Fractal Analysis

Fractal analysis is becoming more and more common in all walks of life. This includes biomedical engineering, steganography and art. Writing one book on all these topics is a very difficult task. For this reason, this book covers only selected topics. Interested readers will find in this book the topics of image compression, groundwater quality, establishing the downscaling and spatio-temporal scale conversion models of NDVI, modelling and optimization of 3T fractional nonlinear generalized magneto-thermoelastic multi-material, algebraic fractals in steganography, strain induced microstructures in metals and much more. The book will definitely be of interest to scientists dealing with fractal analysis, as well as biomedical engineers or IT engineers. I encourage you to view individual chapters

Machine Learning of Scientific Events: Classification, Detection, and Verification

Classification and segmentation of objects using machine learning algorithms have been widely used in a large variety of scientific domains in the past few decades. With the exponential growth in the number of ground-based, air-borne, and space-borne observatories, Heliophysics has been taking full advantage of such algorithms in many automated tasks, and obtained valuable knowledge by detecting solar events and analyzing the big-picture patterns. Despite the fact that in many cases, the strengths of the general-purpose algorithms seem to be transferable to problems of scientific domains where scientific events are of interest, in practice there are some critical issues which I address in this dissertation. First, I discuss the four main categories of such issues and then in the proceeding chapters I present real-world examples and the different approaches I take for tackling them. In Chapter II, I take a classical path for classification of three solar events; Active Regions, Coronal Holes, and Quiet Suns. I optimize a set of ten image parameters and improve the classification performance by up to 36%. In Chapter III, in contrast, I utilize an automated feature extraction algorithm, i.e., a deep neural network, for detection and segmentation of another solar event, namely solar Filaments. Using an off-the-shelf algorithm, I overcome several of the issues of the existing detection module, while facing an important challenge; lack of an appropriate evaluation metric for verification of the segmentations. In Chapter IV, I introduce a novel metric to provide a more accurate verification especially for salient objects with fine structures. This metric, called Multi-Scale Intersection over Union (MIoU), is a fusion of two concepts; fractal dimension from Geometry, and Intersection over Union (IoU) which is a popular metric for segmentation verification. Through several experiments I examine the advantages of using MIoU over IoU, and I conclude this chapter by a follow-through on the segmentation results of the previously implemented filament detection module

The Role of Material Structure in Compacted Earthen Building Materials: Implications for Design and Construction

Rammed earth is an earthen construction material and an ancient construction technique. It is formed by compacting layers of moist sandy loam subsoil into formwork which is then removed, exposing the material and creating a freestanding, monolithic structure. In this thesis, the behaviour of rammed earth is investigated in terms of unsaturated soil mechanics of compacted earthen materials. Basic unsaturated soil mechanics theory is discussed and a method for linking the behaviour and material structure of an unsaturated soil is presented through the development of a model for predicting a soil's water retention curve using the soil pore size distribution and capillary and adsorption phenomena. A series of experiments is then performed in order to explain the behaviour of rammed earth in tension and compression under varying conditions in terms of the material micro-- and macrostructures. An analysis of the sample manufacturing process is presented in order to understand formation of rammed earth's structure in both natural and laboratory-prepared materials. The effects of temperature and humidity, related to a number of sites around the world, on the compressive strength and of changing water content and clay flocculation on the tensile strength of rammed earth are then investigated and combined in order to determine the sources of strength in rammed earth. The pore networks of several rammed earth samples under compression and those of rammed earth samples comprising multiple compacted layers are then investigated using X-Ray computed tomography in order to determine the effects of loading and layering on the material macrostructure and to support results presented in previous chapters. In the final chapter, implications for the design, construction and conservation of rammed earth structures are discussed based on the findings of investigations presented in the preceding chapters

Experimental & Numerical Investigation of Pool Boiling on Engineered Surfaces with Integrated Thin-flim Temperature Sensors

