonance (SPR). SPR is a non-radiative electromagnetic surface wave that propagates in a direction parallel to the negative…
The generalized polarization tensors for resolved imaging. Part I: Shape reconstruction of a conductivity inclusion
- MathematicsMath. Comput.
- 2012
This paper designs an optimization approach which solves the problem of recovering finer details of the shape of a given domain using higher-order polarization tensors by minimizing a weighted discrepancy functional.