Conformal field theories (CFT) constitute an interesting class of twodimensionalquantum field theories, with applications in string theoryas well as condensed matter physics. The symmetries of a CFT can beencoded in the mathematical structure of a conformal vertex algebra.The rational CFT’s are distinguished by the property that the categoryof representations of the vertex algebra is a modular tensor category.The solution of a rational CFT can be split off into two separate tasks, apurely complex analytic and a purely algebraic part. The TFT-construction gives a solution to the second part of the problem.This construction gets its name from one of the crucial ingredients,a three-dimensional topological field theory (TFT). The correlators obtainedby the TFT-construction satisfy all consistency conditions of thetheory. Among them are the factorization constraints, whose implicationsfor boundary conditions are the main topic of this thesis. The main result reviewed in this thesis is that the factorization constraintsgive rise to a semisimple commutative associative complex algebrawhose irreducible representations are the so-called reflection coefficients.The reflection coefficients capture essential information aboutboundary conditions, such as ground-state degeneracies and Ramond-Ramond charges of string compactifications. We also show that the annuluspartition function can be derived fromthis classifying algebra andits representation theory.

In this thesis a set of boundary conditions for multiphase flow is suggested. Characteristic-based boundary conditions are reviewed for single-phase flow. The problem of open-boundary conditions is investigated, and to avoid drifting values, the use of control functions is proposed. The use of control functions is also verified with a new test which assesses the quality of the boundary conditions. Particularly, P- and PI-control functions are examined. PI-controllers have the ability to specify a given variable exactly at the outlet as well as at the inlet, without causing spurious reflections which are amplified. Averaged multiphase flow equations are reviewed, and a simplified model is established. This model is used for the boundary analysis and the computations. Due to the averaging procedure, signal speeds are reduced to the order of the flow speed. This leads to numerical challenges. For a horizontal channel flow, a splitting of the interface pressure model is suggested. This bypasses the numerical problems associated with separation by gravity, and a physical realistic model is used. In this case, the inviscid model is shown to possess complex eigenvalues, and still the characteristic boundary conditions give reasonable results. The governing equations are solved with a Runge-Kutta scheme for the time integration. For the spatial discretisation, a finite-volume and a finite-difference method are used. Both implementations give equivalent results. In single-phase flow, the results improve significantly when a numerical filter is applied. For two-dimensional two-phase flow, the computations are unstable without a numerical filter.

