Dissertation
Long wave approximations of the Fermi-Pasta-Ulam-Tsingou lattice under planar motion
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2020
DOI:
https://doi.org/10.17918/00001071
Abstract
We study the behavior of a generalized Fermi-Pasta-Ulam-Tsingou lattice with planar motion. This is a homogeneous 1-dimensional mass-spring lattice of infinite length which permits motion in a plane. We derive equations of motion for the lattice operating under several force models and conduct a linear stability analysis for each model. We show that the system is stable under the condition of a taut lattice. We prove rigorous estimates that show that solutions to the system can be approximated by the linear superposition of 2-component, small amplitude, long wavelength counter-propagating wave sets which satisfy a pair of KdV-like Hirota-Satsuma systems.
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Details
- Title
- Long wave approximations of the Fermi-Pasta-Ulam-Tsingou lattice under planar motion
- Creators
- Joshua C. Carmichael
- Contributors
- Jay Douglas Wright (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- vii, 54 pages
- Format
- Dissertation
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 991014695538704721