Geodesic
Formation of the structure of an annual ring in conifers: optimizational mathematical modeling
Matematičeskaâ biologiâ i bioinformatika, Tome 2 (2007) no. 2, pp. 319-326.

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The model of formation of an annual growth layer in the tree, a tree-ring, is proposed. The structure of the annual ring is presented to consist of two types of cells. The first type of cells carries out conductive function; the second type carries out supporting (mechanical) function. The choice of a type of cells is based on maximization of contribution of a certain type of cells into the total utility function. The proposed model is proved to be in agreement with the actual data on the tree-ring structure. The existence of the annual ring as a layered structure of conductive cells (early wood) and supporting cells (later wood) is explained in respect to correlations between two fundamental physical regularities – Poiseuille's law for fluid flow and the material strength law. 
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E. Yu. Shipitsina; I. V. Sviderskaya; V. G. Suhovol'skii. Formation of the structure of an annual ring in conifers: optimizational mathematical modeling. Matematičeskaâ biologiâ i bioinformatika, Tome 2 (2007) no. 2, pp. 319-326. http://geodesic.mathdoc.fr/item/MBB_2007_2_2_a1/

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