Geometric Quantum Computation (GQC) is one of the effective methods to realizequantum computation. By using geometric phases, it shows robustness to certainerrors. This thesis aims to develop a new systematic technique for implementing GQC,especially in non-adiabatic systems. First, we examine the nature of the geometric phasewith differential geometry. Then, we give a general theoretical method to realize a givenquantum gate with a geometric phase through reverse engineering. We examine themethod in the constant frequency quantum system with 2 or 3 energy levels. Finally, weanalyze the non-Abelian case where some of the frequencies are degenerate. / Geometrisk kvantberäkning (GQC) är en av de effektiva metoderna för att förverkligakvantberäkningar. Genom att använda geometriska faser visar den sig vara robustmot vissa fel. Syftet med denna avhandling är att utveckla en ny systematisk teknikför att genomföra GQC, särskilt i icke-adiabatiska system. Först undersöker vi dengeometriska fasens natur. med hjälp av differentiell geometri. Därefter ger vi en allmänteoretisk metod för att realisera en given kvantgrind med en geometrisk fas genomreverse engineering. Vi undersöker metoden i kvantsystemet med konstant frekvensoch med 2 eller 3 energinivåer. Slutligen analyserar vi det icke-Abeliska fallet där vissaav frekvenserna är degenererade.

This thesis aimed to look at the behaviours of the water beneath waves from a modeling and simulations point of view. We have investigated how to use Linear wave theory (LWT) to model the kinematic movements in water governed by free ocean waves. The model assumes the surface to consist of a superposition of sinusoidal waves. We have used fast Fourier transform (FFT) to move the surface waves from the space domain to the frequency domain from which we used the components to transform back with the inverses described by LWT. We recreated the surface with the expression for surface elevation for both two and three dimensions, and compared to the original surface. Then the same transformed components could be used to calculate the velocity fields beneath the surface. We found that the recreated surface aligns with the original surface in two and three dimensions. For the three dimensional surface we also found that the error is larger on the peaks of the waves and that at the boundary where the surface ends the error is significant due to some implementation error which we disregard. The calculated velocity fields has the expected circular movement over time and it decreases with depth. We found that a surface described with few discrete points significantly overestimates the velocities close to the surface. By increasing the number of points on the surface with simple linear interpolation this issue was resolved. The algorithms used to calculated the inverse transforms had complexity Ο(N) where N is the number of points for which to calculate the velocity, and the FFT has complexity Ο(N log N) where N is the amount of points that the surface consists of. The performance test seems to follow this trend. For applications of the methodology some future work is advised. Firstly the velocities need to be compared to some data to validate the method. Secondly some further time needs to be spent on the three dimensional case to verify that that the velocity fields behave properly and that the cross sections match with the two dimensional case. And finally, we apprehended an issue on which wavenumber to use for each wave component. Since the positive and negative wavenumber is possible and determines the propagation direction of that wave, we need to find a way to make sure that we are using the correct one for each wave component of an unknown surface.

No description available.

