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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.01734 |
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| _version_ | 1866918226028396544 |
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| author | Huang, Yi Li, Bowen Liu, Ping Shao, Yingjie |
| author_facet | Huang, Yi Li, Bowen Liu, Ping Shao, Yingjie |
| contents | This work analyzes the scattering resonances of general acoustic media in a one-dimensional setting using the propagation matrix approach. Specifically, we characterize the resonant frequencies as the zeros of an explicit trigonometric polynomial. Leveraging Nevanlinna's value distribution theory, we establish the distribution properties of the resonances and demonstrate that their imaginary parts are uniformly bounded, which contrasts with the three-dimensional case. In two classes of high-contrast regimes, we derive the asymptotics of both subwavelength and non-subwavelength resonances with respect to the contrast parameter. Furthermore, by applying the Newton polygon method, we recover the discrete capacitance matrix approximation for subwavelength Minnaert resonances in both Hermitian and non-Hermitian cases, thereby establishing its connection to the propagation matrix framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resonance analysis of one-dimensional acoustic media: a propagation matrix approach Huang, Yi Li, Bowen Liu, Ping Shao, Yingjie Analysis of PDEs 34L20, 34E05, 15A18, 11L03, 30D35 This work analyzes the scattering resonances of general acoustic media in a one-dimensional setting using the propagation matrix approach. Specifically, we characterize the resonant frequencies as the zeros of an explicit trigonometric polynomial. Leveraging Nevanlinna's value distribution theory, we establish the distribution properties of the resonances and demonstrate that their imaginary parts are uniformly bounded, which contrasts with the three-dimensional case. In two classes of high-contrast regimes, we derive the asymptotics of both subwavelength and non-subwavelength resonances with respect to the contrast parameter. Furthermore, by applying the Newton polygon method, we recover the discrete capacitance matrix approximation for subwavelength Minnaert resonances in both Hermitian and non-Hermitian cases, thereby establishing its connection to the propagation matrix framework. |
| title | Resonance analysis of one-dimensional acoustic media: a propagation matrix approach |
| topic | Analysis of PDEs 34L20, 34E05, 15A18, 11L03, 30D35 |
| url | https://arxiv.org/abs/2512.01734 |