This is an ethnographic study that focuses on Zahmanê Êzîdîa Li Dalarna, the Yezidi cemetery, in Borlänge. The Swedish town of Borlänge has one of the largest Yezidi diaspora communities in Western Europe; a majority emigrated from the Northern Iraqi region of Sheikhan during the 1990s and early 2000s. The overall aim of this project is to investigate how the Yezidi community in Borlänge puts Zahmanê Êzîdîa Li Dalarna into use, the meanings ascribed to the site by individual interviewees, and how these relate to ritual places and practices in Sheikhan. The empirical material stems from observations and interviews among members of three extended Yezidi families in Borlänge and in Sheikhan, and archival material from the Church of Sweden. Fieldwork in Sheikhan focused on the valley of Lalish and the cemetery sites in the Yezidi villages in Sheikhan. The empirical material is presented, analysed and discussed through a theoretical framework of place, creation and maintenance of social memory through ritual practice, and the concept of transfer of ritual. The empirical material reveals that salient ritual actions and elements from ceremonies in Lalish and the Yezidi villages in Sheikhan are transferred to Borlänge, and there put into use for ritual practices and for creating and maintaining a collective identity outside of Iraq.

Kronecker structured representations are used to cope with the state space explosion problem in Markovian modeling and analysis. Currently an open research problem is that of devising strong preconditioners to be used with projection methods for the computation of the stationary vector of Markov chains (MCs) underlying such representations. This paper proposes a block SOR (BSOR) preconditioner for hierarchical Markovian Models (HMMs) that are composed of multiple low level models and a high level model that defines the interaction among low level models. The Kronecker structure of an HMM yields nested block partitionings in its underlying continuous-time MC which may be used in the BSOR preconditioner. The computation of the BSOR preconditioned residual in each iteration of a preconditioned projection method becoms the problem of solving multiple nonsingular linear systems whose coefficient matrices are the diagonal blocks of the chosen partitioning. The proposed BSOR preconditioner solvers these systems using sparse LU or real Schur factors of diagonal blocks. The fill-in of sparse LU factorized diagonal blocks is reduced using the column approximate minimum degree algorithm (COLAMD). A set of numerical experiments are presented to show the merits of the proposed BSOR preconditioner.

Hierarchical Markovian Models (HMMs) are composed of multiple low level models (LLMs) and high level model (HLM) that defines the interaction among LLMs. The essence of the HMM approach is to model the system at hand in the form of interacting components so that its (larger) underlying continous-time Markov chain (CTMC) is not generated but implicitly represented as a sum of Kronecker products of (smaller) component matrices. The Kronecker structure of an HMM induces nested block partitionings in its underlying CTMC. These partitionings may be used in block versions of classical iterative methods based on splittings, such as block SOR (BSOR), to solve the underlying CTMC for its stationary vector. Therein the problem becomes that of solving multiple nonsingular linear systems whose coefficient matrices are the diagonal blocks of a particular partitioning. This paper shows that in each HLM state there may be diagonal blocks with identical off-diagonal parts and diagonals differing from each other by a multiple of the identity matrix. Such diagonal blocks are named candidate blocks. The paper explains how candidate blocks can be detected and how the can mutually benefit from a single real Schur factorization. It gives sufficient conditions for the existence of diagonal blocks with real eigenvalues and shows how these conditions can be checked using component matrices. It describes how the sparse real Schur factors of candidate blocks satisfying these conditions can be constructed from component matrices and their real Schur factors. It also demonstrates how fill in- of LU factorized (non-candidate) diagonal blocks can be reduced by using the column approximate minimum degree algorithm (COLAMD). Then it presents a three-level BSOR solver in which the diagonal blocks at the first level are solved using block Gauss-Seidel (BGS) at the second and the methods of real Schur and LU factorizations at the third level. Finally, on a set of numerical experiments it shows how these ideas can be used to reduce the storage required by the factors of the diagonal blocks at the third level and to improve the solution time compared to an all LU factorization implementation of the three-level BSOR solver.