Den kopparbindande egenskapen hos prionproteiner är sannolikt kopplad till proteinets funtion. Det mänskliga prionproteinet innehåller ett kopparbindande oktapeptidområde, där PHGGGWGQ-sekvensen upprepas fyra gånger i följd. Syftet med detta arbete är att undersöka strukturen och dynamiken i oktapeptidområdet genom att använda teoretiska metoder. Med kvantkemisk strukturoptimering genomfördes en detaljerad jämförelse av växelverkan mellan flera katjoner och det kopparbindande området. Enligt dessa beräkningar är rodium(III) en möjlig ersättare för koppar(II) i NMR-specktroskopiska koordinationsstudier. Alternativa solvatiseringsmodeller i molekyldynamiksimuleringar har också jämförts. Periodiska randvillkor är mest lämpade för användning i de system som undersöks i detta arbete. Molekyldynamiksimuleringar användes för att jämföra oktapeptidområdets struktur och dynamik med och utan kopparjoner. Växelverkan mellan aminosyrornas ringar påverkar starkt strukturen i detta område i frånvaro av kopparjoner. Fyra olika icke-bindande och bindande modeller har studerats, vilka skiljer i sin beskrivning av växelverkan mellan koppar och proteinet. Teoretiska EXAFS spektra beräknades från dem simulerade strukturerna. Spektra som genererats för den bindande modellen är nästan identiska med experimentiella resultat, vilket stöder användandet av den bindande modellen. Detta arbete visar att kopparjoner interagerar med histidin imidazolringens Nδ, deprotonerade amidkväven hos de därpå följande glycinerna samt karbonylsyret hos den andra glycinen. Simuleringarna kunde visa att kopparjonen inte stabilt binder några axiella vattenmolekyler i lösning, till skillnad från en kristallstruktur av koordinationsstrukturen. Indolringen hos tryptofan interagerar direkt med kopparjonen genom stabiliserande katjon-π växelverkan utan direkt medverkan av någon vattenmolekyl. Växelverkan mellan indolringen och kopparjonen var väldefinierad och observerades kunna ske på båda sidor av koordinationsplanet. Molekyldynamiksimuleringarna med kopparjoner och oktapeptidområdet visade hur närvaron av kopparjoner ledde till ett mer strukturerat oktapeptidområde. / The copper-binding ability of the prion protein is thought to be closely related to its function. The human prion protein contains a copper-binding octapeptide region, where the octapeptide PHGGGWGQ is repeated four times consecutively. This work focuses on investigation of the structure and the dynamics of the octapeptide region by means of theoretical methods. Quantum chemical structural optimization allowed a detailed comparison of the interaction of several cations at the copper coordination site. These calculations identified rhodium(III) as a potent substitute for copper(II) that could be used to study the coordination site with NMR-spectroscopic methods. Solvation models that could be used in molecular dynamics simulations as an alternative to periodic boundary conditions were evaluated. Periodic boundary conditions are the best method for modeling the aqueous bulk in the kind of systems that are studied in this work. Molecular dynamics simulations were used to compare the behavior of the octapeptide region in the absence and presence of copper ions. Interaction between nonpolar rings strongly influences the structure of the region in the absence of copper ions. Four different non-bonded and bonded models for describing the interaction between copper and the protein were evaluated. Theoretical EXAFS spectra were calculated from the simulated structures. The results obtained for the bonded model are nearly identical with experimental data, which validates the use of the bonded model. This work thus shows strong evidence for copper(II) ions interacting with the octapeptide region through the histidine imidazole Nδ, the deprotonated nitrogen atoms of the following two glycine residues and the carbonyl oxygen atom of the second glycine residue. Notably, the simulations show that the axial sites of the copper ion do not stably coordinate water molecules in solution, as opposed to the crystal structure reported for the coordination site. Instead, the tryptophan indole ring interacted directly with the copper ion through stabilizing cation-π interaction without water mediation. The interaction of the indole ring with the copper ion was well-defined and was observed to occur on both sides of the coordination plane. The investigations of the interaction between copper ions and the octapeptide region with molecular dynamics simulations show how the presence of copper ions results in a more structured octapeptide region. / QC 20100816

Surface Acoustic Wave (SAW) devices are key components in RF and IF stages of many electronic systems. A Surface Acoustic wave is a mechanical wave, which is excited on the surface of a piezoelectric substrate, when an alternating electric voltage is applied through a comb-like interdigital transducer (electrodes) patterned on it. Most SAW applications to date have been in the sub-2GHz region, but emerging applications require SAW devices at higher frequencies. The traditional models are inadequate to account for pronounced second order effects at the GHz range and also new microfabrication techniques are required to obtain quality devices as the critical dimensions shrink into the nano-scale range at these frequencies. The finite element method (a numerical method of solving differential equations) has the potential to account for these effects and ever increasing sub-micron processing capabilities of LIGA (X-ray lithography) present a promising outlook for high frequency SAW device modeling and fabrication respectively. <p>A finite element model has been developed using commercial software ANSYS for one port SAW resonators and is presented in this thesis. The one port SAW resonators are generally connected in form of ladder networks to form low-loss SAW filters. The spacing between the electrodes and the velocity of the SAW determine the frequency of operation of these devices. A finite element model has been developed for three different types of SAWdevices namely Rayleigh, leaky and longitudinal leaky SAW (LLSAW). The LLSAW has higher velocity as compared to other two types and hence considered in this work as a good prospect for high frequency SAW devices. <p>A full finite element model could not be solved due to high computing requirements and hence some assumptions were made and the results were validated against published results in the literature. The results indicate that even with simplifying assumptions and approximations FE model provides reasonably accurate results, that can be used in device design. Some of the simulations (in LLSAW based devices) in this work were also done with a view towards using LIGA (X-ray lithography) for fabrication of high frequency devices as they have the capability for high aspect ratios.

