Abstract
This paper focuses on three groups of geometrical problems, closely related to material sciences in general and particularly to crystal/quasicrystal structures along with their formations and fullerenes. Some new results in mathematics are presented and discussed, for example, in section one, new estimates of minimum radius of local identity that guarantee that a Delone set is a point regular set. New results related to locally rigid packings are discussed in section two. One of the goals of the paper is to establish some internal (mathematically) and external (applications to material science) connections between research agendas of various studies in geometry and material sciences.
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Acknowledgments
The work has been supported in part by the grant of RF Government N 11.G34.31.0053 (Delaunay Laboratory of Yaroslavl University) and RFBR grant 11-01-00633-a and USA NSF grant DMS-1101688.
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Bouniaev, M.M., Dolbilin, N.P., Musin, O.R., Tarasov, A.S. (2016). Geometrical Problems Related to Crystals, Fullerenes, and Nanoparticle Structure. In: Chen, K., Ravindran, A. (eds) Forging Connections between Computational Mathematics and Computational Geometry. Springer Proceedings in Mathematics & Statistics, vol 124. Springer, Cham. https://doi.org/10.5176/2251-1911_CMCGS14.06_13
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DOI: https://doi.org/10.5176/2251-1911_CMCGS14.06_13
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