Many studies of natural landscape preference have demonstrated that qualities such as 'complexity' and 'naturalness' are associated with preference, but have struggled to define the key characteristics of these qualities. Recently, the development of software programs and digital techniques has offered researchers new ways of quantifying the landscape qualities associated with preference. Among them fractal geometry offers the most promising approach. Fractals have been defined as mathematical models of organic objects and patterns as opposed to the straight lines and perfect circles of Euclidean geometry found in man-made environments. Fractal patterns are mainly characterized by their dimension, which could be described as a statistical quantification of complexity. By applying this mathematical concept to digital images, several studies claim to have found a correlation between the fractal dimensions of a set of images and the images' preference ratings. Such studies have particularly focussed on demonstrating support for the hypothesis that patterns with a fractal dimension of around 1.3 induce better responses than others. However, much of this research so far has been carried out on abstract or computer-generated images. Furthermore, the most commonly used method of fractal analysis, the box-counting method, has many limitations in its application to digital images which are rarely addressed. The aim of this thesis is to explore empirically the suggestion that landscape preference could be influenced by the fractal characteristics of landscape photographs. The first part of this study was dedicated to establishing the robustness and validity of the box-counting method, and apply it to landscape images. One of the main limitations of the box-counting method is its need for image pre-processing as it can only be applied to binary (black and white) images. Therefore, to develop a more reliable method for fractal analysis of landscapes, it was necessary to compare different methods of image segmentation, i.e the reduction of greyscale photographs into binary images. Each method extracted a different structure from the original photograph: the silhouette outline, the extracted edges, and three different thresholds of greyscale. The results revealed that each structure characterized a different aspect of the landscape: the fractal dimension of the silhouette outline could quantify the height of the vegetation, while the fractal dimension of the extracted edges characterized complexity. The second part of the study focused on collecting preference ratings for the landscape images previously analysed, using an online survey disseminated in France and the UK. It was found that different groups of participants reacted differently to the fractal dimensions, and that some of those groups were significantly influenced by those characteristics while others were not. Unexpectedly, the variable most correlated with preference was the fractal dimension of the image's extracted edges, although this variable's predictive power was relatively low. The study concludes by summarising the issues involved in estimating the fractal dimensions of landscapes in relation to human response. The research offers a set of reliable and tested methods for extracting fractal dimensions for any given image. Using such methods, it produces results which challenge previous hypotheses and findings in relation to fractal dimensions that predict human preference, identifying gaps in understanding and promising future areas of research.

Visually complex objects with infinitesimally fine features, naturally call for mathematical representations. The geometrical property of self-similarity - the whole similar to its parts - when iterated to infinity generates such features. Finite sets of affine contractions called Iterated Function Systems (IFS), with their compact attractors IFS fractals, can be applied to represent detailed self-similar shapes, such as trees or mountains. The fine local features of such attractors prevent their straightforward geometrical handling, and often imply a non-integer Hausdorff dimension. The main goal of the thesis is to develop an alternative approach to the geometry of IFS fractals in the classical sense via bounding sets. The results are obtained with the objective of practical applicability. The thesis thus revolves around the central problem of determining bounding sets to IFS fractals - and the convex hull in particular - emphasizing the fundamental role of such sets in their geometry. This emphasis is supported throughout the thesis, from real-life and theoretical applications to numerical algorithms crucially dependent on bounding.

