Minnaert resonances for acoustic waves in bubbly media

被引：58

作者：

Ammari, Habib ^{[1
]}

Fitzpatrick, Brian ^{[1
]}

Gontier, David ^{[1
]}

Lee, Hyundae ^{[2
]}

Zhang, Hai ^{[3
]}

机构：

[1] Swiss Fed Inst Technol, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

[2] Inha Univ, Dept Math, 253 Yonghyun Dong, Incheon 402751, South Korea

[3] HKUST, Dept Math, Kowloon, Clear Water Bay, Hong Kong, Peoples R China

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2018年 / 35卷 / 07期

关键词：

Minnaert resonance; Bubble; Monopole approximation; Layer potentials; Acoustic waves; PLASMON RESONANCE; SPECTRAL PROPERTIES; AIR BUBBLES; EQUATION; FREQUENCY; LAYER; NANOPARTICLES; PROPAGATION; SCATTERING; LIQUIDS;

D O I：

10.1016/j.anihpc.2018.03.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Through the application of layer potential techniques and Gohberg-Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. We also provide a mathematical justification for the monopole approximation of scattering of acoustic waves by bubbles at their Minnaert resonant frequency. Our results are complemented by several numerical examples which serve to validate our formula in two dimensions. (C) 2018 Elsevier Masson SAS. All rights reserved.

引用

页码：1975 / 1998

页数：24

共 37 条

[1] Boundary layer techniques for solving the Helmholtz equation in the presence of small inhomogeneities
Ammari, H
Kang, HB
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 296 (01) : 190 - 208
[2] Ammari H., 2007, Applied Mathematical Sciences
[3] Ammari H., 2009, MATH SURV MONGR AM M, V153
[4] A MATHEMATICAL AND NUMERICAL FRAMEWORK FOR BUBBLE META-SCREENS
Ammari, Habib
Fitzpatrick, Brian
Gontier, David
Lee, Hyundae
Zhang, Hai
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2017, 77 (05) : 1827 - 1850
[5] EFFECTIVE MEDIUM THEORY FOR ACOUSTIC WAVES IN BUBBLY FLUIDS NEAR MINNAERT RESONANT FREQUENCY
Ammari, Habib
Zhang, Hai
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2017, 49 (04) : 3252 - 3276
[6] Mathematical Analysis of Plasmonic Nanoparticles: The Scalar Case
Ammari, Habib
Millien, Pierre
Ruiz, Matias
Zhang, Hai
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2017, 224 (02) : 597 - 658
[7] Mathematical analysis of plasmonic resonances for nanoparticles: The full Maxwell equations
Ammari, Habib
Ruiz, Matias
Yu, Sanghyeon
Zhang, Hai
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (06) : 3615 - 3669
[8] Surface Plasmon Resonance of Nanoparticles and Applications in Imaging
Ammari, Habib
Deng, Youjun
Millien, Pierre
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2016, 220 (01) : 109 - 153
[9] Super-resolution in high-contrast media
Ammari, Habib
Zhang, Hai
[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2015, 471 (2178):
[10] A Mathematical Theory of Super-Resolution by Using a System of Sub-Wavelength Helmholtz Resonators
Ammari, Habib
Zhang, Hai
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 337 (01) : 379 - 428

← 1 2 3 4 →