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Dissertations / Theses on the topic 'Plane Wake'

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Published: 10 December 2022
Last updated: 28 January 2023

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1

Janajreh, Isam M. "Quantification of linear and nonlinear energy transfer processes in a plane wake." Thesis, Virginia Tech, 1994. http://hdl.handle.net/10919/41943.

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The transition to turbulence of plane wakes is characterized by the development of the velocity-fluctuation field from a spectrum of weak random background noise in the initial laminar wake to a nearly featureless broad spectrum of intense fluctuations within the turbulent wake. This transition has also been described as a sequence of instabilities and wave-wave interactions. In the initial small-amplitude stage,. a narrow, but continuous, band of dominant instability modes centered near the most unstable mode, known also as the fundamental mode, grow exponentially at rates that can be calculated from the linearized Navier-Stokes equations. As these modes grow, the nonlinear terms become more important and cannot be neglected anymore. The effect of these terms is to introduce wave-wave interactions that lead to quadratic energy transfer between the different spectral components of the velocity-fluctuation field. While the consequences of these interactions, such as broadening of the power spectra, have been observed in many experiments, the characteristics of these interactions have only been examined in limited cases. Previous measurements of the auto-bispectrum showed that three-wave interaction processes are important in the transitioning wake. However, quantification of these processes can only be obtained from measurement of the nonlinear energy transfer rates resulting from the nonlinear wave-wave interactions. Such quantification is very important for understanding the effects of the different mechanisms involved in the transition and final breakdown to turbulence. An understanding of these mechanisms and their effects can then be used to control the transition by enhancing certain mechanisms and reducing the role of others through external excitation. In this work, quantitative estimates of the auto-bispectrum, linear and quadratic coupling coefficients and the resulting energy transfer rates between the interacting waves at different locations are presented in controlled and natural transitions of the plane wake. The results show that, in both natural and controlled transitions, the underlying nonlinear dynamics are similar. Basically, nonlinear interactions between the instability modes result in energy transfer to harmonic bands as well as low-frequency difference components. These components play an important role in the transfer of energy to the sidebands and the valleys between the peaks. The results also show that, while energy-transfer rates in natural transition are lower than in controlled transition, the random nature of wave excitation in natural transition causes energy transfer to a band of low-frequency components which leads to energy transfer to many sidebands and results in a spectrum that differs dramatically from the one obtained in the controlled case where two instabilities are excited.
Master of Science

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2

Riba, Chad Alan. "Circulation control for download wake reduction on a scaled V-22 model." Morgantown, W. Va. : [West Virginia University Libraries], 2003. http://etd.wvu.edu/templates/showETD.cfm?recnum=2902.

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Thesis (M.S.)--West Virginia University, 2003.
Title from document title page. Document formatted into pages; contains x, 87 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 72-73).
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3

O'Hara, Brian. "Comparison of numerical simulation to existing experimental data involving downwash wake reduction for the V-22 Osprey." Morgantown, W. Va. : [West Virginia University Libraries], 2005. https://eidr.wvu.edu/etd/documentdata.eTD?documentid=4355.

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Thesis (M.S.)--West Virginia University, 2005.
Title from document title page. Document formatted into pages; contains viii, 53 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 45-46).
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4

Gibbs, Jason. "Experimental Determination of Lift and Lift Distributions for Wings In Formation Flight." Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/31301.

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Experimental methods for the investigation of trailing vortex strengths, total lift, and lift distributions for three-dimensional wings in close proximity flight were developed. With these experiments we model compound aircraft flight either docked tip-to-tip, or flying in formation. There is a distinct lack of experimental formation flight data using three-dimensional wing models for tests. The absence of fixed walls on either end of the wing permits the development of the asymmetric shedding of vortices, and the determination of the asymmetric circulation distribution induced by the proximity of the leading wing. The pair consisted of a swept NACA-0012 non-cambered wing simulating one half of a leading aircraft and a rectangular cambered NACA 63-420 wing simulating the trailing aircraft. Important aspects of the work included theoretical development, experimental setup, data acquisition and processing, and results validation. Experimentally determining the lift for formation flight, in addition to the local flow behavior for a pair of wings, can provide valuable insight for the proposition of flying actual aircraft in formation to increase mission efficiency. To eliminate the need for bulky mounting stings and direct load measurement devices that can potentially interfere with the local flowfield, a minimally invasive velocity probe method is developed. A series of experiments were performed to assist with the development of the method. Velocity and vorticity distributions obtained along a near-field plane were processed to calculate wingtip vortex strengths. Additionally, vortex position instabilities and the shedding of vorticity inboard of the wingtips were observed. To determine the circulation distributions for the trailing wing, the initial method is modified. By processing velocity information acquired in a near-field plane, both the lift and induced drag were calculated for the trailing airfoil. Comparisons are made to directly measured loads and to results reported earlier. Directly measured lift and drag coefficients were found to agree with existing literature.
Master of Science
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5

Kisiel, Thomas K. "Study of plane wave impingement on a thin plate capable of deformation." Thesis, Monterey, California. Naval Postgraduate School, 1991. http://hdl.handle.net/10945/26798.

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6

Subaschandar, N. "Turbulent Near Wake Behind An Infinitely Yawed Flat Plate." Thesis, Indian Institute of Science, 1995. http://hdl.handle.net/2005/146.

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Near wake is the region of wake flow just behind the trailing edge of the body where the flow is strongly influenced by the upstream flow conditions and also perhaps by the charac­teristics of the body. The present work is concerned with the study of the development of turbulent near wake behind an infinitely yawed flat plate. The turbulent near wake behind an infinitely yawed flat plate is the simplest of the three-dimensional turbulent near wake flows. The present study aims at providing a set of data on the turbulent near wake behind an infinitely yawed flat plate and also at understanding the development and structure of the near wake. Detailed measurements of mean and turbulent quantities have been made using 3-hole probe, X-wire and 3-wire hotwire probes. Further an asymptotic analysis of the two-dimensional turbulent near wake flow has been formulated for the near wake behind an infinitely yawed flat plate. The feature that the near wake which is dominated by mixing of the oncoming turbulent boundary layer retains, to a large extent, the memory of the turbulent structure of the boundary layer, has been exploited to develop this analysis. The analysis leads to three regions of the wake flow (the inner near wake, the outer near wake and the far wake) for which the governing equations are derived. The matching conditions among these regions lead to logarithmic variations in both normal and longitudinal directions in the overlapping regions surrounding the inner wake. These features are validated by the present results. A computational study involving seven well known turbulence models was also under­taken in order to assess the performance of the existing turbulence models in the prediction of the turbulent near wake behind an infinitely yawed flat plate. In this study all the seven models are implemented into a common flow solver code, thus eliminating the influence of grid size, initial conditions and different numerical schemes while making the comparison. This study shows that the K - e model performs better than other models in predicting the near wake behind an infinitely yawed flat plate.
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7

Le-Witt, Julian Alexander. "Asmptotically plane wave spacetimes." Thesis, Durham University, 2009. http://etheses.dur.ac.uk/251/.

