Optimal Packing of Two Disks on Torus

Authors

Zh. Kh. Zhunussova, Institute of mathematics and mathematical modeling, 050010, Almaty, Republic of Kazakhstan\\ Al-Farabi Kazakh National University, 050040, Almaty, Republic of KazakhstanFollow
Ye. K. Ashimov, Institute of mathematics and mathematical modeling, 050010, Almaty, Republic of Kazakhstan\\ Al-Farabi Kazakh National University, 050040, Almaty, Republic of KazakhstanFollow
K. A. Dosmagulova, Institute of mathematics and mathematical modeling, 050010, Almaty, Republic of Kazakhstan\\ Al-Farabi Kazakh National University, 050040, Almaty, Republic of KazakhstanFollow
L. Kh. Zhunussova, Abai Kazakh National Pedagogical University, 050010, Almaty, Republic of KazakhstanFollow

Author Country (or Countries)

Republic of Kazakhstan

Abstract

The article is devoted to recently established connection between the packing problem of disks on torus and the effective conductivity of composites with circular inclusions. The packing problem is usually investigated by geometrical arguments, the conductivity problem by means of elliptic functions. An algorithm is developed in order to determine the optimal location of two disks on torus formed by the hexagonal lattice and square lattice. The corresponding minimization function is constructed in terms of expressions consisting of elliptic functions with unknown arguments. The numerically found roots coincide with the previously established optimal points by a pure geometrical study.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/160407

Recommended Citation

Kh. Zhunussova, Zh.; K. Ashimov, Ye.; A. Dosmagulova, K.; and Kh. Zhunussova, L. (2022) "Optimal Packing of Two Disks on Torus," Applied Mathematics & Information Sciences: Vol. 16: Iss. 4, Article 7.
DOI: http://dx.doi.org/10.18576/amis/160407
Available at: https://digitalcommons.aaru.edu.jo/amis/vol16/iss4/7