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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Main Authors: Nikita Dmitriev, Vadim Sakharov, Alexey Tikhonov
Format: Article
Language:English
Published: Shahid Chamran University of Ahvaz 2025-10-01
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.
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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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