Dans cette thèse, une étude des microstructures périodiques et de leurs applications à la modulation optique par ondes acoustiques est présentée. Plus spécifiquement, le sujet traite du couplage opto-mécanique dans les cavités des cristaux phoXoniques. Cette étude montre comment la théorie des perturbations fournit un outil efficace d’analyse et de prédiction du comportement de la modulation dans de telles structures. Cette méthode permet également d’économiser du temps de calcul en comparaison aux calculs numériques purs. L'étude théorique de la propagation des ondes dans les milieux périodiques est d'abord introduite, puis les paramètres de l'existence simultanée des bandes interdites photoniques et phononiques sont déduites. Le développement d’une méthode semi-analytique ayant pour but d’analyser l'efficacité du couplage acousto-optique dans les structures périodiques artificielles est ensuite réalisé. La théorie des perturbations est développée jusqu'au 2ème ordre. Celle-ci, associée à des considérations de symétrie, est utilisée pour l'interprétation des résultats. Une illustration de la versatilité de la méthode, basée d'une cavité ponctuelle L1 sur substrat silicium, est présentée. Les résultats obtenus sont en accord avec ceux donnés par une méthode purement numérique. / In this thesis, a study of periodic microstructures and their applications to optical modulation by acoustical waves is presented. More specifically, it deals with opto-mechanical coupling in phoXonic crystal cavities. This study shows how the perturbation theory provides an efficient tool to analyse and predict the behaviour of modulation in such structures. Moreover, when compared to pure numerical ones, this method leads to calculation time saving. The theory of periodic media is first introduced and then we derive the parameters for the simultaneous existence of photonic and phononic bandgaps. We end up by the development of a semi-analytical method to analyze acousto-optical coupling efficiency in artificial periodic structures. The perturbation theory is developed up to 2nd order and is used together with symmetry considerations for interpretations. An illustration of the versatility of the developed method is presented using an L1 point defect cavity on silicon substrate and validated with classical numerical results.

In this thesis, the synchronization in the arrays of identical and non-identical coupled harmonic oscillators is studied. Both linear and nonlinear coupling is considered. The study consists of two main parts. The first part concentrates on theoretical analysis and the second part contains the simulation results. The first part begins with introducing the harmonic oscillators and the basics of synchronization. Then some theoretical aspects of synchronization of linearly and nonlinearly coupled harmonic oscillators are presented. The theoretical results say that linearly coupled identical harmonic oscillators synchronize for any frequency of oscillation. For nonlinearly coupled identical harmonic oscillators, synchronization is shown to occur at large enough frequency values. In the second part, the simulator and simulation results are presented. A GUI is designed in MATLAB to run the simulations. In the simulations, synchronization of coupled harmonic oscillators are studied according to different coupling strength values, different frequency values, different coupling graph types (e.g. all-to-all, ring, tree) and different coupling function types (e.g. linear, saturation, cubic). The simulation results do not only support the theoretical part of the thesis but also give some idea about the part of the synchronization of coupled harmonic oscillators uncovered by theory.

This work begins by establishing the necessary and sufficient conditions for hygrothermal stability of composite laminates. An investigation is performed into the range of coupling achievable from within all hygrothermally stable families. The minimum number of plies required to create an asymmetric hygrothermally stable stacking sequence is found to be five. Next, a rigorous and general approach for determining designs corresponding to optimal levels of coupling is established through the use of a constrained optimization procedure. Couplings investigated include extension-twist, bend-twist, extension-bend, shear-twist, and anticlastic. For extension-twist and bend-twist coupling, specimens from five- through ten-ply laminates are manufactured and tested to demonstrate hygrothermal stability and achievable levels of coupling. Nonlinear models and finite element analysis are developed, and predictions are verified through comparison with test results. Sensitivity analyses are performed to demonstrate the robustness of the hygrothermal stability and couplings to deviations in ply angle, typical of manufacturing tolerances. Comparisons are made with current state-of-the-art suboptimal layups, and significant increases in coupling over previously known levels are demonstrated.

