No description available.

An alternative road traffic noise barrier using an array of periodically arranged vertical cylinders known as a Sonic Crystal (SC) is investigated. As a result of multiple (Bragg) scattering, SCs exhibit a selective sound attenuation in frequency bands called band gaps or stop bands related to the spacing and size of the cylinders. Theoretical studies using Plane Wave Expansion (PWE), Multiple Scattering Theory (MST) and Finite Element Method (FEM) have enabled study of the performance of SC barriers. Strategies for improving the band gaps by employing the intrinsic acoustic properties of the scatterer are considered. The use of the tube cavity (Helmholtz type) resonances in Split Ring Resonator (SRR) or the breathing mode resonances observed in thin elastic shells is shown to increase Insertion loss (IL) in the low-frequency range below the first Bragg stop band. Subsequently, a novel design of composite scatterer uses these 2 types of cylindrical scatterer in a concentric configuration with multiple symmetrical slits on the outer rigid shell. An array of composite scatterers forms a system of coupled resonators and gives rise to multiple low-frequency resonances. Measurements have been made in an anechoic chamber and also on a full-scale prototypes outdoors under various meteorological conditions. The experimental results are found to confirm the existence of the Bragg band gaps for SC barriers and the predicted significant improvements when locally resonant scatterers are used. The resonant arrays are found to give rise to relatively angle-independent stop bands in a useful range of frequencies. Good agreement between computational modelling and experimental work is obtained. Studies have been made also of the acoustical performances of regular arrays of cylindrical elements, with their axes aligned and parallel to a ground plane including predictions and laboratory experiment.

Seismic imaging is a technique that uses seismic echoes to map and detect underground geological structures. The conventional seismic image has the resolution limit of λ/2, where λ is the wavelength associated with the seismic waves propagating in the subsurface. To exceed this resolution limit, this thesis develops a new imaging method using resonant multiples, which produces superresolution images with twice or even more the spatial resolution compared to the conventional primary reflection image. A resonant multiple is defined as a seismic reflection that revisits the same subsurface location along coincident reflection raypath. This reverberated raypath is the reason for superresolution imaging because it increases the differences in reflection times associated with subtle changes in the spatial location of the reflector. For the practical implementation of superresolution imaging, I develop a post-stack migration technique that first enhances the signal-to-noise ratios (SNRs) of resonant multiples by a moveout-correction stacking method, and then migrates the post-stacked resonant multiples with the associated Kirchhoff or wave-equation migration formula. I show with synthetic and field data examples that the first-order resonant multiple image has about twice the spatial resolution compared to the primary reflection image. Besides resolution, the correct estimate of the subsurface velocity is crucial for determining the correct depth of reflectors. Towards this goal, wave-equation migration velocity analysis (WEMVA) is an image-domain method which inverts for the velocity model that maximizes the similarity of common image gathers (CIGs). Conventional WEMVA based on subsurface-offset, angle domain or time-lag CIGs requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, I present a new WEMVA method using plane-wave CIGs. Plane-wave CIGs reduce the computational cost and memory storage because they are directly calculated from prestack plane-wave migration, and the number of plane waves is often much smaller than the number of shots. In the case of an inaccurate migration velocity, the moveout of plane-wave CIGs is automatically picked by a semblance analysis method, which is then linked to the migration velocity update by a connective function. Numerical tests on synthetic and field datasets validate the efficiency and effectiveness of this method.

<p> This thesis describes some modifications to the orthogonalized plane wave method designed to make the method applicable to calculating the band structure of transition metals. The procedure is to augment the basis set of OPW's by including functions which vanish in the interstitial regions but represent well the outer core functions and the d-band states near the nucleus. The method is applied to the transition metal niobium, with emphasis on the applicability of the procedure. The convergence of the method is discussed and the resulting band structure of niobium is presented.</p> / Thesis / Doctor of Philosophy (PhD)

<p>Photonic crystals are periodic structures that offers the possibility to control the propagation of light.</p><p>The revised plane wave method has been implemented in order to compute band structures for photonic crystals. The main advantage of the revised plane wave method is that it can handle lossless dispersive materials. This can not be done with a conventional plane wave method. The computational challenge is comparable to the conventional plane wave method.</p><p>Band structures have been calculated for a square lattice of cylinders with different parameters. Both dispersive and non-dispersive materials have been studied as well as the influence of a surface roughness.</p><p>A small surface roughness does not affect the band structure, whereas larger inhomogeneities affect the higher bands by lowering their frequencies.</p>

