3 resultados para Fractional Laplacian

em CORA - Cork Open Research Archive - University College Cork - Ireland


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Wireless sensor networks (WSN) are becoming widely adopted for many applications including complicated tasks like building energy management. However, one major concern for WSN technologies is the short lifetime and high maintenance cost due to the limited battery energy. One of the solutions is to scavenge ambient energy, which is then rectified to power the WSN. The objective of this thesis was to investigate the feasibility of an ultra-low energy consumption power management system suitable for harvesting sub-mW photovoltaic and thermoelectric energy to power WSNs. To achieve this goal, energy harvesting system architectures have been analyzed. Detailed analysis of energy storage units (ESU) have led to an innovative ESU solution for the target applications. Battery-less, long-lifetime ESU and its associated power management circuitry, including fast-charge circuit, self-start circuit, output voltage regulation circuit and hybrid ESU, using a combination of super-capacitor and thin film battery, were developed to achieve continuous operation of energy harvester. Low start-up voltage DC/DC converters have been developed for 1mW level thermoelectric energy harvesting. The novel method of altering thermoelectric generator (TEG) configuration in order to match impedance has been verified in this work. Novel maximum power point tracking (MPPT) circuits, exploring the fractional open circuit voltage method, were particularly developed to suit the sub-1mW photovoltaic energy harvesting applications. The MPPT energy model has been developed and verified against both SPICE simulation and implemented prototypes. Both indoor light and thermoelectric energy harvesting methods proposed in this thesis have been implemented into prototype devices. The improved indoor light energy harvester prototype demonstrates 81% MPPT conversion efficiency with 0.5mW input power. This important improvement makes light energy harvesting from small energy sources (i.e. credit card size solar panel in 500lux indoor lighting conditions) a feasible approach. The 50mm × 54mm thermoelectric energy harvester prototype generates 0.95mW when placed on a 60oC heat source with 28% conversion efficiency. Both prototypes can be used to continuously power WSN for building energy management applications in typical office building environment. In addition to the hardware development, a comprehensive system energy model has been developed. This system energy model not only can be used to predict the available and consumed energy based on real-world ambient conditions, but also can be employed to optimize the system design and configuration. This energy model has been verified by indoor photovoltaic energy harvesting system prototypes in long-term deployed experiments.

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A digital differentiator simply involves the derivation of an input signal. This work includes the presentation of first-degree and second-degree differentiators, which are designed as both infinite-impulse-response (IIR) filters and finite-impulse-response (FIR) filters. The proposed differentiators have low-pass magnitude response characteristics, thereby rejecting noise frequencies higher than the cut-off frequency. Both steady-state frequency-domain characteristics and Time-domain analyses are given for the proposed differentiators. It is shown that the proposed differentiators perform well when compared to previously proposed filters. When considering the time-domain characteristics of the differentiators, the processing of quantized signals proved especially enlightening, in terms of the filtering effects of the proposed differentiators. The coefficients of the proposed differentiators are obtained using an optimization algorithm, while the optimization objectives include magnitude and phase response. The low-pass characteristic of the proposed differentiators is achieved by minimizing the filter variance. The low-pass differentiators designed show the steep roll-off, as well as having highly accurate magnitude response in the pass-band. While having a history of over three hundred years, the design of fractional differentiator has become a ‘hot topic’ in recent decades. One challenging problem in this area is that there are many different definitions to describe the fractional model, such as the Riemann-Liouville and Caputo definitions. Through use of a feedback structure, based on the Riemann-Liouville definition. It is shown that the performance of the fractional differentiator can be improved in both the frequency-domain and time-domain. Two applications based on the proposed differentiators are described in the thesis. Specifically, the first of these involves the application of second degree differentiators in the estimation of the frequency components of a power system. The second example concerns for an image processing, edge detection application.

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Very Long Baseline Interferometry (VLBI) polarisation observations of the relativistic jets from Active Galactic Nuclei (AGN) allow the magnetic field environment around the jet to be probed. In particular, multi-wavelength observations of AGN jets allow the creation of Faraday rotation measure maps which can be used to gain an insight into the magnetic field component of the jet along the line of sight. Recent polarisation and Faraday rotation measure maps of many AGN show possible evidence for the presence of helical magnetic fields. The detection of such evidence is highly dependent both on the resolution of the images and the quality of the error analysis and statistics used in the detection. This thesis focuses on the development of new methods for high resolution radio astronomy imaging in both of these areas. An implementation of the Maximum Entropy Method (MEM) suitable for multi-wavelength VLBI polarisation observations is presented and the advantage in resolution it possesses over the CLEAN algorithm is discussed and demonstrated using Monte Carlo simulations. This new polarisation MEM code has been applied to multi-wavelength imaging of the Active Galactic Nuclei 0716+714, Mrk 501 and 1633+382, in each case providing improved polarisation imaging compared to the case of deconvolution using the standard CLEAN algorithm. The first MEM-based fractional polarisation and Faraday-rotation VLBI images are presented, using these sources as examples. Recent detections of gradients in Faraday rotation measure are presented, including an observation of a reversal in the direction of a gradient further along a jet. Simulated observations confirming the observability of such a phenomenon are conducted, and possible explanations for a reversal in the direction of the Faraday rotation measure gradient are discussed. These results were originally published in Mahmud et al. (2013). Finally, a new error model for the CLEAN algorithm is developed which takes into account correlation between neighbouring pixels. Comparison of error maps calculated using this new model and Monte Carlo maps show striking similarities when the sources considered are well resolved, indicating that the method is correctly reproducing at least some component of the overall uncertainty in the images. The calculation of many useful quantities using this model is demonstrated and the advantages it poses over traditional single pixel calculations is illustrated. The limitations of the model as revealed by Monte Carlo simulations are also discussed; unfortunately, the error model does not work well when applied to compact regions of emission.