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The principal aim of this thesis was to develop and implement a standardised protocol for the fractal analysis of cancellous bone architecture. Cancellous bone structure from different skeletal sites in groups of osteoporotic, osteoarthritic and normal individuals was analysed. The results of fractal analysis were explained in the context of conventional bone histomorphometry and a priori knowledge to advance the understanding of cancellous bone architecture. There has been much effort devoted to the pursuit of descriptors of cancellous bone complexity. The aim of these endeavours has been to develop morphological descriptors of bone quality that explain the functional properties of the cancellous bone structure for age-related changes, the effect of disease processes or the effect of therapeutic agents on the diseased skeleton. The fractal analysis of the complexity of cancellous bone architecture promises to be an exciting addition to existing analytical techniques. The establishment of a standardised methodology for the fractal analysis of cancellous bone encompassed many components. Knowledge of the stereological and histomorphometric principles that are employed in currently available techniques enabled a comprehensive examination of the factors that effect the measurement of the fractal dimensions. The methodology presented in this thesis has been optimised specifically for measuring sectional fractal dimensions in histological sections of cancellous bone. The sectional fractal dimensions show that, over three ranges of scale, cancellous bone is effectively fractal at multiple sites in the normal skeleton. The three sectional fractal dimensions describe different morphological compartments of the cancellous bone structure. Fractal 1 describes the surface texture of the trabeculae, fractal 2 describes the shape or form of individual trabeculae and fractal 3 describes the spatial arrangement or overall architecture of the cancellous bone. This thesis reports that in the normal skeleton there are differences between skeletal sites for the fractal dimensions, which are dependent on the functional properties of the skeletal sites. Fractal 2 and fractal 3 for subchondral cancellous bone is greater than vertebral body and iliac crest cancellous bone, which indicates greater morphological complexity. Also, fractal 2 and fractal 3 in subchondral cancellous bone show an age-related decrease, which suggests that the cancellous bone structure becomes less complex with age. This interostotic variability in response to ageing is indicative of the heterogeneity in functional properties of cancellous bone in the skeleton. In this thesis, fractal analysis has been shown to detect morphological differences in the cancellous bone between normals, osteoporotics and osteoarthritics in the compressive and tensile trabeculae of the femoral head and the iliac crest. These data have provided new insights into the mechanisms of change to cancellous bone structure in ageing and in disease. Age-related changes in the structural parameters of cancellous bone are seen at all the skeletal sites in the normals but are only present in the compressive trabeculae of the femoral head in the osteoporotics and not at all in the osteoarthritics. These observations indicate that these disease processes are associated with an uncoupling of the control mechanisms that affect cancellous bone structural complexity. In the normals, the fractal dimensions only show age-related change in the tensile trabeculae of the femoral head, suggesting that fractal analysis is not suitable for detecting the age-related changes that are quantified by the structural parameters of cancellous bone in these study groups but the fractal dimensions detect underlying cancellous bone complexity independent of age. For the osteoporotics, fractal 1 is the same at all skeletal sites. This suggests that the relative levels of remodeling activity are the same for both normals and osteoporotics. Fractal 2 for both the compressive and tensile trabeculae in the femur is significantly lower for the osteoporotics than the normals but in the iliac crest, fractal 2 is the same. This implies that in the femoral head the osteoporotics have trabeculae that are significantly less complex in shape than the normals. This phenomenon is not seen in the iliac crest, which is usually the site of diagnostic biopsy. Therefore, biopsies for diagnosis of osteoporosis may not show changes in cancellous bone structural complexity that are evident in disease affected sites. The structural parameters of cancellous bone show that osteoporotics lose whole trabeculae due to perforation of trabeculae, through decreased Tb.N and increased Tb.Sp. This leads to less interconnection between trabeculae, loss of branching and more rounded trabeculae, hence the trabeculae are less complex in shape. For fractal 3, in compressive and tensile regions of the femur the osteoporotics are significantly lower than the normals and in the iliac crest the osteoporotics are the same as the normals. This indicates that in the femoral head the spatial arrangement of the trabeculae within the cancellous structure of the osteoporotics is less complex. The structural parameters of cancellous bone show that there is loss of whole trabeculae, which is associated with increased spatial separation between the trabeculae as bone is lost. For the osteoarthritics, fractal 1 is the same as the normals at all skeletal sites. Fractal 2 for the compressive trabeculae in the femoral head is significantly higher for the osteoarthritics than the normals but in the tensile trabeculae of the femoral head and the iliac crest fractal 2 for the osteoarthritics is the same as the normals. This implies that in the compressive trabeculae of the femoral head the osteoarthritics have trabeculae that are significantly more complex in shape than the normals. The structural parameters of cancellous bone show that the compressive trabeculae of the femoral head are thicker, more numerous and less widely separated with greater BV/TV than the normals. This leads to greater interconnectivity between trabeculae and more complex branching, hence the trabeculae are more complex in shape. For fractal 3, in the compressive and tensile regions of the femoral head the osteoarthritics and the normals are the same but in the iliac crest the osteoarthritics are lower than the normals. This indicates that the spatial arrangement of the trabeculae within the cancellous structure of the osteoarthritics does not change in response to the disease process in subchondral cancellous bone adjacent to the articular lesion but in the iliac crest the spatial arrangement of the trabeculae in osteoarthritics is less complex in shape. The structural parameters of cancellous bone show that BV/TV is increased in the compressive and tensile trabeculae of the femoral head but not in the iliac crest of the osteoarthritics. This indicates that the spatial complexity of the trabecular arrangement within the cancellous structure of osteoarthritics changes independently of changes in cancellous bone structure detected by the structural parameters of cancellous bone. The sectional fractal dimensions have detected differences in morphological complexity between the normals and disease groups and between the skeletal sites. These novel data have been obtained using an innovative technique that is not dependent on assumptions based on conceptual models of cancellous bone structure. A priori knowledge of bone biology is utilised to enable the fractal analysis to measure specific morphological entities within the cancellous bone structure. The fractal dimensions have identified changes in the morphological complexity of specific components of the cancellous structure, which are not identified by existing model-based morphometric techniques. This has enabled new understanding of how change to cancellous bone structure occurs as a result of a disease process. Fractal analysis is a novel tool that will prove useful for the study of changes in cancellous bone structure due to disease and to study the use of therapies to alter or maintain the quality of cancellous bone architecture. / Thesis (Ph.D.)--Medical School, 2002.