This thesis concerns the study of time reversal and plane-wave decomposition in various geophysical applications. Time reversal is a key step in seismic interferometry, reverse time migration and full waveform inversion. The plane-wave transform, also known as the tau-p transform or slant-stack, can separate waves based on their ray parameters or their emergence angles at the surface. I propose a new approach to retrieve virtual full-wave seismic responses from crosscorrelating recorded seismic data in the plane-wave domain. Unlike a traditional approach where the correlogram is obtained from crosscorrelating recorded data, which contains the full range of ray parameters, this method directly chooses common ray parameters to cancel overlapping ray paths. Thus, it can sometime avoid spurious arrivals when the acquisition requirement of seismic interferometry is not strictly met. I demonstrate the method with synthetic examples and an ocean bottom seismometer data example. I show a multi-scale application of plane-wave based full waveform inversion (FWI) with the aid of frequency domain forward modeling. FWI uses the two-way wave-equation to produce high-resolution velocity models for seismic imaging. This technique is implemented by an adjoint-state approach, which viii involves a time-reversal propagation of the residual wavefield at receivers, similar to seismic interferometry. With a plane-wave transformed gather, we can decompose the data by ray parameters and iteratively update the velocity model with selected ray parameters. This encoding approach can significantly reduce the number of shots and receivers required in gradient and Hessian calculations. Borrowing the idea of minimizing different data residual norms in FWI, I study the effect of different scaling methods to the receiver wavefield in the reverse time migration. I show that this type of scaling is able to significantly suppress outliers compared to conventional algorithms. I also show that scaling by its absolute norm generally produces better results than other approaches. I propose a robust stochastic time-lapse seismic inversion strategy with an application of monitoring Cranfield CO2 injection site. This workflow involves two steps. The first step is the baseline inversion using a hybrid starting model that combines a fractal prior and the low-frequency prior from well log data. The second step is to use a double-difference inversion scheme to focus on the local areas where time-lapse changes have occurred. Synthetic data and field data show the effectiveness of this method. / text

Photonic crystals are periodic structures that offers the possibility to control the propagation of light. The revised plane wave method has been implemented in order to compute band structures for photonic crystals. The main advantage of the revised plane wave method is that it can handle lossless dispersive materials. This can not be done with a conventional plane wave method. The computational challenge is comparable to the conventional plane wave method. Band structures have been calculated for a square lattice of cylinders with different parameters. Both dispersive and non-dispersive materials have been studied as well as the influence of a surface roughness. A small surface roughness does not affect the band structure, whereas larger inhomogeneities affect the higher bands by lowering their frequencies.

<p> The Augmented Plane Wave method has been used to calculate the one-electron energy band structure of MnF2 . The bands were computed at the r point and along the ^ line for cases representing the "paramagnetic" and anti-ferromagnetic states of MnF2.</p> / Thesis / Master of Science (MSc)

Modeling and analysing materials with theoretical tools is of great use when finding new systems for applications, for example, semiconductors with point defects can be used for quantum applications, like single photon emitters. One important aspect to consider symmetry, which can yield useful information about the properties of a system. To perform symmetry analysis, a code was developed that takes the orbitals of atomic structures, as calculated with Density Functional Theory simulations, as input. Specifically, the orbitals of molecules, and defects in solids are in focus. The symmetry analysis code calculates overlap of orbitals and their symmetry transformed counterpart, maps these overlaps to characters, finds the irreducible representations, and also finds which optical transitions are allowed. The code was tested on CH4 and SF6 molecules, and the divacancy defect in 4H-SiC. The symmetry analysis is performed easily and produces results that coincide well with other theoretical results. Furthermore, symmetry matrices can be approximated to be integer matrices, and the wave functions can be approximated with less accurate plane wave expansions by reducing the cutoff energy, and thus reducing the number of plane waves. These approximations shorten the calculation time and do not compromise the accuracy of the overlap. The code automates the symmetry analysis and is intended to be used in a high-throughput manner. / <p>2021-10-12          </p><p>The student thesis was first published online. </p><p>2022-02-25          </p><p>The student thesis was updated with an errata list which is downloadable from the permanent link.</p>