Ce mémoire traite de l’influence des Lumières sur la pensée philosophique et musicale du compositeur et guitariste Fernando Sor (1778-1839). Cette influence peut être déclinée en trois thèmes, autour desquels le présent travail est structuré. Le premier thème, qui est omniprésent dans la Méthode pour la guitare de Sor (Paris, 1830), est celui de l’usage de la raison opposé à l’obéissance aveugle à une autorité. Le deuxième thème, présent lui aussi dans la Méthode, est celui de l’harmonie conçue comme une science permettant d’établir les rapports naturels qui existent entre les sons. Le troisième thème, présent quant à lui dans des chansons à caractère politique composées par Sor entre 1808 et 1832, est celui de la recherche de liberté face à l’oppression. Nous verrons dans ce mémoire que la manière dont la raison, l’harmonie et la liberté se manifestent dans les écrits et les œuvres de ce pionnier de la guitare classique est similaire à la manière dont ces trois mêmes notions sont représentées dans l’Encyclopédie de Diderot et d’Alembert, Sor faisant d’ailleurs référence à cet ouvrage emblématique du siècle des Lumières dans sa Méthode. D’autre part, nous verrons que le guitariste a aussi été influencé par les écrits de figures importantes associées au classicisme français, comme Descartes en ce qui concerne la raison et Rameau en ce qui concerne la notion de basse fondamentale (ces deux auteurs étant d’ailleurs cités dans l’Encyclopédie). En somme, ce mémoire permet de mieux définir le concept d’« influence des Lumières chez Sor » qui restait autrement plutôt flou dans la littérature secondaire publiée à ce jour. / This master’s thesis deals with the influence of the Enlightenment on the philosophical and musical thought of the composer and guitarist Fernando Sor (1778-1839). This influence can be divided into three themes, around which this project is structured. The first theme, which is omnipresent in Sor’s Méthode pour la guitare (Paris, 1830), is that of the use of reason opposed to a blind submission to authority. The second theme, also present in the Méthode, is that of harmony seen as a science that establishes the natural relationships that exist between sounds. The third theme, present in political songs composed by Sor between 1808 and 1832, is that of the struggle of freedom against tyranny. In this thesis, we will see that the way reason, harmony and freedom are conceived in Sor’s work is heavily influenced by Diderot and d’Alembert’s Encyclopédie, which is mentioned in the Méthode. On the other hand, we will see that the guitarist was also influenced by the writings of major figures associated with French classicism, such as Descartes when it comes to reason and Rameau when it comes to the notion of basse fondamentale (both of whom are mentioned in the Encyclopédie). In short, this master’s thesis helps to better understand how the Enlightenment influenced Sor, a subject that was otherwise mostly absent from the secondary literature.

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The pressure on clean and sustainable energy supplies is increasing. In this regard energy conversion by electrochemical processes plays a major role, for both fuel cell reactions and electrolysis reactions. The sulphur dioxide oxidation reaction (SOR) is a common reaction found in the Hybrid Sulphur Cycle (HyS) and the HyS is a way to produce large-scale hydrogen (H2). The problem with the use of the HyS and fuel cells is the cost involved as large amounts of Pt are required for effective operation. The aim of the study was to determine whether there was an alternative catalyst which was more efficient and cost-effective than Pt. The oxygen reduction reaction (ORR), the ethanol oxidation reaction (EOR) and SOR were studied by means of different electrochemical techniques (cyclovoltammetry (CV), linear polarization (LP) and rotating disk electrode (RDE)) on polycrystalline platinum (Pt) and palladium (Pd). The SRR and EOR are common reactions occurring at the cathode and anode, respectively, in fuel cells and these reactions have been investigated extensively. The reason for studying the reactions was as a preparation for the SOR. This study compared polycrystalline Pt and Pd for the different reactions, with the main focus on the SOR as Pd is considerably cheaper than Pt, and for the SOR polycrystalline Pd has by no means been investigated intensively. Polycrystalline Pt and Pd were compared by different electrochemical techniques and analyses. The Koutecky-Levich and Levich analyses were used to (i) calculate the number of e- involved in the relevant reaction, (ii) to determine whether the reaction was mass transfer controlled at high overpotentials and (iii) whether the reaction mechanism changed with potential. Next the kinetic current density ( k) was calculated from Koutecky-Levich analyses, which was further used for Tafel slope analyses. If it was not possible to carry out the analyses, the activation energy (Ea) was used to determine the electrocatalytic activity of the catalyst. The electrocatalytic activity was also determined by comparing onset potentials (Es), peak potentials (Ep) and limited/maximum current density ( b/ p) of each catalyst. This study was only a preliminary study for the SOR and therefore, further studies are certainly required. It seemed Pd shows better electrocatalytic activity than Pt for the SRR in an alkaline electrolyte because of similar Es, but Pd produced a higher cathodic current density. Pt showed a lower Es than Pd for the SRR in an acid electrolyte, but Pd delivered a higher cathodic current density. This, therefore, means that the SRR in an acid