Bispectral and trispectral characterization of transition to chaos in the Duffing oscillator

Higher-order spectral (bispectral and trispectral) analyses of numerical solutions of the Duffing equation with a cubic stiffness are used to isolate the coupling between the triads and quartets, respectively, of nonlinearly interacting Fourier components of the system. The Duffing oscillator follows a period-doubling intermittency catastrophic route to chaos. For period-doubled limit cycles, higher-order spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. However, when the Duffing oscillator becomes chaotic, global behavior of the cubic nonlinearity becomes dominant and quadratic nonlinear interactions are weak, while cubic interactions remain strong. As the nonlinearity of the system is increased, the number of excited Fourier components increases, eventually leading to broad-band power spectra for chaos. The corresponding higher-order spectra indicate that although some individual nonlinear interactions weaken as nonlinearity increases, the number of nonlinearly interacting Fourier modes increases. Trispectra indicate that the cubic interactions gradually evolve from encompassing a few quartets of Fourier components for period-1 motion to encompassing many quartets for chaos. For chaos, all the components within the energetic part of the power spectrum are cubically (but not quadratically) coupled to each other.

Higher-Order spectra of nonlinear polynomial models for Chua's circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

Fundus image registration algorithms for a pc-based image processing system

We have developed digital image registration program for a MC 68000 based fundus image processing system (FIPS). FIPS not only is capable of executing typical image processing algorithms in spatial as well as Fourier domain, the execution time for many operations has been made much quicker by using a hybrid of "C", Fortran and MC6000 assembly languages.

Instantaneous phase of the autocorrelation and robustness to signal-dependent noise

The phase of an analytic signal constructed from the autocorrelation function of a signal contains significant information about the shape of the signal. Using Bedrosian's (1963) theorem for the Hilbert transform it is proved that this phase is robust to multiplicative noise if the signal is baseband and the spectra of the signal and the noise do not overlap. Higher-order spectral features are interpreted in this context and shown to extract nonlinear phase information while retaining robustness. The significance of the result is that prior knowledge of the spectra is not required.

On the behaviour of higher-order spectral features for object recognition in the presence of various types of noise

This paper presents results on the robustness of higher-order spectral features to Gaussian, Rayleigh, and uniform distributed noise. Based on cluster plots and accuracy results for various signal to noise conditions, the higher-order spectral features are shown to be better than moment invariant features.

Ocular aberrations in the peripheral visual field

We modified a commercial Hartmann-Shack aberrometer and used it to measure ocular aberrations across the central 42º horizontal x 32º vertical visual fields of five young emmetropic subjects. Some Zernike aberration coefficients show coefficient field distributions that were similar to the field dependence predicted by Seidel theory (astigmatism, oblique astigmatism, horizontal coma, vertical coma), but defocus did not demonstrate such similarity.