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In this thesis we study aspects of plane wave spacetimes in the hope of shedding light of the nature of holography for plane waves. In particular, we would like to understand better the space of asymptotically plane wave solutions. We first review the necessary background on plane waves, variational principles for gravity and black holes in higher dimensions. We then propose a definition of asymptotically plane wave spacetimes in vacuum gravity in terms of the asymptotic fall-off of the metric and discuss the relation to previously constructed exact solutions. We construct a well-behaved action principle for such spacetimes, using the formalism developed by Mann and Marolf. We show that the action is finite on-shell and that the variational principle is well-defined for solutions of vacuum gravity satisfying our asymptotically plane wave fall-off conditions. Next we investigate the construction of black holes and black strings in vacuum plane wave spacetimes using the method of matched asymptotic expansions. We find solutions of the linearised equations of motion in the asymptotic region for a general source on a plane wave background. We observe that these solutions have some unusual propeties and do not satisfy our previously defined conditions for being asymptotically plane wave. Hence, the space of asymptotically plane solutions is restricted. We consider the solution in the near horizon region, treating the plane wave as a perturbation of a black object, and find that there is a regular black string solution. We find that no regular black hole solution exists, which is a counter-example to the conjecture of Emparan et. al. We end with a discussion of our results and suggest possible directions for future work.
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8

Pankiewicz, Ari. "Strings in plane wave backgrounds." Doctoral thesis, [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968799981.

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9

Pena, Moises. "Geodesics on Generalized Plane Wave Manifolds." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/866.

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A manifold is a Hausdorff topological space that is locally Euclidean. We will define the difference between a Riemannian manifold and a pseudo-Riemannian manifold. We will explore how geodesics behave on pseudo-Riemannian manifolds and what it means for manifolds to be geodesically complete. The Hopf-Rinow theorem states that,“Riemannian manifolds are geodesically complete if and only if it is complete as a metric space,” [Lee97] however, in pseudo-Riemannian geometry, there is no analogous theorem since in general a pseudo-Riemannian metric does not induce a metric space structure on the manifold. Our main focus will be on a family of manifolds referred to as a generalized plane wave manifolds. We will prove that all generalized plane wave manifolds are geodesically complete.
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10

Myung, Noh Hoon. "A high frequency analysis of electromagnetic plane wave scattering by perfectly-conducting semi-infinite parallel plate and rectangular waveguides with absorber coated inner walls /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487267546980859.

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11

Ding, Anli [Verfasser], and Oliver [Akademischer Betreuer] Ambacher. "Surface acoustic wave devices based on c-plane and a-plane AlScN." Freiburg : Universität, 2020. http://d-nb.info/1228786887/34.

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12

Burmaster, Charles Lyman. "Reciprocity calibration in a plane wave resonator." Thesis, Monterey, California. Naval Postgraduate School, 1985. http://hdl.handle.net/10945/21518.

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13

Sinha, Aninda. "Aspects of IIB plane wave string theory." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.614759.

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14

Harris, Paul Jeffrey 1970. "Numerical investigation of transitional compressible plane wakes." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/282531.

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Air flow in the wake region of a two-dimensional (plane) body with a blunt base has been studied using numerical simulations. The objective of this study is (1) to observe the behavior of large dynamic structures in the plane wake at several Mach numbers from low (almost incompressible) up to M = 2.46 and examine their effect on the base pressure, and (2) to address the nature of the instability in the shear layers bounding the wake flow at M = 2.46 and observe the structures that arise from this instability. A code was developed for this study which solves the compressible Navier-Stokes equations in two or three dimensions. This code may be used for either Direct Numerical Simulations (DNS) or Large Eddy Simulations (LES). A spatial model is used, with the computational domain arranged around the trailing edge of a two-dimensional flat plate with a blunt base. Two-dimensional simulations were carried out at Mach numbers of M = 0.25, M = 1.20, and M = 2.46. At all Mach numbers, the flow was found to be unstable with respect to sinuous (antisymmetric) disturbances, with the critical Reynolds number increasing with increasing Mach number. These disturbances grow to a periodic state, and a Karman vortex street is formed. Examination of the supersonic cases revealed that expansion fans in the flow at the corners are the primary cause of the low base pressure, and that disruptions in the expansions raise the base pressure. At M = 2.46 and Reynolds numbers starting at Re = 100, 000, an intermittent shear layer instability was also found, excited by sinuous disturbances. The two instability 2 modes interact to produce a chaotic behavior. Above Re = 200, 000, the shear layer instability appears close to the base without sinuous disturbances, forming rows of vortices in the shear layers. Preliminary three-dimensional simulations were carried out at M = 2.46, examining the variation in the growth rate of three-dimensional disturbances with spanwise wavelength.
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15

Magrini, Samantha H. "Bone Growth: The Wake of the Growth Plate." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent162669258742215.

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16

Cabrera, Gomez Jose Julian. "Velocity-dip analysis in the plane-wave domain." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/30604.