electrolyte is kinetically more favourable on Pd than on Pt. For the EOR better electrocatalytic activity was obtained with Pd than with Pt in an alkaline electrolyte due to higher current densities at lower potentials and Pd showed lower Ea values than Pt in the potential range normally used for fuel cells. Pd was inactive for EOR in an acid electrolyte, while a reaction occurred on Pt. A possible reason for this observation may be due to the H2 absorbing strongly on Pd thus blocking the active positions on the electrode surfaces, preventing further reaction. Pd showed higher electrocatalytic activity for the SOR due to lower Es and higher current densities at low potentials. From the RDE studies it was established that the SRR in an alkaline electrolyte on polycrystalline Pt and Pd was mass transfer controlled at low potentials (high overpotentials), but the SRR in an acid electrolyte was only mass transfer controlled on Pt. The SOR was not mass transfer controlled on polycrystalline Pt and Pd at high potentials (high overpotentials). These assumptions were confirmed by Levich analysis. Using Koutecky-Levich analysis, it was determined that the reaction mechanism on polycrystalline Pt and Pd changed with potential for SRR in an alkaline electrolyte and the SOR. For the SRR in an acid electrolyte the reaction mechanism remained constant with changes in potential on polycrystalline Pd, but the reaction mechanism on polycrystalline Pt changed with potential. These assumptions were confirmed by the number of e-, calculated using Koutecky-Levich analyses. Levich and Koutecky-Levich analyses were not performed for EOR as an increase in rotation speed did not produce an increase in current density. Tafel slope analyses were conducted by making use of overpotentials and k, where possible. As in the case of ethanol, it was not possible to execute Koutecky-Levich analyses and, therefore, it was not possible to perform Tafel slope analyses using k. Tafel slope analyses for the EOR was therefore performed with normal current densities at 0 rotations per minute (rpm). The reaction mechanisms on Pt and Pd for the SRR in alkaline and acidic electrolytes differed due to different Tafel slopes. Pt and Pd displayed similar Tafel slopes for the EOR in alkaline electrolyte, thus suggesting that the reaction mechanisms on Pt and Pd were the same. For the SOR it seemed that the reaction mechanism on Pt and Pd were similar because of similar Tafel slopes. This was only a preliminary and comparative study for polycrystalline Pt and Pd, and the reaction mechanism was not further studied by means of spectroscopic techniques. / MSc (Chemistry), North-West University, Potchefstroom Campus, 2014

The pressure on clean and sustainable energy supplies is increasing. In this regard energy conversion by electrochemical processes plays a major role, for both fuel cell reactions and electrolysis reactions. The sulphur dioxide oxidation reaction (SOR) is a common reaction found in the Hybrid Sulphur Cycle (HyS) and the HyS is a way to produce large-scale hydrogen (H2). The problem with the use of the HyS and fuel cells is the cost involved as large amounts of Pt are required for effective operation. The aim of the study was to determine whether there was an alternative catalyst which was more efficient and cost-effective than Pt. The oxygen reduction reaction (ORR), the ethanol oxidation reaction (EOR) and SOR were studied by means of different electrochemical techniques (cyclovoltammetry (CV), linear polarization (LP) and rotating disk electrode (RDE)) on polycrystalline platinum (Pt) and palladium (Pd). The SRR and EOR are common reactions occurring at the cathode and anode, respectively, in fuel cells and these reactions have been investigated extensively. The reason for studying the reactions was as a preparation for the SOR. This study compared polycrystalline Pt and Pd for the different reactions, with the main focus on the SOR as Pd is considerably cheaper than Pt, and for the SOR polycrystalline Pd has by no means been investigated intensively. Polycrystalline Pt and Pd were compared by different electrochemical techniques and analyses. The Koutecky-Levich and Levich analyses were used to (i) calculate the number of e- involved in the relevant reaction, (ii) to determine whether the reaction was mass transfer controlled at high overpotentials and (iii) whether the reaction mechanism changed with potential. Next the kinetic current density ( k) was calculated from Koutecky-Levich analyses, which was further used for Tafel slope analyses. If it was not possible to carry out the analyses, the activation energy (Ea) was used to determine the electrocatalytic activity of the catalyst. The electrocatalytic activity was also determined by comparing onset potentials (Es), peak potentials (Ep) and limited/maximum current density ( b/ p) of each catalyst. This study was only a preliminary study for the SOR and therefore, further studies are certainly required. It seemed Pd shows better electrocatalytic activity than Pt for the SRR in an alkaline electrolyte because of similar Es, but Pd produced a higher cathodic current density. Pt showed a lower Es than Pd for the SRR in an acid electrolyte, but Pd delivered a higher cathodic current density. This, therefore, means that the SRR in an acid electrolyte is kinetically more favourable on Pd than on Pt. For the EOR better electrocatalytic activity was obtained with Pd than with Pt in an alkaline electrolyte due to higher current densities at lower potentials and Pd showed lower Ea values than Pt in the potential range normally used for fuel cells. Pd was inactive for EOR in an acid