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[pt] A obtenção de estruturas mais resistentes e rígidas, e economicamente viáveis, é uma preocupação cada vez maior na construção civil. Sob essa ótica, este trabalho tem o objetivo de avaliar o comportamento de pilares mistos de seção composta através de uma modelagem numérica. Foram estudados dois tipos de seções, uma composta por dois perfis I laminados, e outra por dois perfis U enrijecidos, em ambos os casos conectados por perfis I e preenchidos com concreto armado. Com o uso do software ABAQUS, foi avaliado o comportamento estrutural dos elementos submetidos a carregamentos de flexão, compressão e flexo-compressão. O modelo foi validado através da comparação com dados experimentais de estudos anteriores e resultados previstos pela norma técnica brasileira, conseguindo representar adequadamente o comportamento das curvas momento-deslocamento e força-deslocamento. As resistências obtidas a partir dos modelos numéricos foram superiores aos valores esperados pela solução teórica, principalmente no carregamento de compressão. De modo a avaliar a viabilidade econômica do sistema misto proposto, foi realizado o dimensionamento de um galpão industrial, que evidenciou ganho significativo de inércia em relação a um sistema composto apenas por perfis de aço, resultando em uma economia de até 11 por cento na massa equivalente em aço. Por fim, desenvolveu-se um estudo paramétrico para investigar a influência do número de conectores, da sua disposição, da resistência do concreto e do diâmetro da armadura na resistência do pilar. / [en] A growing concern in civil construction is to obtain structures that are more resistant, rigid and economically feasible. This study aims to evaluate the behavior of steel-concrete columns of composite section, through numerical modeling. The studied cross-sections were composed of two rolled I profiles, and other with C-lip channels, connected by I profiles, and filled with reinforced concrete. The ABAQUS software was used to evaluate the structural behavior of the columns subjected to flexural, compression and eccentric compression loads. The model was calibrated through experimentally obtained data from previous studies, and results provided by the Brazilian National Standards, and it was able to properly reproduce the moment-displacement and load-displacement curves. The obtained resistances from the numerical models were greater than the ones expected by the theoretical solution, especially under compression load. In order to evaluate the economic feasibility of the proposed composite model, a design example of an industrial shed was conducted, and it showed a significant increase in moment of inertia when compared to steel-only box sections, which resulted in savings of up to 11 percent in equivalent mass of steel. Finally, a parametric study was made to investigate the influence of the number and disposition of the connectors, and the contribution of the concrete resistance and reinforcement s diameter in the strength of the columns.

O Presente trabalho é o estudo das funcionalidades de um descritor e sua aplicabilidade em análise musical tendo como ponto de partida a obra a Ladainha de Nossa Senhora de Faustino Xavier do Prado. Utilizaremos os intervalos melódicos existentes na Ladainha como padrões para verificar similaridades nos contextos; Brasil, Itália e Portugal. Utilizaremos como ferramenta de busca de padrões o software MelodicMatch e desenvolveremos um software para tratar os resultados obtidos organizando-os em uma proposta metodológica que estará descrita na própria aplicação. / The present work is the study of the features of a descriptor and its use in musical analysis taking as its starting point the work of the Ladainha de Nossa Senhora - Faustino Xavier del Prado. We will use existing melodic intervals in the Ladainha as standards for checking similarities in the contexts; Brazil, Italy and Portugal. We will use as standards search tool MelodicMatch the software and develop software to handle the results organizing them into a methodology that will be described in the application itself.