Diffusion in bulk has been well studied and our understanding may be said to be adequate if not complete. Similarly, surface diffusion has been investigated by a number of workers and a fair understanding of it has emerged. When guest particles are confined within the micropores of solids such as zeolites, the resulting phase is neither bulk nor an adsorbed phase but something in between. Properties of such a phase have not been understood sufficiently. Such phase found within these porous solids display rich variety in their property. In part, such a variety arises from the large number of factors that determine their properties. Present thesis attempts to study the relationship of some of these factors, viz., the pore size and the disorder in the pore sizes, the sorbate sizes, the role of orienta-tional motion, the inhomogeneities in temperature etc. to diffusion of the guest molecules in porous solids. Chapter 1 gives a brief overview of the literature and the present understanding in the field of diffusion of spherical atoms and small molecules in microporous materials with special attention to zeolites.,The discussion is focussed on the experimental, theoretical and computer simulation results reported in the last few years. In chapter 2 an analytic expression is derived for the diffusion coefficient of a sorbate in a crystalline porous solid with bottlenecks. This is done by assuming a situation of quasiequi-Hbrium and by applying some elementary results of kinetic theory of gases. The diffusion coefficients obtained from the analytic expression is found to agree well with the molecular dynamics results. Further, it is found to reproduce the diffusion anomaly and its temperature dependence for different zeolites such as Y, A and p. The present calculations provide a strong theoretical support for the levitation effect obtained so far purely from molecular dynamics calculations. The computational effort involved in evaluating the derived expression is at least an order of magnitude less as compared to the molecular dynamics simulations. Levitation effect is found to exist in crystalline porous solids, irrespective of the geometry and topology of the void network of the host - the zeolite. Does levitation effect exist in non-crystalline porous solids where a distribution of pore sizes is seen instead of a single size? Chapter 3 attempts to answer this question via detailed molecular dynamics simulations on zeolite Y whose perfectly crystalline pore structure has been modified by introducing disorder. A normal distribution characterized by its width <TQ of 12-ring window diameters has been generated. Investigation of motion of spherical sorbates within such a disordered host suggests that levitation effect persists although the intensity of the anomalous peak is reduced compared to crystalline faujasite. Further, there is a breakdown of the linear relationship between the self-diffusivity D and 1 /^ where a99 is the sorbate diameter in the disordered host. Comparison of similarity between the effect of temperature and that of disorder are discussed. Chapter 4 investigates the role of orientation on diffusion of methane in zeolite NaCaA during intercage and intracage migration. In this work, diffusion of a five site model of methane within porous zeolite A has been investigated by molecular dynamics simulation. Methane exhibits interesting orientational preference during its passage through the 8-membered window, the rate determining step for overall diffusion: (2+2) (or scissor) orientation is preferred to (1+3) (or inverted umbrella) orientation. This suggests strong translational-orientational coupling. This is supported by ab initio mixed basis calculations thereby suggesting that the results are not a consequence of the classical potential employed. Partial freezing of certain rotational degrees of freedom is observed during the passage of methane through the 8-ring window. Intracage motion of methane shows that methane performs a rolling motion rather than a sliding motion within the supercage. In Chapter 5, diffusion of methane and neopentane through the pores of zeolite NaY has been investigated by means of molecular dynamics simulation. Intercage motion consisting of diffusion through 12-ring window of zeolite NaY is seen to occur with strong orientational preference for (2+2) orientation in the case of neopentane but not methane. Comparison of the result with methane diffusion through the 8-ring window of zeolite NaCaA reported