Applications of fractals to image data compression

Digital image processing is exploited in many diverse applications but the size of digital images places excessive demands on current storage and transmission technology. Image data compression is required to permit further use of digital image processing. Conventional image compression techniques based on statistical analysis have reached a saturation level so it is necessary to explore more radical methods. This thesis is concerned with novel methods, based on the use of fractals, for achieving significant compression of image data within reasonable processing time without introducing excessive distortion. Images are modelled as fractal data and this model is exploited directly by compression schemes. The validity of this is demonstrated by showing that the fractal complexity measure of fractal dimension is an excellent predictor of image compressibility. A method of fractal waveform coding is developed which has low computational demands and performs better than conventional waveform coding methods such as PCM and DPCM. Fractal techniques based on the use of space-filling curves are developed as a mechanism for hierarchical application of conventional techniques. Two particular applications are highlighted: the re-ordering of data during image scanning and the mapping of multi-dimensional data to one dimension. It is shown that there are many possible space-filling curves which may be used to scan images and that selection of an optimum curve leads to significantly improved data compression. The multi-dimensional mapping property of space-filling curves is used to speed up substantially the lookup process in vector quantisation. Iterated function systems are compared with vector quantisers and the computational complexity or iterated function system encoding is also reduced by using the efficient matching algcnithms identified for vector quantisers.

Data transmission by pulse compression

Pulse compression techniques originated in radar.The present work is concerned with the utilization of these techniques in general, and the linear FM (LFM) technique in particular, for comnunications. It introduces these techniques from an optimum communications viewpoint and outlines their capabilities.It also considers the candidacy of the class of LFM signals for digital data transmission and the LFM spectrum. Work related to the utilization of LFM signals for digital data transmission has been mostly experimental and mainly concerned with employing two rectangular LFM pulses (or chirps) with reversed slopes to convey the bits 1 and 0 in an incoherent node.No systematic theory for LFM signal design and system performance has been available. Accordingly, the present work establishes such a theory taking into account coherent and noncoherent single-link and multiplex signalling modes. Some new results concerning the slope-reversal chirp pair are obtained. The LFM technique combines the typical capabilities of pulse compression with a relative ease of implementation. However, these merits are often hampered by the difficulty of handling the LFM spectrum which cannot generally be expressed closed-form. The common practice is to obtain a plot of this spectrum with a digital computer for every single set of LFM pulse parameters.Moreover, reported work has been Justly confined to the spectrum of an ideally rectangular chirp pulse with no rise or fall times.Accordingly, the present work comprises a systerratic study of the LFM spectrum which takes the rise and fall time of the chirp pulse into account and can accommodate any LFM pulse with any parameters.It· formulates rather simple and accurate prediction criteria concerning the behaviour of this spectrum in the different frequency regions. These criteria would facilitate the handling of the LFM technique in theory and practice.

Vergence analysis reveals the influence of axial distances on accommodation with age and axial ametropia

Despite numerous investigations, the aetiology and mechanism of accommodation and presbyopia remains equivocal. Using Gaussian first-order ray tracing calculations, we examine the contribution that ocular axial distances make to the accommodation response. Further, the influence of age and ametropia are also considered. The data show that all changes in axial distances during accommodation reduce the accommodation response, with the reduction in anterior chamber depth contributing most to this overall attenuation. Although the total power loss due to the changes in axial distances remained constant with increasing age, hyperopes exhibited less accommodation than myopes. The study, therefore, enhances our understanding of biometric accommodative changes and demonstrates the utility of vergence analysis in the assessment of accommodation.