The thesis focuses on the application of force measurements with atomic force microscopy (AFM) on materials with a few surface contacts/asperities and chemically modified surfaces. The technique allows measurements of ultra-small intermolecular and surface forces, down to the piconewton level. The force measurements between surfaces of well-defined geometry are often used to measure and model the interaction between different systems of charged and neutral surfaces in various environments. However, detailed knowledge of the contacting surface profile geometry and surface properties is required to model the fundamental forces involved in the interaction. The preparation of such well-defined and idealized surfaces is often time consuming and the surfaces may not possess the behavior and properties of a source material in real processes, such as in industry. Moreover, external factors such as magnetic fields, ionic strengths and pH-values in a solution, may further complicate the evaluation. Hence, it is desirable to explore and develop techniques for trustable measurements of forces between “real” surfaces. These are often a complex composition of various force interactions and multiple surface contacts.The AFM probe technique was explored to measure force interactions between “real” particle surfaces. The work shows the applicability of the AFM technique to study the interaction forces despite the forecasted difficulties with the roughness of the particles.A technique to measure the adhesion and work of adhesion from AFM force curves was implemented and used. The thermal tune method was implemented in our commercial NT-MDT microscope to determine cantilever spring constants. The force interactions between natural microsize (m-s) magnetite particles and synthetic nanosize (n-s) magnetite particles were studied in calcium solution with concentrations of 1, 10, 100 mM and at pH values 4, 6 and 10. The changes in force interactions, due to variations in calcium concentration and pH were investigated. The adhesion force change with the concentration and pH was similar for m-s/m-s and m-s/n-s systems, and the adhesion force increased with the concentration at pH 6, except for the highest calcium concentration of 100 mM at pH 10. It was found that the magnetite surface modification could appear at the highest calcium concentration at pH 10. Moreover, the thesis contains preliminary results of the force interaction study between natural and synthetic bentonite-magnetite particles in calcium solution with concentrations of 1, 10 and 100 mM at pH 6.The influence of roughness on the calculation of contact mechanics parameters were studied with AFM and Vertical Scanning Interferometry (VSI). This is important for future development of a model to describe and characterize the force interaction between samples with multiple surface contacts. It was found that the optical artifacts, induced by VSI, have a large influence on all the roughness parameters calculated on the calibration grids, which represent extreme surface topographies.

Carbon nanotubes (CNTs) have attracted attention over the past decade because of their outstanding mechanical and electronic properties. These tiny tubular shells made of carbon atoms can be metallic or semiconducting and while having diameters of only about one nanometer (10-9 m), they can be up to centimeters in length, making them quasi one-dimensional (molecular wires). Along with a Young's modulus several times that of steel, CNTs are close to perfect (ballistic) electric conductors and conduct heat better than diamond. This makes them candidates for a variety of applications from nanoscale electronics and composites reinforced with CNTs on the molecular level to nano-actuators and high performance flatscreen displays.Beside electron microscopy, no other experimental method has been employed more in research on carbon nanotubes than Raman spectroscopy since it can noninvasively probe single CNTs and provide direct information about their molecular properties, for example, diameter and chirality. That is possible because in the case of CNTs Raman scattering is resonantly enhanced, giving an increase in signal by a factor of 106. Due to their high surface energy and the van der Waals inter-tube interactions, carbon nanotubes naturally form bundles of up to hundreds of tubes. Heat dissipation in CNT bundles is inefficient and, as a result, their exposure to high incident laser power causes overheating and results in several thermal effects dominating the Raman spectrum. The high cost of CNT production has strongly impeded design of "pure nanotube" functional materials, thus shifting the focus of CNT materials research to creation of CNT-based composites. Such new multifunctional materials, based on the outstanding physical properties of nanotubes, are created by mixing relatively small amounts of CNTs with polymers or metals (matrix). This is still a big challenge because of poor dispersion of CNT bundles in the matrix and weak bonding of the nanotubes to the surrounding host (matrix) molecules. One proposed solution to solve the latter problem is to establish bonding of CNTs to the matrix via functional groups covalently attached to the CNT surface, i.e., to use so-called "functionalized" CNTs in composites.The aim of this work is to explore the possibilities of using Raman spectroscopy for expressive characterization of functionalized CNTs, the source material for synthesis of CNT-based composites. CNTs produced by two synthesis techniques, with different diameter distributions, were probed using several laser excitations. Evaluating the efficiency of the functionalization process requires first determination of the intrinsic spectroscopic properties of the pristine (non-functionalized) CNTs. Because functionalization is carried out on bundled CNTs, a detailed investigation of whether the incident laser irradiation causes thermal effects in the sample during Raman experiments was performed in order to find experimental protocols for recording the intrinsic (unperturbed by heating) spectrum of the CNT bundles. From this study a set of "reference conditions" defining laser irradiance levels that do not result in overheating of the CNT bundles was established. Exceeding these laser irradiation levels (thresholds) first results in reversible changes of the Raman spectrum due to heating, while further increase of the laser irradiation leads to irreversible changes in the spectra and, hence, destruction of the CNTs in the sample. Evaluation of this destruction demonstrates its dependence on CNT diameter and high sensitivity to photon energy. Additional experiments show that in some cases a similar instability of the Raman spectra and irreversible destruction of the CNTs occur at laser irradiation levels below those that increase sample temperature. Finally, we used the "reference" laser irradiation regimes to characterize the effects of CNT sidewall functionalization. Specifically, HiPCO-produced, single-walled CNTs functionalized by methoxypenyl functional groups were studied in detail and the influence on the three main vibrational bands investigated. Results from analysis of the radial breathing mode band show that the functionalization process is selective and depends on both nanotube diameter and type.

