Modeling of branching and plant growth via a modified elastica.

摘要

One of the most remarkable sites in nature is the branched structure of plants. The branching enables the plant to increase its capability to photosynthesize and to support its flowering structures. The shape of a plant's branches depend on a wide range of factors, some of which vary with the growth stage of the plant.To accommodate the factors featured in plant growth, Euler's original theory is modified to include the effects of lateral accretion, tip growth, and residual (or growth) stresses. As a result, a theory of deformable rods featuring time-varying intrinsic curvature, flexural rigidity, moment of inertia, mass density, and length is developed. The resulting theory is supplemented by a novel growth evolution equation. This equation is used to control the evolution of the intrinsic curvature in response to changes in flexural rigidity and moment of inertia. We also introduce a novel control curvature to address the deficiency in accommodating residual (growth) stresses that are inherent in any rod theory. The novel growth law is illustrated with a range of examples. It is also compared and related to earlier published works on plant stem growth modeling.Another contribution of the thesis is the development of a graphical technique to determine the shape of branched structures. Here, a plant with multiple stem bifurcations is considered and the graphical technique is used to explain the multiplicity of static configurations that the plant can display. We close the dissertation with an outline of future work on the modeling of plant growth and branching.