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    Plant patterns

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    Author
    Shipman, Patrick Daniel
    Issue Date
    2004
    Keywords
    Biology, Botany.
    Mathematics.
    Biology, Plant Physiology.
    Advisor
    Newell, Alan C.
    
    Metadata
    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    The hexagons on a pineapple contrast with the ribs observed, for example, on pumpkins or saguaro cacti. This dissertation demonstrates how these various configurations, and also the related patterns of phyllotaxis (the arrangement of leaves into whorls or spirals) can be understood as the energy-minimizing buckling pattern of a compressed shell (the plant's tunica) on an elastic foundation. The key new idea is that the elastic energy is minimized by special triads or sequences of triads of periodic deformations whose local wavevectors add to zero. Although triad configurations arise from a variety of microscopic mechanisms in natural and laboratory systems, we show that the particular choices of wavevectors that are observed on plants arise in a nontrivial way from properties specific to a mechanical model. Furthermore, the theory predicts correlations between types of phyllotaxis and shapes of plant surface configurations and suggests experiments that can further test the mechanical theory of plant pattern formation. The dissertation concludes with a derivation of Cross-Newell equations governing pattern formation far from onset in nonisotropic systems and in systems with hexagonal planforms.
    Type
    text
    Dissertation-Reproduction (electronic)
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Graduate College
    Mathematics
    Degree Grantor
    University of Arizona
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