Since the identification of carbon nanotubes (CNTs) by Ijima in 1991, this material has become a subject of great interest and effort in science because of the outstanding physical properties it exhibits. CNTs can be thought of as graphene sheets rolled into seamless cylinders of various diameters and in principle infinite length. Depending on the number of concentrically arranged tubes, CNTs are termed single‐walled (SWCNT), double‐walled (DWCNT), and multi‐walled (MWCNT) CNTs. Moreover SWCNTs exist as semiconducting or metallic types, depending on the orientation of the hexagonal lattice relative to the tube axis, as classified by the chiral indices (n, m). Their extraordinary mechanical, electrical, thermal, and optical properties render them very attractive for a wide range of applications including advanced composite materials. However synthesis of CNT‐based composite materials still remains a big challenge. In particular it remains to overcome the difficulties in achieving good nanotubes dispersion within the matrix material. The fact that present synthesis routes produce SWCNTs in a bundled state due to van der Waals intertube interaction is another serious hurdle, as SWCNT bundles do not exhibit the excellent properties of their individual components. Thus special treatment has to be applied in order to break these bundles. In an ideal composite material, the individual SWCNTs would be homogeneously dispersed in the matrix. A second issue is the interaction between the CNTs and the host: to improve the load transfer between host and filler covalent linking between the two components is desirable. One approach to solve these problems is functionalization of the CNT source material prior to its incorporation into the polymer matrix. Optimization is required to maximize the transfer from the polymer to the CNTs but minimize the number of wall defects created by the covalent grafting of the functional groups on the CNT sidewalls. Moreover appropriate functional groups have to be chosen to assure compatibility with the polymer being used. Synthesis of the polymethyl methacrylate (PMMA) composite material used here, based on functionalized SWCNTs, was reported recently and its study revealed inhomogeneities in the CNT distribution within the polymer and associated degradation in the mechanical properties suggested as being attributed to the presence of CNT agglomerates. Since Raman spectroscopy, as a mostly non‐destructive analysis method, has proven to be a powerful tool for studying both pure CNT materials and CNT‐based composites, it was used in this work along with supporting methods (scanning electron microscopy (SEM) and focused ion beam (FIB)) for extended characterization of the composite material, including analysis of the source SWCNT material before and after functionalization. Employment of different laser excitation energies (1.96eV and 2.33eV) allowed to separately probe metallic and semiconducting CNTs in the composite samples. The CNT distribution in the samples was illustrated by Raman spectral mapping of the G+‐ peak intensity as a function of position, thus elucidating the presence of CNT agglomerates of different size and shape. At both photon energies, spectral line scans across the boundary regions were performed revealing a substantial drop in intensity of G+ CNT Raman mode and an increase of the D/G+‐intensity ratio. Examination of the D/G+‐ intensity ratio of the SWCNT material before incorporation into the composite showed a higher value for functionalized than for the raw SWCNTs. Furthermore, the metallic nanotubes exhibited a higher degree of functionalization. Raman spectral imaging revealed some inhomogeneities of the CNT distribution in the composite material: the spectra of the areas with good CNT dispersion in the composite exhibit a higher D/G+‐ intensity ratio than in areas with CNT agglomerates indicating that functionalized CNTs are preferentially dispersed in the polymer matrix while non functionalized ones tend to group together in agglomerates. Furthermore significant laser heating of the SWCNTs in composites has been revealed resulting in a downshift of the G+‐ peak position which was much more pronounced in agglomerates than in the areas with dispersed CNTs and detected at the very lowest laser irradiances. SEM/FIB dual beam technique was employed as a supplementary analysis tool. The composites microstructure in CNT agglomerates as well as in the dispersed area was investigated by acquisition of SEM crossectional images confirming the different local CNT concentrations.

