Far Eastern Mathematical Journal

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Mechanical characteristics of molecular dynamics model and Korobov polynomials

Guzev M.A., Ustinov A.V.

2016, issue 1, P. 39-43

Abstract

We use the number theory methods for explicit calculation of a static stress field in the system of a 1D chain harmonic oscillators. The sums defining stress field are presented in terms of Korobov polynomials for arbitrary number of oscillators and arbitrary averaging scale.

Keywords: molecular dynamics, Fourier series, Korobov polynomials

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References

[1] M.A. Guzev, Ju.G. Izrail'skij, M.A. Shepelov, «Molekuljarno-dinamicheskie harakteristiki odnomernoj tochno reshaemoj modeli na razlichnyh masshtabah», Fizicheskaja mehanika, 9:5 (2006), 53–57. [2] N.M. Korobov, «Special'nye polinomy i ih prilozhenija», Diofantovy priblizhenija. Matem. zapiski, 2 (1996), 77–89. [3] A.V. Ustinov, «O formulah summirovanija i interpoljacii», Chebyshevskij sbornik, 1 (2001), 52–71. [4] N.M. Korobov, «O nekotoryh svojstvah special'nyh polinomov», Chebyshevskij sbornik, 1 (2001), 40–49. [5] A.V. Ustinov, «Ob odnom obobshhenii chisel Stirlinga», Chebyshevskij sbornik, 3:2(4) (2002), 107–122. [6] A.V. Ustinov, «Polinomy Korobova i tenevoj analiz», Chebyshevskij sbornik, 4:4(8) (2003), 137–152.

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