The Method of Zero Tangential Strengths in the Problem of Charge Distribution over the Surfaces of Two Interacting Tori
In this paper, a system of two circular concentric non-touching tori is considered. An electrostatic charge can be applied to each of the tori. The problem is to find the density of charge distribution over the surfaces of the tori, taking into account the Coulomb interaction between the surfaces. T...
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Shahid Chamran University of Ahvaz
2025-10-01
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| Series: | Journal of Applied and Computational Mechanics |
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| Online Access: | https://jacm.scu.ac.ir/article_19460_0a5a75a8082ef8de7c2b0bc8a01c2272.pdf |
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| author | Nikita Dmitriev Vadim Sakharov Alexey Tikhonov |
| author_facet | Nikita Dmitriev Vadim Sakharov Alexey Tikhonov |
| author_sort | Nikita Dmitriev |
| collection | DOAJ |
| description | In this paper, a system of two circular concentric non-touching tori is considered. An electrostatic charge can be applied to each of the tori. The problem is to find the density of charge distribution over the surfaces of the tori, taking into account the Coulomb interaction between the surfaces. The required density is found numerically by the method of successive approximations based on the fact that in the static case, the total tangential strength of the Coulomb forces is zero at each of the points on the surface of each of the tori. The corresponding functional is constructed, the problem of numerical minimization of which is solved by the gradient descent method. |
| format | Article |
| id | doaj-art-e238e36fc04147ea979e6d4f43fb959a |
| institution | Kabale University |
| issn | 2383-4536 |
| language | English |
| publishDate | 2025-10-01 |
| publisher | Shahid Chamran University of Ahvaz |
| record_format | Article |
| series | Journal of Applied and Computational Mechanics |
| spelling | doaj-art-e238e36fc04147ea979e6d4f43fb959a2025-08-20T03:50:58ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362025-10-011141196120610.22055/jacm.2025.48138.500919460The Method of Zero Tangential Strengths in the Problem of Charge Distribution over the Surfaces of Two Interacting ToriNikita Dmitriev0Vadim Sakharov1Alexey Tikhonov2Saint Petersburg State University, 7-9 Universitetskaya nab., Saint Petersburg, 199034, RussiaSaint Petersburg State University, 7-9 Universitetskaya nab., Saint Petersburg, 199034, RussiaSaint Petersburg State University, 7-9 Universitetskaya nab., Saint Petersburg, 199034, RussiaIn this paper, a system of two circular concentric non-touching tori is considered. An electrostatic charge can be applied to each of the tori. The problem is to find the density of charge distribution over the surfaces of the tori, taking into account the Coulomb interaction between the surfaces. The required density is found numerically by the method of successive approximations based on the fact that in the static case, the total tangential strength of the Coulomb forces is zero at each of the points on the surface of each of the tori. The corresponding functional is constructed, the problem of numerical minimization of which is solved by the gradient descent method.https://jacm.scu.ac.ir/article_19460_0a5a75a8082ef8de7c2b0bc8a01c2272.pdftoruselectrostatic chargecharge distributiontangential stressessurface densitygradient descent method |
| spellingShingle | Nikita Dmitriev Vadim Sakharov Alexey Tikhonov The Method of Zero Tangential Strengths in the Problem of Charge Distribution over the Surfaces of Two Interacting Tori Journal of Applied and Computational Mechanics torus electrostatic charge charge distribution tangential stresses surface density gradient descent method |
| title | The Method of Zero Tangential Strengths in the Problem of Charge Distribution over the Surfaces of Two Interacting Tori |
| title_full | The Method of Zero Tangential Strengths in the Problem of Charge Distribution over the Surfaces of Two Interacting Tori |
| title_fullStr | The Method of Zero Tangential Strengths in the Problem of Charge Distribution over the Surfaces of Two Interacting Tori |
| title_full_unstemmed | The Method of Zero Tangential Strengths in the Problem of Charge Distribution over the Surfaces of Two Interacting Tori |
| title_short | The Method of Zero Tangential Strengths in the Problem of Charge Distribution over the Surfaces of Two Interacting Tori |
| title_sort | method of zero tangential strengths in the problem of charge distribution over the surfaces of two interacting tori |
| topic | torus electrostatic charge charge distribution tangential stresses surface density gradient descent method |
| url | https://jacm.scu.ac.ir/article_19460_0a5a75a8082ef8de7c2b0bc8a01c2272.pdf |
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