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Plane-wave decomposition and slant stack transformation have recently gained much interest as viable routes to perform a variety of prestack processing tasks, such as velocity estimation, migration, filtering, deconvolution, and velocity inversion. To further complement the current advances, the problem of earth model parameter estimation and prestack structural imaging are addressed in this work. Unlike existing methods, the algorithms presented here make a novel and systematic use of the plane-wave domain to determine migration and interval velocities, interface dip angles and common-shot gather reflector images. To start, a method is developed to estimate migration velocities and interface dip angles in earth models composed of planar, dipping reflecting interfaces separating homogeneous layers, and where straight-ray travelpaths to the reflecting interfaces can be assumed. The method consists of transforming a common-shot gather into the plane-wave domain, where a semblance analysis search along cosinusoid trajectories is performed. Since the cosinusoid trajectories are functions of the migration velocity and interface dip angle, selection of the maximum semblance values yields the best estimates to the desired earth model parameters. To remove the straight-ray assumption of the velocity-dip analysis method, a recursive technique is developed to estimate interval velocities and interface dip angles via a ray tracing algorithm. This technique essentially generates plane-wave domain traveltimes for a range of interval velocities and interface dip angles, and computes the error between the generated and observed plane-wave traveltimes. The minimum error determines the best estimates of the earth model parameters. With the information attained in the velocity-dip analysis algorithm, a plane-wave based imaging method is developed to produce prestack common-shot gather images of the reflecting interfaces. The method consists of transforming a common-shot gather into the plane-wave domain, where a velocity-dip semblance analysis is performed. Then, the plane-wave components are downward extrapolated and recombined via a dip-incorporated inverse slant-stack transformation to produce the spherical-wave field that would have been recorded by receivers placed on the reflecting interfaces. The dip incorporation consists of redefining the angle of emergence of the plane waves. Finally, a simple mapping algorithm converts the offset and time coordinates of the reconstructed wave field to the true horizontal location and two-way vertical time of the reflection points. This results in the desired prestack migrated images of the reflecting interfaces. In this thesis, a novel algorithm to perform plane-wave decomposition via Fourier transforms is also proposed. This algorithm consists of the application of the double fast Fourier transform to the input data, followed by complex vector multiplications with essentially the Fourier representation of the Bessel function J0 . A numerical singularity is avoided by applying an analytical expression that approximately accounts for the singular point contribution. An inverse fast Fourier transform from frequency to time gives the desired plane-wave seismogram. The techniques proposed in this work have yielded encouraging results on synthetic and field data examples. The examples demonstrate, for the first time, the systematic use of the plane-wave domain in processing seismic reflection data from common-shot gather data to the plane-wave domain, to velocity and dip angle analysis and to prestack structural imaging. It is believed that the results from this work will help researchers as well as practising geophysicists to become better acquainted with plane-wave domain processing.
Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate
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17

Pairor, Puangratana. "In-plane tunneling spectroscopy of d-wave superconductors." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ63754.pdf.

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18

Philip, Simon. "Plane-wave limits and homogeneous M-theory backgrounds." Thesis, University of Edinburgh, 2005. http://hdl.handle.net/1842/15645.

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In this thesis we study plane-wave limits and M-theory vacua. We consider several hereditary properties of the plane-wave limit but focus on that of homogeneity. We show that a sufficient condition for a plane-wave limit along a particular geodesic of any spacetime to be homogeneous is that the geodesic be homogeneous. On reductive homogeneous spacetimes we reduce the calculation to a set of algebraic formulae by two different methods; the first uses the covariant description of the plane-wave limit [Blau, O’Loughlin, Papadopoulos. JHEP,01:047,2002] and the second employs a non-adapted coordinate description of the plane-wave limit. We study how the homogeneous structure on a reductive homogeneous spacetime behaves under the plane-wave limit and apply our formulae to many relevant examples. We then consider supersymmetric M-theory vacua and the Lie supersymmetry superalgebra on these backgrounds. We show that those backgrounds which preserve more than 24 of the supersymmetries are necessarily homogeneous and provide some evidence that this boundary is sharp. The symmetric square of the spinor bundle of an 11-dimensional spacetime is isomorphic to a particular bundle of differential forms, this can be used to interpret Killing spinors as differential forms satisfying a system of first order equations [Gauntlett, Gutowski, Pakis. JHEP,12:049,2003]. We use this technique to investigate both the geometric and algebraic nature of the 24+ supergravity solutions, in particular those which are plane-waves. Finally we consider some more general homogeneous supergravity solutions, including homogeneous 5-dimensional supergravity.
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19

Garcia, Samuel. "Plane-Wave Scattering of a Periodic Corrugated Cylinder." Thesis, Florida Atlantic University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10610475.

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In this dissertation, a novel approach to modeling the scattered field of a periodic corrugated cylinder, from an oblique incident planewave, is presented. The approach utilizes radial waveguide approximations for fields within the corrugations, which are point matched to approximated scattered fields outside of the corrugation to solve for the expansion coefficients. The point matching is done with TMz and TEz modes simultaneously, allowing for hybrid modes to exist.

The derivation of the fields and boundary conditions used are discussed in detail. Axial and radial propagating modes for the scattered fields are derived and discussed. Close treatment is given to field equations summation truncation and conversion to matrix form, for numerical computing. A detailed account of the modeling approach using Mathematica® and NCAlgebra for the noncommutative algebra, involved in solving for the expansion coefficients, are also given.

The modeling techniques offered provide a full description and prediction of the scattered field of a periodic corrugated cylinder. The model is configured to approximate a smooth cylinder, which is then compared against that of a textbook standard smooth cylinder. The methodology and analysis applied in this research provide a solution for computational electromagnetics, RF communications, Radar systems and the like, for the design, development, and analysis of such systems. Through the rapid modeling techniques developed in this research, early knowledge discovery can be made allowing for better more effective decision making to be made early in the design and investigation process of an RF project.

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20

Pearce, Gregory John. "Plane-wave methods for modelling photonic crystal fibre." Thesis, University of Bath, 2006. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.436875.

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21

Speirs, Lucinda J. "Wake dispersion on process plant : enhancing VOC emissions control." Thesis, University of Surrey, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265655.

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22

Bolat, Beldek Tugba. "Short Wave Infrared Camera Design And Focal Plane Analysis." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614150/index.pdf.

