Modeling of spatial variations of growth within apical domes by means of the growth tensor. Pt. 1. Growth specified on dome axis

Abstract

By using the growth tensor and a natural curvilinear coordinate system for description of the distribution of growth in plant organs, three geometrie types of shoot apical domes (parabolic, clliptical and hyperbolic) were modcled. It was assumed that apical dome geometry remains unchanged during growth and that the natural coordinate systems are paraboloidal and prolate spheroidal. Two variants of the displacement yelocity fields V were considered. One yariant is specified by a constant relative elemental ratę of growth along the axis of the dome. The second is specified by a ratę inereasing proportionally with distance from the geometrie focus of the coordinate systems (and the apical dome). The growth tensor was used to calculate spatial yariations of growth rates for each yariant of each dome type. There is in both yariants a elear tendency toward lower growth rates in the distal region of the dome. A basie condition for the existence of a tunica is met.