No description available.

The role of hydroelectricity in the Swedish energy system is increasing rapidly as the share of renewable energy sources in the country grows. Meanwhile, the dams are under current revision as ecology and safety requirements has changed since most of them were built. The need for research regarding the Swedish hydroelectric dams is higher than ever.  Historically, such research has been made through measurements in physical laboratory models – scaled down several times to reasonable sizes. However, these models become problematic in cases of very shallow waters. Distorted scaling allows the flows to keep necessary depths to remain representative for the prototype flows, however, research on such distorted flows are quite limited and moreover limited to models with completely free surface flows.  In this study the effects of distortion upon physical as well as numerical measurements of water depths and velocities are analyzed for a dam with a tunnel outlet at the bottom. Measurements were made in a distorted physical model with a distortion ratio of 3, the values of which were later compared to measurements conducted in an earlier study of the same dam in an undistorted model. Furthermore, results of numerical simulations for both the earlier mentioned scales as well as measurements in two models with distortion ratios of 2 and 4 were added to the comparison.  The purpose of the study is to widen the knowledge of distorted models and flows, as well as the knowledge of which situations CFD can perform satisfactory results and not. Numerically conducted values seem to match physical ones well, whereas the differences increased rapidly following an increased distortion ratio. Initially a goal of the study was to find a suitable distortion-ratio to obtain differences of a maximum of 10%, however, as the study came to show consistently much larger differences than that regarding water depths, the question of why these large differences occur rose to become the more significant one. The leading theory of why the differences increase as the distortion ratio becomes greater is that of the decreased utilization of the cross-sectional tunnel area, which leads to higher velocities and thereby higher tunnel resistance.

In recent decades, spinor-helicity formalism has gained popularity as a useful tool for studyingscattering amplitudes in four dimensions. This formalism has been extended to higher dimensions,but there is still much work to be done around its application. This thesis explores a new approachto extending the spinor-helicity formalism to ten dimensions by breaking the Lorentz symmetryinto two five-dimensional subspaces. We use this approach to express the ten-dimensional dynamical variables in terms of five-dimensional spinor helicities. We divide the polarization vectorsinto a direct sum of two massive polarization vectors, each living in five dimensions. We thenapply this new spinor-helicity formalism in ten dimensions to construct the YM, SYM, and higherderivative amplitudes. The results obtained in this thesis suggest that this approach may providea promising avenue for extending the spinor-helicity formalism relevant to SYM, supergravity, andsuperstring theory.

The use of exhaled breath analysis in assessing the health status of human individuals is an intriguing concept that has attracted more and more attention during recent years. Although detection of species in breath can, to a certain extent, be made by both electrochemical and mass spectrometric techniques, these do not always provide sufficient sensitivity, selectivity and speed. Due to the development of new laser sources in the (MIR) wavelength region, absorption spectrometry (AS) has shown such good performance that MIR-AS techniques start to become more viable alternatives to breath analysis. Of the large number of species exhaled  (major species, which are in %-concentrations, e.g. H2O and CO2, minor species, which exist in ppm concentrations, e.g. CO and CH4, and trace species, which exist in low or sup-ppb concentrations), some are more important than others, such as Carbonyl Sulfide, Ethane, Ethylene and Formaldehyde, since they are important biomarkers for various diseases e.g. chronic respiratory diseases, acute lung transplant rejection, UV-radiation damage of the skin and gastro-esophageal/breast cancer. The present thesis consists of a compilation and analysis of possible transitions primarily in the 3-4 µm region that can be used for detecting such species by MIR-AS techniques.