The method of zero tangential strengths in the problem of charge distribution over the surfaces of two interacting tori

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The method of zero tangential strengths in the problem of charge distribution over the surfaces of two interacting tori. / Дмитриев, Никита Николаевич ; Сахаров, Вадим Юрьевич ; Тихонов, Алексей Александрович.

In: Journal of Applied and Computational Mechanics, Vol. 11, No. 4, 01.10.2025, p. 1196-1206.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{caf2706b78594c9a90764fadb66d4b96,

title = "The method of zero tangential strengths in the problem of charge distribution over the surfaces of two interacting tori",

abstract = "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.",

keywords = "Torus, charge distribution, electrostatic charge, gradient descent method, surface density, tangential stresses",

author = "Дмитриев, {Никита Николаевич} and Сахаров, {Вадим Юрьевич} and Тихонов, {Алексей Александрович}",

year = "2025",

month = oct,

day = "1",

doi = "10.22055/JACM.2025.48138.5009",

language = "English",

volume = "11",

pages = "1196--1206",

journal = "Journal of Applied and Computational Mechanics",

issn = "2383-4536",

publisher = "Shahid Chamran University of Ahvaz",

number = "4",

}

RIS

TY - JOUR

T1 - The method of zero tangential strengths in the problem of charge distribution over the surfaces of two interacting tori

AU - Дмитриев, Никита Николаевич

AU - Сахаров, Вадим Юрьевич

AU - Тихонов, Алексей Александрович

PY - 2025/10/1

Y1 - 2025/10/1

N2 - 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.

AB - 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.

KW - Torus

KW - charge distribution

KW - electrostatic charge

KW - gradient descent method

KW - surface density

KW - tangential stresses

UR - https://www.mendeley.com/catalogue/85a763e1-9b64-3aa1-a4bf-aac7f2ea8ce3/

U2 - 10.22055/JACM.2025.48138.5009

DO - 10.22055/JACM.2025.48138.5009

M3 - Article

VL - 11

SP - 1196

EP - 1206

JO - Journal of Applied and Computational Mechanics

JF - Journal of Applied and Computational Mechanics

SN - 2383-4536

IS - 4

ER -

ID: 132267819