Geodesic
Ring statistics in disordered solids: a parallel algorithm for clusters with hundred thousands of atoms
Numerical methods and programming, Tome 18 (2017) no. 4, pp. 447-454.

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The rings consisting of various number of atoms are basic structural elements in many disordered solids. In this paper, a parallel algorithm for calculating an approximate ring distribution function by the number of atoms is proposed. The algorithm is based on the Monte Carlo method and is applied to SiO$_2$ clusters consisting of up to $10^6$ atoms. The efficiency of the algorithm is studied using up to 1024 computational cores.
Keywords: structures of glasses and films, molecular dynamics, glassy silicon dioxide, ring statistic. 
@article{VMP_2017_18_4_a9,
     author = {G. F. Grigor'ev and V. B. Sulimov and A. V. Tikhonravov},
     title = {Ring statistics in disordered solids: a parallel algorithm for clusters with hundred thousands of atoms},
     journal = {Numerical methods and programming},
     pages = {447--454},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2017_18_4_a9/}
}
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G. F. Grigor'ev; V. B. Sulimov; A. V. Tikhonravov. Ring statistics in disordered solids: a parallel algorithm for clusters with hundred thousands of atoms. Numerical methods and programming, Tome 18 (2017) no. 4, pp. 447-454. http://geodesic.mathdoc.fr/item/VMP_2017_18_4_a9/