The critical conduction mode (CRM) power factor correction converters (PFC) are widely used in industry for low power offline switching mode power supplies. For the CRM PFC, the main advantage is to reduce turn-on loss of the main switch. However, the large inductor current ripple in CRM PFC creates huge DM EMI noise, which requires a big EMI filter. The switching frequency of the CRM PFC is variable in half line cycle which makes the EMI characteristics of the CRM PFC are not clear and have not been carefully investigated. The worst case of the EMI noise, which is the baseline to design the EMI filter, is difficult to be identified. In this paper, an approximate mathematical EMI noise model based on the investigation of the principle of the quasi-peak detection is proposed to predict the DM EMI noise of the CRM PFC. The developed prediction method is verified by measurement results and the predicted DM EMI noise is good to evaluate the EMI performance. Based on the noise prediction, the worst case analysis of the DM EMI noise in the CRM PFC is applied and the worst case can be found at some line and load condition, which will be a great help to the EMI filter design and meanwhile leave an opportunity for the optimization of the whole converter design. What is more, the worst case analysis can be extended to 2-channel interleaved CRM PFC and some interesting characteristics can be observed. For example, the great EMI performance improvement through ripple current cancellation in traditional constant frequency PFC by using interleaving techniques will not directly apply to the CRM PFC due to its variable switching frequency. More research needs to be done to abstract some design criteria for the boost inductor and EMI filter in the interleaved CRM PFC. / Master of Science

Modelling of volcanic ashfall has been attempted by volcanologists but very little work has been done by mathematicians. In this thesis we show that mathematical models can accurately describe the distribution of particulate materials that fall to the ground following an eruption. We also report on the development and analysis of mathematical models to calculate the ash concentration in the atmosphere during ashfall after eruptions. Some of these models have analytical solutions. The mathematical models reported on in this thesis not only describe the distribution of ashfall on the ground but are also able to take into account the effect of variation of wind direction with elevation. In order to model the complexity of the atmospheric flow, the atmosphere is divided into horizontal layers. Each layer moves steadily and parallel to the ground: the wind velocity components, particle settling speed and dispersion coefficients are assumed constant within each layer but may differ from layer to layer. This allows for elevation-dependent wind and turbulence profiles, as well as changing particle settling speeds, the last allowing the effects of the agglomeration of particles to be taken into account.