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Linear Nearest Neighbor Flocks With All Distinct Agents, Robert G. Lyons
Linear Nearest Neighbor Flocks With All Distinct Agents, Robert G. Lyons
Dissertations and Theses
This dissertation analyzes the global dynamics of 1-dimensional agent arrays with nearest neighbor linear couplings. The equations of motion are second order linear ODE's with constant coefficients. The novel part of this research is that the couplings are different for each agent. We allow the forces to depend on the relative position and relative velocity (damping terms) of the agents, and the coupling magnitudes differ for each agent. Further, we do not assume that the forces are "Newtonian'" (i.e., the force due to A on B equals minus the force of B on A) as this assumption does not apply …
Error Propagation And Algorithmic Design Of Contour Integral Eigensolvers With Applications To Fiber Optics, Benjamin Quanah Parker
Error Propagation And Algorithmic Design Of Contour Integral Eigensolvers With Applications To Fiber Optics, Benjamin Quanah Parker
Dissertations and Theses
In this work, the finite element method and the FEAST eigensolver are used to explore applications in fiber optics. The present interest is in computing eigenfunctions u and propagation constants β satisfing [sic] the Helmholtz equation Δu + k2n2u = β2u. Here, k is the freespace wavenumber and n is a spatially varying coefficient function representing the refractive index of the underlying medium. Such a problem arises when attempting to compute confinement losses in optical fibers that guide laser light. In practice, this requires the computation of functions u referred to as …