The goal of this thesis is to introduce the finite difference method (FDM) adjusted for usage in modeling of sound propagation, and other approaches that are used together with this method. These approaches include selective filtering and time integration using the Runge-Kutta method, which has low computer memory requirements. An important topic in modeling sound propagation are boundary conditions. The thesis examines and verifies several types of boundary conditions. Included in the thesis are solutions to example problems implemented in Matlab.

風力発電システムは、現在世界中で普及しているが、その地上高と立地条件からしばしば落雷の被害を受け、稼働率の低下が問題視されている。本論文は、垂直導体である風力発電タワーにおける雷サージ解析の高精度化、高速化を目的とした垂直導体回路解析モデルの提案、およびその有用性のについて述べるとともに、風力発電所や洋上風車への拡張性についてまとめたものである。 / 博士(工学) / Doctor of Philosophy in Engineering / 同志社大学 / Doshisha University

In this thesis we study the optimal stochastic control problem of the drift of a Lévy process. We show that, for a broad class of Lévy processes, the partial integro-differential Hamilton-Jacobi-Bellman equation for the value function admits classical solutions and that control policies exist in feedback form. We then explore the class of Lévy processes that satisfy the requirements of the theorem, and find connections between the uniform integrability requirement and the notions of the score function and Fisher information from information theory. Finally we present three different numerical implementations of the control problem: a traditional dynamic programming approach, and two iterative approaches, one based on a finite difference scheme and the other on the Fourier transform. / text

Šiame darbe pristatomi nauji rezultatai, gauti tiriant diskretųjį Šturmo ir Liuvilio uždavinį su viena klasikine o kita nelokaliąja integraline kraštine sąlyga. Pirmoje dalyje pristatomas diferencialinis Šturmo ir Liuvilio uždavinys su nelokaliąja integraline kraštine sąlyga. Šio uždavinio kompleksinė spektro dalis buvo ištirta bakalauro darbe. Antroje darbo dalyje diferencialinis uždavinys suvedamas į antros eilės baigtinių skirtumų schemą, kai nelokalioji integralinė sąlyga aproksimuojama pagal trapecijų arba Simpsono formulę. Ištirta skirtuminių operatorių su nelokaliosiomis kraštinėmis sąlygomis spektro struktūra, tikrinių reikšmių priklausomybė nuo parametrų γ ir ξ esančių nelokaliosiose sąlygose, reikšmių ir pasirinkto tinklo taškų skaičiaus n. Rezultatai pateikiami charakteristinių funkcijų grafikais ir jų projekcijomis. / In this paper we present a new result of the investigation discrete Sturm--Liuoville problem with one classical and the other nonlocal integral boundary condition. The first part of paper presents differential Sturm Liuoville problem with integral boundary condition. Complex part of spectrum for Sturm Liuoville problem with integral boundary condition was investigated in Bachelor Thesis. The second part of paper present result of investigation second-order finite difference scheme, when the integral conditions condition is approximated by the Trapezoid or Simpson's rules. There are investigated the spectrum of the finite-difference schemes and it dependence on the parameters γ and ξ from nonlocal boundary condition n,where n number of grid points. Simulation results are presented as graphs and projections of characteristic functions.