in chapter 4 suggests that such a preferential orientation is a typical characteristic of systems whose levitation parameter is close to unity. Temperature dependence of translational-orientational coupling during the passage through the bottleneck has been obtained. As seen earlier, partial freezing of certain rotational degrees of freedom also exists. Little or no freezing is observed around the molecular axis of symmetry parallel to the vector, ft, perpendicular to the window plane since it does the orientation of the molecule with respect to fi. Analysis of intracage motion suggests existence of rolling motion in preference to sliding motion both in methane and neopentane. It is suggested that globular molecules show a predominance of rolling motion in comparison to anisotropic molecules such as benzene. Chapter 6 reports results from molecular dynamics(MD) simulations and its comparison to the quasi-elastic neutron scattering (QENS) measurements of the diffusion of propane, NaY zeolite, at different temperatures and at a relatively high loading. The contributions to S(Q, cu) from ballistic and diffusive motions are analysed. The self-diffusivity D has been calculated from mean squared displacement (MSD) as well as from the dynamic structure factor (S(Q,cu)) computed from the MD simulation. Both the values are consistent with each other. Also, they are in reasonable agreement with the experimental QENS results. The MD results indicate a fixed jump length diffusion process, whereas, the QENS data fits well to a jump diffusion model with a Gaussian distribution of jump lengths. Diffusion is often accompanied by a reaction or sorption which in turn can induce temperature inhomogeneities. In chapter 7 Monte Carlo simulations of Lennard-Jones atoms in zeolite NaCaA are reported for the presence of a hot zone presumed to be created by a reaction. Our simulations show that the presence of localized hot regions can alter both the kinetic and transport properties such as diffusion. An enhancement in diffusion coefficient is seen in the presence of a local hot spot. Further, the enhancement of the diffusion constant is greater for systems with larger barrier height, a surprising result that may be of considerable significance to many chemical and biological processes. We find an unanticipated coupling between reaction and diffusion due to the presence of hot or cold zone in addition to that which normally exists between them via concentration. Chapter 8 explores the possibility of exploiting a judicial combination of levitation effect and blow-torch effect for the separation of mixtures. In this study, Monte Carlo simulations have been carried out for three different binary mixtures in zeolite NaCaA with hot spot placed just before the position of the window along one direction. The binary mixture consisting of two types of particles both of which are from the linear regime does not separate well while the separation achieved of the mixture with one component from the linear regime and another from the anomalous regime is excellent. The separation factors obtained in the case of the latter mixture is more than an order of magnitude larger than that of the conventional separation methods. In the case of Ne-Ar mixture in NaCaA also, where Ne is in the linear regime and Ar is in the anomalous regime, the separation attained is excellent. These results suggest that a combination of levitation and blow-torch effects can be used to obtain extraordinary separation. Here the levitation effect specifies the sign and the magnitude of the energy barrier. The blow-torch drives the component in positive or negative direction depending on the energy barrier of the guest species. An appendix describes an additional but unrelated work carried out: a Monte Carlo study of the orthorhombic(fJ), monoclinic(ct) and liquid phases of toluene in the isobaric isothermal ensemble employing variable shape simulation cell. The structure has been characterized in terms of the radial distribution functions and orientational correlation functions. The transition from the orthorhombic low temperature (3-phase to the high temperature monoclinic cc-phase has been successfully simulated. The transition is first order and lies between 140 and 145K in agreement with experiment. The reverse transition from the a-to the (3-phase does not take place in agreement with experiment. The liquid phase density and the heat of vapourization are in good agreement with the experimental values.

