Funct. Mater. 2016; 23 (4): 592-598.
Symmetry of life in crystals
1State University of Airspace Instrumentation,67 Bolshaya Morskaya Str., 190000 St.-Petersburg, Russian Federation
2Institute for Scintillation Materials, STC Institute for Single Crystals, National Academy of Sciences of Ukraine, 60 Nauky Ave., 61001 Kharkiv, Ukraine
The results of the study of quasicrystals matrix models are presented, which confirm the hypothesis that each quasicrystal has corresponding quasiorthogonal matrix associated with it, the golden ratio matrix meets the D.Shechtman quasicrystal. It is concluded that for the ordered structures consisting of two endlessly recurring units, a modular two-level golden ratio matrix may be a model reflecting the structure elements. The main interest here is in the indication of the prospects: both the materials and the matrices can have different structures, and the matrices can be involved in predicting the existence and then in analyzing the materials.
1. D.Shechtman, I.Blech, D.Gratias, J.W.Cahn, Phys. Rev. Lett., 53, 1951 (1984). https://doi.org/10.1103/PhysRevLett.53.1951
2. R.Penrose, Evreka, 39, 16 (1978).
3. Yu.Kh.Vekilov, M.A.Chernikov, Succ. Phys. Sci., 180, 561 (2010).
4. A.E.Madison, Sol. State Phys., 55, 784 (2013). https://doi.org/10.1134/S1063783413040185
5. W.Steurer, S.Deloudi, Concepts, Methods and Structures, Springer, New York (2009).
6. S.Hyde, S.Andersson, K.Larsson et al., The Language of Shape. The Role of Curvature in Condensed Matter Physics, Chemistry and Biology, Elsevier, Amsterdam (1997).
7. E.A.Lord, A.L.Mackay, S.Ranganathan, New Geometries for New Materials, Cambridge University Press (2006).
8. N.A.Balonin, M.B.Sergeyev, Inf. Contr. Syst., 5, 2 (2013).
9. N.A.Balonin, M.B.Sergeyev, Inf. Contr. Syst, 1, 2 (2014).
10. N.A.Balonin, M.B.Sergeev, Informatsionno-upravliaiushchie Sistemy, 6, 2 (2013). https://doi.org/10.15217/issn1684-8853.2015.6.2