Document Type

Thesis

Date of Degree Completion

Winter 2014

Degree Name

Master of Science (MS)

Department

Computational Science

Committee Chair

Filip Jagodzinski

Second Committee Member

James Bisgard

Third Committee Member

Aaron Montgomery

Abstract

There are many equations in the applied sciences whose solutions correspond to critical points of a function describing specific phenomenon. For example, molecules have a unique potential energy, and one stable conformation of a molecule can be thought of as a low point on a potential energy surface. Finding the mountain pass point between two confirmations of a molecule is analogous to finding the energy of a biological structure that is an intermediate conformation between two stable states. Mathematicians have developed theorems and abstract techniques to find these mountain pass points. However, using such approaches is often difficult, especially because a specific technique is often tailor-made for a specific application domain. Therefore, it is not possible to port the approach from one application domain to another. This thesis investigates approximating mountain passes using a computer algorithm implemented in Mathematica. This research gives insight on how to find mountain pass critical points in the general sense. An implementation is presented and the efficiency of this mountain pass approximation algorithm is investigated.

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