One performed a more modern approach on such heat stress to find changes out to compact morphometry in spermatozoon head by computational analysis. One aimed in this work to assess how to compact chromatin and sperm morphometry after have risen testicular temperature, by using experimental cryptorchidism in rabbits (Oryctolagus cuniculus), as well as used 30 rabbits: wild rabbit, white, adult, located in the rabbit keeping of University of Uberaba, Uberaba (city), MG (State of Minas Gerais), Brazil. One classified the rabbits into two groups of 15. Both groups were anesthetised, but only the experimental cryptorchidism one underwent a surgical operation. One gathered semen samples within a total of 69 days. One both dyed semen smear of all rabbits by using a toluidine blue dye and afterwards analysed it with a digital microcomputer to assess compacting chromatin and sperm morphometry. Chromatin varied regarding compact intensity (Diff%), homogeneity by coefficient of variation (CV) and aberrant chromatin (AbChr). By analysing morphometrically one assessed: area, perimeter (Perim.), width (w.), length (l.), ratio width:length (w./l.), ellipsity (E.), form factor (FF), lateral symmetry (LatSym), antero-posterior symmetry (A-PSym), and Fourier descriptors with amplitude from 0 to 2. Testicular temperature rise swayed the concentration, motility, and vigour adversely. Chromatin structure becomes aberrant when affected by testicular heat stress. And spermatozoon head tends to lessen. / Uma abordagem mais moderna sobre a elevação da temperatura foi realizada, visando detectar alterações na compactação e morfometria da cabeça do espermatozoide pela análise computacional. O objetivo do trabalho foi avaliar a compactação da cromatina e a morfometria espermática após a elevação da temperatura testicular, por meio de criptorquidismo experimental, em coelhos. Foram utilizados 30 coelhos da raça Nova Zelândia, brancos, adultos, situados no coelhário da Universidade de Uberaba, Uberaba, MG, Brasil. Os coelhos foram separados em dois grupos de 15. Ambos os grupos foram anestesiados, mas somente um deles sofreu intervenção cirúrgica, o criptorquidismo experimental. Foram coletadas amostras de sêmen durante 69 dias. Esfregaços de sêmen de todos os coelhos foram corados com azul de toluidina e, posteriormente, analisados digitalmente por meio de microcomputador para avaliar a compactação de cromatina e morfometria. A cromatina foi avaliada quanto à intensidade de compactação (Dif%), homogeneidade pelo coeficiente de variação (CV) e cromatina anômala (Cr. An.). Na análise morfométrica foram avaliados: área, perímetro (Per.), largura (Larg.), comprimento (Comp.), razão largura:comprimento (L/C), elipsidade (E), fator forma (FF), simetria lateral (Sim. Lat.), simetria ântero posterior (Sim. A-P) e descritores Fourier com amplitude de 0 a 2. A elevação da temperatura testicular influenciou negativamente a concentração, motilidade, vigor, torna-se anômala a estrutura da cromatina e a cabeça do espermatozoide tende a diminuir. / Mestre em Ciências Veterinárias

O Presente trabalho é o estudo das funcionalidades de um descritor e sua aplicabilidade em análise musical tendo como ponto de partida a obra a Ladainha de Nossa Senhora de Faustino Xavier do Prado. Utilizaremos os intervalos melódicos existentes na Ladainha como padrões para verificar similaridades nos contextos; Brasil, Itália e Portugal. Utilizaremos como ferramenta de busca de padrões o software MelodicMatch e desenvolveremos um software para tratar os resultados obtidos organizando-os em uma proposta metodológica que estará descrita na própria aplicação. / The present work is the study of the features of a descriptor and its use in musical analysis taking as its starting point the work of the Ladainha de Nossa Senhora - Faustino Xavier del Prado. We will use existing melodic intervals in the Ladainha as standards for checking similarities in the contexts; Brazil, Italy and Portugal. We will use as standards search tool MelodicMatch the software and develop software to handle the results organizing them into a methodology that will be described in the application itself.

[pt] Essa dissertação realiza uma análise do escoamento reativo e turbulento no interior do combustor de um estato reator a combustível sólido. Investiga-se diferentes modelos para prever a pirólise do combustível sólido. O modelo matemático é baseado na solução numérica das equações de conservação de massa, quantidade de movimento linear, energia e equações de transporte para quantidades escalares. O modelo de turbulência empregado é o (constante de Von Kármán -taxa de dissipação da energia cinética turbulenta) para altos Reynolds e na modelagem da combustão emprega-se o formalismo da fração de mistura/função densidade de probabilidade prescrita. Próximo às paredes, a lei da parede é usada, sendo a camada limite dividida em duas regiões, uma subcamada laminar e uma região totalmente turbulenta. As transferências de calor e massa para as paredes são calculadas utilizando-se a lei da parede modificada com uso de um parâmetro de transferência de massa. Os resultados obtidos através do modelo proposto foram comparados com os resultados obtidos anteriormente com outros modelos e com dados experimentais, verificando-se que os mesmos apresentam um boa concordância com os dados existentes na literatura, concluindo-se que o modelo é satisfatório para o problema proposto. / [en] This dissertation presents an analysis of reactive and turbulent flow field in a solid fuel ramjet combustor. The ability of different models to predict solid fuel pyrolysis is investigated. The mathematical model is based on the numerical solution of the conservation equations of mass, momentum, energy and transport equations for scalar quantities. The energia cinética turbulenta - taxa de dissipação da energia cinética turbulenta for high Reynolds turbulence model is employed and the combustion is modeled with the mixture fraction/prescribed probability density function formalism. Close to the walls the law-of-the-wall is specified, with the boundary layer divided into two regions, a viscous sublayer and a fully turbulent region. Heat and mass transfer at the walls are calculated using a modified law-of-the-wall based on a blowing parameter. The results obtained using the proposed model were compared with other earlier models predictions and with empirical data. It was verified that the results are in good agreement with literature data, allowing to conclude that the model presented is suitable for the prediction of the mas s transfer and flow field in a solid fuel ramjet combustor.