We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove the completeness of root functions related to L.

Surface Acoustic Wave (SAW) devices are key components in RF and IF stages of many electronic systems. A Surface Acoustic wave is a mechanical wave, which is excited on the surface of a piezoelectric substrate, when an alternating electric voltage is applied through a comb-like interdigital transducer (electrodes) patterned on it. Most SAW applications to date have been in the sub-2GHz region, but emerging applications require SAW devices at higher frequencies. The traditional models are inadequate to account for pronounced second order effects at the GHz range and also new microfabrication techniques are required to obtain quality devices as the critical dimensions shrink into the nano-scale range at these frequencies. The finite element method (a numerical method of solving differential equations) has the potential to account for these effects and ever increasing sub-micron processing capabilities of LIGA (X-ray lithography) present a promising outlook for high frequency SAW device modeling and fabrication respectively. <p>A finite element model has been developed using commercial software ANSYS for one port SAW resonators and is presented in this thesis. The one port SAW resonators are generally connected in form of ladder networks to form low-loss SAW filters. The spacing between the electrodes and the velocity of the SAW determine the frequency of operation of these devices. A finite element model has been developed for three different types of SAWdevices namely Rayleigh, leaky and longitudinal leaky SAW (LLSAW). The LLSAW has higher velocity as compared to other two types and hence considered in this work as a good prospect for high frequency SAW devices. <p>A full finite element model could not be solved due to high computing requirements and hence some assumptions were made and the results were validated against published results in the literature. The results indicate that even with simplifying assumptions and approximations FE model provides reasonably accurate results, that can be used in device design. Some of the simulations (in LLSAW based devices) in this work were also done with a view towards using LIGA (X-ray lithography) for fabrication of high frequency devices as they have the capability for high aspect ratios.

Articular cartilage has a limited ability to heal due to its avascular, aneural, and alymphatic nature. Currently, there is a need for alternative therapies for diseases that affect articular cartilage such as osteoarthritis. Recently, it has been shown that tissue constructs, which resemble cartilage in structure and function, can be cultured in vitro in a cell-polymer bioreactor system. Bioreactors provide a three dimensional environment that promotes cell proliferation and matrix production. The primary objective of this study is to accurately simulate fluid mechanics using the lattice Boltzmann method for application to a cell-polymer bioreactor system. Lattice Boltzmann (LB) is a flexible computation technique that will allow for the simulation of a moving construct under various bioreactor conditions. The method predicts macroscopic hydrodynamics by considering virtual particle interactions. Derived from the Lattice Gas Automata, lattice Boltzmann allows for mass transfer, complex geometries, and particle dynamics. A primary goal is to characterize the accuracy of the LB implementation and eventually the shear stresses felt by a tissue construct in this dynamic environment. This information is important since recent studies show that chondrocytic function may depend on the mechanical stimuli produced by fluid flow. Hence, shear stress may affect the final mechanical properties of tissue constructs. In this study, numerical simulations are done first in 2D and then extended to 3D to test the LB implementation. Simulations of the rotating wall vessel (RWV) bioreactor are then undertaken. The results are benchmarked against computations done with a commercial CFD package, FLUENT, and compared with analytic solutions and experimental data.

