Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2017
Committee Chair or Co-Chairs
Jeff Knisley
Committee Members
Jeff Knisley, Michele Joyner, Robert Gardner
Abstract
Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic integrators, and often, these techniques are developed for well-understood Hamiltonian systems such as Hill’s lunar equation. In this presentation, we explore how well symplectic techniques developed for well-understood systems (specifically, Hill’s Lunar equation) address discretization errors in MD systems which fail for one or more reasons.
Document Type
Thesis - unrestricted
Recommended Citation
Frazier, William, "Application of Symplectic Integration on a Dynamical System" (2017). Electronic Theses and Dissertations. Paper 3213. https://dc.etsu.edu/etd/3213
Copyright
Copyright by the authors.
Included in
Algebra Commons, Dynamic Systems Commons, Non-linear Dynamics Commons, Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons