Geodesic
Application of optimization methods for finding equilibrium states of two-dimensional crystals
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2032-2041

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A two-dimensional model of a multilayer material and a procedure for simulating its properties based on global optimization methods are proposed. This model is applied for the case of a two-dimensional crystal. Global minima of the interaction energy of the material's atoms are found, and geometric characteristics of its corresponding equilibrium states are described. The resulting lattices, in particular graphene's lattices, agree with experimental data, which confirms the validity of the proposed approach. This approach can be extended to a wider class of layered structures, and it can be used for determining the mechanical properties of materials. 
@article{ZVMMF_2016_56_12_a3,
     author = {Yu. G. Evtushenko and S. A. Lurie and M. A. Posypkin and Yu. O. Solyaev},
     title = {Application of optimization methods for finding equilibrium states of two-dimensional crystals},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2032--2041},
     publisher = {mathdoc},
     volume = {56},
     number = {12},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a3/}
}
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Yu. G. Evtushenko; S. A. Lurie; M. A. Posypkin; Yu. O. Solyaev. Application of optimization methods for finding equilibrium states of two-dimensional crystals. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2032-2041. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a3/