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The subject of this study is the design of a camera, which has maximum volume of 50 mm x 50 mm x 300 mm, using short infrared wavelength providing Rayleigh criteria. Firstly, the required flux per pixel has been calculated. Throughout these calculations, atmospheric losses have been obtained by MODTRAN program. Also signal to noise ratio has been examined at minimum and maximum integration time intervals. The focal length of the camera has been calculated as it receives 1 m resolution from 8 km distance. Moreover, the lens materials have been used as N-F2, LIF and BaF2 in this six lens system. The design has been done using ZEMAX optical design program and the performance of the system at focal plane was investigated by the help of Seidel aberrations, Modulation transfer Function (MTF), Spot diagram and Optical Path Difference (OPD) fan plot analyses.
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23

Llewellyn, Smith Stefan Gregory. "Vortices and Rossby-wave radiation on the beta-plane." Thesis, University of Cambridge, 1996. https://www.repository.cam.ac.uk/handle/1810/244817.

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The Earth’s atmosphere and oceans contain strongly swirling coherent structures. The sphericity of the Earth’s surface, which may be modelled by the beta-effect, is responsible for the motion of these vortices, and also for the existence of Rossby waves. This dissertation examines the evolution of distributed vortices on the beta-plane when the vortices are much stronger than the background beta-effect. There is a small nondimensional parameter ε , and a solution to the problem may be sought as an asymptotic expansion in ε. The near-field equation is then, to first order, a forced radial Rayleigh equation. For the nondivergent case, with no vortex stretching, a different dynamical balance holds in the far field. Chapter 2 derives an exact mode-one solution for the radial Rayleigh operator and completely solves the classical inviscid instability initial-value problem for mode-one disturbances to a circular basic state. Disturbances tend to a steady-state solution if the basic state circulation is nonzero, and grow algebraically without bound otherwise. Chapter 3 examines properties of the causal Green’s function for the far-field Rossby wave equation. Chapter 4 calculates the first-order solution to the global problem in the nondivergent case by the method of Matched Asymptotic Expansions. For zero circulation, there is no far field. The resulting trajectory of vortices is computed; several ways of identifying the centre of the vortices are presented. Trajectories are calculated for the Rankine and Gaussian vortices. Chapter 5 calculates the asymptotic behaviour of the second-order solution, and examines the nonuniformity of the asymptotic expansion. In the case of nonzero circulation, the expansion loses validity for times t = 0( ε -2/3 ) and spatial scales r = 0( ε -1/3 ), rather than t = 0( ε -1) and r = 0(1) respectively. Chapter 6 solves the divergent problem numerically to first order, and also analytically for asymptotically large Rossby radii of deformation. The order of breakdown is then t = 0( ε -1). Chapter 7 presents conclusions and suggestions for further research.
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24

Whitmore, Norman Daniel. "An imaging hierarchy for common-angle plane wave seismograms /." Access abstract and link to full text, 1995. http://0-wwwlib.umi.com.library.utulsa.edu/dissertations/fullcit/9605996.

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25

Alomari, Zainab Rami Saleh. "Plane wave imaging beamforming techniques for medical ultrasound imaging." Thesis, University of Leeds, 2017. http://etheses.whiterose.ac.uk/18127/.

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In ultrasound array imaging, the beamforming operation is performed by aligning and processing the received echo signals from each individual array element to form a complete image. This operation can be performed in many different ways, where adaptive and non-adaptive beamformers are considered as the main categories. Adaptive beamformers exploit the statistical correlation between the received data to find a weighting value at the focal point, instead of using a fixed weighting window in non-adaptive beamforming. This results in a significant improvement in the image quality in terms of resolution and sidelobes reduction. This improvement is necessary for ultrafast imaging because of the lack of focusing in Plane Wave Imaging (PWI) that results in lowering the SNR, and thus the produced imaging quality is reduced. This thesis analyses different adaptive beamforming techniques for ultrafast imaging. For accurate medical diagnosis, the frame rate, the imaging resolution, contrast and speckle homogeneity are all considered as important parameters that contribute to the final imaging result. To be able to evaluate each technique by minimizing the effect of external parameters, two different analysis were performed. First an empirical expression for PWI lateral resolution is produced after studying the effect of the imaging parameters on this imaging method. Then a method for selecting the suitable steering angles in Compound Plane- Wave Imaging (CPWI) is introduced, with a detailed explanation for the effect of the compound angles on resolution and sidelobes level. In order to add the contrast improvement to the properties of adaptive beamformers, some techniques like the coherence-based factors and Eigenspace-Based Minimum Variance (ESBMV) are produced in the literature. After demonstrating the principle of Minimum Variance adaptive beamformer, a detailed comparison for the types of coherence-based factors is given. In addition, a new technique of Partial-ESBMV is introduced to modify reference ESBMV so that no Black Box Region artefacts nor dark spots appear when using this method in medical imaging. After explaining its background and properties using cystic and wire phantoms, the proposed method is applied to the real RF data of carotid artery, as an application to clarify the efficiency of this method in medical ultrasound imaging.
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Friday, Brian Matthew. "VANISHING LOCAL SCALAR INVARIANTS ON GENERALIZED PLANE WAVE MANIFOLDS." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/884.

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Characterizing a manifold up to isometry is a challenging task. A manifold is a topological space. One may equip a manifold with a metric, and generally speaking, this metric determines how the manifold “looks". An example of this would be the unit sphere in R3. While we typically envision the standard metric on this sphere to give it its familiar shape, one could define a different metric on this set of points, distorting distances within this set to make it seem perhaps more ellipsoidal, something not isometric to the standard round sphere. In an effort to distinguish manifolds up to isometry, we wish to compute meaningful invariants. For example, the Riemann curvature tensor and its surrogates are examples of invariants one could construct. Since these objects are generally too complicated to compare and are not real valued, we construct scalar invariants from these objects instead. This thesis will explore these invariants and exhibit a special family of manifolds that are not flat on which all of these invariants vanish. We will go on to properly define, and gives examples of, manifolds, metrics, tangent vector fields, and connections. We will show how to compute the Christoffel symbols that define the Levi-Civita connection, how to compute curvature, and how to raise and lower indices so that we can produce scalar invariants. In order to construct the curvature operator and curvature tensor, we use the miracle of pseudo-Riemannian geometry, i.e., the Levi-Civita connection, the unique torsion free and metric compatible connection on a manifold. Finally, we examine Generalized Plane Wave Manifolds, and show that all scalar invariants of Weyl type on these manifolds vanish, despite the fact that many of these manifolds are not flat.
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27

Busch, John Robert. "All-polymer flexural plate wave sensors." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/38144.

