Design of digital differentiators

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.

Optical micro- and nanofibres: Higher mode generation and particle manipulation studies

This thesis is centred on two experimental fields of optical micro- and nanofibre research; higher mode generation/excitation and evanescent field optical manipulation. Standard, commercial, single-mode silica fibre is used throughout most of the experiments; this generally produces high-quality, single-mode, micro- or nanofibres when tapered in a flame-heated, pulling rig in the laboratory. Single mode fibre can also support higher transverse modes, when transmitting wavelengths below that of their defined single-mode regime cut-off. To investigate this, a first-order Laguerre-Gaussian beam, LG01 of 1064 nm wavelength and doughnut-shaped intensity profile is generated free space via spatial light modulation. This technique facilitates coupling to the LP11 fibre mode in two-mode fibre, and convenient, fast switching to the fundamental mode via computer-generated hologram modulation. Following LP11 mode loss when exponentially tapering 125μm diameter fibre, two mode fibre with a cladding diameter of 80μm is selected fir testing since it is more suitable for satisfying the adiabatic criteria for fibre tapering. Proving a fruitful endeavour, experiments show a transmission of 55% of the original LP11 mode set (comprising TE01, TM01, HE21e,o true modes) in submicron fibres. Furthermore, by observing pulling dynamics and progressive mode-lass behaviour, it is possible to produce a nanofibre which supports only the TE01 and TM01 modes, while suppressing the HE21e,o elements of the LP11 group. This result provides a basis for experimental studies of atom trapping via mode-interference, and offers a new set of evanescent field geometries for sensing and particle manipulation applications. The thesis highlights the experimental results of the research unit’s Cold Atom subgroup, who successfully integrated one such higher-mode nanofibre into a cloud of cold Rubidium atoms. This led to the detection of stronger signals of resonance fluorescence coupling into the nanofibre and for light absorption by the atoms due to the presence of higher guided modes within the fibre. Theoretical work on the impact of the curved nanofibre surface on the atomic-surface van der Waals interaction is also presented, showing a clear deviation of the potential from the commonly-used flat-surface approximation. Optical micro- and nanofibres are also useful tools for evanescent-field mediated optical manipulation – this includes propulsion, defect-induced trapping, mass migration and size-sorting of micron-scale particles in dispersion. Similar early trapping experiments are described in this thesis, and resulting motivations for developing a targeted, site-specific particle induction method are given. The integration of optical nanofibres into an optical tweezers is presented, facilitating individual and group isolation of selected particles, and their controlled positioning and conveyance in the evanescent field. The effects of particle size and nanofibre diameter on pronounced scattering is experimentally investigated in this systems, as are optical binding effects between adjacent particles in the evanescent field. Such inter-particle interactions lead to regulated self-positioning and particle-chain speed enhancements.

Physicochemical characterisation of protein ingredients prepared from milk by ultrafiltration or microfiltration for application in formulated nutritional products

Formulated food systems are becoming more sophisticated as demand grows for the design of structural and nutritional profiles targeted at increasingly specific demographics. Milk protein is an important bio- and techno-functional component of such formulations, which include infant formula, sports supplements, clinical beverages and elderly nutrition products. This thesis outlines research into ingredients that are key to the development of these products, namely milk protein concentrate (MPC), milk protein isolate (MPI), micellar casein concentrate (MCC), β-casein concentrate (BCC) and serum protein concentrate (SPC). MPC powders ranging from 37 to 90% protein (solids basis) were studied for properties of relevance to handling and storage of powders, powder solubilisation and thermal processing of reconstituted MPCs. MPC powders with ≥80% protein were found to have very poor flowability and high compressibility; in addition, these high-protein MPCs exhibited poor wetting and dispersion characteristics during rehydration in water. Heat stability studies on unconcentrated (3.5%, 140°C) and concentrated (8.5%, 120°C) MPC suspensions, showed that suspensions prepared from high-protein MPCs coagulated much more rapidly than lower protein MPCs. β-casein ingredients were developed using membrane processing. Enrichment of β-casein from skim milk was performed at laboratory-scale using ‘cold’ microfiltration (MF) at <4°C with either 1000 kDa molecular weight cut-off or 0.1 µm pore-size membranes. At pilot-scale, a second ‘warm’ MF step at 26°C was incorporated for selective purification of micellised β-casein from whey proteins; using this approach, BCCs with β-casein purity of up to 80% (protein basis) were prepared, with the whey protein purity of the SPC co-product reaching ~90%. The BCC ingredient could prevent supersaturated solutions of calcium phosphate (CaP) from precipitating, although the amorphous CaP formed created large micelles that were less thermo-reversible than those in CaP-free systems. Another co-product of BCC manufacture, MCC powder, was shown to have superior rehydration characteristics compared to traditional MCCs. The findings presented in this thesis constitute a significant advance in the research of milk protein ingredients, in terms of optimising their preparation by membrane filtration, preventing their destabilisation during processing and facilitating their effective incorporation into nutritional formulations designed for consumers of a specific age, lifestyle or health status