Traditional 1H lung imaging using MRI faces numerous challenges and difficulties due to low proton density and air-tissue susceptibility artifacts. New imaging techniques using inhaled xenon gas can overcome these challenges at the cost of lower signal to noise ratio. The signal to noise ratio determines reconstructed image quality and is an essential parameter in ensuring reliable results in MR imaging. The traditional RF surface coils used in MR imaging exhibit an inhomogeneous field, leading to reduced image quality. For the last few decades, fractal-shaped antennas have been used to optimize the performance of antennas for radiofrequency systems. Although widely used in radiofrequency identification systems, mobile phones, and other applications, fractal designs have yet to be fully researched in the MRI application space. The use of fractal geometries for RF coils may prove to be fruitful and thus prompts an investiga- tion as the main goal of this thesis. Preliminary simulation results and experimental validation results show that RF coils created using the Gosper and pentaflake offer improved signal to noise ratio and exhibit a more homogeneous field than that of a traditional circular surface coil. / Thesis / Master of Applied Science (MASc)

Yes / A decoupling metamaterial (MTM) configuration based on fractal electromagnetic-bandgap (EMBG) structure is shown to significantly enhance isolation between transmitting and receiving antenna elements in a closely-packed patch antenna array. The MTM-EMBG structure is cross-shaped assembly with fractal-shaped slots etched in each arm of the cross. The fractals are composed of four interconnected-`Y-shaped' slots that are separated with an inverted-`T-shaped' slot. The MTM-EMBG structure is placed between the individual patch antennas in a 2 × 2 antenna array. Measured results show the average inter-element isolation improvement in the frequency band of interest is 17, 37 and 17 dB between radiation elements #1 & #2, #1 & #3, and #1 & #4, respectively. With the proposed method there is no need for using metallic-via-holes. The proposed array covers the frequency range of 8-9.25 GHz for X-band applications, which corresponds to a fractional-bandwidth of 14.5%. With the proposed method the edge-to-edge gap between adjacent antenna elements can be reduced to 0.5λ 0 with no degradation in the antenna array's radiation gain pattern. Across the array's operating band, the measured gain varies between 4 and 7 dBi, and the radiation efficiency varies from 74.22 and 88.71%. The proposed method is applicable in the implementation of closely-packed patch antenna arrays used in SAR and MIMO systems. / Partially supported by innovation programme under grant agreement H2020-MSCA-ITN-2016 SECRET-722424 and the financial support from the UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/E022936/1.

Wavelet Modulation (WM)---also referred to as fractal modulation---simultaneously sends data at multiple rates through an unknown channel. This novel multirate diversity strategy offers improved message recovery over conventional modulation techniques: if the message is not received at one rate due to the channel disturbances, it can be received at another rate where the channel is clear. Previous research has demonstrated the performance of wavelet modulation in Gaussian channels. This paper extends the investigation to the performance of wavelet modulation in time varying channels. We show that bit error rate (BER) wavelet demodulation performance in the additive, white, Gaussian noise (AWGN) channel is comparable to theoretical binary phase shift keying. Our results depict the improvement in performance that can be realized for time varying channels by utilizing the various rates of wavelet modulation; BER versus SNR curves for each fading channel show how the message at one rate can be more accurately recovered than at another rate. Furthermore, we also present results indicating the dramatic improvement in wavelet demodulation performance when multiple rates are available and utilized for demodulation. This improvement in performance is highly visible in BER performance for the AWGN and flat fading channels. Finally, a comparison of binary phase shift keying (BPSK) and WM in a frequency selective channel is performed. The BER improvement of WM is shown when demodulation is done at rates which are least corrupted by ISI. We illustrate our new algorithm that: identifies the channel characteristics; determines which rates are maximally corrupted by ISI; and, utilizes only those uncorrupted copies in demodulation. / Master of Science