Properties of lignin and poly(hydroxybutyrate) blends

The Queensland University of Technology (QUT) allows the presentation of a thesis for the Degree of Doctor of Philosophy in the format of published or submitted papers, where such papers have been published, accepted or submitted during the period of candidature. This thesis is composed of Seven published/submitted papers and one poster presentation, of which five have been published and the other two are under review. This project is financially supported by the QUTPRA Grant. The twenty-first century started with the resurrection of lignocellulosic biomass as a potential substitute for petrochemicals. Petrochemicals, which enjoyed the sustainable economic growth during the past century, have begun to reach or have reached their peak. The world energy situation is complicated by political uncertainty and by the environmental impact associated with petrochemical import and usage. In particular, greenhouse gasses and toxic emissions produced by petrochemicals have been implicated as a significant cause of climate changes. Lignocellulosic biomass (e.g. sugarcane biomass and bagasse), which potentially enjoys a more abundant, widely distributed, and cost-effective resource base, can play an indispensible role in the paradigm transition from fossil-based to carbohydrate-based economy. Poly(3-hydroxybutyrate), PHB has attracted much commercial interest as a plastic and biodegradable material because some its physical properties are similar to those of polypropylene (PP), even though the two polymers have quite different chemical structures. PHB exhibits a high degree of crystallinity, has a high melting point of approximately 180°C, and most importantly, unlike PP, PHB is rapidly biodegradable. Two major factors which currently inhibit the widespread use of PHB are its high cost and poor mechanical properties. The production costs of PHB are significantly higher than for plastics produced from petrochemical resources (e.g. PP costs $US1 kg-1, whereas PHB costs $US8 kg-1), and its stiff and brittle nature makes processing difficult and impedes its ability to handle high impact. Lignin, together with cellulose and hemicellulose, are the three main components of every lignocellulosic biomass. It is a natural polymer occurring in the plant cell wall. Lignin, after cellulose, is the most abundant polymer in nature. It is extracted mainly as a by-product in the pulp and paper industry. Although, traditionally lignin is burnt in industry for energy, it has a lot of value-add properties. Lignin, which to date has not been exploited, is an amorphous polymer with hydrophobic behaviour. These make it a good candidate for blending with PHB and technically, blending can be a viable solution for price and reduction and enhance production properties. Theoretically, lignin and PHB affect the physiochemical properties of each other when they become miscible in a composite. A comprehensive study on structural, thermal, rheological and environmental properties of lignin/PHB blends together with neat lignin and PHB is the targeted scope of this thesis. An introduction to this research, including a description of the research problem, a literature review and an account of the research progress linking the research papers is presented in Chapter 1. In this research, lignin was obtained from bagasse through extraction with sodium hydroxide. A novel two-step pH precipitation procedure was used to recover soda lignin with the purity of 96.3 wt% from the black liquor (i.e. the spent sodium hydroxide solution). The precipitation process is presented in Chapter 2. A sequential solvent extraction process was used to fractionate the soda lignin into three fractions. These fractions, together with the soda lignin, were characterised to determine elemental composition, purity, carbohydrate content, molecular weight, and functional group content. The thermal properties of the lignins were also determined. The results are presented and discussed in Chapter 2. On the basis of the type and quantity of functional groups, attempts were made to identify potential applications for each of the individual lignins. As an addendum to the general section on the development of composite materials of lignin, which includes Chapters 1 and 2, studies on the kinetics of bagasse thermal degradation are presented in Appendix 1. The work showed that distinct stages of mass losses depend on residual sucrose. As the development of value-added products from lignin will improve the economics of cellulosic ethanol, a review on lignin applications, which included lignin/PHB composites, is presented in Appendix 2. Chapters 3, 4 and 5 are dedicated to investigations of the properties of soda lignin/PHB composites. Chapter 3 reports on the thermal stability and miscibility of the blends. Although the addition of soda lignin shifts the onset of PHB decomposition to lower temperatures, the lignin/PHB blends are thermally more stable over a wider temperature range. The results from the thermal study also indicated that blends containing up to 40 wt% soda lignin were miscible. The Tg data for these blends fitted nicely to the Gordon-Taylor and Kwei models. Fourier transform infrared spectroscopy (FT-IR) evaluation showed that the miscibility of the blends was because of specific hydrogen bonding (and similar interactions) between reactive phenolic hydroxyl groups of lignin and the carbonyl group of PHB. The thermophysical and rheological properties of soda lignin/PHB blends are presented in Chapter 4. In this chapter, the kinetics of thermal degradation of the blends is studied using thermogravimetric analysis (TGA). This preliminary investigation is limited to the processing temperature of blend manufacturing. Of significance in the study, is the drop in the apparent energy of activation, Ea from 112 kJmol-1 for pure PHB to half that value for blends. This means that the addition of lignin to PHB reduces the thermal stability of PHB, and that the comparative reduced weight loss observed in the TGA data is associated with the slower rate of lignin degradation in the composite. The Tg of PHB, as well as its melting temperature, melting enthalpy, crystallinity and melting point decrease with increase in lignin content. Results from the rheological investigation showed that at low lignin content (.30 wt%), lignin acts as a plasticiser for PHB, while at high lignin content it acts as a filler. Chapter 5 is dedicated to the environmental study of soda lignin/PHB blends. The biodegradability of lignin/PHB blends is compared to that of PHB using the standard soil burial test. To obtain acceptable biodegradation data, samples were buried for 12 months under controlled conditions. Gravimetric analysis, TGA, optical microscopy, scanning electron microscopy (SEM), differential scanning calorimetry (DSC), FT-IR, and X-ray photoelectron spectroscopy (XPS) were used in the study. The results clearly demonstrated that lignin retards the biodegradation of PHB, and that the miscible blends were more resistant to degradation compared to the immiscible blends. To obtain an understanding between the structure of lignin and the properties of the blends, a methanol-soluble lignin, which contains 3× less phenolic hydroxyl group that its parent soda lignin used in preparing blends for the work reported in Chapters 3 and 4, was blended with PHB and the properties of the blends investigated. The results are reported in Chapter 6. At up to 40 wt% methanolsoluble lignin, the experimental data fitted the Gordon-Taylor and Kwei models, similar to the results obtained soda lignin-based blends. However, the values obtained for the interactive parameters for the methanol-soluble lignin blends were slightly lower than the blends obtained with soda lignin indicating weaker association between methanol-soluble lignin and PHB. FT-IR data confirmed that hydrogen bonding is the main interactive force between the reactive functional groups of lignin and the carbonyl group of PHB. In summary, the structural differences existing between the two lignins did not manifest itself in the properties of their blends.