Prostate Cancer (PCa) is the second most diagnosed cancer in men across the world; it is considered the fifth leading cause of cancer related death according to cancer statistics 2012. Being a member of the internal parts in males reproductive system, testing any abnormality with the prostate gland remains both troublesome and inconvenient, and foremost inaccurate. The diagnostic practice starts with prostate-specific antigen (PSA) level testing, which in return is highly indecisive, provoking an over diagnosis and treatment. Genomic alteration and Single Nucleotide Variants (SNV s) are assumed to play a role during PCa progression. On behalf of the RIBOLUTION project, a project with the aim of finding diagnostic biomarkers from RNA sequences, SNV s in RNA sequences were analysed to pinpoint potential candidate genes in PCa. The fact that the cohort provides whole-transcriptome data of pro- static tissue promotes the possibility to obtain comprehensive knowledge of the cancerous changes. The advantage of detecting SNV s in RNA sequences relies in focusing on only those, which could be relevant to the gene’s func- tion. However, methods for detecting and analysing SNV s solely in RNA sequences are currently not yet established. This study aimed to (1) establish fitting and applicable assays to identify, inspect and conclude the potential role of SNV s in RNA sequences, (2) use the obtained knowledge to single out the genes that are potentially relevant for PCa. SNV s in the RIBOLUTION cohort were investigated. Prostate tissue was obtained from 40 PCa patients, and then RNA was sequenced using Next Generation Sequencing. In 16 patients, a pairwise prostatic tissue was taken, one a confirmed tumor tissue and the second a tumor-free tissue. As a control, samples from 8 men with benign prostatic hyperplasia were likewise sequenced. Different computational pipelines were established and successfully fulfilled the aim. The CVR Module (Calling Variants in RNA-Seq) is a computer- based pipeline intended to identify SNV s and discriminate between false positive and true positive calls. Validating the SNV s reported by the accomplished Module has shown high sensitivity (> 80% validated SNV s). Much as novel SNV s that had ∼ 101% higher median calling quality in comparison to SNV s found in dbSNP, the Single Nucleotide Polymorphism Database. In agreement with current knowledge, novel SNV s was observed in tumor samples with slight but significant increase vs. tfree tissue (P < 0.05, testing on proportion). On top of that, positive correlation between non-silent effect and novel SNV in tumor samples was also observed (P < 0.05, r = 0.33, Pearson’s correlation). Moreover, more than 40% of the candidate genes were found in COSMIC, the Catalog Of Somatic Mutations In Cancer; some of them are confirmed somatic mutation (cancer associated). About 11% were also reported in studies to be disease associated or observed in other diseases, mostly heredity related. Potential PCa associated genes were identified via combination of three different systematic methods: mutational clustering, mutational functional bias, and covariates of the mutated genes. The first method (mutational clustering), however, did not reveal any significant insight. The top candidate genes were then selected in accordance with the latter methods. The list of top candidate genes includes > 50% genes with direct association with PCa; > 80% genes previously reported in other cancer types, while ∼ 35% that are in- volved in PCa associated complexes. Besides well known and validated PCa biomarker (alpha-methylacyl-CoA racemase (AMACR)), we identify for the first time, from mutational prospective, 22% of the genes to be potentially associated with PCa. Among those, one of the most promising candidate genes is NWD1 (NACHT and WD repeat domain containing 1). This gene was mentioned in a previous study to be a potential player in PCa prognosis. We add to this our novel observation, NWD1 was found significantly mutated in the entire tumor samples. These significant findings were proven to be tumor-specific when they were compared to the available control and tumor-free (P < 0.05, non-parametric ranking). We conclude that analyzing SNV s from RNA is as useful and informative as DNA-based ones, and accomplish further benefits that could be gained once the suggested methods are adapted.