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This thesis investigates the underlying causes of friction and ine ciency within an internal combustion engine, focusing on the ring-liner conjunction in the vicinity of the power-stroke top dead centre reversal. In such lubricated contacts, friction is the result of the interplay between numerous kinetics, with those at micro- and nano-scale interactions being signi cantly di erent than the ones at larger scales. A modi ed Elrod's cavitation algorithm is developed to determine the microscopic tribological characteristics of the piston ring-liner contact. Predicting lubricant tran- sient behaviour is critical when the inlet reversal leads to thin lms and inherent metal-to-metal interaction. The model clearly shows that cavitation at the trailing edge of the ring-liner contact generated pre-reversal, persists after reversal and pro- motes starvation and depletion of the oil lm. Hence, this will lead to boundary friction. A fractal based boundary friction model is developed for lightly loaded asperity con- tacts, separated by diminishing small lms, usually wetted by a layer of molecules adsorbed to the tips of the asperities. In nano-scale conjunctions, a lubricant layering e ect often takes place due to the smoothness of surfaces, which is governed by the surface and lubricant properties. A molecularly thin layer of lubricant molecules can adhere to the asperities, being the last barrier against direct surface contact. As a result, boundary friction (prevailing in such diminishing gaps) is actually determined by a combination of shearing of a thin adsorbed lm, adhesion of approaching as- perities and their plastic deformation. A model for physio-chemical hydrodynamic mechanism is successfully established, describing the formation of thin adsorbed lms between asperities. This model is e ectively integrated with separately devel- oped models that predict the adhesive and plastic contact of asperities.

The goals of this thesis were: (1) to develop a data acquisition system for measuring gait parameters and (2) to determine the effect of knee pads on gait and comfort. The data acquisition system consisted of a data acquisition card that was inserted in the PC card (PCMCIA) slot of a laptop computer, a knee goniometer, foot switches, and pressure sensors. Various drive circuits were designed to connect the different sensors to the data acquisition card. The gait analysis results showed that the knee pads do not have a significant effect on long range gait correlations calculated from the stride interval. Pressure measurements between the knee pads and the knee showed that a pressure in the range of 0 to 8.31 psi occurred when kneeling. The maximum pressure for the sensor located under the top strap of the knee pad occurred when getting into and out of the kneeling stance. The data acquisition system successfully met the design objectives. The stride interval was recorded and analyzed, and pressures were successfully measured and analyzed.

O presente trabalho tem como objetivo caracterizar e correlacionar formas de onda de sinais de emissÃo acÃstica, utilizando mÃtodos de anÃlise espectral e fractal, em corpos de prova previamente soldados com seus respectivos defeitos, avaliando assim a integridade estrutural do material aÃo carbono ASTM 516 Grau 60, utilizado em vasos de pressÃo, tubulaÃÃes, esferas de armazenamento, etc. Os sinais de emissÃo acÃstica foram gerados submetendo os corpos de prova a ensaios de traÃÃo. Para anÃlise dos sinais no domÃnio dos tempos, foram utilizados o mÃtodo de contagem de caixas, que fornece a dimensÃo fractal, e o de intervalo re-escalado de Hurst, e no domÃnio das freqÃÃncias o mÃtodo espectral de Fourier. AtravÃs das relaÃÃes previstas pelas leis de escala, concluiu-se que os expoentes calculados pelos mÃtodos espectral de Fourier e reescalado de Hurst, correlacionam-se entre si, bem como com a dimensÃo fractal obtida pelo mÃtodo de contagem de caixas. Mostrou-se tambÃm a existÃncia de duas regiÃes de escala distintas que caracterizam a mudanÃa do regime elÃstico para o regime plÃstico quando as amostras foram submetidas ao carregamento de traÃÃo. Verificou-se ainda que este comporta-mento foi caracterÃstico tanto para os materiais soldados como para o metal de base. / The present work aims to characterize and correlate waveforms of acoustic emission signals, using methods of spectral analysis and fractal in specimens previously soldiers with their defects, thus evaluating the structural integrity of the material carbon steel ASTM 516 Grade 60 used in pressure vessels, piping, storage spheres, etc.. The acoustic emission signals were generated by subjecting the specimens to tensile tests. For analysis of the signals in the time domain, we used the method of box counting, which provides the fractal dimension, and re-scaled range of Hurst, and in the frequency domain the Fourier spectral method. Through the relations laid down by law scale, it was concluded that the exponents calculated by Fourier transform and spectral methods reescalado Hurst, are correlated with each other as well as the fractal dimension obtained from a box counting. It was also shown existence of two regions of different scale characterizing the change of the elastic to the plastic regime when the samples were subjected to traction. It was further found that this behavior is characteristic for both the welded material as for the parent metal.