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京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24738号 / 情博第826号 / 新制||情||138(附属図書館) / 京都大学大学院情報学研究科先端数理科学専攻 / (主査)教授 磯 祐介, 准教授 吉川 仁, 准教授 藤原 宏志, 教授 西村 直志(京都大学 名誉教授) / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

This dissertation describes new methods for measuring surface forces using evanescent waves, and applications to non-DLVO forces. An evanescent wave, generated at a solid-liquid interface, is scattered by AFM tips or particles attached to AFM cantilevers. The scattering of this wave is used to determine absolute separation between surfaces and/or the refractive index as a function of separation in AFM measurements. This technique is known as evanescent wave atomic force microscopy (EW-AFM). The scattering of an evanescent wave by Si3N4 AFM tips is large and decays exponentially with separation from a refractive index boundary. Thus, scattering is a useful method for measuring the separation between a Si3N4 tip and sample. This method has been used to measure the absolute separation between a tip and sample in the presence of an irreversibly adsorbed polymer film. Measurement of the film thickness and time response of the polymer to applied loads has also been studied. These measurements are not possible using current AFM techniques. In addition to measurements in polymer systems, the simple scattering profile from Si3N4 tips was used to re-examine short range hydration forces between hydrophilic surfaces. Results presented in this thesis suggest this force does not depend on the hydrated radius of the ion between glass and silicon nitride. The scattering generated by a Si3N4 tip has also been used to measure the refractive index of bulk fluids and thin films between hydrophobic surfaces. Based on these results, I have shown that a long-range attraction between hydrophobic surfaces is accompanied by an increase in the refractive index between the tip and surface. From this I have concluded that the attractive force, measured in this study, is the result of an increase in the concentration of organic material between surfaces. Finally, I have shown that the scattering profile depends on the material and size of the scattering object. Scattering from silicon nitride tips is exponential with separation. In contrast, the scattering profile from silicon tips, which are similar in size and geometry, is not a simple exponential. The scattering profile of larger spherical particles attached to cantilevers is also not exponential. It is approximately the sum of two exponentials. The functional form of the scattering profile with separation is consistent with the transmission of evanescent light through flat planar films. This result would suggest that a re-examination of the separation-dependence of scattering in TIRM measurements is necessary. / Ph. D.

To investigate seismic resolution of deep mantle plumes as well as the robustness of the anti-correlation between bulk sound speed and S wave speed imaged in the lowermost mantle, we use a Spectral Element Method (SEM) to simulate global seismic wave propagation in 3-D wavespeed models and measure frequency-dependent P-, S-, Pdiff- and Sdiff-wave traveltime anomalies caused by plume structures in the lowermost mantle. We compare SEM time delay measurements with calculations based on ray theory and show that an anti-correlation between bulk sound speed and S-wave speed could be produced as an artifact. This is caused by different wavefront healing effects between P waves and S waves in thermal plume models. The bulk sound speed structure remains poorly resolved when P-wave and S-wave measurements are at different periods with similar wavelength. The differences in wave diffraction between the two types of waves depend on epicentral distance and wave frequency. The artifact in anti-correlation is also confirmed in tomographic inversions based on ray theory using Pdiff and Sdiff time delay measurements made on the SEM synthetics. This indicates a chemical origin of "superplumes" in the lowermost mantle may not be necessary to explain observed seismic traveltimes. The same set of Pdiff and Sdiff measurements are inverted using finite-frequency tomography based on Born sensitivity kernels. We show that wavefront healing effects can be accounted for in finite-frequency tomography to recover the true velocity model. / Master of Science

