In the first part of the dissertation, a novel stochastic averaging technique based on a Hilbert transform definition of the oscillator response displacement amplitude is developed. In comparison to standard stochastic averaging, the requirement of “a priori” determination of an equivalent natural frequency is bypassed, yielding flexibility in the ensuing analysis and potentially higher accuracy. Further, the herein proposed Hilbert transform based stochastic averaging is adapted for determining the time-dependent survival probability and first-passage time probability density function of stochastically excited nonlinear oscillators, even endowed with fractional derivative terms. To this aim, a Galerkin scheme is utilized to solve approximately the backward Kolmogorov partial differential equation governing the survival probability of the oscillator response. Next, the potential of the stochastic averaging technique to be used in conjunction with performance-based engineering design applications is demonstrated by proposing a stochastic version of the widely used incremental dynamic analysis (IDA). Specifically, modeling the excitation as a non-stationary stochastic process possessing an evolutionary power spectrum (EPS), an approximate closed-form expression is derived for the parameterized oscillator response amplitude probability density function (PDF). In this regard, IDA surfaces are determined providing the conditional PDF of the engineering demand parameter (EDP) for a given intensity measure (IM) value. In contrast to the computationally expensive Monte Carlo simulation, the methodology developed herein determines the IDA surfaces at minimal computational cost. In the second part of the dissertation, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear and time-variant oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear sub-systems. Next, a recently developed L1-norm minimization procedure based on compressive sensing theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Several numerical examples are considered for assessing the reliability of the technique, even in the presence of incomplete and corrupted data. These include a 2-DOF time-variant Duffing oscillator endowed with fractional derivative terms, as well as a 2-DOF system subject to flow-induced forces where the non-stationary sea state possesses a recently proposed evolutionary version of the JONSWAP spectrum. In the third part of this dissertation, a joint time-frequency analysis technique based on generalized harmonic wavelets (GHWs) is developed for dynamic cerebral autoregulation (DCA) performance quantification. DCA is the continuous counter-regulation of the cerebral blood flow by the active response of cerebral blood vessels to the spontaneous or induced blood pressure fluctuations. Specifically, various metrics of the phase shift and magnitude of appropriately defined GHW-based transfer functions are determined based on data points over the joint time-frequency domain. The potential of these metrics to be used as a diagnostics tool for indicating healthy versus impaired DCA function is assessed by considering both healthy individuals and patients with unilateral carotid artery stenosis. Next, another application in biomedical engineering is pursued related to the Pulse Wave Imaging (PWI) technique. This relies on ultrasonic signals for capturing the propagation of pressure pulses along the carotid artery, and eventually for prognosis of focal vascular diseases (e.g., atherosclerosis and abdominal aortic aneurysm). However, to obtain a high spatio-temporal resolution the data are acquired at a high rate, in the order of kilohertz, yielding large datasets. To address this challenge, an efficient data compression technique is developed based on the multiresolution wavelet decomposition scheme, which exploits the high correlation of adjacent RF-frames generated by the PWI technique. Further, a sparse matrix decomposition is proposed as an efficient way to identify the boundaries of the arterial wall in the PWI technique.

The concern of this thesis was to investigate the nonlinear dynamics inherent in oscillating waterfalls.

Computational fluid dynamics (CFD) analysis was performed in order to compare the solutions of oscillating wings with Prandtl’s lifting-line theory. Quasi-steady and steady-periodic simulations were completed using the CFD software Star-CCM+. The simulations were performed for a number of frequencies in a pure plunging setup. Additional simulations were then completed using a setup of combined pitching and plunging at multiple frequencies. Results from the CFD simulations were compared to the quasi-steady lifting-line solution in the form of the axial-force, normal-force, power, and thrust coefficients, as well as the efficiency obtained for each simulation. The mean values were evaluated for each simulation and compared to the quasi-steady lifting-line solution. It was found that as the frequency of oscillation increased, the quasi-steady lifting-line solution was decreasingly accurate in predicting solutions.

