Perversions and whips: Static and dynamic problems of elastic filaments

Persistent Link:
http://hdl.handle.net/10150/280309
Title:
Perversions and whips: Static and dynamic problems of elastic filaments
Author:
McMillen, Tyler K.
Issue Date:
2003
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:
Two problems of elastic filaments are considered, one a problem of determining the static shape of a filament with intrinsic curvature tinder constant force, and one a problem of determining the dynamical behavior of a planar rod. In the first problem, examining the phenomenon of perversion, methods of dynamical systems are used to examine the static equations of elastic filaments, in which the arc-length of the filament plays the role of time. The phenomenon of perversion, in which two oppositely handed helices are connected by an inversion of chirality, is represented by a heteroclinic orbit of the dynamical system. The second problem is an examination of a whip wave, the propagation of a loop in a whip as it travels the length of the whip to create a sharp crack as the loop reaches the end of the rod and accelerates to supersonic speeds. This study is undertaken in two stages: first we examine the propagation of the loop as it travels down the rod far from the end of the rod, and then we examine the behavior of the rod as the loop reaches the end of the rod and unfolds, accelerating the tip. In the first stage we use techniques of asymptotic analysis and perturbation methods to determine the relationship of the speed of the loop to the radius of the rod. In the second stage we employ a numerical technique to compute the behavior of the loop as it unfolds to determine the relationship of the maximal speed of the tip of the rod to the characteristics of the rod and the forces applied to the handle.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Goriely, Alain

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titlePerversions and whips: Static and dynamic problems of elastic filamentsen_US
dc.creatorMcMillen, Tyler K.en_US
dc.contributor.authorMcMillen, Tyler K.en_US
dc.date.issued2003en_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.abstractTwo problems of elastic filaments are considered, one a problem of determining the static shape of a filament with intrinsic curvature tinder constant force, and one a problem of determining the dynamical behavior of a planar rod. In the first problem, examining the phenomenon of perversion, methods of dynamical systems are used to examine the static equations of elastic filaments, in which the arc-length of the filament plays the role of time. The phenomenon of perversion, in which two oppositely handed helices are connected by an inversion of chirality, is represented by a heteroclinic orbit of the dynamical system. The second problem is an examination of a whip wave, the propagation of a loop in a whip as it travels the length of the whip to create a sharp crack as the loop reaches the end of the rod and accelerates to supersonic speeds. This study is undertaken in two stages: first we examine the propagation of the loop as it travels down the rod far from the end of the rod, and then we examine the behavior of the rod as the loop reaches the end of the rod and unfolds, accelerating the tip. In the first stage we use techniques of asymptotic analysis and perturbation methods to determine the relationship of the speed of the loop to the radius of the rod. In the second stage we employ a numerical technique to compute the behavior of the loop as it unfolds to determine the relationship of the maximal speed of the tip of the rod to the characteristics of the rod and the forces applied to the handle.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_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.advisorGoriely, Alainen_US
dc.identifier.proquest3089989en_US
dc.identifier.bibrecord.b44425107en_US
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