Ground-Penetrating Radar (GPR) is a non-destructive electromagnetic investigative tool used in many applications across the fields of engineering and geophysics. The propagation of electromagnetic waves in lossy materials is complex and over the past 20 years, the computational modelling of GPR has developed to improve our understanding of this phenomenon. This research focuses on the development of accurate numerical models of widely-used, high-frequency commercial GPR antennas. High-frequency, highresolution GPR antennas are mainly used in civil engineering for the evaluation of structural features in concrete i. e., the location of rebars, conduits, voids and cracking. These types of target are typically located close to the surface and their responses can be coupled with the direct wave of the antenna. Most numerical simulations of GPR only include a simple excitation model, such as an infinitesimal dipole, which does not represent the actual antenna. By omitting the real antenna from the model, simulations cannot accurately replicate the amplitudes and waveshapes of real GPR responses. Numerical models of a 1.5 GHz Geophysical Survey Systems, Inc. (GSSI) antenna and a 1.2 GHz MALÅ GeoScience (MALÅ) antenna have been developed. The geometry of antennas is often complex with many fine features that must be captured in the numerical models. To visualise this level of detail in 3d, software was developed to link Paraview—an open source visualisation application which uses the Visualisation Toolkit (VTK)—with GprMax3D—electromagnetic simulation software based on the Finite-Difference Time-Domain (FDTD) method. Certain component values from the real antennas that were required for the models could not be readily determined due to commercial sensitivity. Values for these unknown parameters were found by implementing an optimisation technique known as Taguchi’s method. The metric used to initially assess the accuracy of the antenna models was a cross-corellation of the crosstalk responses from the models with the crosstalk responses measured from the real antennas. A 98 % match between modelled and real crosstalk responses was achieved. Further validation of the antenna models was undertaken using a series of laboratory experiments where oil-in-water (O/W) emulsions were created to simulate the electrical properties of real materials. The emulsions provided homogeneous liquids with controllable permittivity and conductivity and enabled different types of targets, typically encountered with GPR, to be tested. The laboratory setup was replicated in simulations which included the antenna models and an excellent agreement was shown between the measured and modelled data. The models reproduced both the amplitude and waveshape of the real responses whilst B-scans showed that the models were also accurately capturing effects, such as masking, present in the real data. It was shown that to achieve this accuracy, the real permittivity and conductivity profiles of materials must be correctly modelled. The validated antenna models were then used to investigate the radiation dynamics of GPR antennas. It was found that the shape and directivity of theoretically predicted far-field radiation patterns differ significantly from real antenna patterns. Being able to understand and visualise in 3d the antenna patterns of real GPR antennas, over realistic materials containing typical targets, is extremely important for antenna design and also from a practical user perspective.

This thesis presents algorithm development in computational chemistry, and applies new computer science concepts to voltammetric simulation. To begin, this thesis discusses why algorithm development is necessary, and inherent problems found in commercial simulation solvers. As a result of this discussion, this thesis describes the need for simulators to keep abreast of recent computational developments. Algorithm development in this thesis is taken through stages. Chapter 3 applies known theory relating to the stripping voltammetry at a macroelectrode to the diffusional model of a microdisk, using finite difference and alternating direction implicit simulation techniques. Chapter 4 introduces the concept of parallel computing, and how computational hardware has developed recently to take advantage of out-of-order calculations, by processing them in parallel to reduce simulation time. The novel area of graphics card simulation for highly parallel algorithms is also explained in detail. Chapter 5 discusses the adaptation of voltammetric finite difference algorithms to a purely parallel format for simulation by explicit solution. Through explicit solution, finite difference algorithms are applied to electrode geometries which necessitate a three-dimensional solution – elliptical electrodes; square, rectangular, and microband electrodes; and dual microdisk electrodes in collector-generator mode. Chapter 6 introduces 'Random Walk' simulations, whereby individual particles in the simulation are modelled and their trajectories over time are calculated. The random walk technique in this thesis is improved for pure three-dimensional diffusion, and adapted to graphics cards, allowing up to a factor 4000 increase in speed over previous computational methods. This method is adapted to various systems of low concentration confined voltammetry (chapter 6.4) and single molecule detection, ultra low concentration cyclic voltammetry (chapter 6.5), and underpotential deposition of thallium on mobile silver nanoparticles (chapter 6.6). Overall, this thesis presents, and applies, a series of algorithm development concepts in computational electrochemistry.

Theoretical and experimental plasmonics is a growing field as a method to create near fields at sub-wavelength distances. In this thesis, a finite-difference time-domain method is used to simulate electromagnetic waves onto a thin film that present of nickel nanorods with sharp apexes. The absorbed, transmitted, and reflected fields were shown to depend linearly on silver film thickness and nanotip length. The electric field is visualized along the tip to show strong charge density along the base of the tip’s apex and how that density changes for wavelength, metal, and source tilt. Lastly, the study shows gold film on the nanotip apex provides the largest enhancement of the electric field for the wavelengths 532, 572, and 633 nm.

