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The Effects Of Viscous Damping On Rogue Wave Formation And Permanent Downshift In The Nonlinear Schrödinger Equation, Evelyn Smith
The Effects Of Viscous Damping On Rogue Wave Formation And Permanent Downshift In The Nonlinear Schrödinger Equation, Evelyn Smith
Honors Undergraduate Theses
This thesis investigates the effect of viscous damping on rogue wave formation and permanent downshift using the higher-order nonlinear Schrödinger equation (HONLS). The strength of viscous damping is varied and compared to experiments with only linear damped HONLS.
Stability analysis of the linear damped HONLS equation shows that instability stabilizes over time. This analysis also provides an instability criterion in the case of HONLS with viscous damping.
Numerical experiments are conducted in the two unstable mode regime using perturbations of the Stokes wave as initial data. With only linear damping permanent downshift is not observed and rogue wave formation is …
Multicolor Ramsey And List Ramsey Numbers For Double Stars, Jake Ruotolo
Multicolor Ramsey And List Ramsey Numbers For Double Stars, Jake Ruotolo
Honors Undergraduate Theses
The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. For a graph H, the k-color Ramsey number r(H; k) of H is the smallest integer n such that every k-edge-coloring of Kn contains a monochromatic copy of H. Despite active research for decades, very little is known about Ramsey numbers of graphs. This is especially true for r(H; k) when k is at least 3, also known as the multicolor Ramsey number of …