Quantitative analysis of the electric field in a two-layer mixed structure and its application

Wanjing Tang; Youjun Deng; Juan Wang; Zaiyun Zhang

doi:10.3934/ipi.2024007

Article Contents

2024, Volume 18, Issue 5: 1078-1095. Doi: 10.3934/ipi.2024007

This issue Previous Article Estimating absorption and scattering in quantitative photoacoustic tomography with an adaptive Monte Carlo method for light transport Next Article On the reconstruction of medium conductivity by integral equation method based on the Levi function

Quantitative analysis of the electric field in a two-layer mixed structure and its application

1.
School of Mathematics and Statistics, Central South University, Changsha, Hunan, China
2.
School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, Hunan, China

^*Corresponding author: Youjun Deng
^*Corresponding author: Youjun Deng

Received: September 2023

Revised: February 2024

Early access: February 2024

Published: October 2024

The work of Y. Deng was supported by NSFC-RGC Joint Research Grant No. 12161160314 and NSF grant of China No. 11971487. The work of Z. Zhang was supported by NSF grant of Hunan Grant No. 2021JJ30297, Scientific Research Fund of Hunan Provincial Education Department No. 22A0478 and Hunan Province Graduate Research Innovation Project No. CX20231208

Abstract / Introduction Full Text(HTML) Related Papers Cited by

Abstract

This paper is concerned with the quantitative analysis of the electric field perturbation in a two-layer structure, where the inner layer is a rod-shape inclusion and the outer layer is an arbitrary inclusion with normal size. By making use of the layer potential techniques and asymptotic estimates, we quantify the relationship of the perturbed electric field on the geometry of the inclusions. Then we use the aforesaid quantitative result to uniquely recover the rod shape inclusion with only one boundary measurement.

Keywords:

Mathematics Subject Classification: Primary: 35C10, 35C20; Secondary: 35P20.

Citation:

Full Text(HTML)

Related Papers

Cited by

References

[1]	H. Ammari and H. Kang, Polarization and Moment Tensors With Applications to Inverse Problems and Effective Medium Theory, Applied Mathematical Sciences, Berlin Heidelberg: Springer-Verlag, 2007.
[2]	Y. Deng, H. Liu and G. Uhlmann, Full and partial cloaking in electromagnetic scattering, Arch. Ration. Mech. Anal., 223 (2017), 265-299. doi: 10.1007/s00205-016-1035-6.
[3]	Y. Deng, H. Liu and G. Uhlmann, On regularized full- and partial-cloaks in acoustic scattering, Comm. Partial Different. Equat., 42 (2017), 821-851. doi: 10.1080/03605302.2017.1286673.
[4]	Y. Deng, H. Liu and G. Zheng, Mathematical analysis of plasmon resonances for curved nanorods, J. Math. Pures Appl., 153 (2021), 248-280. doi: 10.1016/j.matpur.2021.07.010.
[5]	Y. Deng, H. Liu and G. Zheng, Plasmon resonances of nanorods in transverse electromagnetic scattering, J. Differ. Equ., 318 (2022), 502-536. doi: 10.1016/j.jde.2022.02.035.
[6]	Y. Deng and W. Tang, Quantitative analysis of the elastic field for rod shape inclusion and uniqueness for related inverse problem, preprint.
[7]	T. V. Duncan, Applications of nanotechnology in food packaging and food safety: Barrier materials, antimicrobials and sensors, J. Colloid Interface Sci., 363 (2011), 1-24. doi: 10.1016/j.jcis.2011.07.017.
[8]	X. Fang, Y. Deng and H. Liu, Sharp estimate of electric field from a conductive rod and application, Stud. Appl. Math., 146 (2021), 279-297. doi: 10.1111/sapm.12348.
[9]	W. Huynh, J. Dittmer and A. Alivisatos, Hybrid nanorod-polymer solar cells, Science, 295 (2002), 2425-2427. doi: 10.1126/science.1069156.
[10]	N. Jana, L. Gearheart and C. Murphy, Wet chemical synthesis of high aspect ratio cylindrical gold nanorods, J. Phys. Chem. B, 105 (2001), 4065-4067. doi: 10.1021/jp0107964.
[11]	S. Lin, X. Wang, Z. Ji, C. H. Chang, Y. Dong, H. Meng, Y. P. Liao, M. Wang, T. B. Song, S. Kohan, T. Xia, J. I. Zink, S. Lin and A. E. Nel, Aspect ratio plays a role in the hazard potential of CeO2 nanoparticles in mouse lung and zebrafish gastrointestinal tract, ACS Nano, 8 (2014), 4450-4464. doi: 10.1021/nn5012754.
[12]	M. Volder, S. Tawfick, R. Baughman and A. Hart, Carbon nanotubes: Present and future commercial applications, Science, 339 (2013), 535-539. doi: 10.1126/science.1222453.