In single phase, steady, turbulent axisymmetric jets, the time-averaged velocity field can be characterised by the decay in centreline velocity and increased spread with increasing distance from the jet orifice. In a two-phase or ‘particle-laden’ jet, the particles will modulate the jet turbulence and exchange momentum with the gas phase. Consequently, these effects reduce both the centreline velocity decay and spreading rates with respect to the single-phase jet. Empirical exponential scaling factors were found by previous authors to describe the reduced centreline decay and spreading rates well for low Stokes numbers. In this thesis, power-law scaling factors are found to scale well a wide range of centreline velocity decay and spreading rate data published over the past 40 years, for a wide range of Stokes numbers. The power-law scaling is composed of three different regimes. For low Stokes numbers St₀ ≲20, it is found that the gas phase centreline velocity, u₀/uc collapses if plotted as a function of x/D(1 + Ø₀)⁻¹, and the velocity profile half widths r₁/ ₂ collapse if plotted as a function of x/D(1+Ø₀)⁻¹. Here, u₀ is the exit velocity, Ø₀ is the exit mass loading, x is the axial coordinate and D is the pipe diameter. For intermediate Stokes numbers, u₀/uc collapses if plotted as a function of x/D(1 + Ø₀)⁻¹ and r₁/ ₂ collapses if plotted as a function of x/D(1 + Ø₀)⁻¹/². For high Stokes numbers St₀ ≳ 200, u₀/uc collapses if plotted as a function of x/D(1 + Ø₀)⁻¹/² and the half width is approximately independent of Ø₀. In addition to the velocity of the gas phase, other aspects of particle- laden jets are found to be amenable to scaling by power-law functions. It is found that reported solid phase mass flux data scales similarly to gas phase measurements. Limited solid phase concentration and entrainment measurements reported in the literature are also found to scale by power-law functions. Whereas that limited data was obtained from the literature, measurements of the distribution of particles in particle-laden jets were conducted to further assess the validity of the scaling regimes to the solid phase. A planar light scattering technique is conducted to measure the distribution of particles in an axisymmetric jet and their subsequent scaling (or lack thereof) are reported for a variation in Ø₀, Stokes number and gas phase jet exit density. For Stokes numbers based on the pipe friction velocity St* ₀ ∼ 1, half widths of particle distributions were found to scale with x/D(1+Ø₀)⁻¹/² . The apparent centreline concentration was found to be independent of Ø₀ at this same St* ₀ . For Stokes numbers based on the pipe friction velocity St*₀ < 1, half widths are independent of Ø₀. The effect of the other parameters, i.e. Stokes number and density ratio, on centreline distributions and half widths are also investigated. Measurements of particle distributions, delivered via an annular channel, in a triangular oscillating jet (OJ) flow are also reported for a variation in momentum ratio, the ratio of OJ momentum to channel momentum and mass loading. The results of the variation in momentum ratio on particle distributions are compared with an existing precessing jet (PJ) study. It is the aim of this study to determine the experimental conditions for which the OJ nozzle is superior to the PJ nozzle. The use of an OJ nozzle is preferable at an industrial scale by virtue of its lower driving pressure compared with a PJ nozzle. It is found that particle distributions in a PJ flow spread at a greater rate with increasing momentum ratio compared with the spread of particles in an OJ flow. However, at momentum ratios approximately less than unity, the absolute spread from an OJ is greater. This also corresponds to nozzle driving pressure less than approximately 10kPA. For an increase in mass loading, the spread of particle distribution in the OJ decreases and recirculation increases. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1337352 / Thesis (M.Eng.Sc.) -- University of Adelaide, School of Mechanical Engineering, 2008