Mechanical properties of sheet metal under forming conditions

In the bulge test, a sheet metal specimen is clamped over a circular hole in a die and formed into a bulge by the hydraulic pressure on one side of the specirnen. As the unsupported part of the specimen is deformed in this way, its area is increased, in other words, the material is generally stretched and its thickness generally decreased. The stresses causing this stretching action are the membrane stresses in the shell generated by the hydraulic pressure, in the same way as the rubber in a toy balloon is stretched by the membrane stresses caused by the air inside it. The bulge test is a widely used sheet metal test, to determine the "formability" of sheet materials. Research on this forming process (2)-(15)* has hitherto been almost exclusively confined to predicting the behaviour of the bulged specimen through the constitutive equations (stresses and strains in relation to displacements and shapes) and empirical work hardening characteristics of the material as determined in the tension test. In the present study the approach is reversed; the stresses and strains in the specimen are measured and determined from the geometry of the deformed shell. Thus, the bulge test can be used for determining the stress-strain relationship in the material under actual conditions in sheet metal forming processes. When sheet materials are formed by fluid pressure, the work-piece assumes an approximately spherical shape, The exact nature and magnitude of the deviation from the perfect sphere can be defined and measured by an index called prolateness. The distribution of prolateness throughout the workpiece at any particular stage of the forming process is of fundamental significance, because it determines the variation of the stress ratio on which the mode of deformation depends. It is found. that, before the process becomes unstable in sheet metal, the workpiece is exactly spherical only at the pole and at an annular ring. Between the pole and this annular ring the workpiece is more pointed than a sphere, and outside this ring, it is flatter than a sphere. In the forming of sheet materials, the stresses and hence the incremental strains, are closely related to the curvatures of the workpiece. This relationship between geometry and state of stress can be formulated quantitatively through prolateness. The determination of the magnitudes of prolateness, however, requires special techniques. The success of the experimental work is due to the technique of measuring the profile inclination of the meridional section very accurately. A travelling microscope, workshop protractor and surface plate are used for measurements of circumferential and meridional tangential strains. The curvatures can be calculated from geometry. If, however, the shape of the workpiece is expressed in terms of the current radial (r) and axial ( L) coordinates, it is very difficult to calculate the curvatures within an adequate degree of accuracy, owing to the double differentiation involved. In this project, a first differentiation is, in effect, by-passed by measuring the profile inclination directly and the second differentiation is performed in a round-about way, as explained in later chapters. The variations of the stresses in the workpiece thus observed have not, to the knowledge of the author, been reported experimentally. The static strength of shells to withstand fluid pressure and their buckling strength under concentrated loads, both depend on the distribution of the thickness. Thickness distribution can be controlled to a limited extent by changing the work hardening characteristics of the work material and by imposing constraints. A technique is provided in this thesis for determining accurately the stress distribution, on which the strains associated with thinning depend. Whether a problem of controlled thickness distribution is tackled by theory, or by experiments, or by both combined, the analysis in this thesis supplies the theoretical framework and some useful experimental techniques for the research applied to particular problems. The improvement of formability by allowing draw-in can also be analysed with the same theoretical and experimental techniques. Results on stress-strain relationships are usually represented by single stress-strain curves plotted either between one stress and one strain (as in the tension or compression tests) or between the effective stress and effective strain, as in tests on tubular specimens under combined tension, torsion and internal pressure. In this study, the triaxial stresses and strains are plotted simultaneously in triangular coordinates. Thus, both stress and strain are represented by vectors and the relationship between them by the relationship between two vector functions. From the results so obtained, conclusions are drawn on both the behaviour and the properties of the material in the bulge test. The stress ratios are generally equal to the strain-rate ratios (stress vectors collinear with incremental strain vectors) and the work-hardening characteristics, which apply only to the particular strain paths are deduced. Plastic instability of the material is generally considered to have been reached when the oil pressure has attained its maximum value so that further deformation occurs under a constant or lower pressure. It is found that the instability regime of deformation has already occurred long before the maximum pressure is attained. Thus, a new concept of instability is proposed, and for this criterion, instability can occur for any type of pressure growth curves.

