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

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

Modeling of spatial variations of growth within apical domes by means of the growth tensor. Pt. 2. Growth specified on dome axis

Variations of the elemental relative rate of growth are modeled for parabolic, elliptic and hyperbolic domes of shoot apices by using the growth tensor in a suitable curvilinear coordinate system when the mode of area growth on the dome surface is known. Variations of growth rates within the domes arc obtained in forms of computer-made maps for the following variants of growth on the dome surface: (I) constant meridional growth rate, (2) isotropic area growth, (3) anisotropy of area growth which becomes more intensive with increasing distance from the vertex. In variants I and 2 a maximum of volumetric growth rate appears in the center of the dome. Such a distribution of growth seems to be unrealistic, However, the corresponding growth tensors are interesting because they can be used in combination with other growth tensors to get the expected minimum volumetric growth rate in the dome center

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

By using the growth tensor and a natural curvilinear coordinate system for description of the distribution of growth in plant organs, three geometric types of shoot apical domes (parabolic, elliptical and hyperbolic) were modeled. 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 velocity fields V were considered. One variant is specified by a constant relative elemental rate of growth along the axis of the dome. The second is specified by a rate increasing proportionally with distance from the geometric focus of the coordinate systems (and the apical dome). The growth tensor was used to calculate spatial variations of growth rates for each variant of each dome type. There is in both variants a clear tendency toward lower growth rates in the distal region of the dome. A basic condition for the existence of a tunica is met