A total synthesis of the complex C-aryl glycoside isokidamycin was achieved during an effort to construct the natural product kidamycin, a member of the pluramycin family of antitumor antibiotics. The angolosamine carbohydrate was appended, along with annelation of a benzene ring by the implementation of the Martin group's silicon tether-directed, intramolecular aryne-furan cycloaddition strategy. The vancosamine-derived carbohydrate was then installed by an O -> C-glycoside rearrangement. A novel protocol for the carbonylative cross-coupling of ortho-disubstituted aryl iodides with aryl boronic acids and alkynyl zinc reagents was also discovered during efforts to introduce the pyranone ring of kidamycin. The reaction proved general, as a variety of electron-rich and electron-poor aryl iodides, boronic acids, and alkynyl-zinc reagents participated in the cross-coupling. / text

Sophisticated electromagnetic pulse sequences that control spin dynamics have been developed in Nuclear Magnetic Resonance (NMR) over the last few decades. However, due to more and more demanding criteria, such as unknown parameters, larger bandwidths, higher signal to noise ratio (SNR), less power consumption, etc., new pulse sequences are constantly needed. This thesis presents new pulse sequences for several important applications of NMR. / Engineering and Applied Sciences

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: The objective of this thesis is to develop a 9.2 GHz low phase noise oscillator with a cylindrical cavity resonator. A cylindrical metal cavity with air as dielectric was used as a resonator. To minimise the phase noise of the oscillator, the resonator must be designed to have a high Q-factor. A high Q-factor was obtained by designing the resonator to operate in the TE011 mode. A tuning screw was used to tune the resonant frequency without significantly affecting the Q-factor. The tuning screw also separates the resonant frequencies of the degenerate TE011 and TM111 modes. The signal is coupled to the resonator by means of rectangular apertures. The coupling was designed to minimise the phase noise of the oscillator. A dual mode waveguide filter was developed and inserted into the oscillator loop in order to prevent oscillation at unwanted frequencies. Due to the excellent phase noise performance of the oscillator, it was not possible to measure the phase noise directly with the available phase noise meter. A measurement setup using two similar oscillators tuned to oscillate at frequencies differing by about 60 MHz was implemented. The output signals were down-converted to the difference frequency where the phase noise could be measured accurately. The output signal of the oscillator was measured at different locations in the loop and clearly showed that the resonator can be used as a filter to minimise the phase noise. The performance of the oscillators met all expectations. Phase noise levels of -115 dBc/Hz and -146 dBc/Hz were obtained at offset frequencies of 10 and 100 kHz. / AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om ‘n 9.2 GHz lae faseruis ossillator met 'n silindriese holte resoneerder te ontwikkel. 'n Silindriese metaal golfleier holte met 'n lug diëlektrikum was gebruik as die resoneerder. Om die faseruis van die ossillator te minimeer moet die resoneerder ontwerp word om 'n hoë Q-faktor te hê. Om 'n hoë Q-faktor te behaal was die resoneerder ontwerp om in die TE011 orde te werk. Die resoneerder is toegerus met 'n verstelskroef wat die bedryfsfrekwensie verstel sonder om die belaste Q-faktor aansienlik te beïnvloed. Die verstelskroef skei ook die frekwensie van die degeneratiewe TE011 en TM111 ordes. Drywing word na die resoneerder gekoppel deur middel van reghoekige openinge. Die koppeling is ontwerp om die faseruis van die ossillator te minimeer. 'n Tweede orde dubbelmodes golfleier filter is ontwerp en in die ossillatorlus ingevoeg om ossillasie by ongewenste frekwensies te voorkom. Vanweë die baie lae faseruis van die ossillator was dit nie moontlik om die faseruis direk met die beskikbare faseruismeter te meet nie. 'n Meetopstelling met twee soorgelyke ossillators waarvan die frekwensies met ongeveer 60 MHz verskil is geïmplementeer. Die uittreeseine van die ossillators is afgemeng na die verskilfrekwensie waar die meetinstrument meer sensitief is en die faseruis akkuraat gemeet kan word. Die uittreesein van die ossillator is by verskillende punte gemeet en het duidelik getoon dat die resoneerder as filter gebruik kan word om die faseruis te minimeer. Die ossillators se werkverrigting het aan die verwagtinge voldoen. Faseruis vlakke van -115 dBc/Hz en -146 dBc/Hz by afsetfrekwensies van onderskeidelik 10 en 100 kHz is verkry.

