Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Dynamical local models for segmentation and prediction of financial time series

In the analysis and prediction of many real-world time series, the assumption of stationarity is not valid. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We introduce a new model which combines a dynamic switching (controlled by a hidden Markov model) and a non-linear dynamical system. We show how to train this hybrid model in a maximum likelihood approach and evaluate its performance on both synthetic and financial data.

Interhemispheric differences of spectral power in expressive language:a MEG study with clinical applications

In the last decade we have seen an exponential growth of functional imaging studies investigating multiple aspects of language processing. These studies have sparked an interest in applying some of the paradigms to various clinically relevant questions, such as the identification of the cortical regions mediating language function in surgical candidates for refractory epilepsy. Here we present data from a group of adult control participants in order to investigate the potential of using frequency specific spectral power changes in MEG activation patterns to establish lateralisation of language function using expressive language tasks. In addition, we report on a paediatric patient whose language function was assessed before and after a left hemisphere amygdalo-hippocampectomy. Our verb generation task produced left hemisphere decreases in beta-band power accompanied by right hemisphere increases in low beta-band power in the majority of the control group, a previously unreported phenomenon. This pattern of spectral power was also found in the patient's post-surgery data, though not her pre-surgery data. Comparison of pre and post-operative results also provided some evidence of reorganisation in language related cortex both inter- and intra-hemispherically following surgery. The differences were not limited to changes in localisation of language specific cortex but also changes in the spectral and temporal profile of frontal brain regions during verb generation. While further investigation is required to establish concordance with invasive measures, our data suggest that the methods described may serve as a reliable lateralisation marker for clinical assessment. Furthermore, our findings highlight the potential utility of MEG for the investigation of cortical language functioning in both healthy development and pathology.

Evaluation of RF power degradation in microwave photonic systems employing uniform period fibre Bragg gratings

The frequency dependent RF power degradation in direct modulated microwave photonic systems employing uniform period fibre Bragg gratingsFBG.as reflective elements is investigated. The results have implications in terms of the available RF bandwidth and the stability requirements for the fibre Bragg gratings.

Impact of longitudinal power budget in coherent transmission systems employing digital back-propagation

We report the impact of longitudinal signal power profile on the transmission performance of coherently-detected 112 Gb/s m-ary polarization multiplexed quadrature amplitude modulation system after compensation of deterministic nonlinear fibre impairments. Performance improvements up to 0.6 dB (Q(eff)) are reported for a non-uniform transmission link power profile. Further investigation reveals that the evolution of the transmission performance with power profile management is fully consistent with the parametric amplification of the amplified spontaneous emission by the signal through four-wave mixing. In particular, for a non-dispersion managed system, a single-step increment of 4 dB in the amplifier gain, with respect to a uniform gain profile, at similar to 2/3(rd) of the total reach considerably improves the transmission performance for all the formats studied. In contrary a negative-step profile, emulating a failure (gain decrease or loss increase), significantly degrades the bit-error rate.

Investigation of EDFA power transients in circuit-switched and packet-switched optical networks

