Closed-form evaluation of 2D static lattice sums
Semyon Yakubovich, Piotr Drygas, Vladimir Mityushev
TL;DR
This paper derives closed-form formulas for 2D static lattice sums using elliptic integrals, with applications to composite materials and discussions on computational methods like Eisenstein and Rayleigh summation.
Contribution
It introduces new closed-form expressions for lattice sums and explores their applications in material science, advancing computational techniques.
Findings
Derived explicit formulas for lattice sums
Applied formulas to composite material properties
Compared Eisenstein and Rayleigh summation methods
Abstract
In the present paper, employing properties of the complete elliptic integrals of the first and second kind, we deduce closed-form formulae for the lattice sums and other new formulae. Applications to the effective properties of regular and random composites are discussed. We also discuss the Eisenstein summation method and the Rayleigh method used in computations.
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