The mechanics of ultrasonic tube bending

The technology of precision bending of tubes has recently increased in importance and is widely demanded for many industrial applications. However, whilst attention has been concentrated on automation and increasing the production rate of the bending machines, it seems that with one exception very little work has been done in order to understand and therefore fundamentally improve the bending process. A new development for the process of draw-bending of tubes, in which the supporting mandrel is axially vibrated at an ultrasonic frequency, has been perfected. A research programme was undertaken to study the mechanics of tube• bending under both vibratory and non-vibratory conditions. For this purpose, a conventional tube-bending machine was modified and equipped with an oscillatory system. Thin-walled mild steel tubes of different diameter to thickness ratios were bent to mean bend radii having various values from 1.5 to 2.0 times the tube diameter. It was found that the application of ultrasonic vibration reduces the process forces and that the force reduction increases with increasing the vibration amplitude. A reduction in the bending torque of up to 30 per cent was recorded and a reduction in the maximum tube-wall thinning of about 15 per cent was observed. The friction vector reversal mechanism as well as a reduction in friction account for the changes of the forces and the strains. Monitoring the mandrel friction during bending showed, in some cases, that the axial vibration reverses the mandrel .mean force from tension to compression and, thus, the mandrel is assisting the tube motion instead of resisting it. A theory has been proposed to describe the mechanics of deformation during draw-bending of tubes, which embodies the conditions of both "with" and "without" mandrel axial vibration. A theoretical analysis, based on the equilibrium of forces approach, has been developed in which the basic process parameters were taken into consideration. The stresses, the strains and the bending torque were calculated utilising this new solution, and a specially written computer programme was used to perform the computations. It was shown that the theory is in good agreement with the measured values of the strains under vibratory and non-vibratory conditions. Also, the predicted bending 'torque showed a similar trend to that recorded experimentally.

Isotropic compression of mixtures of hard and soft spheres

The compaction behaviour of powders with soft and hard components is of particular interest to the paint processing industry. Unfortunately, at the present time, very little is known about the internal mechanisms within such systems and therefore suitable tests are required to help in the interpretative process. The TRUBAL, Distinct Element Method (D.E.M.) program was the method of investigation used in this study. Steel (hard) and rubber (soft) particles were used in the randomly-generated, binary assemblies because they provided a sharp contrast in physical properties. For reasons of simplicity, isotropic compression of two-dimensional assemblies was also initially considered. The assemblies were first subject to quasi-static compaction, in order to define their behaviour under equilibrium conditions. The stress-strain behaviour of the assemblies under such conditions was found to be adequately described by a second-order polynomial expansion. The structural evolution of the simulation assemblies was also similar to that observed for real powder systems. Further simulation tests were carried out to investigate the effects of particle size on the compaction behaviour of the two-dimensional, binary assemblies. Later work focused on the quasi-static compaction behaviour of three-dimensional assemblies, because they represented more realistic particle systems. The compaction behaviour of the assemblies during the simulation experiments was considered in terms of percolation theory concepts, as well as more familiar macroscopic and microstructural parameters. Percolation theory, which is based on ideas from statistical physics, has been found to be useful in the interpretation of the mechanical behaviour of simple, elastic lattices. However, from the evidence of this study, percolation theory is also able to offer a useful insight into the compaction behaviour of more realistic particle assemblies.

Deformation of sand in plane strain and oxisymmetric compression

Small scale laboratory experiments, in which the specimen is considered to represent an element of soil in the soil mass, are essential to the evolution of fundamental theories of mechanical behaviour. In this thesis, plane strain and axisymmetric compression tests, performed on a fine sand, are reported and the results are compared with various theoretical predictions. A new apparatus is described in which cuboidal samples can be tested in either axisymmetric compression or plane strain. The plane strain condition is simulated either by rigid side platens, in the conventional manner, or by flexible side platens which also measure the intermediate principal stress. Close control of the initial porosity of the specimens is achieved by a vibratory method of sample preparation. The strength of sand is higher in plane strain than in axisymmetric compression, and the strains required to mobilize peak strength are much smaller. The difference between plane strain and axisymmetric compression behaviour is attributed to the restrictions on particle movement enforced by the plane strain condition; this results in an increase in the frictional component of shear strength. The stress conditions at failure in plane strain, including the intermediate principal stress, are accurately predicted by a theory based on the stress- dilatancy interpretation of Mohr's circles. Detailed observations of rupture modes are presented and measured rupture plane inclinations are predicted by the stress-dilatancy theory. Although good correlation with the stress-dilatancy theory is obtained during virgin loading, in both axisymmetric compression and plane strain, the stress-dilatancy rule is only obeyed during reloading if the specimen has been unloaded to approximate ambient stress conditions. The shape of the stress-strain curves during pre-peak deformation, in both plane strain and axisymmetric compression, is accurately described bv a combined parabolic-hyperbolic specification.