Speckle reduction in optical coherence tomography imaging by affine-motion image registration

Signal-degrading speckle is one factor that can reduce the quality of optical coherence tomography images. We demonstrate the use of a hierarchical model-based motion estimation processing scheme based on an affine-motion model to reduce speckle in optical coherence tomography imaging, by image registration and the averaging of multiple B-scans. The proposed technique is evaluated against other methods available in the literature. The results from a set of retinal images show the benefit of the proposed technique, which provides an improvement in signal-to-noise ratio of the square root of the number of averaged images, leading to clearer visual information in the averaged image. The benefits of the proposed technique are also explored in the case of ocular anterior segment imaging.

Congo Red adsorption by ball-milled sugarcane bagasse

The adsorption of Congo Red (CR) by ball-milled sugarcane bagasse was evaluated in an aqueous batch system. CR adsorption capacity increased significantly with small changes in bagasse surface area. CR removal decreased with increasing solution pH from 5.0 to 10.0. Maximum adsorption capacity was 38.2 mg/g bagasse at a CR concentration of 500 mg/L. The equilibrium isotherm fitted the Freundlich model and the adsorption kinetics obeyed pseudo-second order equation. CR adsorption obeyed the intra-particle diffusion model very well with bagasse surface area in the range of 0.58–0.66 m2/g, whereas it was controlled by multi-adsorption stages with bagasse surface area in the range of 1.31–1.82 m2/g. Thermodynamic analysis indicated that the adsorption process is an exothermic and spontaneous process. Fourier transform infrared analysis of bagasse containing adsorbed CR indicated interactions between the carboxyl and hydroxyl groups of bagasse and CR function groups.

