Clustered eigenvalue problem for glassy state relaxation and its inverse problem
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918144926285824 |
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| author | Chen, Shuli de Hoop, Maarten V. Deng, Youjun Lin, Ching-Lung Nakamura, Gen |
| author_facet | Chen, Shuli de Hoop, Maarten V. Deng, Youjun Lin, Ching-Lung Nakamura, Gen |
| contents | For computational convenience, a Prony series approximation of the stretched exponential relaxation function of homogeneous glasses has been proposed (J. Mauro, Y. Mauro, 2018), which is the extended Burgers model known for viscoelasticity equations. The authors of [P. Loreti and D. Sforza, 2019] initiated a spectral analysis of glass relaxation along this line, and gave some numerical results on clusters of eigenvalues. A theoretical justification of the results and development of further numerical studies were left open. In this paper, we provide a complete theoretical justification of their results and their numerical verification. Besides these, we solve an inverse spectral problem for clusters of eigenvalues associated with the glass relaxation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Clustered eigenvalue problem for glassy state relaxation and its inverse problem Chen, Shuli de Hoop, Maarten V. Deng, Youjun Lin, Ching-Lung Nakamura, Gen Analysis of PDEs For computational convenience, a Prony series approximation of the stretched exponential relaxation function of homogeneous glasses has been proposed (J. Mauro, Y. Mauro, 2018), which is the extended Burgers model known for viscoelasticity equations. The authors of [P. Loreti and D. Sforza, 2019] initiated a spectral analysis of glass relaxation along this line, and gave some numerical results on clusters of eigenvalues. A theoretical justification of the results and development of further numerical studies were left open. In this paper, we provide a complete theoretical justification of their results and their numerical verification. Besides these, we solve an inverse spectral problem for clusters of eigenvalues associated with the glass relaxation. |
| title | Clustered eigenvalue problem for glassy state relaxation and its inverse problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.16714 |