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

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.

Thesis (M. Eng.(Mechanical Engineering))--University of Pretoria, 2004. / Includes bibliographical references.

Laplacian differential operator -- Vibrations of plucked strings and Hollow cylinders.

[Truncated abstract] This thesis is split into two parts. In part one; A 50 K dual mode oscillator, the aim of the project was to build a 50 K precision oscillator with frequency stability on the order of 1014 from 1 to 100 seconds. A dual-mode temperature compensation technique was used that relied on a turning point in the frequency-temperature relationship of the difference frequency between two orthogonal whispering gallery modes in a single sapphire crystal. A cylindrical sapphire loaded copper cavity resonator was designed, modelled and built with a turning point in the difference frequency between an E-mode and H-mode pair at approximately 52.5 K . . . The frequencies and Q-factors of whispering spherical modes in the 3-12 GHz range in the fused silica resonator are measured at 6, 77 and 300 K and the Q-factor is used to determine the loss tangent at these temperatures. The frequency and Q-factor temperature dependence of the TM2,1,2 whispering gallery mode at 5.18 GHZ is used to characterise the loss tangent and relative permittivity of the fused silica from 4-300 K. Below 22 K the frequency-temperature dependence of the resonator was found to be consistent with the combined effects of the thermal properties of the dielectric and the influence of an unknown paramagnetic impurity, with a spin resonance frequency at about 138 ± 31 GHz. Below 8 K the loss tangent exhibited a 9th order power law temperature dependence, which may be explained by Raman scattering of Phonons from the paramagnetic impurity ions. A spherical Bragg reflector resonator made from multiple concentric dielectric layers loaded in a spherical cavity that enables confinement of field in the centre of the resonator is described. A set of simultaneous equations is derived that allow the calculation of the required dimensions and resonance frequency for such a resonator and the solution is confirmed using finite element analysis. A spherical Bragg reflector resonator is constructed using Teflon and free-space as the dielectric materials. A Q-factor of 22,000 at 13.87 GHz was measured and found to compare well with the design values.

Piezoelectricity crystal is used in different area in industry, such as downhole oil, gas industry, and ballistics. The piezoelectricity crystals are able to create electric fields due to mechanical deformation called the direct piezoelectric effect, or create mechanical deformation due to the effect of electric field called the indirect piezoelectric effect. In this thesis, piezoelectricity effect is the core part. There are 4 parts in the frequency output pressure transducer: two crystal oscillators, phase-locked loop (PLL), mixer, frequency counter. Crystal oscillator is used to activate the piezoelectricity crystal which is made from quartz. The resonance frequency of the piezoelectricity crystal will be increased with the higher pressure applied. The signal of the resonance frequency will be transmitted to the PLL. The function of the PLL is detect the frequency change in the input signal and makes the output of the PLL has the same frequency and same phase with the input signal. The output of the PLL will be transmitted to a Mixer. The mixer has two inputs and one output. One input signal is from the pressure crystal oscillator and another one is from the reference crystal oscillator. The frequency difference of the two signal will transmitted to the frequency counter from the output of the mixer. Thus, the frequency output pressure transducer with a frequency counter is a portable device which is able to measure the pressure without oscilloscope or computer.

Indiana University-Purdue University Indianapolis (IUPUI) / In order to conform to pollutant-control regulations and minimize NOx emissions, modern household boilers and central heating systems are moving toward premixed combustors. These combustors have been successful with regards to emissions along with efficiency. However, their implementation has been associated with acoustical instability problems that could be solved through precise optimization in design rather than trial and error experimentation. This thesis introduces an experimental apparatus, which is designed to investigate the acoustic instability problem at the flame level. The goal is an experimental determination of the flame transfer function and comparison of the experimental data with a theoretical model of the flame. An experimental procedure is designed to diagnose the origins of the combustion instabilities by measurement of the flame transfer function. This research is carried out in three steps. The first step is to understand the acoustic instability problem through study of the theoretical models of the flame transfer function and selection of a model, which is most functional in industrial applications. A xiii measurement technique for the flame transfer function is developed according to the required accuracy in measurements, repeatability, and configurability for a wide range of operating conditions. Subsequently, an experimental apparatus is designed to accommodate the flame transfer function measurement technique. The components of the acoustic system are carefully sized to achieve precise measurement of the system parameters such as flows, pressures, and acoustic responses, and the apparatus is built. The apparatus is operated to measure the flame transfer function at several operating conditions. The experimentally measured flame transfer function is compared with a theoretical model for further verification. The experimental apparatus provides an improved assessment of the acoustic instability problem for industrial applications.