Persistent Link:
http://hdl.handle.net/10150/290129
Title:
Plant patterns
Author:
Shipman, Patrick Daniel
Issue Date:
2004
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)
Keywords:
Biology, Botany.; Mathematics.; Biology, Plant Physiology.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Newell, Alan C.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titlePlant patternsen_US
dc.creatorShipman, Patrick Danielen_US
dc.contributor.authorShipman, Patrick Danielen_US
dc.date.issued2004en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © 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.en_US
dc.description.abstractThe 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.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectBiology, Botany.en_US
dc.subjectMathematics.en_US
dc.subjectBiology, Plant Physiology.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorNewell, Alan C.en_US
dc.identifier.proquest3145130en_US
dc.identifier.bibrecord.b47210357en_US
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