The strength of column-to-foundation joints in reinforced concrete

This thesis is concerned with the experimental and theoretical investigation into the compression bond of column longitudinal reinforcement in the transference of axial load from a reinforced concrete column to a base. Experimental work includes twelve tests with square twisted bars and twenty four tests with ribbed bars. The effects of bar size, anchorage length in the base, plan area of the base, provision of bae tensile reinforcement, links around the column bars in the base, plan area of column and concrete compressive strength were investigated in the tests. The tests indicated that the strength of the compression anchorage of deformed reinforcing steel in the concrete was primarily dependent on the concrete strength and the resistance to bursting, which may be available within the anchorage . It was shown in the tests without concreted columns that due to a large containment over the bars in the foundation, failure occurred due to the breakdown of bond followed by the slip of the column bars along the anchorage length. The experimental work showed that the bar size , the stress in the bar, the anchorage length, provision of the transverse steel and the concrete compressive strength significantly affect the bond stress at failure. The ultimate bond stress decreases as the anchorage length is increased, while the ultimate bond stress increases with increasing each of the remainder parameters. Tests with concreted columns also indicated that a section of the column contributed to the bond length in the foundation by acting as an extra anchorage length. The theoretical work is based on the Mindlin equation( 3), an analytical method used in conjunction with finite difference calculus. The theory is used to plot the distribution of bond stress in the elastic and the elastic-plastic stage of behaviour. The theory is also used to plot the load-vertical displacement relationship of the column bars in the anchorage length, and also to determine the theoretical failure load of foundation. The theoretical solutions are in good agreement with the experimental results and the distribution of bond stress is shown to be significantly influenced by the bar stiffness factor K. A comparison of the experimental results with the current codes shows that the bond stresses currently used are low and in particular, CPIlO(56) specifies very conservative design bond stresses .

The effects of solid contamination in hydraulic fluids on axial piston pumps

The fluids used in hydraulic systems inevitably contain large numbers of small, solid particles, a phenomenon known as 'fluid contamination'. Particles enter a hydraulic system from the environment, and are generated within it by processes of wear. At the same time, particles are removed from the system fluid by sedimentation and in hydraulic filters. This thesis considers the problems caused by fluid contamination, as they affect a manufacturer of axial piston pumps. The specific project aim was to investigate methods of predicting or determining the effects of fluid contamination on this type of pump. The thesis starts with a theoretical analysis of the contaminated lubrication of a slipper-pad bearing. Statistical methods are used to develop a model of the blocking, by particles, of the control capillaries used in such bearings. The results obtained are compared to published, experimental data. Poor correlation between theory and practice suggests that more research is required in this area before such theoretical analysis can be used in industry. Accelerated wear tests have been developed in the U.S.A. in an attempt to predict pump life when operating on contaminated fluids. An analysis of such tests shows that reliability data can only be obtained from extensive test programmes. The value of contamination testing is suggested to be in determining failure modes, and in identifying those pump components which are susceptible to the effects of contamination. A suitable test is described, and the results of a series of tests on axial piston pumps are presented and discussed. The thesis concludes that pump reliability data can only be obtained from field experience. The level of confidence which can be placed in results from normal laboratory testing is shown to be too low for the data to be of real value. Recommendations are therefore given for the ways in which service data should be collected and analysed.