The surfaces of rivers are hotspots for biogeochemical exchange and emit significant amounts of greenhouse gases globally. Estimates of river surface area are critical to determining fluvial greenhouse gas evasion yet are currently poorly constrained. The relative abundance of narrow rivers to wide rivers is commonly assumed to be fractal, or scale invariant. This assumption aids in statistical estimates of river surface area but has not been tested across spatial scales. We measured river size in four nested basins within the Mississippi River Basin using a combination of remote sensing and field surveying to determine the statistical size distribution of rivers from continental to headwater scales. We found that the relative abundance of narrow rivers to wide rivers consistently fits a log-normal probability density function, supporting the assumption of fractal river size. Using the fractal size distribution of rivers, we estimated a total river surface area of 17,828 ± 5,126 km2 (0.54 ± 0.16 % of land surface area) in the Mississippi River Basin which is comparable to previous studies. Our multi-scale approach revealed the fractal nature of river size and allowed for a more accurate accounting of river surface area with implications for the role of rivers in biogeochemical cycling. / Master of Science / Greenhouse gases and other gaseous chemicals enter the atmosphere at the surfaces of rivers. Knowing the total surface area of rivers can help us figure out how much greenhouse gas comes from rivers, but there is a wide range of estimates for the total river surface area. Some estimates of total river surface area rely on the assumption that river networks look similar when zoomed in or zoomed out, like the leaves of a fern or the crystals in a snowflake. To test this assumption, we measured the size of rivers in the Mississippi River Basin at large and small scales using satellite and aerial imagery as well as by hand in the field. We found evidence that supports the assumption that river networks look similar at all scales. We also used our measurements to make a statistical estimate of total river surface area in the Mississippi River Basin: 17,828 ± 5,126 km2, or 0.54 ± 0.16 % of the total land surface area, which is a similar percentage to what other researchers have found. This approach gave us a clearer picture of the surface area of rivers of all sizes which is important because small rivers emit greenhouse gases at a faster rate than large rivers.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第25283号 / 工博第5242号 / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 藤本 健治, 准教授 丸田 一郎, 教授 大塚 敏之, 教授 青井 伸也(大阪大学) / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Yes / The development of ultra-high performance cementitious composite (UHPCC) represents a significant advancement in the field of concrete science and technology, but insufficient hydration and high autogenous shrinkage relatively increase the pores inside UHPCC, in turn, affecting the macro-performance of UHPCC. This paper, initially, optimized the pore structure of UHPCC using different types and dimensions of nanofillers. Subsequently, the pore structure characteristics of nano-modified UHPCC were investigated by the mercury intrusion porosimeter method and fractal theory. Finally, the fluid permeability of nano-modified UHPCC was estimated by applying the Katz-Thompson equation. Experimental results showed that all incorporated nanofillers can refine the pore structure of UHPCC, but nanofillers with different types and dimensions have various effects on the pore structure of UHPCC. Specifically, CNTs, especially the thin-short one, can significantly reduce the porosity of UHPCC, whereas nanoparticles, especially nano-SiO2, are more conducive to refine the pore size. Among all nanofillers, nano-SiO2 has the most obvious effect on pore structure, reducing the porosity, specific pore volume and most probable pore radius of UHPCC by 31.9%, 35.1% and 40.9%, respectively. Additionally, the pore size distribution of nano-modified UHPCC ranges from 10-1nm to 105nm, and the gel pores and fine capillary pores in the range of 3-50nm account for more than 70% of the total pore content, confirming nanofillers incorporation can effectively weaken pore connectivity and induce pore distribution to concentrate at nanoscale. Fractal results indicated the provision of nanofillers reduces the structural heterogeneity of gel pores and fine capillary pores, and induces homogenization and densification of UHPCC matrix, in turn, decreasing the UHPCC fluid permeability by 15.7%-79.2%. / National Science Foundation of China (51978127, 52178188 and 51908103), the China Postdoctoral Science Foundation (2022M720648 and 2022M710973) and the Fundamental Research Funds for the Central Universities (DUT21RC(3)039).