In single phase, steady, turbulent axisymmetric jets, the time-averaged velocity field can be characterised by the decay in centreline velocity and increased spread with increasing distance from the jet orifice. In a two-phase or ‘particle-laden’ jet, the particles will modulate the jet turbulence and exchange momentum with the gas phase. Consequently, these effects reduce both the centreline velocity decay and spreading rates with respect to the single-phase jet. Empirical exponential scaling factors were found by previous authors to describe the reduced centreline decay and spreading rates well for low Stokes numbers. In this thesis, power-law scaling factors are found to scale well a wide range of centreline velocity decay and spreading rate data published over the past 40 years, for a wide range of Stokes numbers. The power-law scaling is composed of three different regimes. For low Stokes numbers St₀ ≲20, it is found that the gas phase centreline velocity, u₀/uc collapses if plotted as a function of x/D(1 + Ø₀)⁻¹, and the velocity profile half widths r₁/ ₂ collapse if plotted as a function of x/D(1+Ø₀)⁻¹. Here, u₀ is the exit velocity, Ø₀ is the exit mass loading, x is the axial coordinate and D is the pipe diameter. For intermediate Stokes numbers, u₀/uc collapses if plotted as a function of x/D(1 + Ø₀)⁻¹ and r₁/ ₂ collapses if plotted as a function of x/D(1 + Ø₀)⁻¹/². For high Stokes numbers St₀ ≳ 200, u₀/uc collapses if plotted as a function of x/D(1 + Ø₀)⁻¹/² and the half width is approximately independent of Ø₀. In addition to the velocity of the gas phase, other aspects of particle- laden jets are found to be amenable to scaling by power-law functions. It is found that reported solid phase mass flux data scales similarly to gas phase measurements. Limited solid phase concentration and entrainment measurements reported in the literature are also found to scale by power-law functions. Whereas that limited data was obtained from the literature, measurements of the distribution of particles in particle-laden jets were conducted to further assess the validity of the scaling regimes to the solid phase. A planar light scattering technique is conducted to measure the distribution of particles in an axisymmetric jet and their subsequent scaling (or lack thereof) are reported for a variation in Ø₀, Stokes number and gas phase jet exit density. For Stokes numbers based on the pipe friction velocity St* ₀ ∼ 1, half widths of particle distributions were found to scale with x/D(1+Ø₀)⁻¹/² . The apparent centreline concentration was found to be independent of Ø₀ at this same St* ₀ . For Stokes numbers based on the pipe friction velocity St*₀ < 1, half widths are independent of Ø₀. The effect of the other parameters, i.e. Stokes number and density ratio, on centreline distributions and half widths are also investigated. Measurements of particle distributions, delivered via an annular channel, in a triangular oscillating jet (OJ) flow are also reported for a variation in momentum ratio, the ratio of OJ momentum to channel momentum and mass loading. The results of the variation in momentum ratio on particle distributions are compared with an existing precessing jet (PJ) study. It is the aim of this study to determine the experimental conditions for which the OJ nozzle is superior to the PJ nozzle. The use of an OJ nozzle is preferable at an industrial scale by virtue of its lower driving pressure compared with a PJ nozzle. It is found that particle distributions in a PJ flow spread at a greater rate with increasing momentum ratio compared with the spread of particles in an OJ flow. However, at momentum ratios approximately less than unity, the absolute spread from an OJ is greater. This also corresponds to nozzle driving pressure less than approximately 10kPA. For an increase in mass loading, the spread of particle distribution in the OJ decreases and recirculation increases. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1337352 / Thesis (M.Eng.Sc.) -- University of Adelaide, School of Mechanical Engineering, 2008

When an intense femtosecond laser pulse propagates in a gas, it undergoes filamentation, a spectacular process where the pulse spatial, spectral and temporal characteristics change considerably. A thin short-lived plasma column is formed in the wake of the propagating pulse. My PhD work has been dedicated to the further understanding of the filamentation process. In a first part, I compare the properties of a usual filament with those of a filament formed by a femtosecond laser pulse with a Bessel beam profile. Using a laser pulse of same intensity and duration, I show that a Bessel beam can form a longer and more uniform plasma column in air, but that the plasma density is significantly lower. In a second part, I show that it is possible to increase considerably the lifetime of the plasma column, using a dual femtosecond/nanosecond laser pulse technique. To obtain an increased lifetime over a significant segment of a plasma column, I rely on the properties of Bessel beams in the nonlinear regime developed in the first chapter. In a third part, I study the dynamics of free electrons that are produced in the filamentation process. To do this, I have developed a specially designed current probe. Experiments reveal a very rich behaviour. The longitudinal displacements of electrons in the plasma column depend sensitively on the nature of the gas and its pressure as well as on the laser polarization of the laser. I propose a model to explain this behaviour. The direction of electron flow results from the competition between pure laser forces and a Coulomb wake field force. In the last chapter, I study filamentation in a Helium gas. This required improving the laser characteristics in order to reach the necessary power for filamentation. Improved characteristics have been achieved by implementing a planar compression stage which shortened the laser pulse from 50 fs to 10 fs without appreciable energy loss. The first experimental evidence for filamentation in He is presented at the end of the thesis. Agreement is found with a numerical simulation.