Thesis (PhD (Physics))--University of Stelllenbosch, 2010. / ENGLISH ABSTRACT: In this dissertation a fully relativistic model for polarized inclusive quasielastic proton-nucleus scattering is developed. Using a standard relativistic impulse approximation (RIA) treatment of quasielastic scattering and a two-body SPVAT form of the current operator, it is shown how the behaviour of projectile and target can be decoupled. Subsequently, different models for projectile and target can be adopted and combined to examine a variety of relativistic effects. The most simplistic model of the target is provided by a mean-field nuclear matter approximation to the relativistic meson-nucleon model, quantum hadrodynamics (QHD). Here relativistic effects manifest as an effective mass, which is lower than the free mass, of the constituent nucleons. This model is improved upon by including many-body correlations through medium-modification of meson propagators in the relativistic random-phase approximation (RPA). Since it is generally accepted that the strong nuclear force and the extended range of the nuclear potential lead to distortion effects on the projectile and ejectile (seen as a modulation of the wave functions), our formalism is geared towards the use of relativistic distorted waves (RDWIA). The distorted waves are written as partial wave expansions and are solutions to the Dirac equation with potentials. The inclusion of distortions, however, greatly increases the computational burden and we show how a number of analytical and numerical techniques can be used to facilitate the process of calculation. It is also shown how the standard relativistic plane wave treatment (RPWIA) can, instead, be easily employed to obtain a baseline for determining the impact of distortions. A calculation is performed for the reaction 40Ca(!p, !p !) at a beam energy of 500 MeV. Here it is found that the effect of correlations on the RPWIA calculation can be seen as a quenching of the cross section that is expected to become more pronounced at lower energies or for higher density targets. A RDWIA calculation shows additional reduction and if target correlations are included this effect is enhanced. To our knowledge this is the first calculation that attempts to include both these effects (RPA and RDWIA) in the context of quasielastic proton-nucleus scattering. / AFRIKAANSE OPSOMMING: In hierdie proefskrif word ’n ten volle relatiwistiese model vir die berekening van inklusiewe kwasielastiese proton-kern verstrooiing daargestel. Deur gebruik te maak van ’n standaard relatiwistiese impulsbenadering (RIA) vir kwasi-elastiese verstrooiing asook ’n twee-deeltjie-SPVAT-vorm vir die stroom-operator, word daar gewys hoedat die gedrag van die projektiel en teiken ontkoppel kan word. Verskillende modelle kan dus vir die projektiel en teiken gebruik word om ’n verskeidenheid relatiwistiese effekte te bestudeer. Die mees simplistiese model vir die teiken word verskaf deur ’n gemiddelde-veld kernmateriaalbenadering tot die relatiwistiese meson-nukleon-model, kwantum-hadrodinamika (QHD). In hierdie model manifesteer relatiwistiese effekte as ’n effektiewe massa, wat kleiner is as die vrye massa, van nukleone in die kern. Hierdie model word verbeter deur die inagneming van veeldeeltjie korrelasies deur medium-gewysigde meson-propagators in die relatiwistiese ewekansige-fase-benadering (RPA). Aangesien dit algemeen aanvaar word dat die sterk-wisselwerking en die reikwydte van die kernpotensiaal aanleiding gee tot vervormingseffekte op die projektiel en ejektiel (gesien as die modulasie van golffunksies), is ons model optimaal geformuleer om gebruik te maak van relatiwistiese vervormde golwe (RDWIA). Die vervormde golwe word geskryf as parsi¨elegolf uitbreidings en dien as oplossings vir die Dirac-vergelyking met potensiale. Insluiting van vervormings vermeerder egter die berekeningslas geweldig en ons toon hoedat ’n aantal analitiese en numeriese tegnieke gebruik kan word om die proses te vergemaklik. Daar word ook aangetoon hoe die standaard- relatiwistiese-vlakgolf-benadering (RPWIA), in plaas van vevormde golwe, maklik gebruik kan word om ’n verwysingspunt vir die meting van die effek van vervormings te bepaal. ’n Berekening vir die reaksie 40Ca(!p, !p !) teen ’n projektiel-energie van 500 MeV word getoon. Hier word dit gevind dat die effek van korrelasies op die RPWIA-berekening gesien kan word as ’n verlaging van die kansvlak. Daar word verwag dat hierdie effek duideliker sal word by laer energie¨e en ho¨er kerndigthede. ’n RDWIA-berekening word getoon wat daarop dui dat addisionele verlaging in die kansvlak voorkom en indien korrelasies hier ingesluit word, word hierdie effek vergroot. Sover ons kennis strek, is hierdie die eerste berekening wat poog om beide hierdie effekte (RPA en RDWIA) in die konteks van kwasi-elastiese proton-kern verstrooiing in te sluit.

A theoretical investigation of acoustic wave interactions with turbulent premixed flames was performed. Such interactions affect the characteristic unsteadiness of combustion processes, e.g., combustion instabilities. The small perturbation method (SPM) was utilized to evaluate the scattered fields as a result of the flame-wave interaction at the instantaneous wrinkling surface of a randomly moving turbulent flame. Stochastic analysis of ensemble-averaged net acoustic energy was conducted to examine coherent and incoherent acoustic energy amplification /damping by the interaction. Net acoustic energy flux out of the flame is due to two factors: the acoustic velocity jump due to unsteady heat release from flame. The other is the flames unsteady motion. Five(5) dimensionless parameters that govern this net acoustic energy were determined: rms height and correlation length of flame front, incident wave frequency, the ratio of flames diffusion time to flame fronts correlation time, and incidence angle. The dependence of net acoustic energy upon these dimensionless parameters was illustrated and discussed by numerical simulations in case of Gaussian statistics of flame front. The laminar flame response to equivalence ratio perturbations was also examined, showing that the overall heat release response is controlled by the superposition of three disturbances: heat of reaction, flame speed, and flame area. Heat of reaction disturbances dominate the flame response at low Strouhal numbers, roughly defined as (frequency x flame length)/(axial flow velocity). All three disturbances play equal roles at Strouhal numbers of O(1). In addition, the mean equivalence ratio exerts little effect upon this transfer function at low Strouhal numbers. At O(1) Strouhal numbers, the flame response increases with decreasing values of the mean equivalence ratio.