The objective of this investigation is to measure and analyze surface temperature fluctuations in pool boiling. The surface temperature fluctuations were recorded on silicon surfaces with and without multi-walled carbon nanotubes (MWCNT). Novel Thin Film Thermocouples (TFT) are micro-fabricated on test substrates to measure surface temperatures. A dielectric liquid refrigerant (PF-5060) is used as test fluid. Both nucleate and lm boiling regimes are investigated for the silicon test substrates. Dynamics of nucleate boiling is investigated on the CNT coated substrates. High frequency temperature fluctuation data is analyzed for the presence of determinism using non-linear time series analysis techniques in TISEAN(copyright) software. The impact of subcooling and micro/nano-scale surface texturing using MWCNT coatings on the dynamics of pool boiling is assessed. Dynamic invariants such as correlation dimensions and Lyapunov spectrum are evaluated for the reconstructed attractor. A non-linear noise reduction scheme is employed to reduce the level of noise in the data. Previous investigations in pool boiling chaos, reported in literature were based on temperature measurements underneath the test surface consisting of single or few active nucleation sites. Previous studies have indicated the presence of low-dimensional behavior in nucleate boiling and high-dimensional behavior in CHF and film boiling. Currently, there is no study detailing the effects of multiple nucleation sites, subcooling and surface texturing on pool boiling dynamics. The investigation comprises of four parts: i) in situ micro-machining of Chromelalumel (K-type) TFT, ii) calibration of these sensors, iii) utilizing these sensors in pool boiling experiments iv) analysis of these fluctuations using techniques of nonlinear time series analysis. Ten TFT are fabricated on a rectangular silicon surface within an area of ~ 3.00 cm x 3.00 cm. The sensing junctions of the TFT measure 50 mm in width and 250 nm in depth. Surface temperature fluctuations of the order of i) 0.65-0.93 degrees C are observed near ONB ii) 2.3-6.5 degrees C in FDNB iii) 2.60-5.00 degrees C at CHF and iv) 2.3-3.5 degrees C in film boiling. Investigations show the possible presence of chaotic dynamics near CHF and in film-boiling in saturated and subcooled pool boiling. Fully-developed nucleate boiling (FDNB) is chaotic. No clear assessment of the dynamics could be made in the onset of nucleate boiling (ONB) and partial nucleate boiling (PNB) regimes due to the effects of noise. However, the frequency spectra in these regimes appear to have two independent frequencies and their integral combinations indicating a possible quasiperiodic bifurcation route to chaos. The dimensionality in FDNB, at CHF and in film-boiling is lower in saturated pool boiling as compared to values in corresponding regimes in subcooled pool boiling. Surface temperature fluctuations can damage electronic components and need to be carefully controlled. Understanding the nature of these fluctuations will aid in deciding the modeling approach for surface temperature transients on an electronic chip. Subsequently, the TFT signals can be employed in a suitable feedback control loop to prevent the occurrence of hotspots

Fractal analyses of some natural systems

Fractal dimensions are estimated by the box-counting method for real world data sets and for mathematical models of three natural systems. 1 he natural systems are nearshore sea wave profiles, the topography of Shei-pa National Park in Taiwan, and the normalised difference vegetation index (NDV1) image of a fresh fern. I he mathematical models which represent the natural systems utilise multi-frequency sinusoids for the sea waves, a synthetic digital elevation model constructed by the mid-point displacement method for the topography and the Iterated Function System (IFS) codes for the fern leaf. The results show that similar fractal dimensions are obtained for discrete sub-sections of the real and synthetic one-dimensional wave data, whilst different fractal dimensions are obtained for discrete sections of the real and synthetic topographical and fern data. The similarities and differences are interpreted in the context of system evolution which was introduced by Mandelbrot (1977). Finally, the results for the fern images show that use of fractal dimensions can successfully separate void and filled elements of the two-dimensional series

Aspectos da variabilidade espacial e arrasto em sítios experimentais da Floresta Amazônica

