A Simple Mathematical Model of Growth Pattern in Tree Stems

Stem formation process is analysed by examining annual ringsfor coniferous and broadleaved trees. Cutting a tree stem intoseveral segments of a constant length, the weight of each segmentis denoted as the stem density (S). In addition the verticallyaccumulated current increment of the stem densities is definedas the cumulative stem increment (CSI). Examining the relationshipsbetween CSI and S for tree stems, it is shown that most of themdepict straight lines. Redefining S as a function with two independentvariables, time t and vertical position z along the stem, thelinear partial differential equation