Ocular characteristics of anisometropia

Animal models of refractive error development have demonstrated that visual experience influences ocular growth. In a variety of species, axial anisometropia (i.e. a difference in the length of the two eyes) can be induced through unilateral occlusion, image degradation or optical manipulation. In humans, anisometropia may occur in isolation or in association with amblyopia, strabismus or unilateral pathology. Non-amblyopic myopic anisometropia represents an interesting anomaly of ocular growth, since the two eyes within one visual system have grown to different endpoints. These experiments have investigated a range of biometric, optical and mechanical properties of anisometropic eyes (with and without amblyopia) with the aim of improving our current understanding of asymmetric refractive error development. In the first experiment, the interocular symmetry in 34 non-amblyopic myopic anisometropes (31 Asian, 3 Caucasian) was examined during relaxed accommodation. A high degree of symmetry was observed between the fellow eyes for a range of optical, biometric and biomechanical measurements. When the magnitude of anisometropia exceeded 1.75 D, the more myopic eye was almost always the sighting dominant eye. Further analysis of the optical and biometric properties of the dominant and non-dominant eyes was conducted to determine any related factors but no significant interocular differences were observed with respect to best-corrected visual acuity, corneal or total ocular aberrations during relaxed accommodation. Given the high degree of symmetry observed between the fellow eyes during distance viewing in the first experiment and the strong association previously reported between near work and myopia development, the aim of the second experiment was to investigate the symmetry between the fellow eyes of the same 34 myopic anisometropes following a period of near work. Symmetrical changes in corneal and total ocular aberrations were observed following a short reading task (10 minutes, 2.5 D accommodation demand) which was attributed to the high degree of interocular symmetry for measures of anterior eye morphology, and corneal biomechanics. These changes were related to eyelid shape and position during downward gaze, but gave no clear indication of factors associated with near work that might cause asymmetric eye growth within an individual. Since the influence of near work on eye growth is likely to be most obvious during, rather than following near tasks, in the third experiment the interocular symmetry of the optical and biometric changes was examined during accommodation for 11 myopic anisometropes. The changes in anterior eye biometrics associated with accommodation were again similar between the eyes, resulting in symmetrical changes in the optical characteristics. However, the more myopic eyes exhibited slightly greater amounts of axial elongation during accommodation which may be related to the force exerted by the ciliary muscle. This small asymmetry in axial elongation we observed between the eyes may be due to interocular differences in posterior eye structure, given that the accommodative response was equal between eyes. Using ocular coherence tomography a reduced average choroidal thickness was observed in the more myopic eyes compared to the less myopic eyes of these subjects. The interocular difference in choroidal thickness was correlated with the magnitude of spherical equivalent and axial anisometropia. The symmetry in optics and biometrics between fellow eyes which have undergone significantly different visual development (i.e. anisometropic subjects with amblyopia) is also of interest with respect to refractive error development. In the final experiment the influence of altered visual experience upon corneal and ocular higher-order aberrations was investigated in 21 amblyopic subjects (8 refractive, 11 strabismic and 2 form deprivation). Significant differences in aberrations were observed between the fellow eyes, which varied according to the type of amblyopia. Refractive amblyopes displayed significantly higher levels of 4th order corneal aberrations (spherical aberration and secondary astigmatism) in the amblyopic eye compared to the fellow non-amblyopic eye. Strabismic amblyopes exhibited significantly higher levels of trefoil, a third order aberration, in the amblyopic eye for both corneal and total ocular aberrations. The results of this experiment suggest that asymmetric visual experience during development is associated with asymmetries in higher-order aberrations, proportional to the magnitude of anisometropia and dependent upon the amblyogenic factor. This suggests a direct link between the development of higher-order optical characteristics of the human eye and visual feedback. The results from these experiments have shown that a high degree of symmetry exists between the fellow eyes of non-amblyopic myopic anisometropes for a range of biomechanical, biometric and optical parameters for different levels of accommodation and following near work. While a single specific optical or biomechanical factor that is consistently associated with asymmetric refractive error development has not been identified, the findings from these studies suggest that further research into the association between ocular dominance, choroidal thickness and higher-order aberrations with anisometropia may improve our understanding of refractive error development.

Effective adsorption of sodium dodecylsulfate (SDS) by hydrocalumite (CaAl-LDH-Cl) induced by self-dissolution and re-precipitation mechanism

Hydrocalumite (CaAl-LDH-Cl) were synthesized through a rehydration method involving a freshly prepared tricalcium aluminate (C3A) with CaCl2 solution. To understand the intercalation behaviour of sodium dodecylsulfate (SDS) with CaAl-LDH-Cl, X-ray diffraction (XRD), Fourier transform infrared (FTIR), scanning electron microscopy (SEM), transmission electron microscope (TEM), X-ray photoelectron spectroscopy (XPS), inductively coupled plasma-atomic emission spectrometer (ICP) and elemental analysis have been undertaken. The sorption isotherms with SDS reveal that the maximum sorption amount of SDS by CaAl-LDH-Cl could reach 3.67 mmol•g-1. The results revealed that CaAl-LDH-Cl holds a self-dissolution property, about 20-30% of which is dissolved. And the dissolved Ca2+, Al3+ ions are combined with SDS to form CaAl-SDS or Ca-SDS precipitation. It has been highlighted that the composition of resulting products is strongly dependent upon the SDS concentration. With increasing SDS concentrations, the main resulting product changes from CaAl-SDS to Ca-SDS, and the value of interlayer spacing increased to 3.27 nm.