This thesis focuses on generating real world turbulence levels in a water tunnel rotor test using fractal grids and characterizing the effect of the fractal grid generated-turbulence on the performance of hydrokinetic turbines. The research of this thesis is divided into three studies: one field study and two laboratory studies. The field study was conducted at the Canadian Hydro Kinetic Turbine Test Centre (CHTTC) on the Winnipeg River. An Acoustic Doppler Velocimeter (ADV) was used in the field study to collect flow measurements in the river. The laboratory studies were conducted at the University of Victoria (UVic) fluids research lab and the Sustainable Systems Design Lab (SSDL). In addition, the Particle Image Velocimetry (PIV) technique was used in the experiential studies to obtain quantitative information about the vector flow field along the test section, both upstream and downstream of the rotor’s plane. The first study is a field study aiming to provide real flow characteristics and turbulence properties at different depths from the free-surface to boundary layer region of a fast river current by conducting a field study in the Winnipeg River using ADV. A novel technique to deploy and control an ADV from free-surface to boundary layer in a fast-current channel is introduced in this work. Flow characteristics in the river, including mean flow velocities and turbulence intensity profiles are analyzed. The obtained results indicate that the maximum mean velocity occurs below the free-surface, suggesting that the mean velocity is independent of the channel depth. From the free-surface to half depth, it was found that changes in both the mean velocity and turbulence intensity are gradual. From mid-depth to the river bed, the mean velocity drops rapidly while the turbulence intensity increases at a fast rate. The turbulent intensity varied from 9% at the free-surface to around 17.5% near the river bed. The results of this study were used in the second lab study to help designing a fractal grid for a recirculating water flume tank. The goal was to modify the turbulence intensity in the water tunnel such that the generated turbulence was similar to that in the river at a location typical of a hydrokinetic device. The properties of fractal-generated turbulence were experimentally investigated by means of 2D Particle Image Velocimetry (PIV). The streamwise turbulent intensity profiles for different grids along the channel are presented. Additionally, visualization of the average and fluctuating flow fields are also presented. The results are in good agreement with results in literature. The third and final study investigated the power coefficient of a scale hydrokinetic turbine rotor in controlled turbulent flow (7.4 % TI), as well as in the low-turbulence smooth flow (0.5% TI) typical of lab scale testing. PIV was employed for capturing the velocity field. The results show that using realistic TI levels in the water tunnel significantly decrease the turbine’s power coefficient compared to smooth flow, highlighting the importance of considering this effect in future experimental campaigns. / Graduate

Made available in DSpace on 2016-04-27T16:57:55Z (GMT). No. of bitstreams: 1 dissertacao_ricardo_ronald_eberson.pdf: 1316160 bytes, checksum: a673a44e8d3259e7d409f1d2d55d1e62 (MD5) Previous issue date: 2004-05-13 / This research concerns the teaching and learning of Mathematics in the presence of computational tools, particularly in relation to the construction of fractals. The main aim of the work is to contribute to the analysis of the computational transposition process (Balacheff, 1994) of Fractal Geometry in four computational learning environments. The study entails an analysis of the nature of the meanings that each of the educational software environments affords for particular mathematical notions, that is, its epistemological domain of validity . Additionally the idea of microworld is used in relation to Dynamic Geometry environments and those based of Turtle Geometry . The theoretical approach adopted warrants and guides the methodological choices, which involve the qualitative analysis of the set of chosen computational environments. The analyses show that the construction of fractals in two of these environments made use of the concept of the Chaos Game. In these two cases, the formal structures of both softwares present tools based on geometrical transformations of the plane, although with distinct kinds of control, especially in terms of the extent to which relationships between tools and the concepts involved are made explicit. The results also enable the proposal of teaching situations concerning the construction of fractals in these environments, aimed at providing a context for the exploration of notions related to geometrical transformations of the plane and their geometrical and algebraic representations / Esta pesquisa insere-se no quadro do ensino e da aprendizagem de Matemática integrando ferramentas computacionais, em particular, no que se refere à construção de objetos fractais. O objetivo principal deste trabalho é contribuir para uma análise, em termos da transposição informática (Balacheff, 1994), da Geometria Fractal em quatro ambientes computacionais de aprendizagem humana. Fundamentado nessa noção, o estudo concentra-se na análise da natureza dos significados que um dado software educativo permite construir para uma determinada noção matemática, isto é, em seu domínio de validade epistemológica . Além disso, utiliza a idéia de micro-mundo no que se refere à ambientes de Geometria Dinâmica e aqueles baseados na Geometria da Tartaruga . Tal abordagem teórica justifica e orienta o desenvolvimento metodológico, voltado à análise qualitativa do conjunto de ambientes informáticos escolhidos. As análises realizadas mostram que a construção de fractais em dois desses ambientes relacionam-se à concepção do Jogo do Caos. Em ambos os casos, as estruturas formais destes softwares apresentam ferramentas baseadas em transformações geométricas no plano, embora com tipos de controle distintos, em particular, no que se refere à explicitação da relação entre as ferramentas e o conceito envolvido. Os resultados também permitem propor situações de ensino envolvendo a construção de fractais nesses ambientes, visando contribuir para a contextualização de noções relacionadas às transformações geométricas no plano, com a exploração de suas representações geométricas e algébricas