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A novel all-polymer flexural plate wave (FPW) sensor from a piezoelectric polyvinylidene fluoride (PVDF) thin-film with poly-(3,4-ethylenedioxythiophene) poly- (styrenesulfonate) (PEDOT:PSS) interdigital transducer (IDT) electrodes has been fabricated and characterized. PVDF films are made piezoelectric by stretching and poling. X-ray diffraction measurements confirm the transition of the PVDF into its piezoelectric β-phase. Inks of PEDOT:PSS, dimethyl sulfoxide and Triton X-100 are deposited on the PVDF films by inkjet printing to produce the IDT patterns. The sensor operates using fundamental frequency, f0, detection of Lamb waves propagating through the PVDF film. Upon the application of a time-varying voltage signal to the input IDT, acoustic waves are generated and measured using a laser Doppler vibrometer, as well as through an electric signal at the output IDT. The output signal is amplified, filtered and processed using an analog to digital converter, digital signal processor and a computer program. The measured fundamental frequencies range from 330 to 1600 kHz for devices with 18 and 125 micron thick PVDF substrates and 800 and 400 micron acoustic wavelengths. These values for fundamental frequency are well predicted by the device geometry using Lamb wave theory. The effect of mass-loading was characterized by inkjet printing layers of polyvinyl alcohol on the sensors and measuring the resulting frequency shift. The devices demonstrate a frequency shift, Δf , to mass loading, m, with a measured resonance frequency mass sensitivity of Δf/(mf0) = -55.9 cm²/g. Temperature sensitivity was measured to be 1870 Hz/ C. Sensors were also coated with a sensing layer of polyvinyl acetate and its response to toluene and acetone vapour concentrations was characterized.
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28

Alzaix, Benjamin. "Mathematical and numerical analysis of the Herberthson integral equation dedicated to electromagnetic plane wave scattering." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0578/document.

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Cette thèse porte sur la diffraction d’une onde plane électromagnétique par une surface lisse parfaitement conductrice (PEC). Elle présente l’analyse des propriétés d’une nouvelle formulation des trois principales équations intégrales de frontières de la théorie de la diffraction électromagnétique (EFIE, MFIE et CFIE). L’idée est d’adapter les équations intégrales conventionnelles à la diffraction d’une onde plane en supposant que la fonction de phase de l’onde plane incidente détermine la fonction de phase de la distribution de courant induit sur la surface.L’idée d’utiliser la phase dans la diffraction d’ondes planes a déjà été étudiée pour les hautes fréquences, notamment dans les thèses de Zhou (1995) et Darrigrand (2002) qui adaptèrent les espaces d’approximation des éléments finis. Dans cette thèse, cependant, nous suivons une formulation plus récente, donnée par Herberthson (2008), où la fonction de phase est incorporée dans la distribution du noyau des opérateurs intégraux.En présentant les versions modifiées de l’EFIE et de la MFIE (dénommées HEFIE et HMFIE)dans des espaces fonctionnels appropriés, nous prouvons ici l’existence d’une solution unique à cette formulation spécifique et présentons une mise en oeuvre pratique originale qui tire parti de l’expérience acquise sur l’EFIE/MFIE. Par la suite, nous explorons une propriété importante offerte par ces nouvelles formulations: la possibilité de réduire le nombre de degrés de liberté requis pour obtenir une solution précise du problème
This thesis is about the scattering of an electromagnetic plane wave incidenton a perfectly conducting smooth surface. It presents the analysis of the properties of a newformulation of the three principal boundary integral equations of electromagnetic scattering theory(EFIE, MFIE and CFIE). The basic idea is to adapt the conventional integral equations toplane-wave scattering by supposing that the phase function of an incident plane wave determinesthe phase function of the induced boundary current distribution.This idea of using the phase in plane wave scattering has previously been studied in highfrequencyscattering, in particular in the theses by Zhou (1995) and Darrigrand (2002) whoadapt the finite element approximation spaces. In this thesis, though, we follow a more recentformulation, given by Herberthson (2008), where the phase function is incorporated in the kerneldistribution of the integral operators.Presenting the modified version of the EFIE and the MFIE (denoted HEFIE and HMFIE) inappropriate function spaces, we prove the existence of a unique solution to this specific formulationand developp an original practical implementation which takes advantage of the gainedexperience on the EFIE/MFIE. Then, we explore another important property provided by thenew formulations: the possibility to reduce the number of degrees of freedom required to get anaccurate solution of the problem
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29

Forslund, Ola. "Scattering and propagation of electromagnetic waves in planar and curved periodic structures - applications to plane wave filters, plane wave absorbers and impedance surfaces." Doctoral thesis, KTH, Alfvén Laboratory, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3825.

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The subject of this thesis is scattering of electromagneticwaves from planar and curved periodic structures. The problemspresented are solved in the frequency domain.

Scattering from planar structures with two-dimensionalperiodic dependence of constitutive parameters is treated. Theconstitutive parameters are assumed to vary continuously orstepwise in a cross section of a periodically repeating cell.The variation along a longitudinal coordinate z is arbitrary. Ageneral skew lattice is assumed. In the numerical examples, lowloss and high loss dielectric materials are considered. Theproblem is solved by expanding the .elds and constitutiveparameters in quasi-periodic and periodic functionsrespectively, which are inserted into Maxwell’s equations.Through various inner products de.ned with respect to the cell,and elimination of the longitudinal vector components, a linearsystem of ordinary di.erential equations for the transversecomponents of the .elds is obtained. After introducing apropagator, which maps the .elds from one transverse plane toanother, the system is solved by backward integration.Conventional thin metallic FSS screens of patch or aperturetype are included by obtaining generalised transmission andre.ection matrices for these surfaces. The transmission andre.ection matrices are obtained by solving spectral domainintegral equations. Comparisons of the obtained results aremade with experimental results (in one particular case), andwith results obtained using a computer code based on afundamentally di.erent time domain approach.

Scattering from thin singly curved structures consisting ofdielectric materials periodic in one dimension is alsoconsidered. Both the thickness and the period are assumed to besmall. The .elds are expanded in an asymptotic power series inthe thickness of the structure, and a scaled wave equation issolved. A propagator mapping the tangential .elds from one sideto the other of the structure is derived. An impedance boundarycondition for the structure coated on a perfect electricconductor is obtained.