Die Genregulation ist ein komplexer Prozess, bei dem Zellen die Menge der Genprodukte steuern, um ihre Identität auszubilden und auf Umweltveränderungen zu reagieren. Die CRISPR-Technologie hat genetische Screens revolutioniert und ermöglicht es, mehrere Transkripte gleichzeitig zu untersuchen. In dieser Arbeit werden die Vorteile und Herausforderungen gepoolter CRISPR-Screens zur Erforschung der Genregulation untersucht. Es wird ein CRISPR-ko-Screen in embryonalen Mausstammzellen (mESCs) beschrieben, der pluripotenzerhaltende Transkriptionsfaktoren identifiziert. Es zeigte sich, dass ein Screening mit einer kleinen Bibliothek den Großteil des biologischen Signals eines genomweiten Screens erfasst und die Identifizierung von Genkandidaten mit kleinen Effektgrößen verbessert. Nachfolgend wird CRISPTimeR, eine neue Methode für die Analyse von Zeitreihen von CRISPR-Screens, vorgestellt. Sie basiert auf gemischten linearen Modellen und ermöglicht es, Treffer zu identifizieren und gleichzeitig zeitlich zu klassifizieren. Als Nächstes wurde CRISPRi verwendet, um für die Pluripotenz von mESCs relevante lncRNAs zu untersuchen, was aufgrund ihrer schlechten Annotation und niedrigen Expressionsniveaus schwierig ist. Eine mögliche Lösung ist eine manuell verfeinerte Annotation von Transkriptionsstartstellen und kleinere Bibliotheks-Screens mit empfindlicherer phänotypischer Auslesung. Zudem wurde ein Sättigungsscreen genomischer Regionen rund um den PHOX2B-Lokus, zur Identifikation cis-regulierender Elemente, durchgeführt. Dabei wurden CRISPRa-reaktive Elemente identifiziert, die Gene in der PHOX2B-TAD regulieren, und mit diesen mittels Einzelzell RNA-seq in Verbindung gebracht. Zusammenfassend zeigt diese Arbeit den Wert gepoolter CRISPR-Screens für die Erforschung der Genregulation und Herausforderungen der Analyse nicht-kodierender Elemente. Zusätzlich beschreibt sie ein neues Tool für die Analyse von kodierenden und nicht-kodierenden CRISPR-Screens in Zeitreihen. / Gene regulation is a complex process in which cells control gene product levels to establish identity and respond to environmental changes. CRISPR technology has revolutionized genetic screening, enabling researchers to study multiple transcripts simultaneously. This thesis explores the advantages and challenges of using pooled CRISPR screens to study gene regulation. First, I describe a CRISPR-ko screen in mouse embryonic stem cells (mESCs) to identify transcription factors involved in pluripotency maintenance. I show that a small-library screen captures most of the biological signal observed in a genome-wide screen, and it improves the identification of candidate genes with small effect sizes. Next, introduce CRISPTimeR, a novel method for the analysis time-series CRISPR screens. CRISPTimeR is based on mixed linear models; it allows to use information from a time-series experiment to identify, and simultaneously perform temporal classification on, hits. Next, I use CRISPRi to study lncRNAs relevant to pluripotency in mESCs. Targeting lncRNAs poses challenges due to poor annotation and low expression levels. I suggest to address these issues by using a hand-refined annotation of transcription start sites and by designing small-library screens with more sensitive phenotypic readout. Finally, I describe a saturation screen targeting large genomic regions around the PHOX2B locus, to identify putative cis-regulatory elements. I identified CRISPRa responsive elements involved in regulating the expression of genes within the PHOX2B TAD, which were then matched with the genes they control using single-cell RNA-seq. Overall, in this thesis I demonstrate the value of CRISPR pooled screens for studying gene regulation, while highlighting the challenges associated with targeting non-coding elements and suggesting possible approaches to address these challenges. Moreover, I introduce a novel tool for the analysis of both coding and non-coding time-series CRISPR screens.

Thesis (DPhil (Electrical and Electronic Engineering))--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: The Karoo Array Telescope (KAT) will be used by South Africa in its bid to host the international Square Kilometre Array (SKA). As the SKA will have orders of magnitude greater sensitivity than existing radio telescopes, it will also be concomitantly more sensitive to radio frequency interference (RFI). The influence of RFI on a differential mode (DM) KAT conductive system is an unavoidable phenomenon. In this context, the conductive or galvanic system can, in its most basic form, consist of a source, a load, and connecting conductors. It can also, in the case of the KAT-7 seven-dish interferometer, consist of each telescope, its functional cabling, and the main correlator connecting the telescopes together. However, additional connections between the system and the environment exist. These might be an intentional connection made to the earthing layout, or unintentional connections due to parasitic capacitances and inductive connections. As a result of this, additional conductive systems are created which carry common mode (CM) currents. Interference present in such CM paths enters the DM system through the transfer impedance (Zt) between them. To reduce or eliminate this interference in the DM system, Zt has to be minimised. The use of an earthed parallel conductor (EPC as commonly referred to) in the form of a cable tray is considered to be one of the principal methods to reduce Zt. The properties of cable trays as EPCs at wavelengths which are greater than the tray length are well documented. One main focus in this dissertation is on cable tray mid-span and end connections. They are not well described in the literature over the wide range of frequencies that is expected for KAT developments. The influence of the most common connections on the measured and computed Zt of the cable tray is determined. Computer Simulation Technology’s Microwave Studio (CST MWS) is employed to validate the measured results and also to enable visualisation of the fields and currents. Recommendations for the best connection to use for any cable tray installation is given. The overall shielding ability of optimally-connected cable trays has been evaluated using a physical and computational model. In both cases the induced voltage on a victim conductor, and far-field gain functions for varying angles of incidence onto the model, are determined. The results also show that for certain scenarios, most of the coupling to the victim conductor, takes place inside the end enclosure and not the cable tray. In general, properly-connected cable trays do provide protection to their enclosed conductors, even at frequencies were the wavelength is much shorter than the width of the tray. The second main focus arises from an on-site radio frequency (RF) current audit undertaken on two of the seven KAT-7 telescopes. Shielding measures, such as interface barriers at the floor and roof of the lower telescope pedestal, are studied. The investigation is facilitated by the development of an accurate physical and computational scale model of the dish. Direct current injection and plane wave illumination methods are used to excite the system. The measured CM current distributions are compared and comments made regarding the validity of the measurement procedure. The CM currents, measured around the outside of the lower pedestal show higher levels when a direct current path to ground is established, as opposed to when no clear path exists. This finding suggests at least two methods of preventing CM interference entering or leaving the pedestal: harden the floor and roof barriers, or manage current paths outside the telescope. Related to this, CM currents measured either side of the telescope interface barriers, are used to determine the level of shielding the interface provides. When compared to the common definition of shielding effectiveness, the current measurement provides more conservative shielding estimates. The research in this dissertation has influenced, and will continue to influence, the layout of galvanic systems for the present KAT-7 structures and the anticipated developments to MeerKAT. / AFRIKAANSE OPSOMMING: Die Karoo Array Telescop (KAT) sal gebruik word deur Suid-Afrika in sy poging om die bod te kry om die internasionale Square Kilometre Array (SKA) te huisves. Aangesien die SKA ordes meer sensitief sal wees as bestaande radioteleskope, sal dit terselfdertyd ook meer sensitief wees vir radio frekwensie steurnisse. Die invloed van radio frekwensie steurnisse op die differentiëlemodus KAT geleidende netwerk is iets onvermydeliks. Binne hierdie konteks kan die geleidende netwerk, in sy mees basiese vorm, bestaan uit ʼn bron, ʼn las, en verbindingsgeleiers. Dit kan ook, in die geval van die KAT-7 sewe-teleskoop interferometer, bestaan uit elke teleskoop, sy funksionele bekabeling, en die korrelator wat die verbinding is tussen al die teleskope. Daar is egter, addisionele verbindings tussen die netwerk en die onmiddellike omgewing rondom dit. Hierdie verbindings kan opsetlik gemaak word deur byvoorbeeld, verbinding van die netwerk se aardkabel aan die res van die beaarding, of onopsetlik deur parasitiese kapasitansies en induktiewe verbindings. As gevolg hiervan word addisionele geledende netwerke geskep waarin gemenemodus strome kan vloei. Indien daar wel strome in die gemenemodus netwerk vloei, word dit oorgedra aan die differentiëlemodus netwerk deur ʼn oordragimpedansie (Zt) wat teenwoordig is tussen die twee. Om dus die steurnisse in die differentiëlemodus netwerk te verminder of te elimineer, moet Zt tot ʼn minimum beperk word. Die gebruik van ʼn geaarde parallelle geleier in die vorm van ʼn kabelkanaal, word beskou as een van die mees doeltreffendste metodes om Zt te verminder. Die eienskappe van kabelkanale as geaarde parallelle geleiers by frekwensies waar die golflengtes langer is as die van die kabelkanaal, is volledig gedokumenteer. Een van die belangrikste fokuspunte in hierdie verhandeling is rakende die kabelkanale se middel en eindpuntverbindings. Hulle word nie goed beskryf in die beskikbare literatuur nie, en weliswaar vir wyeband doeleindes wat vir KAT ontwikkelinge verwag word. Die invloed van die mees algemeenste kabelkanaal verbindings op gemete en berekende Zt word bepaal. Computer Simulation Technology’s Microwave Studio (CST MWS) word eerstens, gebruik om die akkuraatheid van die gemete resultate te bewys en tweedens, deur visualisering van E-veld en gemenemodus oppervlak strome. Aanbevelings vir die beste verbindings vir enige kabelkanaal opstelling word gegee. Die algemene afskerminsvermoeë van ʼn idiaal-verbinde kabelkanaal word bepaal deur middel van metings en simulasies. In beide gevalle word die geïnduseerde spanning op ʼn slagoffer kabel, en die verveld aanwins funksie bepaal vir verskillende invalshoeke op die model. Die resultate toon verder dat vir spesifieke gevalle wat beskou word, die meeste koppeling binne die kabinet aan die einde van die kabelkanaal plaasvind. Oor die algemeen verskaf goed verbinde kabelkanale wel ʼn sekere vlak van beskerming aan kabels binne die kabelkanaal, selfs by frekwensies waar die golflengte baie korter is as die breedte van die kabelkanaal. Die tweede belangrike fokuspunt spruit voort uit ʼn radio frekwensie stroomoudit, wat twee van die KAT-7 teleskope evalueer het. Afskermingsmatreëls soos die kabelhindernisse op die vloer en dak van die onderste teleskoop voetstuk, word bestudeer. Tesame met die metings op die werklike teleskoop wat geneem is, word ʼn akkurate fisiese en simulasie skaalmodel geskep om die metings beter te analiseer. Direkte stroominspuitings metode en platvlakgolf beligting word gebruik om gemenemodus strome op die teleskoop se struktuur te induseer. Die gemenemodus stroomverspreiding vir beide tegnieke word vergelyk in ʼn poging om kommentaar te lewer rakende die geldigheid van die meettegniek. Die gemenemodus strome wat aan die buitekant van die teleskoop voetstuk gemeet word, is hoër wanneer ʼn direkte stroompad na grond op die voetstuk geskep word in vergelyking met ʼn ongedefinieerde pad. Hierdie verskynsel dui daarop dat ten minste twee metodes bestaan om die ongevraagde gemenemodus strome te verhoed om aan die binnekant van die teleskoop voetstuk te vloei. Die een is die verbetering van die vloer en dak kabelhindernisse, en die ander is verbetering van die stroompad (stroompaaie) aan die buitekant van die voetstuk sodat ʼn meer direkte pad na grond geskep word. Die gemiddelde gemenemodus strome weerskante van die kabelhindernis, kan gebruik word op te bepaal hoeveel afskerming die hindernis bied. Indien die berekende waardes by verskillende frekwensies vergelyk word met die tradisionele filter doeltreffendheid (Zt), word ʼn meer konserwatiewe beraming verkry. Die navorsing in hierdie verhandeling het alreeds, maar sal ook die toekomstige uitleg van galvaniese stelsels vir KAT-7 asook die verwagte MeerKAT beïnvloed.

This work is a numerical and analytical study of wave motion through dynamic materials (DM). This work focuses on showing several results that greatly extend the applicability of the checkerboard focusing effect. First, it is shown that it is possible to simultaneously focus dilatation and shear waves propagating through a linear elastic checkerboard structure. Next, it is shown that the focusing effect found for the original €œperfect€� checkerboard extends to the case of the checkerboard with smooth transitions between materials, this is termed a functionally graded (FG) checkerboard. With the additional assumption of a linear transition region, it is shown that there is a region of existence for limit cycles that takes the shape of a parallelogram in (m,n)-space. Similar to the perfect case, this is termed a €œplateau€� region. This shows that the robustness of the characteristic focusing effect is preserved even when the interfaces between materials are relaxed. Lastly, by using finite volume methods with limiting and adaptive mesh refinement, it is shown that energy accumulation is present for the functionally graded checkerboard as well as for the checkerboard with non-matching wave impedances. The main contribution of this work was to show that the characteristic focusing effect is highly robust and exists even under much more general assumptions than originally made. Furthermore, it provides a tool to assist future material engineers in constructing such structures. To this effect, exact bounds are given regarding how much the original perfect checkerboard structure can be spoiled before losing the expected characteristic focusing behavior.