In this doctoral thesis is characterized and studies the forest-atmosphere interaction through nonlinear tools using data from micrometeorological towers and high-resolution environmental satellites images. We analyzed the forest-atmosphere interaction and characteristics of horizontal heterogeneity regarding the Amazonian experimental sites Sustainable Development Reserve Uatumã (1 56 'S 2 21' S and 59 16 'W 57 57' W) and the Biological Reserve in Jarú Rondônia (10 05 'S 10 19' S and 61 35 'W 61 57' W), which contain primary forest. We analyzed the average aspect vertical wind profile above and inside the canopy structure, such as analytical expressions for it, for example, a hyperbolic tangent function and its variant, considering also the variability of the inflection point of the height of the profile and its relation to the scale of the occurrence of coherent structures. We studied aspects of surface drag and consequences of its existence drains above dense forests. We have investigated the occurrence of gravity waves (GWs) above experimental site in central Amazonia, generated by the ground swell in the nocturnal boundary layer (NBL). We used the number of internal waves to classify Scorer forced by gravity or no topography. To this were certain characteristic scales of rolling terrain for various wind directions between wind north-east and south-east, which are prevalent in the region. Altimetric data were used with a resolution of 30 m, which provided information to detect the characteristic length scales of the terrain undulations in specific directions via multi-scale analysis using the Continuous Wavelet Transform with a Morlet wavelet analyzer. Were also used meteorological data measured in a tower 80 meters high (2 08 '40.0 "S 59 ° 00' 10.0" W) which lies approximately 130 meters above sea level, as part of German-Brazilian scientific project "ATTO" (Amazonian Tall Tower Observatorium) in experimental site of Sustainable Development Reserve Uatumã, northeast of Amazonas. The results showed that most of the GWs detected satisfied the criterion Steeneveld et al. (2009) to characterize waves induced Orografically. Those who did not meet this criterion were detected preferably in two arcs centered on meteorological tower, the first in which the wind direction was between 0° to 45°, and the second, with the wind direction between 120° and 180°. WGs events not forced by the topography are associated with the "Night Regime Turbulence 3" proposed by Sun et al. (2012), where the local effects do not predominate in the generation of turbulence, but effects associated with strong descending air movements and located in time (the top-down phenomena). As part of the characterization of horizontal heterogeneity of the land, we used high spatial resolution satellite imagery (IKONOS, 1 -4 m) to investigate aspects of variability in scale texture regions covered by the forest and deforested area in the Rebio- Jarú. We sought to determine the existence of possible variability patterns in the texture of vegetation cover for scale in both regions covered by forest, pasture, forestpasture, cultivated area and water bodies. The detection of texture characteristic scales was developed through directional study based on the application of Continuous Wavelet Transform Two-dimensional, using the Morlet wavelet function of analyzer. The Recurrence Analysis and its quantifiers was a method of analysis of nonlinear time series used to discriminate regions covered by forests of others with different land uses in the area located west of the Brazilian Amazon from a satellite image of high resolution . This was done as part of efforts to identify and characterize heterogeneity patterns of tropical forest and other areas with coverage in the Amazon region. The results suggest the existence of possible preferential axes of texture patterns in forested areas and specific standards for areas with different land cover and water bodies. In addition to these results and innovative methodologies, the conclusion of this study highlights the importance of adequately characterize the horizontal variability of the land and to investigate aspects of the relationship between this variability and the occurrence of specific physical phenomena in the atmospheric boundary layer. This type of research will point certainly innovative ways to identify the most appropriate parameterization of forest-atmosphere exchange processes in complex terrain.Nesta tese de doutorado caracteriza-se e estuda-se a interação floresta-atmosfera por meio de ferramentas não-lineares utilizando dados de torres micrometeorológicas e de imagens de alta