Growth in Root Apices. II. Deformation and Rate of Deformation

Publisher Website
Google Scholar
Abstract
The description of deformation and of the rate of deformation in the growth of a root is discussed. Deformation involves the displacement of particles from an initial configuration, and the stretch and rotation of material elements in the vicinity of particles. These effects may be described using vector operators such as the material displacement gradient tensor, K, or the material deformation gradient tensor, F, which associate an infinitesimal vector element in the deformed configuration with its initial position. In 1 dimension, both operators have simple forms: K is the slope of the displacement function u(X,t), which relates displacement u to initial position, X, and time; and F is the slope of the deformation function x(X,t), which relates deformed position, x, to initial position and time. The rate of deformation at a point is described using the rate of deformation tensor, which, in one dimension, is the instantaneous rate of elongation of an infinitesimal vector element relative to its length. This quantity is Erickson''s relative elemental rate of elongation (RELEL), and it is evaluated by calculating the divergence of the spatial velocity field at a point on the growing axis. The growth rates and specific growth of regions of the root are then defined as spatial averages of the RELEL. The measures of deformation and rate of deformation are illustrated with data from Erickson and Sax''s paper on the growth of seedling roots of Zea mays L. and are discussed in relation to concepts in the literature.

This publication has 3 references indexed in Scilit: