Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The nite size of nucleons should play an important role in the description of high density nuclear matter as found in astro-physical objects. Yet we see that the Walecka model, which is generally used to describe these systems, treats the nucleons as point particles. Here we argue that a non-commutative version of the Walecka model may be a consistent and appropriate framework to describe nite nucleon size e ects. In this framework the length scale introduced through the non-commutative parameter plays the role of the nite nucleon size. To investigate the consequences of this description, the equations of motion and energy-momentum tensor for the non-commutative Walecka model are derived. We also derived an expression for the total energy of the system, as a function of the non-commutative parameter, in a spatially non-uniform matter approximation. The non-commutative parameter, as a variable dependent on the dynamics of the system, remains to be solved self-consistently. / AFRIKAANSE OPSOMMING: Die eindige grootte van nukleone moet 'n belangrike rol speel in die beskrywing van ho e-digtheid kern materie soos gevind in astro- siese voorwerpe. Tog sien ons dat die Walecka model, wat in die algemeen gebruik word om hierdie stelsels te beskryf, die nukleone as punt deeltjies hanteer. Ons redeneer dus dat 'n nie-kommutatiewe weergawe van die Walecka model 'n konsistente en gepaste raamwerk is om die e ekte van eindige nukleon grootte te beskryf. In hierdie raamwerk speel die lengte-skaal wat ingevoer word deur die nie-kommutatiewe parameter die rol van eindige grootte vir nukleone. Om die gevolge van hierdie beskrywing te ondersoek, word die vergelykings van beweging en die energie-momentum tensor afgelei vir die nie-kommutatiewe Walecka model. Ons het ook 'n uitdrukking vir die totale energie van die stelsel, as 'n funksie van die niekommutatiewe parameter, afgelei in 'n ruimtelik nie-uniforme materie benadering. Die niekommutatiewe parameter, as 'n veranderlike afhanklik van die dinamika van die stelsel, bly steeds om self-konsistent opgelos te word.

This thesis is divided into two parts: In the first one (Chapters 1 and 2), we deal with problems arising from quantitative homogenization of the random elliptic operator in divergence form $-\\nabla \\cdot a \\nabla$. In Chapter 1 we study existence and stochastic bounds for the Green function $G$ associated to $-\\nabla \\cdot a \\nabla$ in the case of systems. Without assuming any regularity on the coefficient field $a= a(x)$, we prove that for every (measurable) uniformly elliptic tensor field $a$ and for almost every point $y \\in \\mathbb^d$, there exists a unique Green\'s function centred in $y$ associated to the vectorial operator $-\\nabla \\cdot a\\nabla $ in $\\mathbb{R}^d$, $d> 2$. In addition, we prove that if we introduce a shift-invariant ensemble $\\langle\\cdot \\rangle$ over the set of uniformly elliptic tensor fields, then $\\nabla G$ and its mixed derivatives $\\nabla \\nabla G$ satisfy optimal pointwise $L^1$-bounds in probability. Chapter 2 deals with the homogenization of $-\\nabla \\cdot a \\nabla$ to $-\\nabla \\ah \\nabla$ in the sense that we study the large-scale behaviour of $a$-harmonic functions in exterior domains $\\{ |x| > r \\}$ by comparing them with functions which are $\\ah$-harmonic. More precisely, we make use of the first and second-order correctors to compare an $a$-harmonic function $u$ to the two-scale expansion of suitable $\\ah$-harmonic function $u_h$. We show that there is a direct correspondence between the rate of the sublinear growth of the correctors and the smallness of the relative homogenization error $u- u_h$. The theory of stochastic homogenization of elliptic operators admits an equivalent probabilistic counterpart, which follows from the link between parabolic equations with elliptic operators in divergence form and random walks. This allows to reformulate the problem of homogenization in terms of invariance principle for random walks. The second part of thesis (Chapters 3 and 4) focusses on this interplay between probabilistic and analytic approaches and aims at exploiting it to study invariance principles in the case of degenerate random conductance models and systems of interacting particles. In Chapter 3 we study a random conductance model where we assume that the conductances are independent, stationary and bounded from above but not uniformly away from $0$. We give a simple necessary and sufficient condition for the relaxation of the environment seen by the particle to be diffusive in the sense of every polynomial moment. As a consequence, we derive polynomial moment estimates on the corrector which imply that the discrete elliptic operator homogenises or, equivalently, that the random conductance model satisfies a quenched invariance principle. In Chapter 4 we turn to a more complicated model, namely the symmetric exclusion process. We show a diffusive upper bound on the transition probability of a tagged particle in this process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent interest. We also show off-diagonal estimates of Carne-Varopoulos type.

I pappersmaskiner används kräppblad för att kräppa av pappret från en stor roterande cylinder, en så kallad yankee-cylinder. Dessa blad utstår stora nötningar och beläggs därför med antingen en kromoxidbeläggning eller en hårdmetallsbeläggning för att öka bladets nötningsbeständighet. Bladen beläggs med termisk sprutning, kromoxiden via plasmasprutning och hårdmetallen via "High-Velocity-Oxy-Fuel"-sprutning (HVOF). I detta arbete har slitagetester utförts på belagda kräppblad genom att använda en "slider-on-flat-surface" (SOFS) tribometer för att ta reda på vilken av dessa beläggningar som är bäst lämpad för att användas på kräppblad. Vid användning av SOFS belastas kräppbladen med en normalkraft och glider mot en platta till önskad total glidsträcka är uppnådd. För att kunna genomföra slitagetesterna i SOFSen behövdes en fixtur konstrueras och tillverkas och kräppblad behövde kapas till önskad geometri. Det skapades tre koncept för fixturen och med en beslutsmatris gjordes valet vilken av dem som skulle tillverkas. Den tillverkade fixturen håller kräppbladen stabila i både sidled och i glidriktningen och håller kräppbladen i en vinkel likt i verkligheten. Slitagetesterna utfördes vid tre olika glidsträckor med konstant normallast. Efter slitagetesterna analyserades bladen i stereomikroskop och svepelektronmikroskop för att identifiera nötningsmekanismer. De dominerande nötningsmekanismerna var abrasiv och adhesiv nötning. På grund av porositet i beläggningarna ökades antalet sprickor och mer och mer fragment lossnade vid ökande glidsträcka under slitagetesterna. Det visade sig efter mätningar av bortnött bredd på bladet att det hårdmetallbelagda kräppbladet hade bäst nötningsbeständighet. Detta på grund av dess hårda tungstenkarbider som minskade den abrasiva nötningen och spricktillväxten i beläggningen och dess högre duktilitet jämfört med kromoxiden. / Creping blades are used in paper machines for creping tissue paper from a rotating cylinder called a yankee cylinder. These blades experience severe wear and are therefore coated by either chromium oxide or a hard metal coating to make the blades more wear resistant. The coatings are sprayed on to the blade by thermal spraying processes, the chromium oxide coating with plasma spraying and the hard metal coating with "High-Velocity-Oxy-Fuel" (HVOF) spraying. In this thesis wear testing of the coated creping blade using a "slider-on-flat-surface" (SOFS) tribometer has been done to find out which of these coatings that is best suited for coating on the creping blade. When using the SOFS, the creping blade is subjected to a chosen normal force and is scraped against a counterface for a set total distance. In order to execute the wear tests in SOFS, construction and manufacturing of a holder for the creping blades was needed and the creping blades had to be cut to correct geometry. Three concepts were created for the holder and the decicion about which one to manufacture was made with a decision matrix. The new holder holds the creping blades stable in side movements and in the sliding direction. It also keeps the blade at a set angle to the counterface as in the real application. The wear tests consisted of three sliding distances with constant normal load. The blades were analyzed in a stereo microscope and in a scanning electron microscope to identify the wear mechanisms when the wear tests were completed. The major wear mechanisms were abrasive and adhesive wear. Because of porosity in the coatings, the number of cracks increased and fragments from the blades came loose when increasing the sliding distance during the wear tests. It showed that by measuring the eroded width on the blades that the hard metal coated blade had the best wear resistance because of the hard tungsten carbides that lowered the abrasive wear and the crack growth in the coating and because of its higher ductility in comparison to chromium oxide.

Cone crushers are widely used in the mining, mineral processing and quarrying segments of the industry to crush ores and large rocks. In such machinery, the load to be carried is rather heavy and the motion is gyratory which creates a need for a bearing set that can withstand such severe conditions. Sandvik AB is a high-technology Swedish engineering group specialized in tools and tooling systems for metal cutting, equipment, as well as tools and services for the mining and construction industries. One of their products relevant to the mining industry is the cone crusher which utilizes a 3-piece bearing set to carry thrust load. This bearing can be classified as a Spiral Groove Bearing \footnote{The abbreviation S.G.B will be used interchangeably throughout the thesis.}, and it has been incurred that it wears out rather quickly and is believed to be running under mixed-lubrication conditions where the interfaces in the bearing-set are not fully lubricated. The aim behind this thesis is to create a multiphysics model of this bearing in order to understand deeply how it works and the reasons why it does not perform as expected as well as to predict design improvements which can improve the performance of the bearing-set, thus increasing its operating life. It has been concluded that the bearing operates under severe mixed-lubrication conditions and that the generation of a squeeze film is the only method by which lubrication takes place due to the excessive depth of the grooves which is needed to allow for an adequate amount of cold oil to flow into the grooves and cool the interface as well as to accommodate for a considerable amount of wear particles. In light of the results and insight gathered from the simulations, possible design variations of the bearing which can be advantageous in terms of mitigating asperity friction in the interfaces of the bearing are discussed and tested.

2 Abstract Multifunctional adapter protein and histone chaperone Daxx has been described in nu- merous cellular processes, including the regulation of apoptotic and stress signalling, antiviral response and processes connected to chromatin (e. g. transcription). Its influ- ence on chromatin-related processes is mainly carried out by several associated en- zymes, such as DNA-methyltransferase-1, histone deacetylases and chromatin- remodelling ATPase ATRX. In the complex with ATRX Daxx functions as a chaperone of histone-3.3, maintaining the constitutive heterochromatin e. g. at centromeric and telomeric regions. The main aim of this Thesis was a better understanding of the Daxx cellular functions through identification and functional characterization of its novel interacting proteins. Using the yeast two-hybrid screen, several such new Daxx-interacting proteins were identified. These proteins were mainly nuclear, connected to the regulation of chroma- tin-related processes. More detailed analysis focused on the interaction of Daxx with chromatin-remodelling ATPase Brg1. This interaction was confirmed both in vitro and in the cells, where Daxx and Brg1 associated mainly in high molecular weight pro- tein complexes. These likely chromatin-remodelling complexes contain, in addition to Brg1, several...

This project has been executed at the forestry machine track manufacturer Olofsfors AB and has been aimed at development of a rig for simulation of the wear that occurs in the linkage of Olofsfors AB forestry machine tracks. The problem is that link hooks in the tracks wears out first, often several times faster than other components. Olofsfors AB want to be able to test this wear in a controlled environment. The purpose of the wear rig is to distinguish what type of wear that is in effect as well as be able to optimize materials for Olofsfors AB: s products.   The project began with an pilot study of different types of relevant wear and different types of complete methods of wear measurement and simulation to better understand the problem. After this a market screening of existing machines and rigs that could be of interest was done. The project continued with creation of concepts of wear rigs and methods of wear. After a selection process the project proceeded with one concept to a 3D prototype.   From the market screening it could be found that the market is very thin with few suppliers. Their products are relatively expensive and need specially made test samples. The recommendation to Olofsfors AB will therefore be to construct a rig themselves. The market screening could be used by Olofsfors AB as a basis if they decide to expand their test activity in the future.    The project reached the overall goals and delivered a prototype that passes the set demands. This means that the project is basically ready to move on to construction of a physical wear rig. There are still some problems to overcome but these will be easiest to solve during the construction phase. / Projektet har utförts hos skogmaskinbandstillverkaren Olofsfors AB och har gått ut på att ta fram en rigg för att simulera den nötning som uppstår i länksystemet på Olofsfors AB:s skogsmaskinband. Problemet är att länkkrokar i banden nöts ut först, ofta flera gånger snabbare än andra komponenter. Nu vill Olofsfors AB kunna testa denna nötning i kontrollerade miljöer. Syftet med nötningsriggen är att kunna avgöra vilken typ av nötning som verkar samt kunna göra materialoptimering för Olofsfors AB:s produkter.   Projektet inleddes med en förstudie av olika typer av relevant nötning samt olika typer av färdiga metoder för att mäta och simulera nötning för att förstå problemet bättre. Efter detta gjordes en marknadsundersökning av befintliga maskiner och riggar som kan vara av intresse. Projektet fortsatte med konceptgenerering av nötningsriggar och nötningsmetoder. Efter utsållning gick projektet vidare med ett koncept till en 3D-prototyp.   Från marknadsundersökningen konstaterades det att marknaden är väldigt smal med få leverantörer. Deras produkter är relativt dyra och kräver speciella provbitar. Rekommendationen till Olofsfors AB blir därför att konstruera en egen rigg. Marknadsundersökningen kan användas som underlag av Olofsfors AB om de vill expandera sin testverksamhet i framtiden.   Projektet nådde de övergripande målen och levererade en prototyp som klarar av uppsatta krav. Detta innebär att projektet är i stort sett redo att gå vidare till konstruktion av en fysisk nötningsrigg. Vissa problem kvarstår, men dessa löses enklast under konstruktionsfasen.

O conceito de que estimulação elétrica promove o reparo de fraturas tem uma longa história, datada de 1812. O mecanismo pelo qual estimulação elétrica promove a osteogênese ainda é assunto de especulação científica, entretanto esse método não farmacológico, utilizado no presente trabalho, já mostrou efeitos positivos na promoção e estímulo da osteogênese. O presente trabalho objetivou analisar a influência da aplicação de campo elétrico pulsado nas características histológicas e propriedades mecânicas do tecido ósseo em osteotomias experimentais realizadas em tíbias de ratos. Foram utilizados 52 ratos com fraturas cirúrgicas unilaterais do terço médio da tíbia, sem lesão dos músculos e do periósteo. Os animais foram divididos em dois grupos: grupo controle, que não recebeu estimulação e grupo tratado com campo elétrico. Esses foram divididos em dois subgrupos: animais sacrificados no 19º pós-operatório e animais sacrificados no 27º pós-operatório. O membro fraturado foi tratado com campo elétrico pulsado com freqüência fundamental de 1,5 MHz e 200 \'mü\'s de largura de pulso, em sessões diárias de 20 minutos. Realizou-se radiografia desse membro no dia da cirurgia e do sacrifício. Após o tratamento sacrificaram-se os ratos e extraíram-se suas tíbias para a obtenção de material para a análise morfométrica e ensaio mecânico de flexão. Os ensaios biomecânicos revelaram que houve diferença significativa entre as médias dos grupos tratado 18 e 12 dias somente para a tensão, sendo esta maior para o grupo tratado 18 dias, para as demais propriedades mecânicas analisadas não houve diferença significativa. A análise morfométrica determinou que a relação entre os grupos controle 18 dias com tratado 18 dias bem como entre os grupos tratado 12 dias e tratado 18 dias das médias das áreas de osso formado apresentaram diferenças estatisticamente significantes. Esses resultados sugerem que existe um incremento na síntese de matriz orgânica no grupo tratado, não acompanhado linearmente pela síntese mineral. A diferença estatisticamente significativa nas tensões de ruptura, por outro lado, sugere que o aumento no grau de mineralização encontra-se em curso. / The concept that electrical stimulation promotes the repair of fractures has a long history, dated of 1812. The mechanism for which electrical stimulation promotes osteogenesis is still subject of scientific speculation, however that method non-pharmacological, used in the present work has already showed positive effects in the promotion and incentive of osteogenesis. The present work objectified to analyze the influence of the application of electric field pulsed in the histological characteristic and mechanical properties of the bone tissue in experimental osteotomy accomplished in tibias of rats. 52 rats were used with unilateral surgical fractures of the medium third of the tibia, without lesion of the muscles and of the periosteum. The animals were divided in two groups: group control, that didn\'t receive stimulation and treated group with electric field. These were divided in two subgroups: animals sacrificed in the 19th after operation and animals sacrificed in the 27th after operation. The fracture member was treated with electric field pulsed with fundamental frequency of 1,5 MHz and 200 \'mü\'s of pulse width, in daily sessions of 20 minutes. The x-ray of that member took place in the day of the surgery and of the sacrifice. After the treatment the rats were sacrificed and their tibias were extracted for the material obtaining for analysis morfometric and mechanical rehearsal of flexion. The mechanical rehearsals revealed that there was only significant difference among the averages of the treated groups 18 and 12 days for the tension, the treated group 18 days had a larger tension, for the other analyzed mechanical properties there was not significant difference. The averages of the moment of inertia and area went significantly larger for the treated group 18 days compared with the respective averages of the control group controls. The treated group 12 days presented averages significantly larger when compared to the properties: moment of inertia, neutral line and area with the control group 12 days. These results suggest that an increment exists in the synthesis of organic matrix in the treated group, not accompanied lineally by the mineral synthesis. The difference significant statistic in the rupture tensions, on the other hand, suggests that the increase in the mineralization degree meets in course.

Nosso objeto de estudo são os sistemas de spins com interações de longo alcance; em particular, estamos interessados em sistemas cuja probabilidade invariante é o modelo de Ising em A^S, onde A = {-1, 1} é o espaço de spins e S = Z^d é o espaço de sítios. Apresentamos dois resultados originais que são consequências da aplicação de algoritmos de simulação perfeita e de acoplamento no contexto da construção deste tipo de sistemas e de suas respectivas probabilidades invariantes. / Our object of interest are spin systems with long-range interactions. As a special case, we are interested in systems whose invariant measure is the Ising model on A^S, where A = {-1, 1} is the space of spins and S = Z^d is the space of sites. We present two original results that are byproducts of the application of Perfect Simulation and Coupling algorithms in the context of the construction of these spin systems and their respective invariant measures.

Nosso trabalho considera o processo de exclusão simples do vizinho mais próximo evoluindo com taxas de salto aleatórias . Demonstramos o limite hidrodinâmico deste processo. Este resultado è obtido através do limite hidrodinâmico do processo de exclusão onde as taxas de salto iniciais são substituidas pelas taxas cx,N que tem a mesma distribuição para cada N maior ou igal a 1. Fazemos algumas suposições no meio c_N e consideramos que as partículas estão inicialmente distribuidas de acordo à medida produto de Bernoulli associada a um perfil inicial. / Consider a Poisson process with rate equal to 1 in IR. Consider the nearest neighbor simple exclusion process with random jump rates § where §x =\\lambda, \\lambda > 0 if there is a Poisson mark between (x, x + 1) and §x = 1 otherwise. We prove the hydrodynamic limit of this process. This result follows from the hydrodynamic limit in the case that the jump rates {§x : x inteiro} are replaced by an array {cx,N : x inteiro} having the same distribution for each N >=1.

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