Using phase-space localized basis functions to obtain vibrational energies of molecules

For decades scientists have attempted to use ideas of classical mechanics to choose basis functions for calculating spectra. The hope is that a classically-motivated basis set will be small because it covers only the dynamically important part of phase space. One popular idea is to use phase space localized (PSL) basis functions. This thesis improves on previous efforts to use PSL functions and examines the usefulness of these improvements. Because the overlap matrix, in the matrix eigenvalue problem obtained by using PSL functions with the variational method, is not an identity, it is costly to use iterative methods to solve the matrix eigenvalue problem. We show that it is possible to circumvent the orthogonality (overlap) problem and use iterative eigensolvers. We also present an altered method of calculating the matrix elements that improves the performance of the PSL basis functions, and also a new method which more efficiently chooses which PSL functions to include. These improvements are applied to a variety of single well molecules. We conclude that for single minimum molecules, the PSL functions are inferior to other basis functions. However, the ideas developed here can be applied to other types of basis functions, and PSL functions may be useful for multi-well systems.

Vibrational Feedback Training System for Use with SEMG Controlled Powered Prostheses

Loss of limb results in loss of function and a partial loss of freedom. A powered prosthetic device can partially assist an individual with everyday tasks and therefore return some level of independence. Powered upper limb prostheses are often controlled by the user generating surface electromyographic (SEMG) signals. The goal of this thesis is to develop a virtual environment in which a user can control a virtual hand to safely grasp representations of everyday objects using EMG signals from his/her forearm muscles, and experience visual and vibrotactile feedback relevant to the grasping force in the process. This can then be used to train potential wearers of real EMG controlled prostheses, with or without vibrotactile feedback. To test this system an experiment was designed and executed involving ten subjects, twelve objects, and three feedback conditions. The tested feedback conditions were visual, vibrotactile, and both visual and vibrotactile. In each experimental exercise the subject attempted to grasp a virtual object on the screen using the virtual hand controlled by EMG electrodes placed on his/her forearm. Two metrics were used: score, and time to task completion, where score measured grasp dexterity. It was hypothesized that with the introduction of vibrotactile feedback, dexterity, and therefore score, would improve and time to task completion would decrease. Results showed that time to task completion increased, and score did not improve with vibrotactile feedback. Details on the developed system, the experiment, and the results are presented in this thesis.