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Spectral Analysis Of Complex Dynamical Systems, Casey Lynn Johnson
Spectral Analysis Of Complex Dynamical Systems, Casey Lynn Johnson
CGU Theses & Dissertations
The spectrum of any differential equation or a system of differential equations is related to several important properties about the problem and its subsequent solution. So much information is held within the spectrum of a problem that there is an entire field devoted to it; spectral analysis. In this thesis, we perform spectral analysis on two separate complex dynamical systems. The vibrations along a continuous string or a string with beads on it are the governed by the continuous or discrete wave equation. We derive a small-vibrations model for multi-connected continuous strings that lie in a plane. We show that …
High Order Explicit Semi-Lagrangian Method For The Solution Of Lagrangian Transport And Stochastic Differential Equations, Hareshram Natarajan
High Order Explicit Semi-Lagrangian Method For The Solution Of Lagrangian Transport And Stochastic Differential Equations, Hareshram Natarajan
CGU Theses & Dissertations
A semi-Lagrangian method is developed for the solution of Lagrangian transport equations and stochastic differential equations that is consistent with Discontinuous Spectral Element Method (DSEM) approximations of Eulerian conservation laws. The method extends the favorable properties of DSEM that include its high-order accuracy, its local and boundary fitted properties and its high performance on parallel platforms for the concurrent semi-Lagrangian and Eulerian solution of a class of time-dependent problems that can be described by coupled Eulerian-Lagrangian formulations. Such formulations include the probabilistic models used for the simulation of chemically reacting turbulent flows or particle-laden flows. Motivated by the high-fidelity simulation …