Optimal Packing of Two Disks on Torus
Zhunussova Zh.Kh. Ashimov Ye.K. Dosmagulova K.A. Zhunussova L.Kh.
July 2022Natural Sciences Publishing
Applied Mathematics and Information Sciences
2022#16Issue 4549 - 554 pp.
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.
Composite , Effective conductivity , Hexagonal lattice , Optimal packing , Square lattice , Torus
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Institute of mathematics and mathematical modeling, Almaty, 050010, Kazakhstan
Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Abai Kazakh National Pedagogical University, Almaty, 050010, Kazakhstan
Institute of mathematics and mathematical modeling
Al-Farabi Kazakh National University
Abai Kazakh National Pedagogical University
10 лет помогаем публиковать статьи Международный издатель
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