Generalized Distribution Function of Relaxation Times with the Davidson-Cole Model as a Kernel
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910295296835584 |
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| author | Allagui, Anis Elwakil, Ahmed |
| author_facet | Allagui, Anis Elwakil, Ahmed |
| contents | In this paper we propose a generalized distribution function of relaxation times (DFRT) considering the Davidson-Cole model as an elementary process instead of the standard Debye model. The distribution function is retrieved from the inverse of the generalized Stieltjes transform expressed in terms of iterated Laplace transforms. We derive computable analytical expressions of the generalized DFRT for some of the most known normalized impedance (or admittance) models including the constant phase element, the Davidson-Cole, Havriliak-Negami and the Kohlrausch-Williams-Watts models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06490 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Distribution Function of Relaxation Times with the Davidson-Cole Model as a Kernel Allagui, Anis Elwakil, Ahmed Chemical Physics Disordered Systems and Neural Networks Mathematical Physics Applied Physics In this paper we propose a generalized distribution function of relaxation times (DFRT) considering the Davidson-Cole model as an elementary process instead of the standard Debye model. The distribution function is retrieved from the inverse of the generalized Stieltjes transform expressed in terms of iterated Laplace transforms. We derive computable analytical expressions of the generalized DFRT for some of the most known normalized impedance (or admittance) models including the constant phase element, the Davidson-Cole, Havriliak-Negami and the Kohlrausch-Williams-Watts models. |
| title | Generalized Distribution Function of Relaxation Times with the Davidson-Cole Model as a Kernel |
| topic | Chemical Physics Disordered Systems and Neural Networks Mathematical Physics Applied Physics |
| url | https://arxiv.org/abs/2401.06490 |