Persistent Link:
http://hdl.handle.net/10150/297062
Title:
A Numerical Study of Pattern Forming Fronts in Phyllotaxis
Author:
Pennybacker, Matthew
Issue Date:
2013
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:
Using a partial differential equation model derived from the ideas of the Meyerowitz and Traas groups on the role of the growth hormone auxin and those of Green and his group on the role compressive stresses can play in plants, we demonstrate how all features of spiral phyllotaxis can be recovered by the passage of a pushed pattern forming front. The front is generated primarily by a PIN1 mediated instability of a uniform auxin concentration and leaves in its wake an auxin fluctuation field at whose maxima new primordia are assumed to be initiated. Because it propagates through a slowly changing metric, the patterns have to make transitions between spirals enumerated by decreasing parastichy numbers. The point configurations of maxima coincide almost exactly with those configurations generated by the use of discrete algorithms based on optimal packing ideas which suggests that pushed pattern forming fronts may be a general mechanism by which natural organisms can follow optimal strategies. We also describe in detail a numerical method that is used to efficiently and accurately integrate the model equations while preserving the variational structure from which they are derived.
Type:
text; Electronic Dissertation
Keywords:
Pattern Formation; Phyllotaxis; Applied Mathematics; Optimal Packing
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Newell, Alan C.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleA Numerical Study of Pattern Forming Fronts in Phyllotaxisen_US
dc.creatorPennybacker, Matthewen_US
dc.contributor.authorPennybacker, Matthewen_US
dc.date.issued2013-
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.abstractUsing a partial differential equation model derived from the ideas of the Meyerowitz and Traas groups on the role of the growth hormone auxin and those of Green and his group on the role compressive stresses can play in plants, we demonstrate how all features of spiral phyllotaxis can be recovered by the passage of a pushed pattern forming front. The front is generated primarily by a PIN1 mediated instability of a uniform auxin concentration and leaves in its wake an auxin fluctuation field at whose maxima new primordia are assumed to be initiated. Because it propagates through a slowly changing metric, the patterns have to make transitions between spirals enumerated by decreasing parastichy numbers. The point configurations of maxima coincide almost exactly with those configurations generated by the use of discrete algorithms based on optimal packing ideas which suggests that pushed pattern forming fronts may be a general mechanism by which natural organisms can follow optimal strategies. We also describe in detail a numerical method that is used to efficiently and accurately integrate the model equations while preserving the variational structure from which they are derived.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectPattern Formationen_US
dc.subjectPhyllotaxisen_US
dc.subjectApplied Mathematicsen_US
dc.subjectOptimal Packingen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorNewell, Alan C.en_US
dc.contributor.committeememberMcLaughlin, Kennethen_US
dc.contributor.committeememberLin, Kevinen_US
dc.contributor.committeememberGlickenstein, Daviden_US
dc.contributor.committeememberNewell, Alan C.en_US
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