Cette thèse est consacrée à des questions d'analyse en amont de la modélisation de structures arborescentes, comme le poumon humain. Plus particulièrement, nous portons notre intérêt sur une classe de domaines ramifiés du plan, dont la frontière comporte une partie fractale auto-similaire. Nous commençons par une étude d'espaces de fonctions dans cette classe de domaines. Nous étudions d'abord la régularité Sobolev de la trace sur la partie fractale de la frontière de fonctions appartenant à des espaces de Sobolev dans les domaines considérés. Nous étudions ensuite l'existence d'opérateurs de prolongement sur la classe de domaines ramifiés. Nous comparons finalement la notion de trace auto-similaire sur la partie fractale du bord à des définitions plus classiques de trace. Nous nous intéressons enfin à un problème de transmission mixte entre le domaine ramifié et le domaine extérieur. L'interface du problème est la partie fractale du bord du domaine. Nous proposons ici une approche numérique, en approchant l'interface fractale par une interface préfractale. La stratégie proposée ici est basée sur le couplage d'une méthode auto-similaire pour la résolution du problème intérieur et d'une méthode intégrale pour la résolution du problème extérieur. / We study some questions of analysis in view of the modeling of tree-like structures, such as the human lungs. More particularly, we focus on a class of planar ramified domains whose boundary contains a fractal self-similar part. We start by studying some function spaces defined for this class of domains. We first study the Sobolev regularity of the traces on the fractal part of the boundary of functions in some Sobolev spaces of the ramified domains. Then, we study the existence of Sobolev extension operators for the ramified domains we consider. Finally, we compare the notion of self-similar trace on the fractal part of the boundary with more classical definitions of trace. In the last part, we focus on a mixed transmission problem between the ramified domain and the exterior domain. The fractal part of the boundary is the interface of the problem. We propose a numerical approach where we approximate the self-similar interface by a prefractal interface. The proposed strategy is based on a self-similar method for the resolution of the inner problem coupled with an integral method for the resolution of the outer problem.

Στη συγκεκριμένη μεταπτυχιακή εργασία γίνεται ανάλυση των ηλεκτροεγκεφαλογραφικών καταγραφών επιληπτικών ασθενών με βάση την κλασματική διάσταση για τον εντοπισμό της έναρξης των επιληπτικών κρίσεων καθώς και για την ανίχνευση των επερχόμενων επιληπτικών κρίσεων. Πιο συγκεκριμένα, χρησιμοποιούνται τέσσερις μέθοδοι υπολογισμού της κλασματικής διάστασης στο πεδίο του χρόνου. Πραγματοποιείται μία συγκριτική μελέτη των συγκεκριμένων μεθόδων χρησιμοποιώντας δύο συνθετικά σήματα γνωστής κλασματικής διάστασης και στη συνέχεια οι μέθοδοι εφαρμόζονται σε ηλεκτροεγκεφαλογραφικές καταγραφές ασθενών που πάσχουν από επιληψία. Η συγκεκριμένη εργασία αποδεικνύει ότι όλες οι μέθοδοι μπορούν και εντοπίζουν την έναρξη των επιληπτικών κρίσεων ενώ η στατιστική ανάλυση δείχνει ότι κάποιες από αυτές τις μεθόδους μπορούν να χρησιμοποιηθούν και ως δείκτες πρόβλεψης των επερχόμενων επιληπτικών κρίσεων. Επίσης, διαπιστώνεται ότι ανάλογα με το είδος των ηλεκτροεγκεφαλογραφικών καταγραφών, το μέγεθος του παραθύρου και τη ζώνη διέλευσης του φίλτρου τα αποτελέσματα της κλασματικής διάστασης που προκύπτουν επηρεάζονται. / Τhe fractal dimension is a powerful tool in the analysis of electroencephalograms. In this work, four methods of estimating the fractal dimension of electroencephaolographic recordings of epileptic patients directly in the time domain are analyzed and compared. The analysis is performed over both synthetic data and real recordings of epileptic patients. The effects of the type of recordings, the window size and the frequencies in the passband filter are examined. This study shows that the four methods detect the beginning of the epileptic seizures, while the statistic analysis proves that some of these methods can be used for the prediction of the next seizures.