Unsteady large-scale vortices, formed by the roll-up of free shear layers separating along sharp edges, are the dominant flow characteristics of the turbulent flow over buildings. These vortical structures interact with each other and with the building surface resulting in secondary separation and severe pressure fluctuations. Moreover, the interaction of the large-scale vortices with the multiplicity of turbulence scales in the incoming wind exacerbates their unsteady motion and hence significantly affects the pressure fluctuations spectra experienced by the building. Large-eddy simulations are conducted to study the interaction of homogeneous turbulence in the incident flow with a surface-mounted prism. A compact fifth-order upwind difference scheme is used to effectively and accurately perform the simulations. Three cases of incident flow are considered. In one case, the prism is placed in a smooth uniform flow. In the second case, homogeneous isotropic turbulence with von Karman spectrum is superimposed on the uniform flow at the inflow boundary. The integral length scale is one-half the prism height. In the third case, the integral length scale is equal to the prism height. The numerical results are compared with experimental measurements reported by Tieleman et al. (2002). The results show that the highest negative mean value of the pressure coefficient on the roof and the sides is about 30% larger in case two of turbulent inflow and takes place closer to the windward edge of the prism. Moreover, the pressure coefficients on the roof and sides of the prism in the case of turbulent inflow show a higher level of variations in comparison with the case of smooth inflow conditions. The predicted mean characteristics of the pressure coefficients in the turbulent case match the experimental values in terms of both magnitude and location on the roof of the prism reported in Tieleman et al. (1998) and Tieleman et al. (2002). As for the peak value, the peak value of -2 obtained in the turbulent inflow case two is about 20% smaller than the values measured experimentally by Tieleman et al. (2002). On the other hand, it is stressed that the peak value in the simulations would increase as the duration of the simulation is increased to match that of the experimental measurement. The results also show that the turbulent case yields a non-exceedence probability for the peak pressure coefficient that is closer to the one obtained from the measured data than the smooth case data. Also, spectral and cross-spectral analysis are carried out using complex Morlet wavelet transform to investigate pressure-velocity relation. The study shows that the nonlinearity in the relationship of velocity-pressure is detected using wavelet bicoherence. / Ph. D.

The ultrasonic NDE technique to characterize the ultrasonic nonlinear response of the cyclically load 7075-T6 aluminum is described in this thesis. In order to estimate the nonlinear relation of the ultrasonic waves due to material fatigue damage or degradation, the spectral analysis techniques such as the power spectrum, bispectrum, and bicoherence spectrum are applied. The ultrasonic nonlinearity parameters by Cantrell and Jhang are introduced and presented as a function of the material fatigue growth, the number of fatigue cycles. This thesis presents the effectiveness of the bispectral analysis for evaluating the nonlinear aspects of the ultrasonic wave propagation. The results show that the nonlinearity parameters by Cantrell and Jhang are responsive to the output amplitude of the received signal and vary for the various materials, and independent of the input frequency and the ultrasonic wave propagation distance. By using the bispectral analysis tools, particularly the bicoherence spectrum, the increase of the coupling levels between the fundamental, its harmonic, and subharmonic frequency components is presented as the number of fatigue cycles is increased. This thesis suggests that the application of the bicoherence spectrum based on the nonlinear wave coupling relations be more effective for estimating the level of the material fatigue life. / Master of Science

Atrial fibrillation (AF) is a troublesome disease often overlooked by more serious myocardial infarctions. Up until now, there has been very little or no use of high order spectral techniques in order to evaluate the organization of the atrium during AF. Cross-bicoherence algorithm can be used alongside a surrogate data threshold in order to determine significant phase coupling interactions, giving rise to an organizational metric. This proposed algorithm is used to show rotigaptide, a gap junction coupling drug, significantly increases the organization of the atria during episodes of AF due to improvement of cell-to-cell coupling.

Higher-order spectral analysis of acoustical waveforms can provide phase information that is not retained in calculations of power spectral density. In the propagation of high intensity sound, nonlinearity can cause substantial changes in the waveform as frequency components interact with one another. The bispectrum, which is one order higher than power spectral density, may provide a useful measure of nonlinearity in propagation by highlighting spectral regions of interaction. This thesis provides a review of the bispectrum, places it in the context of nonlinear acoustic propagation, and presents spectra calculated as a function of distance for numerically propagated acoustic waveforms. The calculated spectra include power spectral density, quad-spectral density, bispectrum, spatial derivative of the bispectrum, bicoherence, and skewness function. / text

In this work, I will describe a new statistical tool: the canonical bicoherence, which is a combination of the canonical coherence and the bicoherence. I will provide its definitions, properties, estimation by multitaper methods and statistics, and estimate the variance of the estimates by the weighted jackknife method. I will discuss its applicability and usefulness in nonlinear quadratic phase coupling detection and analysis for multivariate random processes. Furthermore, I will develop the time-varying canonical bicoherence for the nonlinear analysis of non-stationary random processes. In this thesis, the canonical bicoherence is mainly applied in two types of data: a) three-component geomagnetic field data, and b) high-dimensional brain electroencephalogram data. Both results obtained will be linked with physical or physiological interpretations. In particular, this thesis is the first work where the novel method of ``canonical bicoherence'' is introduced and applied to the nonlinear quadratic phase coupling detection and analysis for multivariate random processes. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2008-10-31 15:03:57.596