electrolyte, while a reaction occurred on Pt. A possible reason for this observation may be due to the H2 absorbing strongly on Pd thus blocking the active positions on the electrode surfaces, preventing further reaction. Pd showed higher electrocatalytic activity for the SOR due to lower Es and higher current densities at low potentials. From the RDE studies it was established that the SRR in an alkaline electrolyte on polycrystalline Pt and Pd was mass transfer controlled at low potentials (high overpotentials), but the SRR in an acid electrolyte was only mass transfer controlled on Pt. The SOR was not mass transfer controlled on polycrystalline Pt and Pd at high potentials (high overpotentials). These assumptions were confirmed by Levich analysis. Using Koutecky-Levich analysis, it was determined that the reaction mechanism on polycrystalline Pt and Pd changed with potential for SRR in an alkaline electrolyte and the SOR. For the SRR in an acid electrolyte the reaction mechanism remained constant with changes in potential on polycrystalline Pd, but the reaction mechanism on polycrystalline Pt changed with potential. These assumptions were confirmed by the number of e-, calculated using Koutecky-Levich analyses. Levich and Koutecky-Levich analyses were not performed for EOR as an increase in rotation speed did not produce an increase in current density. Tafel slope analyses were conducted by making use of overpotentials and k, where possible. As in the case of ethanol, it was not possible to execute Koutecky-Levich analyses and, therefore, it was not possible to perform Tafel slope analyses using k. Tafel slope analyses for the EOR was therefore performed with normal current densities at 0 rotations per minute (rpm). The reaction mechanisms on Pt and Pd for the SRR in alkaline and acidic electrolytes differed due to different Tafel slopes. Pt and Pd displayed similar Tafel slopes for the EOR in alkaline electrolyte, thus suggesting that the reaction mechanisms on Pt and Pd were the same. For the SOR it seemed that the reaction mechanism on Pt and Pd were similar because of similar Tafel slopes. This was only a preliminary and comparative study for polycrystalline Pt and Pd, and the reaction mechanism was not further studied by means of spectroscopic techniques. / MSc (Chemistry), North-West University, Potchefstroom Campus, 2014

The thesis involves computer simulation and theoretical studies of dynamics of water under confinement and structural transformation in different complex systems. Based on the systems and phenomena of interest, the work has been classified in to three major parts: I. Dynamics of water under confinement II. Dynamics of water in presence of amphiphilic solutes III. Structural transformation in complex systems The three parts have further been divided into nine chapters. Brief chapter wise outline of the thesis is discussed below. Part I deals with the dynamics of water in confined systems. In Chapter I.1, we provide a brief introduction of water dynamics inc on fined systems. We also give a brief outline of relevant experimental and theoretical techniques used to study the water dynamics under confinement. Chapter I.2 describes a model based analytical study of dynamical correlation in confined systems. Here, we introduce a novel one dimensional Ising model to investigate the propagation and annihilation of dynamical correlations in confined systems and to understand the intriguing shortening of the orientational relaxation time that has been reported for small sized reverse micelles (RMs).In our model, the two spins located at the two end cells are oriented in the opposite directions to mimic the surface effects present in the real systems. These produce opposing polarizations which propagate from the surface to the center, thus producing bulk like condition at the center. This model can be solved analytically for short chains. For long chains, we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm).We show that the model satisfactorily reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is non-exponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of the relaxation of spins undergoes a change with the emergence of homogeneous dynamics, where the decay is predominantly exponential. In Chapter I.3, layer-wise distance dependent orientation relaxation of water confined in reverse micelle s(RM)is studied using theoretical and computational tools. We use both a newly constructed spins on a ring (SOR) Ising-type model with modified Shore-Zwanzig rotational dynamics and atomistic simulations with explicit water. Our study explores the size effect of RMs and the role of intermolecular correlations, compromised by the presence of a highly polar surface, on the distance (from the surface) dependence of water relaxation. The SOR model can capture some aspects of distance dependent orientation relaxation, such as acceleration of orientation relaxation at intermediate layers. In atomistic simulations, layer-wise decomposition of hydrogen bond (H-bond) formation pattern clearly reveal that the H-bond arrangement of water at a certain distance away from the surface can remain frustrated due to interaction with the polar surface head groups. We show that this layer-wise analysis also reveals the presence of a non-monotonic, slow relaxation component which can be attributed to the frustration effect and is accentuated in small to intermediate size RMs. For larger RMs, the long-time component decreases monotonically from the interface to the interior of the RMs with slowest relaxation observed at the interface. In ChapterI.4, we present theoretical two dimensional infrared