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Geometrical Models Some of Microstructure Using Tessellation

Year 2022, Issue: 15, 40 - 46, 22.06.2022

Abstract

The physical, biological and functional properties of many materials in nature depend on the size, shape, and spatial distribution of their microstructures, as well as their location. This distribution of layout corresponds to the concept of tessellation, which is expressed by formulas in geometry. This concept has been defined in botany by the term "mosaic" for morphological structures such as a flower petal, bark, or fruit. It is easier to determine the productivity of materials with known microstructures at the macro scale. In many areas, the geometry of the microstructures of materials can be clarified and their usability can be increased. Similar research has been done in the food field. The stability, transport properties, structural integrity or nutritional quality of food materials are reflections of microstructure communities, and when they are embedded, they reveal the engineering structures we call macrostructure (tissue and organ). As a result, when the micro-geometrical structures of the materials are known and considered, the productivity parameters at the macro scale become determinable. The transition from microstructure to macrostructure can then be achieved by appropriate homogenization procedures. Since the microstructures that make up the materials make up the whole of that material, the shape of the connection between them is important. Plant tissues also have a micromorphological structure consisting of many cells. Therefore, the characteristics of the plant depend not only on the characteristics of individual cells, but also on the connection, location, and interactions between the cellular components. In this study, it has been tried to determine the geometric models of the cells that make up the microscopic structures of some plants by using the geometric definitions of tessellation, which is a mathematical concept.

References

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  • [6] Tanvir R.F, Nicolay H, Alejandro D. R, Tamara L. W, Damiano P (2012). Experimental determination of Philodendron melinonii and Arabidopsis thaliana tissue microstructure and geometric modeling via finite-edge centroidal Voronoi tessellation. Physical Review. 86, 031921.
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Year 2022, Issue: 15, 40 - 46, 22.06.2022

Abstract

References

  • [1] Aguilera J. M (2005). Why food microstructure? J. Food Eng. 67, 3-11.
  • [2] Ghosh S, Le K, Moorthy S (1996). Two scale analysis of heterogeneous elasticplastic materials with asymptotic homogenization and Voronoi cell finite element model. Comput. Methods Appl. Mech. Eng. 132, 63–116.
  • [3] Tanvir R.F, Nicolay H, Alejandro D. R, Tamara L. W, Damiano P (2014). Computational study of the elastic properties of Rheum rhabarbarum tissues via surrogate models of tissue geometry. Journal of Structural Biology 185 285–294.
  • [4] Gibson L. J, Ashby M. F, (1999). Cellular Solids: Structure and Properties, 2nd ed., Cambirdge Solid State Science series (Cambridge University Press, Cambridge, New York.
  • [5] Silva M. J, Hayes W. C, Gibson L. J (1995). The effects of non-periodic microstructure on the elastic properties of two-dimensional cellular solids. Int. J. Mech. Sci., 37, 1161-77.
  • [6] Tanvir R.F, Nicolay H, Alejandro D. R, Tamara L. W, Damiano P (2012). Experimental determination of Philodendron melinonii and Arabidopsis thaliana tissue microstructure and geometric modeling via finite-edge centroidal Voronoi tessellation. Physical Review. 86, 031921.
  • [7] Cohn H, Larsen M, Propp J (1998). The Shape of a Typical Boxed Plane Partition." New York J. Math. 4, 137-166.
  • [8] Algan, G (1981). Bitkisel Dokular İçin Mikroteknik. Fırat Üniv. Fen-Ed.Fak.Yayın. Bot. No:1, İstanbul.
  • [9] Baytop A (1981). Bitkisel Drogların Anatomik Yapısı. İstanbul Üniv. Yay. 6, Baskı No: 32, İstanbul.
  • [10] Conway R, Burgiel H, Goodman-Strauss G (2008). The Symmetries of Things. Peters.D. Pasini, Journal of Design & Nature and Ecodynamics 3, 1.
  • [11] Gardner M (1988). Tilings with Convex Polygons. Ch. 13 in Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, pp. 162-176.
  • [12] Weisstein, Eric W (2007). Hexagon Tiling. From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HexagonTiling.html.
  • [13] Ghyka, M. C (1977). The Geometry of Art and Life, 2nd ed. New York: Dover.
  • [14] Williams, R (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. New York: Dover.
  • [15] Weisstein, Eric W (2020). "Dodecagon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Dodecagon.html.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Ali Özdemir 0000-0001-9330-7084

Canan Özdemir

Early Pub Date June 17, 2022
Publication Date June 22, 2022
Submission Date March 4, 2022
Acceptance Date April 7, 2022
Published in Issue Year 2022 Issue: 15

Cite

APA Özdemir, A., & Özdemir, C. (2022). Geometrical Models Some of Microstructure Using Tessellation. Journal of New Results in Engineering and Natural Sciences(15), 40-46.