Parametric excitation can occur when the value of a parameter of an oscillator is modulated at twice the natural frequency of the oscillator. The response grows exponentially and is only limited by a nonlinearity of the system, so large response amplitudes typically occur. However, there is no response unless the parametric drive amplitude is above a threshold value that is dictated by the damping. We investigate parametric excitation in three physical systems. The first involves an acoustic standing wave in a pipe that is driven by a piston at one end. An analysis shows that parametric excitation is not feasible in this system unless one uses a very large-excursion piston (for example, from an aircraft engine). The second system is an inductor-capacitor circuit which can undergo oscillations of the current. An analysis of capacitance modulation with a bank of alternate rotating and stationary parallel plates shows that parametric excitation would be very difficult to achieve. Finally, we describe the construction of a torsional oscillator whose length is modulated. Parametric excitation is successfully demonstrated in this system. A comparison of data to predictions of the standard theory of parametric excitation reveals significant deviations.

Thesis (M.S. in Applied Physics)--Naval Postgraduate School, June 2002. / Thesis advisor(s): Bruce Denardo, Andres Larraza. Includes bibliographical references (p. 55). Also available online.

Thesis (M.S. in Engineering Acoustics)--Naval Postgraduate School, June 2005. / Thesis Advisor(s): Includes bibliographical references (p. 59). Also available online.

Vita. / Digitized by Kansas Correctional Industries

This thesis pertains to the uses of functional data analysis and nonlinear mixed-effects model with applications to PET data. In the first part of this dissertation, we consider a permutation-based inference for function-on-scalar regression. While PET imaging data analysis is most commonly performed on data that are aggregated into several discrete a priori regions of interest, our primary interest is on measures of 5-HTT binding potential that are made at many locations along a continuous anatomically defined tract, one that was chosen to follow serotonergic axons. Our goal is to characterize the binding patterns along this tract, determine how such patterns differ between diagnostic groups, and also to investigate the question of homogeneity. We utilize function-on-scalar regression modeling to make optimal use of our data and inference is made using permutation testing strategies that do not require distributional assumptions. Simulations are conducted to examine the validity of our methods and compare the performance of competing methods. We illustrate this approach by applying it to PET data. In the second part of this dissertation, we introduce shape-based distance metrics for comparison of IRFs. The common practice involves summarizing the estimated IRF using a single scalar measure, such as VT, and comparing it across subjects/groups using standard univariate analyses. However, this approach neglects the nature and structure of the IRFs and overlooks their shapes. We propose a k-nearest-neighbor ensemble approach that optimally combines distance metrics based on principles of functional data analysis and shape data analysis. Simulations are conducted to compare the predictive performance of our approach to the traditional approach of using VT. We illustrate this approach by applying it to PET data. In the third part of this dissertation, we discuss the a nonlinear mixed-effects modeling approach for PET data analysis under the assumption of a simplified reference tissue model. The conventional two-stage approach uses NLS estimates of the population parameters, although statistically valid, it is possible to allow for more complex models that consider all subjects simultaneously. We propose a nonlinear mixed-effects (NLME) model that can estimate not only the individual-level parameters, but also the effects of covariates on the parameters. In this way, estimation of kinetic parameters and statistical inference can be performed simultaneously. Simulations are conducted to compare the power for detection of group differences and population- and individual-level parameter estimation for both NLS and NLME models. We apply our NLME approach to PET data to illustrate the modeling procedure.