In this thesis, we study the scattering problem of a vertically offset dielectric slab waveguide, using continuous radiation modes. The calculation of radiation modes of an arbitrarily layered waveguide has been thoroughly investigated in the literature. Most approaches were based on launching two incident waves: one from above and one from below, resulting in two transmitted waves and two reflected waves. Radiation modes were obtained by algebraic adjustments of each incident wave¡¦s amplitude and phase. These radiation modes formed standing waves in both the substrates and superstrates. This implies that walls are located an infinite distance far from the first and the last interfaces. In addition to physical conflicts of simultaneous existence of the incident wave and the walls, the derivation details are complicated and non-intuitive. In our thesis, with a given propagation constant for an arbitrarily layered dielectric waveguide, we propose an intuitive method to obtain two independent radiation mode solutions. We also construct a specific procedure to orthogonalize and normalize these two radiation modes. The second part of this thesis is focused on applying these radiation modes into a customized coupled transverse mode integral equation formulation (CTMIE), to the study of vertically offset slab waveguides. CTMIE requires two artificial boundaries placed in the substrate and superstrate. We choose to compute discretized radiation modes with the periodic boundary conditions. Under these circumstances, modes correspond to different spatial frequencies and thereby do not inter-couple. This means the matrix of the overlap integral between these two groups of modes (slightly vertically shifted) are block-diagonally dominated. The off-diagonal elements are two orders of magnitude smaller than the diagonal ones. As a result, when the two artificial boundaries are pushed towards infinity in the CTMIE formulation, we may obtain an exact inverse of the Greene¡¦s matrix without relying on numerical inversion.

Adini¡¦s elements are applied to Poisson¡¦s eigenvalue problems in the unit square with periodical boundary conditions and the leading eigenvalues are obtained from the Rayleigh quotient. The penalty techniques are developed to copy with periodical boundary conditions, and superconvergence is also explored for leading eigenvalues. The optimal convergence O(h^6) are obtained for quasiuniform elements (see [2, 21]). When the uniform rectangular elements are used, the superconvergence O(h^6+p) with p = 1 or p = 2 of leading eigenvalues is proved, where h is the maximal boundary length of Adini¡¦s elements. Numerical experiments are carried to verify the analysis made. Keywords. Adini¡¦s elements, Poisson¡¦s equation, periodical boundary conditions, eigenvalue problems.

Both Gauss-Seidel Iterative 3D deconvolution and Richardson-Lucy like algorithms are used due to their stability and high quality results in high noise microscopic medical image processing. An approach to determine the difference between these two algorithms is presented in this paper. It is shown that the convergence rate and the quality of these two algorithms are influenced by the size of the point spread function (PSF). Larger PSF sizes causes faster convergence but this effect falls off for larger sizes . It is furthermore shown that the relaxation factor and the number of iterations are influencing the convergence rate of the two algorithms. It has been found that increasing relaxation factor and number of iterations improve convergence and can reduce the error of the deblurred image. It also found that overrelaxation converges faster than underrelaxation for small number of iterations. However, it can be achieved smaller final error with under-relaxation. The choice of underrelaxation factor and overrelaxation factor value are highly problem specific and different from one type of images. In addition, when it comes to 3D iterative deconvolution, the influence of boundary conditions for these two algorithms is discussed. Implementation aspects are discussed and it is concluded that cache memory is vital for achieving a fast implementation of iterative 3D deconvolution. A mix of the two algorithms have been developed and compared with the previously mentioned Gauss-Seidel and the Richardson-Lucy-like algorithms. The experiments indicate that, if the value of the relaxation parameter is optimized, then the Richardson-Lucy-like algorithm has the best performance for 3D iterative deconvolution. / Upplösningen på bilder tagna med mikroskop är idag begränsad av diffraktion. För att komma runt detta förbättras bilden digitalt utifrån en matematisk modell av den fysiska processen. Den här avhandlingen jämför två algoritmer för att lösa ekvationerna: Richardson-Lucy och Gauss-Seidel. Vidare studeras effekten av parametrar såsom utbredningen av ljusspridfunktionen och regularisering av ekvationslösaren. / Mobile: (0046)762778136