Date of Award

1-2015

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

David Trubatch

Committee Member

Bogdan Nita

Committee Member

Ashwin Vaidya

Subject(s)

Lattice theory, Experimental mathematics

Abstract

In a 1955 paper, Enrico Fermi, John Pasta, and Stanislaw Ulam studied a one dimensional, nonlinear dynamical system on an early electronic computer. They were surprised to see the system’s original energy configuration recur. The experiment, which has since become known as the “FPU Problem”, initiated the field of experimental mathematics, is at the origin of the soliton concept and chaos theory, has sparked revolutions in modem science, and called into question the equipartition hypothesis.

The FPU experiment still has many open questions, not the least of which is an explanation for the recurrence.

In this work, we compare the FPU chain to similar two-dimensional FPU lattices. We did not find original energy configuration recurrence in any of the two dimensional systems we studied, but we note that the systems also did not reach equipartition. Our observations were limited due to accuracy issues with the integrator for some of our systems. We also observed that large, 1024 mass one-dimensional FPU systems acted nearly identical to linear systems.

File Format

PDF

Included in

Mathematics Commons

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