<p>The running of gas turbines with low emissions causes high pressure pulsations to arise in the combustion chamber. These pulsations are high amplitude sound vibrations. At some frequencies these are harmful to the gas turbine. Hence these pulsations are monitored to avoid operating conditions where pulsations are specifically harmful. It is necessary to expose the system of known pulsations to verify the functionality of the monitoring process. </p><p>This report describes the development of a generator of pressure pulsations to verify the monitoring system. The output should be of harmonic form with a frequency of greater than 160 Hz and 15 mbar in amplitude. To begin with, a few alternatives to a pulsation generator are described. In light of studies of these possibilities the alternative based on a roller bearing is selected. This is considered as one of the easier alternatives to design. </p><p>An existing generator of pressure pulsations has been analyzed. The calculations from this analysis supported the construction of the new device. The new generator far exceeded the specification regarding frequency, amplitude and harmonics of the pulsations. With a few modifications, such as encapsulation, the pulsation generator will be ready for usage. It could then serve as a mobile device for the inspection of the pulsation monitoring system. Possibly the device could be equipped with a faster and stronger motor. This would permit the device to be used for the calibration of pulsation monitoring sensors.</p>

Self-oscillating reactions have been widely observed and studied since the last century because they exhibit unique behaviors different from the traditional chemical reactions. Self-oscillating systems, such as the Belousov-Zhabotinsky (BZ) reaction, oxidation reaction of CO on single crystal Pt, and calcium waves in the heart tissue, are of great interest in a variety of scientific areas. This thesis contributes to the understanding of wave transition in BZ reaction, and to possible applications of non-equilibrium behaviors of polymer systems. In BZ reaction, two types of wave patterns, target and spiral, are frequently observed. The transition from one to another is not fully understood. Hence, a systematic investigation has been performed here to investigate the mechanism by which heterogeneity affects the formation of wave patterns. A BZ reaction catalyst was immobilized in ion exchange polystyrene beads to form active beads. Then active and inactive beads with no catalyst loading were mixed together with various ratios to achieve various levels of heterogeneity. In the same reaction environment, different wave patterns were displayed for the bead mixtures. We observed a transition from target patterns to spiral patterns as the percentage of the active beads in the beads mixture decreased. The increase of the heterogeneity led to wave pattern transition. Heterogeneity hindered the propagation of target waves and broke them into wavelets that generated spiral waves. In an effort to develop practical applications based on non-equilibrium phenomena, we have established a novel drug delivery system. A proton generator Zirconium Phosphate (ZrP) was imbedded inside a pH sensitive polymer matrix, poly acrylic acid (PAA). Through the ion exchange with sodium cation (Na+), ZrP generates protons to control the swelling/shrinking behaviors of PAA. The drug encapsulated in the matrix can be released in a controlled manner by adjusting the supply of Na+. This system might be developed into vehicles to deliver drugs to specific targets and release at a proper time. This new delivery technique will be convenient and significantly increase the efficiency of medicines.

The thesis is devoted to the study of spontaneous synchronization of coupled nonlinear oscillators. It consists of two major parts. The first describes synchronization of Josephson junctions embedded in a transmission line. I consider in detail a new phenomenon ??eation of inert oscillator pairs ??ich was observed in analytical studies. The second part of the thesis describes synchronization of an array of single mode fiber lasers, with special interest in the phenomenon of synchronization of subsets of fiber lasers in a two dimensional array through a specific arrangement of the under-pumped lasers.

An interest in vehicle efficiency improvement drives a need for research in the field of light metal alloys. Current industrially-available technologies do not include warm-forming of metal alloy sheet materials. The obstacles to the technology may be potentially overcome with granular media, which could be used as an alternative force transfer medium. However, some granular material properties like force chain formation require further investigation before forming technology using granular media may be developed. Throughout the course of this study, a direct shear cell instrument was designed and fabricated. This instrument was used to measure the basic mechanical properties of granular media. A 3D CAD model of the direct shear cell instrument and operating procedures are presented in this study. Different granular materials, such as steel bearing balls and sand, were tested under conditions simulating granular media flow behavior expected for the working medium in warm-forming of metal alloys sheet materials. The experiments were conducted under both static and oscillating normal loads. The static load experiments were conducted for various normal loads and shear rates, and oscillating normal load experiments were conducted under various oscillation frequencies, average normal loads and load amplitudes. During dense-packed spherical granular media flow experiments, shear stress oscillations were observed. These are attributed to the force-chain jamming behavior occurring within the granular media structure. It was also observed that granular media flow properties can be controlled by an oscillating normal load applied to the granular media. From the experimental and simulation studies it may be concluded that normal load oscillations should enhance granular media flow, which could be a great advantage for using granular media as working fluid for sheet metal forming. / text