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![Nanopteron-Stegoton Traveling Waves in Mass and Spring Dimer Fermi-Pasta-Ulam-Tsingou Lattices için kapak resmi Nanopteron-Stegoton Traveling Waves in Mass and Spring Dimer Fermi-Pasta-Ulam-Tsingou Lattices için kapak resmi](/client/assets/d79c3e4af2b6d196/ctx/images/no_image.png)
Nanopteron-Stegoton Traveling Waves in Mass and Spring Dimer Fermi-Pasta-Ulam-Tsingou Lattices
Başlık:
Nanopteron-Stegoton Traveling Waves in Mass and Spring Dimer Fermi-Pasta-Ulam-Tsingou Lattices
Yazar:
Faver, Timothy E., author.
ISBN:
9780438129498
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (177 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Doug Wright.
Özet:
We study the existence of traveling waves in mass and spring dimer Fermi-Pasta- Ulam-Tsingou (FPUT) lattices. These are infinite, one-dimensional lattices of particles connected by nonlinear springs, in which either the masses alternate (the mass dimer or diatomic lattice) or the spring forces alternate (the spring dimer). Under the classical "long wave" scaling, the lattice equations of motion turn out to be sin- gularly perturbed. In response to this complication, we apply a method of Beale to produce nanopteron traveling wave solutions with wave speed slightly greater than the lattice's speed of sound. The nanopteron wave profiles are the superposition of an exponentially decaying term (which itself is a small perturbation of a KdV soliton) and a periodic term of very small amplitude.
This dissertation builds on the previous work of Faver and Wright on mass dimer lattices to treat spring dimer lattices. Further generalizing the spring forces from the mass dimer case, we allow the springs' nonlinearity to contain higher order terms be- yond the quadratic. This necessitates the use of composition operators to phrase the long wave problem, and these operators require delicate estimates due to the characteristic superposition of different function types from Beale's ansatz. Additionally, the value of the leading order term in the spring dimer traveling wave profiles alternates between particle sites, so that, unlike in the mass dimer, the spring dimer traveling waves are also "stegotons."
Notlar:
School code: 0065
Konu Başlığı:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(695412.1) | 695412-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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