This thesis describes the combination of non-stabilized nucleophiles and prochiral/racemic electrophiles in transition metal catalyzed asymmetric transformations. These enantioselective reactions have tremendous potential for the formation of chiral building blocks and new structural motifs that can be found in a variety of natural products and their derivatives. The first part of the thesis focuses on the synthetic approach towards anti-cancer active diterpenoid structures. The two key steps involve a Cu-catalyzed asymmetric conjugate addition of alkylzirconocenes to enones and an intramolecular oxidative cyclisation. Particular investigations into the cyclisation are made with organocatalysis, transition metal catalysis and electrochemistry for the formation of these tricyclic scaffolds. In the second part this work builds on the Rh-catalyzed asymmetric Suzuki-Miyaura coupling of benzeneboronic acids and cyclic allyl chlorides, which has been developed in our group. Here, the main point is to use more challenging coupling partners, such as heteroaromatic boronic acids, which are coupled to racemic cyclic allyl halides. The utility of this method is demonstrated by performing further transformations and an asymmetric synthesis of the natural product (+)- isoanabasine. The last chapter describes the development of a new asymmetric Hiyama coupling of arylsiloxanes with racemic cyclic allyl chloride. Attempts are made to generate substrates that are not accessible via the asymmetric Suzuki - Miyaura reaction. After extensive optimisation a variety of arylsiloxanes is generated and tested with the best conditions to prove its utility in comparison to the asymmetric Suzuki-Miyaura coupling.

The work presented in this thesis focuses on the total synthesis of (-)-6,7- Dideoxysqualestatin H5. Particular emphasis was the development of a cross- coupling strategy for direct delivery of the side chain towards the end of the synthesis. Various methods investigated to perform the key Csp3-Csp2 coupling initially led to the Fu variant of the Negishi coupling at elevated temperatures and subsequent cross- electrophile coupling at rt. Key features of the asymmetric synthesis of (-)-6,7- dideoxysqualestatin H5, include: (1) highly diastereoselective n-alkylation of a tartrate acetonide enolate and subsequent oxidation-hydrolysis to provide an asymmetric entry to a Î2-hydroxy-α-ketoester motif; (2) facilitation of Rh(II)-catalysed cyclic carbonyl ylide formation-cycloaddition by cogeneration of keto and diazo functionality through ozonolysis of an unsaturated hydrazone; and (3) stereoretentive Ni-catalysed Csp³-Csp² cross-electrophile coupling between tricarboxylate core and unsaturated side-chain to complete the natural product. Following completion of the natural product, further work was carried out on the ozonolysis of unsaturated tosylhydrazones as a direct approach to diazocarbonyls. The scope and limitations of reacting unsaturated tosylhydrazones with O₃ followed by Et₃N for the generation of 1,4- and 1,5-diazocarbonyl systems were explored. Tosylhydrazones, from tosylhydrazide condensation with readily available Î ́- and Îμ- unsaturated α-ketoesters, led in the former case to a 2-pyrazoline whereas the latter cases led to α-diazo-Îμ-ketoesters, although a terminal alkene produced a tetrahydropyridazinol. Tosylhydrazones from cyclic enones also allowed access to 1,4- and 1,5-diazocarbonyl systems using the ozonolysis-Et₃N strategy.

We study a new method for the strong approximate solution of stochastic differential equations using coupling and we prove order one error bounds for the new scheme in Lp space assuming the invertibility of the diffusion matrix. We introduce and implement two couplings called the exact and approximate coupling for this scheme obtaining good agreement with the theoretical bound. Also we describe a method for non-invertibility case (Combined method) and we investigate its convergence order which will give O(h3/4 √log(h)j) under some conditions. Moreover we compare the computational results for the combined method with its theoretical error bound and we have obtained a good agreement between them. In the last part of this thesis we work out the performance of the multilevel Monte Carlo method using the new scheme with the exact coupling and we compare the results with the trivial coupling for the same scheme.