Corrosion often occurs in the inner aluminum lining of the HB-53 helicopter external fuel tank, resulting in fuel leaks. This project centers on developing an in-situ ultrasonic inspection technique to detect corroded areas inside the fuel tank. Due to the complexity of the composite structure of the tank, the ultrasonic inspection is carried out from inside the tank using a monostatic backscattering technique. The backscattered field contains information related to the insonified surface properties (surface roughness scales). Numerical predictions are implemented with a simplified model of backscattered intensity (Ogilvy, 1991). Experimental results are obtained on artificially corroded plates, and on the actual fuel tank of the HB-53 helicopter. Signal processing techniques (Envelope Correlation and Inverse Technique) are used to detect corroded surfaces with data obtained with a focused 10 MHz pulsed transducer.

Wave scattering by arrays of cylinders has received special attention by many authors and analytical solutions have been derived. The investigation of optical and acoustical analogies to the problem of interaction of water waves with rigid and flexible cylinder arrays is the main focus of this thesis. In acoustics, a sound may be attenuated while it propagates through a layer of bubbly liquid. In fact, if the natural frequency of the bubbles is in the range of the wave periods, the attenuation becomes more evident. The ultimate objective of the research described herein is to determine if this phenomenon may also be found in the interaction between water waves and arrays of flexible cylinders. In a first approach, arrays of rigid cylinders are studied in shallow water. The array is treated as an effective medium, which allows for the definition of reflection and transmission coefficients for the array, and theories from Hu and Chan (2005) associated with the Fabry-Perot interferometer are compared against direct computations of wave scattering using the commercial code WAMIT. Reflection and transmission coefficients from WAMIT are evaluated by applying a Maximum Likelihood Method. The results from WAMIT were found to be in good agreement with those obtained from the effective medium theory. Due to observed inconsistencies for short wave periods and small incident angles, the effective width of the medium is defined and corrected. For the case of a flexible cylinder, generalized modes corresponding to deformations of the cylinder's surface are formulated and added to WAMIT's subroutine. Equations of motion are derived from the theory of vibration for thin shells and mass and stiffness matrices are defined. The objective is to maximize wave attenuation from the array of flexible cylinders. Therefore, the natural periods of the "breathing" mode for these cylinders is set in the range of the studied wave periods. Then, material properties, as well as mass and stiffness matrices, are chosen to achieve this effect.

Computer simulation of wave propagation is an active research area as wave phenomena are prevalent in many applications. Examples include wireless communication, radar cross section, underwater acoustics, and seismology. For high frequency waves, this is a challenging multiscale problem, where the small scale is given by the wavelength while the large scale corresponds to the overall size of the computational domain. Research into wave equation modeling can be divided into two regimes: time domain and frequency domain. In each regime, there are two further popular research directions for the numerical simulation of the scattered wave. One relies on direct discretization of the wave equation as a hyperbolic partial differential equation in the full physical domain. The other direction aims at solving an equivalent integral equation on the surface of the scatterer. In this dissertation, we present three new techniques for the frequency domain, boundary integral equations. / text

Efficient electromagnetic solvers based on surface integral equations (SIEs) are developed for the analysis of scattering from large-scale and complex composite structures that consist of piecewise homogeneous magnetodielectric and perfect electrically/magnetically conducting (PEC/PMC) regions. First, a multiple-grid extension of the adaptive integral method (AIM) is presented for multi-region problems. The proposed method accelerates the iterative method-of-moments solution of the pertinent SIEs by employing multiple auxiliary Cartesian grids: If the structure of interest is composed of K homogeneous regions, it introduces K different auxiliary grids. It uses the k^{th} auxiliary grid first to determine near-zones for the basis functions and then to execute AIM projection/anterpolation, propagation, interpolation, and near-zone pre-correction stages in the k^{th} region. Thus, the AIM stages are executed a total of K times using different grids and different groups of basis functions. The proposed multiple-grid AIM scheme requires a total of O(N^{nz,near}+sum({N_k}^Clog{N_k}^C)) operations per iteration, where N^{nz,near} denotes the total number of near-zone interactions in all regions and {N_k}^C denotes the number of nodes of the k^{th} Cartesian grid. Numerical results validate the method’s accuracy and reduced complexity for large-scale canonical structures with large numbers of regions (up to 10^6 degrees of freedom and 10^3 regions). Then, a Green function modification approach and a scheme of Hankel- to Teoplitz-matrix conversions are efficiently incorporated to the multiple-grid AIM method to account for a PEC/PMC plane. Theoretical analysis and numerical examples show that, compared to a brute-force imaging scheme, the Green function modification approach reduces the simulation time and memory requirement by a factor of (almost) two or larger if the structure of interest is terminated on or resides above the plane, respectively. In addition, the SIEs are extended to cover structures composed of metamaterial regions, PEC regions, and PEC-material junctions. Moreover, recently introduced well-conditioned SIEs are adopted to achieve faster iterative solver convergence. Comprehensive numerical tests are performed to evaluate the accuracy, computational complexity, and convergence of the novel formulation which is shown to significantly reduce the number of iterations and the overall computational work. Lastly, the efficiency and capabilities of the proposed solvers are demonstrated by solving complex scattering problems, specifically those pertinent to analysis of wave propagation in natural forested environments, the design of metamaterials, and the application of metamaterials to radar cross section reduction. / text