Plant oils as fuels for compression ignition engines: a technical review and life-cycle analysis

As an alternative fuel for compression ignition engines, plant oils are in principle renewable and carbon-neutral. However, their use raises technical, economic and environmental issues. A comprehensive and up-to-date technical review of using both edible and non-edible plant oils (either pure or as blends with fossil diesel) in CI engines, based on comparisons with standard diesel fuel, has been carried out. The properties of several plant oils, and the results of engine tests using them, are reviewed based on the literature. Findings regarding engine performance, exhaust emissions and engine durability are collated. The causes of technical problems arising from the use of various oils are discussed, as are the modifications to oil and engine employed to alleviate these problems. The review shows that a number of plant oils can be used satisfactorily in CI engines, without transesterification, by preheating the oil and/or modifying the engine parameters and the maintenance schedule. As regards life-cycle energy and greenhouse gas emission analyses, these reveal considerable advantages of raw plant oils over fossil diesel and biodiesel. Typical results show that the life-cycle output-to-input energy ratio of raw plant oil is around 6 times higher than fossil diesel. Depending on either primary energy or fossil energy requirements, the life-cycle energy ratio of raw plant oil is in the range of 2–6 times higher than corresponding biodiesel. Moreover, raw plant oil has the highest potential of reducing life-cycle GHG emissions as compared to biodiesel and fossil diesel.

A micro-compression study of shape-memory deformation in U-13 at.% Nb

Microcompression specimens, 10–15 µm in diameter by 20–30 µm in height, were produced from individual parent grains in a polycrystalline U–13 at.%Nb shape-memory alloy using the focused ion beam technique. The specimens were tested in a nanoindentation instrument with a flat diamond tip to investigate stress–strain behavior as a function of crystallographic orientation. The results are in qualitative agreement with a single-crystal accommodation strain (Bain strain) model of the shape-memory effect for this alloy.

New fiber laser architecture with transform-limited nonlinear spectral compression

We numerically demonstrate a new fiber laser architecture supporting spectral compression of negatively chirped pulses in passive normally dispersive fiber. Such a process is beneficial for improving the energy efficiency of the cavity as it prevents narrow spectral filtering from being highly dissipative. The proposed laser design provides an elegant way of generating transform-limited picosecond pulses. © 2012 IEEE.

Amplifier similariton fiber laser with nonlinear spectral compression

We propose a new concept of a fiber laser architecture supporting self-similar pulse evolution in the amplifier and nonlinear spectral pulse compression in the passive fiber. The latter process allows for transform-limited picosecond pulse generation, and improves the laser’s power efficiency by preventing strong spectral filtering from being highly dissipative. Aside from laser technology, the proposed scheme opens new possibilities for studying nonlinear dynamical processes. As an example, we demonstrate a clear period-doubling route to chaos in such a nonlinear laser system.

Performance, emission and combustion characteristics of an indirect injection (IDI) multi-cylinder compression ignition (CI) engine operating on neat jatropha and karanj oils preheated by jacket water

Renewable non-edible plant oils such as jatropha and karanj have potential to substitute fossil diesel fuels in CI engines. A multi-cylinder water cooled IDI type CI engine has been tested with jatropha and karanj oils and comparisons made against fossil diesel. The physical and chemical properties of the three fuels were measured to investigate the suitability of jatropha and karanj oils as fuels for CI engines. The engine cooling water circuit and fuel supply systems were modified such that hot jacket water preheated the neat plant oil prior to injection. Between jatropha and karanj there was little difference in the performance, emission and combustion results. Compared to fossil diesel, the brake specific fuel consumption on volume basis was around 3% higher for the plant oils and the brake thermal efficiency was almost similar. Jatropha and karanj operation resulted in higher CO 2 and NO x emissions by 7% and 8% respectively, as compared to diesel. The cylinder gas pressure diagram showed stable engine operation with both plant oils. At full load, the plant oils gave around 3% higher peak cylinder pressure than fossil diesel. With the plant oils, cumulative heat release was smaller at low load and almost similar at full load, compared to diesel. At full load, the plant oils exhibited 5% shorter combustion duration. The study concludes that the IDI type CI engine can be efficiently operated with neat jatropha (or karanj) oil preheated by jacket water, after small modifications of the engine cooling and fuel supply circuits. © 2012 Elsevier Ltd.