Magnetic deflection techniques have been employed to measure proton angular distributions from some (d,p) and (t,p) reactions. In many cases the distributions exhibit typical stripping patterns and their analysis in terms of plane wave and distorted wave theories of stripping has enabled spin and parity assignments to be made for a number of excited nuclear levels. These theories are briefly outlined in Chapter 1 of this thesis and the experimental procedures are described in Chapter 2. The (d,p) reaction has been studied at an incident energy of 3 MeV with target nuclei B¹⁰, B¹¹, C¹², C¹⁴ and O¹⁶ and an account of this investigation is given in Chapter 3. Although the plane wave theory gives a good account of the angular distributions corresponding to the low-Q transitions (say Q ≤ 2 MeV) it is not a good approximation for the high-Q transitions. This is in accord with Wilkinson's suggestion that distortion effects should be quite small even at low deuteron bombarding energies providing also that the reaction Q-value is low. Agreement with the high-Q ground state distribution for B¹¹ could only be obtained with distorted wave theory if a cut-off radius were used. This may indicate the need for taking into account finite range effects in this theory. The Se⁷⁶(d,p)Se⁷⁷ reaction has been studied at 7.8 MeV bombarding energy and eleven angular distributions corresponding to the ground and ten excited states of Se⁷⁷ have been analysed using distorted wave theory. This investigation is described in Chapter 4. Deuteron and proton elastic scattering measurements have also been made from Se⁷⁶ and Se⁷⁷, respectively. The optical model potentials required to describe the stripping distributions are found to be entirely consistent with those derived from the elastic scattering data. In Chapter 5 an account is given of a systematic study of the (t,p) reaction for target nuclei B¹⁰, B¹¹, C¹², C¹⁴, O¹⁸, Si²⁸, Si²⁹ and Ca⁴⁰. This investigation was carried out at triton energies between 8 and 13 MeV. In the majority of cases the angular distributions are observed to be strongly forward peaked and these have been analysed in terms of Newn's plane wave theory of double stripping. With the exception of the B¹⁰(t,p)B¹² and C¹²(t,p)C¹⁴ reactions the agreement in general is found to be very satisfactory. In addition to the ground state, nine excited states of B¹³ were observed and information on the spins and parities of six of them have been obtained. The excitation energies of only four excited states were previously known. C¹⁶ had not previously been observed and the present investigation has shown this to be stable by 4.25 MeV against neutron emission, in good agreement with the predicitons of Zel'dovich. The ground state was confirmed to be O⁺ and the first excited state at 1.753 MeV excitation is probably 2⁺. The delayed neutron emission for C¹⁶ has also been studied and its measured half-life found to be 0.74 ± 0.03 seconds. Angular distributions were measured for the ground and nine excited states of O¹⁸ and ground and four excited states of O²⁰. Only one state, at 4.45 MeV excitation in O¹⁸, could not be interpreted by a double stripping process. Spin-parity assignments from the reactions Si²⁸(t,p)Si³⁰, Si²⁹(t,p)Si³¹ and Ca⁴⁰(t,p)Ca⁴² are in good agreement with earlier measurements. The Be¹¹ nucleus has been studied using the Be⁹(t,p)Be¹¹ reaction at 6 and 10 MeV triton energies. This investigation is described in Chapter 6. At the higher bombarding energy six energy levels of Be¹¹ were observed and three of these were found to have natural widths in excess of 10 keV. Proton distributions were measured at both energies for the ground and first excited states. Their interpretation in terms of a double-stripping mechanism is complicated by the presence of large backward peaks but the distributions are not inconsistent with the spins of 1/2 ^- and 1/2 ⁺, respectively, predicted by Talmi and Unna. Angular distributions from the C¹²(t,α)B¹¹ reaction at 10 MeV triton energy were also studied in an attempt to obtain information on the spins and parities of some of the states in B¹¹ which are involved in the beta-decay of Be¹¹. In Chapter 7 an account is given of triton elastic scattering measurements made at incident energies 6.4, 6.8 and 7.2 MeV from C¹², O¹⁶, O¹⁸, F¹⁹ and Ca⁴⁰. Only the scattering from F¹⁹ and Ca⁴⁰ can be described by the optical model, although the optical parameters are ambiguous. The scattering distributions from O¹⁶ at all three energies exhibit large backward peaks suggestive of compound resonance scattering. Optical model parameters derived from the triton scattering data have been uesd by Rook and Mitra to analyse the proton distributions from Ca⁴⁰(t,p)Ca⁴², using distorted wave theory. A brief account of the results is given in Appendix C.