Erbium-doped fibre amplifiers (EDFA’s) are a key technology for the design of all optical communication systems and networks. The superiority of EDFAs lies in their negligible intermodulation distortion across high speed multichannel signals, low intrinsic losses, slow gain dynamics, and gain in a wide range of optical wavelengths. Due to long lifetime in excited states, EDFAs do not oppose the effect of cross-gain saturation. The time characteristics of the gain saturation and recovery effects are between a few hundred microseconds and 10 milliseconds. However, in wavelength division multiplexed (WDM) optical networks with EDFAs, the number of channels traversing an EDFA can change due to the faulty link of the network or the system reconfiguration. It has been found that, due to the variation in channel number in the EDFAs chain, the output system powers of surviving channels can change in a very short time. Thus, the power transient is one of the problems deteriorating system performance. In this thesis, the transient phenomenon in wavelength routed WDM optical networks with EDFA chains was investigated. The task was performed using different input signal powers for circuit switched networks. A simulator for the EDFA gain dynamicmodel was developed to compute the magnitude and speed of the power transients in the non-self-saturated EDFA both single and chained. The dynamic model of the self-saturated EDFAs chain and its simulator were also developed to compute the magnitude and speed of the power transients and the Optical signal-to-noise ratio (OSNR). We found that the OSNR transient magnitude and speed are a function of both the output power transient and the number of EDFAs in the chain. The OSNR value predicts the level of the quality of service in the related network. It was found that the power transients for both self-saturated and non-self-saturated EDFAs are close in magnitude in the case of gain saturated EDFAs networks. Moreover, the cross-gain saturation also degrades the performance of the packet switching networks due to varying traffic characteristics. The magnitude and the speed of output power transients increase along the EDFAs chain. An investigation was done on the asynchronous transfer mode (ATM) or the WDM Internet protocol (WDM-IP) traffic networks using different traffic patterns based on the Pareto and Poisson distribution. The simulator is used to examine the amount and speed of the power transients in Pareto and Poisson distributed traffic at different bit rates, with specific focus on 2.5 Gb/s. It was found from numerical and statistical analysis that the power swing increases if the time interval of theburst-ON/burst-OFF is long in the packet bursts. This is because the gain dynamics is fast during strong signal pulse or with long duration pulses, which is due to the stimulatedemission avalanche depletion of the excited ions. Thus, an increase in output power levelcould lead to error burst which affects the system performance.

Practical methods of tracking of nonstationary time series applied to real-world data

In this paper, we discuss some practical implications for implementing adaptable network algorithms applied to non-stationary time series problems. Two real world data sets, containing electricity load demands and foreign exchange market prices, are used to test several different methods, ranging from linear models with fixed parameters, to non-linear models which adapt both parameters and model order on-line. Training with the extended Kalman filter, we demonstrate that the dynamic model-order increment procedure of the resource allocating RBF network (RAN) is highly sensitive to the parameters of the novelty criterion. We investigate the use of system noise for increasing the plasticity of the Kalman filter training algorithm, and discuss the consequences for on-line model order selection. The results of our experiments show that there are advantages to be gained in tracking real world non-stationary data through the use of more complex adaptive models.

Optimized design of high power mid-infrared Er3+, Pr3+ -codoped ZBLAN fiber laser

Based on the rate equations describing the operation of the Er3+, Pr3+ -codoped ZBLAN fiber lasers with different pump configurations, theoretical calculations that relate to the population characteristics and optimization of CW operation of high power Er3+, Pr3+ :ZBLAN double-clad fiber lasers are presented. Using the measured ET (energy-transfer), ETU (energy-transfer-upconversion) and CR (cross-relaxation) parameters relevant to Er3+, Pr3+ -codoped ZBLAN, a good agreement between the theoretical results from the model and recently reported experimental measurements is obtained. The effects on the slope efficiency of a number of laser parameters including fiber length, reflectance of the output mirror and pumping configuration are quantitatively analyzed and used for the design and optimization of high power Er3+, Pr3+ -codoped ZBLAN fiber lasers.

Information and behavioural instruction along the health-care pathway:the perspective of people undergoing hernia repair surgery and the role of formal and informal information sources

Provision of information and behavioural instruction has been demonstrated to improve recovery after surgery. However, patients draw on a range of information sources and it is important to establish which sources patients use and how this influences perceptions and behaviour as they progress along the surgical pathway. In this qualitative, exploratory and longitudinal study, the use of information and instruction were explored from the perspective of people undergoing inguinal hernia repair surgery. Seven participants undergoing inguinal hernia repair surgery were interviewed using semi-structured interviews 2 weeks before surgery and 2 weeks and 4 months post-surgery. Nineteen interviews were conducted in total. Topic guides included sources of knowledge, reasons for help-seeking and opting for surgery and factors influencing return to activity. Data were analysed thematically according to Interpretative Phenomenological Analysis. Participants sought information from a range of sources, focusing on informal information sources before surgery and using information and instruction from health-care professionals post-surgery. This information influenced behaviours including deciding to undergo surgery, use of pain medication and returning to usual activity. Anxiety and help-seeking resulted when unexpected post-surgical events occurred such as extensive bruising. Findings were consistent with psychological and sociological theories. Overall, participants were positive about the information and instruction they received but expressed a desire for more timely information on post-operative adverse events.

Independent component analysis and feature extraction of financial time series

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