Keywords:electromagnetic scattering, periodicstructure, frequency selective structure, frequency selectivesurface, grating, coupled wave analysis, electromagneticbandgap, photonic bandgap, asymptotic boundary condition,impedance boundary condition, spectral domain method,homogenisation

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30

Chang, Ike Yi. "Plane electromagnetic wave scattering by a coated perfectly conducting cylinder." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/14505.

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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1989.
Title as it appeared in M.I.T. Graduate List, June 1989: Electromagnetic plane wave scattering by a coated perfectly conducting cylinder.
Includes bibliographical references (leaves 72-75).
by Ike Yi Chang, Jr.
M.S.
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31

Betts, Juan Fernando. "Finite Element Study of Plane Wave Acoustic Phenomena in Ducts." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/9584.

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This thesis studied the finite element modeling of plane wave acoustic phenomena in ducts. The study looked into finite element factors such as shape functions, mesh refinement, and element distortion. The study concluded that the higher order shape function eight-node quadrilateral element gave considerably better results than lower order shape function four-node quadrilateral element. The eight-node element converged much faster to the analytical solution than the four-node element. The average error, taking all the cases in consideration, for the four-node element was around 30 % for a mesh refinement of about 14 elements per wavelength at 100 Hz frequency. The eight-node element in the other hand had average absolute errors of less than 1% under the same conditions. This section also found that the eight-node element was substantially more resistant to solution deterioration due to element distortion than the four-node element. For example distorting the four-node element up to 60* degrees usually increased errors very rapidly to above 100 % errors. The eight-node element on the other hand usually produced errors of less than 5 % for the same level of distortion. The study showed that the type of boundary condition used had a significant effect on the solution accuracy. The study demonstrated that the effect of the natural boundary conditions was more global. Meeting this kind of boundary condition through mesh convergence produced accurate results throughout the duct.
Master of Science
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32

Cardell, Gregory Scott Roshko A. "Flow past a circular cylinder with a permeable wake splitter plate /." Diss., Pasadena, Calif. : California Institute of Technology, 1993. http://resolver.caltech.edu/CaltechETD:etd-04012005-092116.

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33

Dratler, David Ira. "Numerical investigation of laminar-turbulent transition in a flat-plate wake." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/184965.

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Laminar-turbulent transition of high-deficit flat plate wakes is investigated by direct numerical simulations using the complete Naver-Stokes equations. The simulations are based on a spatial model so that both the base flow and the disturbance flow can develop in the downstream direction. The Navier-Stokes equations are used in a vorticity-velocity form and are solved using a combination of finite-difference and spectral approximations. Fourier series are used in the spanwise direction. Second-order finite-differences are used to approximate the spatial derivatives in the streamwise and transverse directions. For the temporal discretization, a combination of ADI, Crank-Nicolson, and Adams-Bashforth methods is employed. The discretized velocity equations are solved using fast Helmholtz solvers. Code validation is accomplished by comparison of the numerical results to both linear stability theory and to experiments. Calculations of two- and/or three-dimensional sinuous mode disturbances in the wake of a flat plate are undertaken. For calculations of two-dimensional disturbances, the wake is forced at an amplitude level so that nonlinear disturbance development may be observed. In addition, the forcing amplitude is varied in order to determine its effect on the disturbance behavior. To investigate the onset of three-dimensionality, the wake is forced with a small-amplitude three-dimensional disturbance and a larger amplitude two-dimensional disturbance. The two-dimensional forcing amplitude is varied in order to determine its influence on the three-dimensional flow field. Two-dimensional disturbances are observed to grow exponentially at small amplitude levels. At higher amplitude levels, nonlinear effects become important and the disturbances saturate. The saturation of the fundamental disturbance appears to be related to the stability characteristics of the mean flow. Larger forcing amplitudes result in the earlier onset of nonlinear effects and saturation. At large amplitude levels, a Karman vortex street pattern develops. When the wake is forced with both two- and three-dimensional disturbances, strong interactions between these disturbances is observed. The saturation of the two-dimensional disturbance causes the three-dimensional disturbance to saturate. However, this is followed by a resumption of strong three-dimensional growth that may be due to a secondary instability mechanism. Larger two-dimensional forcing amplitudes accelerate the saturation of the two-dimensional and three-dimensional disturbances as well as accelerate the resumption of strong three-dimensional growth. These interactions also result in complicated distributions of vorticity and in a significant increase in the wake width.
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34

Almén, Fredrik. "Band structure computations for dispersive photonic crystals." Thesis, Linköping University, Department of Science and Technology, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-9610.

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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.

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35

Kanellopoulos, Vassilios N. "Vectorial finite element analysis of E-plane waveguide junctions." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=64027.

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36

Abraham, Aliza Opila. "Extreme wave impact on a flexible plate." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104117.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2016.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 99-102).
This thesis describes the use of a combination of various visual techniques to characterize the flow-structure interaction of a breaking wave impacting a flexible vertically mounted plate. Several experiments were conducted on a simulated dam break in which water was rapidly released from a reservoir to generate a wave, which impinged on a cantilevered stainless steel plate downstream. Two high speed cameras collected data on the water and the plate simultaneously. Manual tracking of the wave front and Particle Image Velocimetry (PIV) were used to gather water height, wave speed, crest speed, vorticity, and particle speed, which were used to determine the pressure exerted by the water on the plate. An algorithm was written to track the edge of the plate to find plate deflection over time. The dynamic beam bending equation was used to find the forces experienced by the plate, which were compared to the pressure results. A series of waves of different heights and breaking locations were tested, controlled by the ratio of the height of water initially in the tank and the height of water in the dam break reservoir, for two different plate locations. The properties of the wave varied depending on these parameters, as did the deflection of the plate. The plate deformed more and the recorded velocities in the wave were higher when the depth ratio decreased and when the plate was moved farther from the reservoir. These results shed light on the effect of breaking wave impacts on offshore structures and ship hulls, taking into account the elasticity of these structures. They also provide a test case for future numerical fluid-structure interaction simulation techniques.
by Aliza Opila Abraham.
S.M.
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37

Grooth, Pieter Jan. "Wave reflection by a flat plate cascade." Thesis, Massachusetts Institute of Technology, 1990. http://hdl.handle.net/1721.1/42459.

