International Geologiical Congress - Oslo 2008

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MAG-04 Scales, scaling, non-linearity and complexity in the geosciences

 

Nature ideas of multiscale surfaces organization

 

Nina L. Smirnova, Moscow State University (Russian Federation)
 

 

The problems of crystal, earth and organism surface organization are studied for hundreds years. It was shown at the last century that different multiscale system organization is the same. We tried to establish the nature ideas of polygonal multiscale surface organization. Different surfaces of hundreds crystals, organizms, atomic polyhedra, calderas, cleavage, hypsometric map, diffuse nervous system, geological column, and so on were studied. All surfaces and sections consist of vertices and n-gons. Every vertex and n-gon have coordination sphere or crown. Every closed crown consists of sequence of n-gons with n=3-8 and more (rare). Every sequence consists of 1-7 different letters (n-gons): a, ab, abc, abab, abac, abcd, ababc, abacd, abcde, ababab, ababac, ababcd, abacad, abacbc, abacbd, abacdc, abacde, abcabc, abcabd, abcade, abcdef, abababc, ababacd, ababcac, ababcad, ababcdc, ababcde, -abacabc, abacabd. abacade, abacbcd, abacbdc, abacbde, abacdce, abacdec, abacdef, -abcabcd, abcabde, abcadbe, abcadef, abcdefg and some else. Formulas contain three modules abab, abac, abc, that frequency is very high. Every letter has coefficient, that means repetition of this letter. Every sequence composition formula consist of 1-7 different letters a, ab, abc, abcd, abcde, abcdef, abcdefg. The system of coefficient sets for these formulas is: 3 - {3, 21, 111}, 4 - {4, 31, 22, 211, 1111}, 5 - {5, 41, 32, 311, 221, 2111, 11111}, 6 - {6, 51, 42, 33, 411, 321, 222, 3111, 2211, 21111, 111111}, 7 - {7, 61, 52, 43, 511, 421, 331, 322, 4111, 3211, 2221, 22111, 21111, 1111111}, 8 - {8, 71, 62, 53, 44, 611, 521, 431, 422, 332, 51111, 4211, 3311, 3221, -2222, 41111, 32111, 22211, 311111, 221111, -211111, -11111111}, minus - not realysed formulas, further - only realised formulas: 9 - {531, 432, 333, 5211, 42111}, 10 - {541, 6211, 3331, 43111}, 11 - {6311}, 12 - {651, 6321, 53211}, 13 - {8221, 5431, 73111}, 14 - {851, 8411, 63221}, 15 - {78}, 16 - {853, 922111}, 17 - {.11.3.3}, 18 - {771111}, 20 - {.14.6, .12.5.3, .11.6.3}, 21 - {.11.6.3.1, 864111}, 24 - {.14.5.3.2}, 29 - {.17.5.5.1.1}. Long sequences that consist of 10 and more letters in total are related to pores, windows. Vertex crowns consist of 1-4 dtfferent n-gons. We concluded that local coordination spheres of regular and irregular polygonal surfaces and sections are organized in the same way.

 

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