Synthesis of one-dimensional nanocomposites based on alumina nanofibres and their catalytic applications

Materials with one-dimensional (1D) nanostructure are important for catalysis. They are the preferred building blocks for catalytic nanoarchitecture, and can be used to fabricate designer catalysts. In this thesis, one such material, alumina nanofibre, was used as a precursor to prepare a range of nanocomposite catalysts. Utilising the specific properties of alumina nanofibres, a novel approach was developed to prepare macro-mesoporous nanocomposites, which consist of a stacked, fibrous nanocomposite with a core-shell structure. Two kinds of fibrous ZrO2/Al2O3 and TiO2/Al2O3 nanocomposites were successfully synthesised using boehmite nanofibers as a hard temperate and followed by a simple calcination. The alumina nanofibres provide the resultant nanocomposites with good thermal stability and mechanical stability. A series of one-dimensional (1D) zirconia/alumina nanocomposites were prepared by the deposition of zirconium species onto the 3D framework of boehmite nanofibres formed by dispersing boehmite nanofibres into a butanol solution, followed by calcination at 773 K. The materials were characterised by X-ray diffraction (XRD), Scanning electron microscopy (SEM), Transmission electron microscope (TEM), N2 adsorption/desorption, Infrared Emission Spectroscopy (IES), and Fourier Transform Infrared spectroscopy (FT-IR). The results demonstrated that when the molar percentage, X, X=100*Zr/(Al+Zr), was > 30%, extremely long ZrO2/Al2O3 composite nanorods with evenly distributed ZrO2 nanocrystals formed on their surface. The stacking of such nanorods gave rise to a new kind of macroporous material without the use of any organic space filler\template or other specific drying techniques. The mechanism for the formation of these long ZrO2/Al2O3 composite nanorods is proposed in this work. A series of solid-superacid catalysts were synthesised from fibrous ZrO2/Al2O3 core and shell nanocomposites. In this series, the zirconium molar percentage was varied from 2 % to 50 %. The ZrO2/Al2O3 nanocomposites and their solid superacid counterparts were characterised by a variety of techniques including 27Al MAS-NMR, SEM, TEM, XPS, Nitrogen adsorption and Infrared Emission Spectroscopy. NMR results show that the interaction between zirconia species and alumina strongly correlates with pentacoordinated aluminium sites. This can also be detected by the change in binding energy of the 3d electrons of the zirconium. The acidity of the obtained superacids was tested by using them as catalysts for the benzolyation of toluene. It was found that a sample with a 50 % zirconium molar percentage possessed the highest surface acidity equalling that of pristine sulfated zirconia despite the reduced mass of zirconia. Preparation of hierarchically macro-mesoporous catalyst by loading nanocrystallites on the framework of alumina bundles can provide an alternative system to design advanced nanocomposite catalyst with enhanced performance. A series of macro-mesoporous TiO2/Al2O3 nanocomposites with different morphologies were synthesised. The materials were calcined at 723 K and were characterised by X-ray diffraction (XRD), Scanning electron microscopy (SEM), Transmission electron microscope (TEM), N2 adsorption/desorption, Infrared Emission Spectroscopy (IES), and UV-visible spectroscopy (UV-visible). A modified approach was proposed for the synthesis of 1D (fibrous) nanocomposite with higher Ti/Al molar ratio (2:1) at lower temperature (<100oC), which makes it possible to synthesize such materials on industrial scale. The performances of a series of resultant TiO2/Al2O3 nanocomposites with different morphologies were evaluated as a photocatalyst for the phenol degradation under UV irradiation. The photocatalyst (Ti/Al =2) with fibrous morphology exhibits higher activity than that of the photocatalyst with microspherical morphology which indeed has the highest Ti to Al molar ratio (Ti/Al =3) in the series of as-synthesised hierarchical TiO2/Al2O3 nanocomposites. Furthermore, the photocatalytic performances, for the fibrous nanocomposites with Ti/Al=2, were optimized by calcination at elevated temperatures. The nanocomposite prepared by calcination at 750oC exhibits the highest catalytic activity, and its performance per TiO2 unit is very close to that of the gold standard, Degussa P 25. This work also emphasizes two advantages of the nanocomposites with fibrous morphology: (1) the resistance to sintering, and (2) good catalyst recovery.

