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 
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/
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     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},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Ferrari A. C. et al., “Science and technology roadmap for graphene, related two-dimensional crystals and hybrid systems”, Nanoscale, 7:11 (2015), 4598–4810 | DOI

[2] Andriotis A. N., Richter E., Menon M., “Prediction of a new graphene like Si 2 BN solid”, Physical Review B, 93:8 (2016), 1413–1414 | DOI

[3] Meyer J. C., Geim A. K., Katsnelson M. I., Novoselov K. S., Booth T. J., Roth S., “The structure of suspended graphene sheets”, Nature, 446:7131 (2007), 60–63 | DOI

[4] Memarian F., Fereidoon A., Ganji M. D., “Graphene Young's modulus: molecular mechanics and DFT treatments”, Superlattices Microstruct., 85 (2015), 348–356 | DOI

[5] Sadeghirad A., Su N., Liu F., “Mechanical modeling of graphene using the three-layer-mesh bridging domain method”, Comput. Methods Appl. Mech. Engng., 294 (2015), 278–298 | DOI | MR

[6] Kiselev S. P., Zhirov E. V., “Chislennoe modelirovanie deformirovaniya i razrusheniya grafena pri odnoosnom rastyazhenii metodom molekulyarnoi dinamiki”, Fiz. mezomekhan., 15:2 (2012), 69–76

[7] Ni Z., Bu H., Zou M., Yi H., Bi K., Chen Y., “Anisotropic mechanical properties of graphene sheets from molecular dynamics”, Phys. B Condens. Matter., 405:5 (2010), 1301–1306 | DOI

[8] Dang K. Q., Simpson J. P., Spearot D. E., “Phase transformation in monolayer molybdenum disulphide (MoS2) under tension predicted by molecular dynamics simulations”, Scr. Mater., 76 (2014), 41–44 | DOI

[9] Tabarraei A., Wang X., “A molecular dynamics study of nanofracture in monolayer boron nitride”, Mater. Sci. Engng. A, 641 (2015), 225–230 | DOI

[10] Seifoori S., Hajabdollahi H., “Impact behavior of single-layered graphene sheets based on analytical model and molecular dynamics simulation”, Appl. Surf. Sci., 351 (2015), 565–572 | DOI

[11] Sfyris D., Sfyris G. I., Galiotis C., “Constitutive modeling of some 2D crystals: Graphene, hexagonal BN, MoS$_2$, WSe$_2$ and NbSe$_2$”, Int. J. Solids Struct., 66 (2014), 98–110 | DOI

[12] Zhang B., Xiao H., Yang G., Liu X., “Finite element modelling of the instability in rapid fracture of grapheme”, Eng. Fract. Mech., 141 (2015), 111–119 | DOI

[13] Lure S. A., Posypkin M. A., Solyaev Yu. O., “Metod identifikatsii masshtabnykh parametrov gradientnoi teorii uprugosti na osnove chislennykh eksperimentov dlya ploskikh kompozitnykh struktur”, Internat. J. of Open Informat. Technol., 3:6 (2015), 1–6

[14] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983 | MR

[15] Panteleev A. V., Letova T. A., Metody optimizatsii v primerakh i zadachakh, Vyssh. shkola, M., 2002

[16] Evtushenko Yu. G., “Chislennyi metod poiska globalnogo ekstremuma funktsii (perebor na neravnomernoi setke)”, Zh. vychisl. matem. i matem. fiz., 11:6 (1971), 1390–1403 | Zbl

[17] Evtushenko Y., Posypkin M., “A deterministic approach to global box-constrained optimization”, Optimizat. Letters, 7:4 (2013), 819–829 | DOI | MR | Zbl

[18] Evtushenko Yu. G., Posypkin M. A., “Primenenie metoda neravnomernykh pokrytii dlya globalnoi optimizatsii chastichno tselochislennykh nelineinykh zadach”, Zh. vychisl. matem. i matem. fiz., 51:8 (2011), 1376–1389 | Zbl

[19] Sergeev Ya. D., Kvasov D. E., Diagonalnye metody globalnoi optimizatsii, Fizmatlit, M., 2008

[20] Pinter J. D., Global optimization in action: continuous and Lipschitz optimization: algorithms, implementations and applications, Kluwer, Dordrecht, 2013 | MR

[21] Abgaryan K. K., Posypkin M. A., “Primenenie optimizatsionnykh metodov dlya resheniya zadach parametricheskoi identifikatsii potentsialov mezhatomnogo vzaimodeistviya”, Zh. vychisl. matem. i matem. fiz., 54:12 (2014), 1994–2001 | DOI | Zbl

[22] Tersoff J., “New empirical approach for the structure and energy of covalent systems”, Physical Review B, 37:12 (1988), 6991 | DOI

[23] Mannix A. J., Zhou X.-F., Kiraly B., Wood J. D., Alducin D., Myers B. D., Liu X., Fisher B. L., Santiago U., Guest J. R., Yacaman M. J., Ponce A., Oganov A. R., Hersam M. C., Guisinger N. P., “Synthesis of borophenes: Anisotropic, two-dimensional boron polymorphs”, Science, 350:6267 (2015), 1513–1516 | DOI