Graduation Year

2015

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Andrew Bernoff

Reader 2

Rob Thompson

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Terms of Use for work posted in Scholarship@Claremont.

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© 2015 Ksenia V Zakirova

Abstract

Chain dynamics have gained renewed interest recently, following the release of a viral YouTube video showcasing a phenomenon called the chain fountain. Recent work in the field shows that there exists unexplained behavior in newly proposed chain systems. We consider a general system of a chain traveling at constant velocity in an external force field and derive steady state solutions for the time invariant shape of the chain. Perturbing the solution introduces moving waves along the steady state shape with components that propagate along and against the direction of travel of the chain. Furthermore, we develop a numerical model using a discrete approximation of the chain in order to empirically test our results. The behavior of the chain fountain and related chain systems is discussed in the context of these findings.

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