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38

Froncioni, Andy M. "A new finite element method for analysis of H-plane waveguide junctions /." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63937.

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39

Borràs, Morales Jan. "Park optimization and wake interaction study at Bockstigen offshore wind power plant." Thesis, Uppsala universitet, Institutionen för geovetenskaper, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-245579.

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Losses for wake effects in offshore wind farms represent about 10% to 20% of the park annual energy production. Several analytical wake models have been developed and implemented to predict the power deficit of a wake-affected wind turbine. Validating and parameterizing the wake models available in the industry is essential to better predict the wake losses and thus maximize the energy yield of future offshore developments. In this study, a wake model validation is undertaken for the three models available in the commercial software WindSim. Data from Horns Rev wind farm is used to that purpose. Next, the models that show the best agreement with the observations are parameterized to better describe the power losses of a future offshore wind farm at Bockstigen. To finish with, an optimization sensitivity study is carried out and a final optimal layout is determined according to the seabed depth.
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40

Shen, G.-C. "The interaction between a plane shock wave and a cylindrical afterbody." Thesis, University of Hertfordshire, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.483961.

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41

Scott, Leigh-Ann. "Plane wave expansion analysis of lossy composite transducers incorporating anisotropic polymers." Thesis, University of Strathclyde, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444097.

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42

Li, Fei 1959. "Flow field modifications and wave development in a plane Poiseuille flow." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/42483.

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43

Murillo, Gomez Diego. "Interactive auralization based on hybrid simulation methods and plane wave expansion." Thesis, University of Southampton, 2016. https://eprints.soton.ac.uk/397273/.

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The reconstruction and reproduction of sound fields have been extensively researched in the last decades leading to an intuitive approach to estimate and evaluate the acoustic properties of enclosures. Applications of auralization can be found in acoustic design, subjective tests, virtual reality and entertainment, among others. Different methodologies have been established to generate auralizations for room acoustics purposes, the most common of them, the use of geometrical acoustics and methods based on the numerical solution of the wave equation to synthesize the room impulse responses. The assumptions and limitations of each approach are well known, which in turn, restrict their application to specific frequency bands. If the aim is to reconstruct accurately the sound field in an extended range of frequencies, a combination of these methodologies has to be performed. Furthermore, recent advances in computational power have enabled the possibility to generate interactive atmospheres where the user is able to interact with the environment. This feature, although it expands the applications of the auralization technique, is nowadays mainly based on geometrical acoustics or interpolation methods. The present research addresses the generation of interactive broadband auralizations of enclosures using a combination of the finite element method and geometrical acoustics. For this, modelling parameters for both simulation methods are discussed making emphasis on the assumptions made in each case. Then, the predicted room impulse responses are represented by means of a plane wave expansion, which in turn, enables interactive features such as translation and rotation of the acoustic fields. An analytical expression is derived for the translation in the plane wave domain. Furthermore, the transformation of the plane wave representation in terms of spherical harmonics is also explored allowing the acoustic fields to be rotated. The effects of assuming a plane wave propagation within small enclosures and the consequences of using a finite number of plane waves to synthesize the sound fields are discussed. Finally, an implementation of an interactive auralization system is considered for different reference cases. This methodology enables reconstruction of the aural impression of enclosures in real-time with higher accuracy at low frequencies compared to only geometrical acoustics techniques. The plane wave expansion provides a convenient sound field representation in which the listener can interact with the acoustics of the enclosure. Furthermore, the sound reconstruction can be performed by implementing several sound reproduction techniques extending the versatility of the proposed approach.
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44

Pao, Hsueh-Yuan. "Interaction between a transient plane wave and a conductive half-space." Diss., The University of Arizona, 1995. http://hdl.handle.net/10150/187405.

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A method which allows for the analytical evaluation of the interaction between a transient plane wave and a conductive half-space is presented. We assume that an electromagnetic plane wave is obliquely incident on a conducting half-space, which is modeled by a frequency independent permittivity and conductivity. The general case of the electromagnetic plane wave is divided into two polarizations: transverse electric (TE) and transverse magnetic (TM). The time-domain expressions for the reflected and transmitted waves are first represented as inverse Laplace transforms. The transient fields are then shown to consist of two canonical integrals, f(β) and e(β)The canonical integrals, in turn, are solved analytically, thereby yielding closed-form solutions involving incomplete Lipschitz-Hankel integrals (ILHIs). The ILHIs are computed numerically using efficient convergent and asymptotic series expansions, thus enabling the efficient computation of the transient fields. The exact, closed-form expressions are verified by comparing with previously published results and with results obtained using standard numerical integration and fast Fourier transform algorithms. An asymptotic series representation for the ILHIs is then employed to obtain a relatively simple late-time approximation for the transient fields. This approximate late-time expression is shown to accurately model the fields over a large portion of their time history. The closed-form transient field expressions are used to investigate the effects of neglecting displacement currents when studying transient wave propagation in the conductive half-space. The diffusion fields are found to yield accurate results at late times.
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45

Mechaik, Mehdi Mohamad 1963. "Surface wave propagation on a perforated ground plane with dielectric coating." Thesis, The University of Arizona, 1991. http://hdl.handle.net/10150/277877.

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In this thesis, the surface wave propagation along a periodically perforated conducting ground plane with dielectric coating has been studied for frequencies low enough for the ground plane to be approximated accurately by two bonded wire arrays. The field components have been obtained by using the z-directed electric and magnetic Hertz potentials which greatly simplify the application of the boundary conditions at the interfaces. The application of the appropriate boundary conditions on both sides of the plane of the wire mesh has resulted in a doubly infinite system of equations which, when truncated, can be solved for the wire currents and the propagation characteristics of the surface wave supported by the perforated ground plane. The plane is then modeled by a tensor impedance matrix relating the tangential components of the electric field to the components of the current density in the plane of the mesh. It has been shown that the surface wave propagation constant and the impedance matrix do not significantly depend on the direction of propagation for electrically small wire spacings. For such cases, it is shown that the components of the electric field can be directly related to the second order derivatives of the components of the current density flowing along the perforated ground plane.
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46

Anderson, Brian Eric. "Derivation of Moving-Coil Loudspeaker Parameters Using Plane Wave Tube Techniques." BYU ScholarsArchive, 2004. https://scholarsarchive.byu.edu/etd/17.