Acoustic emission for diesel engine monitoring: A review and preliminary

Vibration analysis has been a prime tool in condition monitoring of rotating machines, however, its application to internal combustion engines remains a challenge because engine vibration signatures are highly non-stationary that are not suitable for popular spectrum-based analysis. Signal-to-noise ratio is a main concern in engine signature analysis due to severe background noise being generated by consecutive mechanical events, such as combustion, valve opening and closing, especially in multi-cylinder engines. Acoustic Emission (AE) has been found to give excellent signal-to-noise ratio allowing discrimination of fine detail of normal or abnormal events during a given cycle. AE has been used to detect faults, such as exhaust valve leakage, fuel injection behaviour, and aspects of the combustion process. This paper presents a review of AE application to diesel engine monitoring and preliminary investigation of AE signature measured on an 18-cylinder diesel engine. AE is compared with vibration acceleration for varying operating conditions: load and speed. Frequency characteristics of AE from those events are analysed in time-frequency domain via short time Fourier trasform. The result shows a great potential of AE analysis for detection of various defects in diesel engines.

Specifying peripheral aberrations in visual science

Purpose: Investigations of foveal aberrations assume circular pupils. However, the pupil becomes increasingly elliptical with increase in visual field eccentricity. We address this and other issues concerning peripheral aberration specification. Methods: One approach uses an elliptical pupil similar to the actual pupil shape, stretched along its minor axis to become a circle so that Zernike circular aberration polynomials may be used. Another approach uses a circular pupil whose diameter matches either the larger or smaller dimension of the elliptical pupil. Pictorial presentation of aberrations, influence of wavelength on aberrations, sign differences between aberrations for fellow eyes, and referencing position to either the visual field or the retina are considered. Results: Examples show differences between the two approaches. Each has its advantages and disadvantages, but there are ways to compensate for most disadvantages. Two representations of data are pupil aberration maps at each position in the visual field and maps showing the variation in individual aberration coefficients across the field. Conclusions: Based on simplicity of use, adequacy of approximation, possible departures of off-axis pupils from ellipticity, and ease of understanding by clinicians, the circular pupil approach is preferable to the stretched elliptical approach for studies involving field angles up to 30 deg.

Eye shape and retinal shape, and their relation to peripheral refraction

Purpose: We provide an account of the relationships between eye shape, retinal shape and peripheral refraction. Recent findings: We discuss how eye and retinal shapes may be described as conicoids, and we describe an axis and section reference system for determining shapes. Explanations are given of how patterns of retinal expansion during the development of myopia may contribute to changing patterns of peripheral refraction, and how pre-existing retinal shape might contribute to the development of myopia. Direct and indirect techniques for determining eye and retinal shape are described, and results are discussed. There is reasonable consistency in the literature of eye length increasing at a greater rate than height and width as the degree of myopia increases, so that eyes may be described as changing from oblate/spherical shapes to prolate shapes. However, one study indicates that the retina itself, while showing the same trend, remains oblate in shape for most eyes (discounting high myopia). Eye shape and retinal shape are not the same and merely describing an eye shape as being prolate or oblate is insufficient without some understanding of the parameters contributing to this; in myopia a prolate eye shape is likely to involve both a steepening retina near the posterior pole combined with a flattening (or a reduction in steepening compared with an emmetrope) away from the pole.