Open Access
Streeter, Willie
Graduate Program:
Mechanical Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
Committee Members:
  • Alok Sinha, Thesis Advisor
  • eigenvectors
  • nonlinear normal modes
  • eigenvalues
  • localizations
The dynamic behavior of deoxyribonucleic acid (DNA) is investigated with a focus on the localized modes of excitation that may occur in a ring of base pairs. It has been suggested that such modes of motion could be involved in the DNA transcription and replication processes required for all know forms of life. The theoretical model analyzed in this study was made up of 10 identical DNA base pairs. The method employed for this investigation initially required identifying the underlying linear system of a nonlinear mathematical DNA model followed by the calculation of this linear system’s eigenvectors and eigenvalues. These were subsequently used as a basis for finding nonlinear periodic solutions commonly referred to as nonlinear normal modes (NNM). Modes of periodic oscillations were identified by first utilizing low energy eigenvectors as assumptions for initial condition vectors that would lead to NNMs. These initial guess values were then corrected to actual vectors that result in NNMs utilizing a shooting corrector method. Curves representing families of NNMs as a function of a particular low energy eigenvector were then obtained utilizing arclength continuation. Bifurcation branches that emanated from these curves were identified through bifurcation branch switching. Through the implementation of these techniques, modes of localized motion were identified for the 10 base pair ring.