ON THE OPTIMAL CONDUCTIVITY OF PACKED TWO-DIMENSIONAL DISPERSED COMPOSITES
Dosmagulova K. Mityushev V. Zhunussova Z.
June 2023Society for Industrial and Applied Mathematics Publications
SIAM Journal on Applied Mathematics
2023#83Issue 3985 - 999 pp.
Optimal packing is applied in physics for investigation of macroscopic properties of composites and porous media. The present paper demonstrates that the optimal packing of perfectly conducting disks on the plane corresponds to the minimal effective conductivity for macroscopically isotropic composites. Such an optimal location is studied and compared to the pure geometric problem for N leq 8 disks packing on the flat torus. The hexagonal (triangular) array of disks solves the problem for the triangle lattice numbers N = 1, 3, 4, 7, . . .. The rest of the cases N = 2, 5, 6, 8 are investigated separately by minimization of structural sums constructed by means of the Eisenstein functions. Copyright
effective conductivity of disks , Eisenstein function , optimal packing of disks on torus , periodic packing , structural sums
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Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Faculty of Computer Science and Telecommunications, Cracow University of Technology, Kraków, 31-155, Poland
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
Faculty of Computer Science and Telecommunications
10 лет помогаем публиковать статьи Международный издатель
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