resolução de satélites ambientais. Foram analisadas a interação floresta-atmosfera e características da heterogeneidade horizontal referentes aos sítios experimentais amazônicos de Reserva de Desenvolvimento Sustentável de Uatumã (1º 56' S 2º 21' S e 59º 16' W 57º 57' W) e da Reserva Biológica do Jarú em Rondônia (10º 05' S 10º 19' S e 61º 35' W 61º 57' W), os quais contêm floresta primária. Foram analisados aspectos do perfil vertical do vento médio acima e no interior do dossel florestal, tais como expressões analíticas para ele, como, por exemplo, a função tangente hiperbólica e variante suas, considerando-se inclusive a variabilidade da altura do ponto de inflexão do perfil e sua relação com a escala de ocorrência de estruturas coerentes. Foram estudados aspectos do arrasto superficial e consequências de sua existência em escoamentos acima de florestas densas. Procurou-se investigar a ocorrência de ondas de gravidade (OGs) acima de sítio experimental na Amazônia central, geradas pela ondulação do terreno na camada limite noturna (CLN). Utilizouse o número de Scorer para classificar ondas internas de gravidade forçadas ou não pela orografia. Para isso foram determinadas escalas características das ondulações do terreno para várias direções do vento compreendidas entre vento de norte-leste e de leste-sul, que são predominantes na região. Foram utilizadas imagens altimétricas com resolução de 30 m, as quais forneceram informações para a detecção de escalas de comprimento características das ondulações do terreno em direções específicas, via análise multi-escala, utilizando-se a Transformada Wavelet Contínua, com uma wavelet analisadora de Morlet. Também foram utilizados dados meteorológicos medidos em uma torre de 80 m de altura (2º 08' 40,0" S 59° 00' 10,0" W) que se encontra aproximadamente a 130 m acima do nível do mar, como parte integrante do projeto científico teuto-brasileiro “ATTO” (Amazonian Tall Tower Observatorium), no sitio experimental da Reserva de Desenvolvimento Sustentável de Uatumã, a nordeste do Amazonas. Os resultados mostraram que a maior parte das OGs detectadas satisfizeram o critério de Steeneveld et al. (2009) para caracterização de ondas induzidas orograficamente. Aquelas que não satisfizeram tal critério foram as detectadas preferencialmente em dois arcos, centrados na torre meteorológica, o primeiro, em que a direção do vento esteve entre 0º a 45º, e o segundo, com a direção do vento entre 120º e 180º. Os eventos de OGs não forçadas pela orografia estão associados ao “Regime Noturno de Turbulência 3” proposto por Sun et al. (2012), em que os efeitos locais não predominam na geração de turbulência, mas efeitos associados a fortes movimentos descendentes de ar bem localizados no tempo (fenômenos do tipo top-down). Como parte da caracterização da heterogeneidade horizontal do terreno, utilizouse imagem de satélite de alta resolução espacial (IKONOS, 1 -4 m) para investigar aspectos da variabilidade em escala da textura de regiões cobertas pela por floresta e desmatadas em área da Rebio-Jarú. Procurou-se determinar a existência de possíveis padrões de variabilidade na textura da cobertura vegetal por escala em regiões tanto cobertas por floresta, pastagem, floresta-pastagem, área cultivada e corpos de água. A detecção de escalas características da textura foi desenvolvida por meio de estudo direcional baseado na aplicação da Transformada Wavelet Contínua Bidimensional, com a utilização da função wavelet analisadora de Morlet. A Análise de Recorrência e de seus quantificadores foi um método de análise de séries temporais não lineares utilizados para discriminar regiões cobertas por florestas de outras com distintos usos da terra em área situada a oeste da Amazônia brasileira a partir de uma imagem de satélite de alta resolução. Isso foi efetuado como parte dos esforços para identificar e caracterizar padrões de heterogeneidade da floresta tropical e de áreas com outras coberturas na região amazônica. Os resultados sugerem a existência de possíveis eixos preferenciais de padrões de textura em áreas cobertas por floresta e de padrões específicos para áreas com diferentes coberturas do solo e com corpos de água. Além desses resultados e metodologias inovadoras, a conclusão deste estudo destaca a importância de caracterizar adequadamente a variabilidade horizontal do terreno e de investigar aspectos da relação entre esta variabilidade e a manifestação de fenômenos físicos específicos na camada limite atmosférica. Tal tipo de investigação certamente apontará caminhos inovadores na busca de parametrizações mais adequadas dos processos de troca floresta-atmosfera em terrenos complexos