An electrical lifetime of polymers in terms of the catastrophe theory
The present study analyzes the known expressions establishing exponential and power relationships between the lifetime of polymer dielectrics and the strength of the electric field acting on them. The work notes the necessity of mathematical substantiation of the known power expression for the field...
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| Format: | Article |
| Language: | English |
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Peter the Great St.Petersburg Polytechnic University
2025-06-01
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| Series: | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
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| Online Access: | https://physmath.spbstu.ru/article/2025.80.09/ |
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| _version_ | 1849434173390979072 |
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| author | Kiselevich Valentin |
| author_facet | Kiselevich Valentin |
| author_sort | Kiselevich Valentin |
| collection | DOAJ |
| description | The present study analyzes the known expressions establishing exponential and power relationships between the lifetime of polymer dielectrics and the strength of the electric field acting on them. The work notes the necessity of mathematical substantiation of the known power expression for the field dependence of electrical lifetime. We obtained the equation of dependence of the electrical lifetime of polymeric dielectrics on the value of the applied electric field strength within the framework of the mathematical catastrophe theory. The study has the performance of quantitative estimation of the parameters of this equation for paper, epoxy and polyethylene terephthalate electrical insulation. We established a good agreement between the literature experimental data and the field dependences of the electrical lifetime of polymers plotted by the proposed equation. The study analyses geometric images of the fold catastrophe function reflecting the nature of the change in the dimensionless parameter of the rate of damage accumulation in a polyethylene terephthalate film under varying electric field strength. The paper shows the prospect of using the mathematical apparatus of catastrophe theory to describe experimental regularities of changes in the electrical strength properties of polymer dielectrics in strong electric fields. |
| format | Article |
| id | doaj-art-0118251c50ca49b98341d763fc752fb5 |
| institution | Kabale University |
| issn | 2405-7223 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Peter the Great St.Petersburg Polytechnic University |
| record_format | Article |
| series | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
| spelling | doaj-art-0118251c50ca49b98341d763fc752fb52025-08-20T03:26:44ZengPeter the Great St.Petersburg Polytechnic UniversitySt. Petersburg Polytechnical University Journal: Physics and Mathematics2405-72232025-06-0118210.18721/JPM.1820920714726An electrical lifetime of polymers in terms of the catastrophe theoryKiselevich Valentin0https://orcid.org/0000-0003-0542-0939Gomel state technical University named after P. O. SukhoiThe present study analyzes the known expressions establishing exponential and power relationships between the lifetime of polymer dielectrics and the strength of the electric field acting on them. The work notes the necessity of mathematical substantiation of the known power expression for the field dependence of electrical lifetime. We obtained the equation of dependence of the electrical lifetime of polymeric dielectrics on the value of the applied electric field strength within the framework of the mathematical catastrophe theory. The study has the performance of quantitative estimation of the parameters of this equation for paper, epoxy and polyethylene terephthalate electrical insulation. We established a good agreement between the literature experimental data and the field dependences of the electrical lifetime of polymers plotted by the proposed equation. The study analyses geometric images of the fold catastrophe function reflecting the nature of the change in the dimensionless parameter of the rate of damage accumulation in a polyethylene terephthalate film under varying electric field strength. The paper shows the prospect of using the mathematical apparatus of catastrophe theory to describe experimental regularities of changes in the electrical strength properties of polymer dielectrics in strong electric fields.https://physmath.spbstu.ru/article/2025.80.09/polymer dielectricelectrical lifetimeelectrical breakdownelectric field strengthcatastrophe theoryfold catastrophe |
| spellingShingle | Kiselevich Valentin An electrical lifetime of polymers in terms of the catastrophe theory St. Petersburg Polytechnical University Journal: Physics and Mathematics polymer dielectric electrical lifetime electrical breakdown electric field strength catastrophe theory fold catastrophe |
| title | An electrical lifetime of polymers in terms of the catastrophe theory |
| title_full | An electrical lifetime of polymers in terms of the catastrophe theory |
| title_fullStr | An electrical lifetime of polymers in terms of the catastrophe theory |
| title_full_unstemmed | An electrical lifetime of polymers in terms of the catastrophe theory |
| title_short | An electrical lifetime of polymers in terms of the catastrophe theory |
| title_sort | electrical lifetime of polymers in terms of the catastrophe theory |
| topic | polymer dielectric electrical lifetime electrical breakdown electric field strength catastrophe theory fold catastrophe |
| url | https://physmath.spbstu.ru/article/2025.80.09/ |
| work_keys_str_mv | AT kiselevichvalentin anelectricallifetimeofpolymersintermsofthecatastrophetheory AT kiselevichvalentin electricallifetimeofpolymersintermsofthecatastrophetheory |