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Small-signal moving-coil loudspeaker driver parameters are traditionally derived through electrical impedance measurement techniques. These parameters are commonly called Thiele/Small parameters, after Neville Thiele and Richard Small who are credited with developing industry-standard loudspeaker modeling techniques. However, because loudspeaker drivers are electro-mechano-acoustical transducers, it should be possible to measure their parameters in physical domains other than the electrical domain. A method of measuring loudspeaker parameters from the acoustical domain will be developed. The technique uses a plane wave tube to measure acoustical properties of a baffled driver under test. Quantities such as the transmission loss through the driver are measured for a driver placed in the tube using the two-microphone transfer-function technique. Models have been developed to curve fit the resulting data, from which small-signal loudspeaker parameters are subsequently derived. This thesis discusses the acoustical measurement theory, apparatus, and system modeling methods (via equivalent circuits). It also compares measured parameters to those derived using electrical techniques. Parameters derived from both approaches are compared with reference values to establish bias errors. Sequential measurements are also compared to reveal random errors in the derivation processes.
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47

Nienhuis, Jaap H. "Plan-view evolution of wave-dominated deltas." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/103250.

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Thesis: Ph. D., Joint Program in Oceanography/Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references.
Ocean waves are a powerful sediment transport mechanism in the coastal zone. This thesis investigates how waves shape deltaic landforms and how small scale river mouth processes affect large-scale delta morphology. I have developed and applied models of plan-view delta shape and their channel dynamics. Simple parameterizations and key insights from these models have allowed us to transcend spatial scales from river mouths to delta plains and make morphologic predictions around the globe for every delta on Earth. I have applied models of delta morphology to backtrack the late Holocene evolution of the Ebro River delta in Spain and estimate timescales and magnitude of past climate change and human impacts. Currently, many deltas around the world face large sediment deficits because of river damming. I model deltaic response to reductions in sediment load and offer frameworks to predict future deltaic change in these dynamic and threatened coastal regions.
by Jaap H. Nienhuis
Ph. D.
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48

Dickman, Edward John. "Microwave Planer-Probe Traveling-Wave Power Dividing-Combining." Thesis, Montana State University, 2005. http://etd.lib.montana.edu/etd/2005/dickman/DickmanE1205.pdf.

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TAs the millimeterwave and sub-millimeterwave portions of the electromagnetic spectrum are increasingly utilized, the need for greater power at those frequencies also increases. Unfortunately, as frequency is increased, the power available from a single solid-state device decreases. Thus, in many applications, the combining of power from several solid-state devices becomes necessary to have usable signal power levels. This thesis presents two such power combining approaches, whose designs are compatible with existing microfabrication techniques that may be used to produce devices operating at 300 GHz and beyond. Additionally, this thesis describes a mathematical modeling procedure that incorporates signal flow and transmission line concepts, and aids in the efficient design of one of these topologies, the Planar-Probe Traveling-Wave Divider- Combiner. Such a modeling approach could be readily applied to traveling wave structures of different topologies. The complete design, simulation, and experimental validation of a conventionally-machined two-way traveling-wave dividing-combining module is demonstrated at X-band frequencies. The demonstrated 15 dB return loss fractional bandwidth was almost 21%, and the insertion loss was found to be better than 0.5 dB throughout most of the operational band. The promising performance of this structure shows that further investigation is merited.
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49

Dupuy, Mi-Song. "Analysis of the projector augmented-wave method for electronic structure calculations in periodic settings." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC073/document.

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Cette thèse est consacrée à l'étude de la méthode PAW (projector augmented-wave) et d'une de ses modifications, baptisée méthode PAW variationnelle (VPAW), pour le calcul de l'état fondamental d'Hamiltoniens en géométrie périodique. Ces méthodes visent à améliorer la vitesse de convergence des méthodes d'ondes planes (ou méthodes de Fourier) en appliquant une transformation inversible au problème aux valeurs propres initial agissant au voisinage de chaque site atomique. Cette transformation permet de capter une partie des difficultés dues aux singularités coulombiennes. La méthode VPAW est analysée pour un opérateur de Schr\"odinger unidimensionnel avec des potentiels de Dirac. Les fonctions propres de ce modèle comprennent des sauts de dérivées similaires aux cusps électroniques. Le saut de dérivée des fonctions propres du problème aux valeurs propres issu de la méthode VPAW est réduit de façon importante. Cela entraîne une accélération de convergence en ondes planes du calcul des valeurs propres corroborée par une étude numérique. Une étude de la méthode VPAW est conduite pour des Hamiltoniens 3D périodiques avec des singularités coulombiennes, parvenant à des conclusions similaires. Pour la méthode PAW, la transformation inversible comporte des sommes infinies qui sont tronquées en pratique. Ceci introduit une erreur, qui est rarement quantifiée en pratique. Elle est analysée dans le cas de l'opérateur de Schrödinger unidimensionnel avec des potentiels de Dirac. Des bornes sur la plus basse valeur propre en fonction des paramètres PAW sont prouvées conformes aux tests numériques
This thesis is devoted to the study of the PAW method (projector augmented-wave) and of a variant called the variational PAW method (VPAW). These methods aim to accelerate the convergence of plane-wave methods in electronic structure calculations. They rely on an invertible transformation applied to the eigenvalue problem, which acts in a neighborhood of each atomic site. The transformation captures some difficulties caused by the Coulomb singularities. The VPAW method is applied to a periodic one-dimensional Schr\"odinger operator with Dirac potentials and analyzed in this setting. Eigenfunctions of this model have derivative jumps similar to the electronic cusps. The derivative jumps of eigenfunctions of the VPAW eigenvalue problem are significantly reduced. Hence, a smaller plane-wave cut-off is required for a given accuracy level. The study of the VPAW method is also carried out for 3D periodic Hamiltonians with Coulomb singularities yielding similar results. In the PAW method, the invertible transformation has infinite sums that are truncated in practice. The induced error is analyzed in the case of the periodic one-dimensional Schrödinger operator with Dirac potentials. Error bounds on the lowest eigenvalue are proved depending on the PAW parameters
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50

Wlodarczyk, A. J. "The application of spectral synthesis in electromagnetic field problems." Thesis, University of Nottingham, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381100.

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