spectroscopic (2D-IR) studies of water confined within RMs of various sizes. Here we focus again mainly on the altered dynamics of confined water by performing a layer-wise decomposition of water. We aim to quantify the relative contributions to the calculated 2D-IR spectra by water molecules located in different layers. The spectra of 0-1 transition clearly show substantial elongation along the diagonal, due to in homogeneous broadening and incomplete spectral diffusion, in the surface water layer of different size of RMs studied in this work. Our study reveals that the motion of the surface water molecules is sub-diffusive, establishing the constrained nature of their dynamics. This is further supported by the two peak nature of the angular analogue of the van Hove correlation function. With increasing system size the motion of water molecules becomes more diffusive in nature and the structural diffusion is observed to be almost completed in the central layer of larger RMs. Comparisons between experiment and simulation help establishing the correspondence between the spectral decomposition available in experimental 2D-IR with the spatial decomposition of simulated 2D-IR. Simulations also allow a quantitative exploration of the relative role of water, sodium ions and sulfonate head groups in irrational dephasing. Interestingly, the negative cross correlation between forces on oxygen and hydrogen of O-H bond in bulk water significantly decreases in the surface layer of different RMs. This negative cross correlation gradually increases in the central layer with increasing size of the RMs and this is found to be partly responsible for the faster relaxation rate of water in the central layer. Part II consists of two chapters and focuses on the dynamics of water in presence of amphiphilic solutes. In Chapter II.1, we present a brief introduction of water – DMSO binary mixture and various anomalous properties of the same. In Chapter II.2, we present theoretical IR study of water dynamics in water–DMSO binary mixtures of different compositions. We show that with increasing DMSO concentration, the IR absorption peak maxima show the presence of structural transformation in similar concentration range, observed in earlier studies. Analysis of H-bonded network near hydrophilic and hydrophobic part of DMSO also suggests that average number of hydrogen bonds near the hydrophobic parts possess maxima at the same concentration range. We also show that with increasing DMSO concentration water dynamics becomes very slow. This has been supported by the diagonal elongation of the 2D-IR spectra and also the slow decay of frequency fluctuation correlation n function (FFCF) and the orientation time correlation function (OTCF). The decoupling of the OTCF establishes that water-DMSOH-bond is much stronger than that of water-water. The last part (Part III) consists of three chapters that deal with structural transformation in various complex systems. In Chapter III.1, we introduce polydisperse systems and present existing theoretical, computer simulation and experimental studies. It also contains the importance and diversity of polydisperse system in nature. In Chapter III.2, we present computer simulation study of melting of polydisperse Lennard-Jones (LJ) system with Gaussian polydispersity in size. The phase diagram reproduces the existence of an early temperature in variant terminal polydispersity (δt0.11), with no signature of re-entrant melting. The absence of re-entrant melting can be attributed to the influence of attractive part of the potential on melting. We find that at terminal polydispersity the fractional density change approaches zero that seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction system undergoes a sharp transition from crystalline solid to disordered state with increasing polydispersity. This has been quantified by second and third order rotational invariant bond orientational orders as well as by the average inherent structure energy. The translational order parameter also indicates similar structural change The free energy calculation further supports the nature of the transition. The third order bond orientational order shows that with increasing polydispersity, local cluster favors more icosahedral-like arrangements and thus the system loses its crystalline symmetry. In Chapter III.3, we present study of phase transition and effect of confinement on it in SOR model. This system is similar to our SOR model discussed in Chapter I.3. The spins execute continuous rotation under a modified XY Hamiltonian. In order to understand the nature of phase transition in such confined spin systems we have performed extensive Monte Carlo simulations. The system size dependence of Binders cumulant, specific heat, order parameter and finite size scaling of order parameter universally suggest the existence of a phase transition. The absence of hysteresis and Scaling of Binders energy cumulant minimum confirm the continuous nature of the transition. The finite size scaling analyses give rise to the mean field nature of the transition. Plausible applications of the proposed model in modeling dipolar liquids in confined systems are also discussed. In Appendix A, we discuss a preliminary study of front propagation in a non-equilibrium system. The model system analogous to the super cooled liquid shows non-Avrami domain growth during rejuvenation. The origin of the non-Avrami nature of the domain growth and the presence of cross over are also discussed. In Appendix B, we discuss umbrella a sampling technique and WHAM analysis which is used in ChapterIII.2 to get the free energy of polydisperse LJ system.