Date of Award
Master of Science (MS)
College of Science and Mathematics
Thesis Sponsor/Dissertation Chair/Project Chair
Lattice theory, Experimental mathematics
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.
Schwarz, Jeffrey A., "FPU Lattices in Multidimensions" (2015). Theses, Dissertations and Culminating Projects. 603.