The world population is expected to increase to approximately 11 billion by 2100. The ageing population (aged 60 and over) is projected to exceed the number of children in 2047. This will be a situation without precedent. The number of citizens with disorders of old age like Dementia will rise to 115 million worldwide by 2050. The estimated cost of Dementia will also increase, from $604 billion in 2010, to $1,117 billion by 2030. At the same time, medical expertise, evidence-driven policymaking and commissioning of services are increasingly evolving the definitive architecture of comprehensive long-term care to account for these changes. Technological advances, such as those provided by computational science and biomedical engineering, will allow for an expansion in our ability to model and simulate an almost limitless variety of complex problems that have long defied traditional methods of medical practice. Numerical methods and simulation offer the prospect of improved clinically relevant predictive information, and of course optimisation, enabling more efficient use of resources for designing treatment protocols, risk assessment and urgently needed management of a long term care system for a wide spectrum of brain disorders. Within this paradigm, the importance of the relationship of senescence of cerebrospinal fluid transport to dementia in the elderly make the cerebral environment notably worthy of investigation through numerical and computational modelling. Hydrocephalus can be succinctly described as the abnormal accumulation (imbalance between production and circulation) of cerebrospinal fluid (CSF) within the brain. Using hydrocephalus as a test bed, one is able to account for the necessary mechanisms involved in the interaction between cerebral fluid production, transport and drainage. The current state of knowledge about hydrocephalus, and more broadly integrative cerebral dynamics and its associated constitutive requirements, advocates that poroelastic theory provides a suitable framework to better understand the disease. In this work, Multiple-network poroelastic Theory (MPET) is used to develop a novel spatio-temporal model of fluid regulation and tissue displacement in various scales within the cerebral environment. The model is discretised in a variety of formats, through the established finite difference method, finite difference – finite volume coupling and also the finite element method. Both chronic and acute hydrocephalus was investigated in a variety of settings, and accompanied by emerging surgical techniques where appropriate. In the coupled finite difference – finite volume model, a key novelty was the amalgamation of anatomically accurate choroid plexuses with their feeding arteries and a simple relationship relaxing the constraint of a unique permeability for the CSF compartment. This was done in order to account for Aquaporin-4 sensitisation. This model is used to demonstrate the impact of aqueductal stenosis and fourth ventricle outlet obstruction. The implications of treating such a clinical condition with the aid of endoscopic third (ETV) and endoscopic fourth ventriculostomy (EFV) are considered. It was observed that CSF velocity in the aqueduct, along with ventricular displacement, CSF pressure, wall shear stress and pressure difference between lateral and fourth ventricles increased with applied stenosis. The application of ETV reduced the aqueductal velocity, ventricular displacement, CSF pressure, wall shear stress and pressure difference within nominal levels. The greatest reversal of the effects of atresia come by opting for ETV rather than the more complicated procedure of EFV. For the finite difference model incorporating nonlinear permeability, qualitatively similar results were obtained in comparison to the pertinent literature, however, there was an overall amplification of ventriculomegaly and transparenchymal pressure difference using this model. A quantitative and qualitative assessment is made of hydrocephalus cases involving aqueductal stenosis, along with the effects to CSF reabsorption in the parenchyma and subarachnoid space. The finite element discretisation template produced for the n^th- dimensional transient MPET system allowed for novel insight into hydrocephalus. In the 1D formulation, imposing the breakdown of the blood-CSF barrier responsible for clearance resulted in an increase in ventricular displacement, transparenchymal venous pressure gradient and transparenchymal CSF pressure gradient, whilst altering the compliance proved to markedly alter the rate of change of displacement and CSF pressure gradient. The influence of Poisson's ratio was investigated through the use of the dual-grid solver in order to distinguish between possible over or under prediction of the ventricular displacement. In the 2D model based on linear triangles, the importance of the MPET boundary conditions is acknowledged, along with the quality of the underlying mesh. Interesting results include that the fluid content is highest in the periventricular region and the skull, whilst after longer time scales, the peak CSF content becomes limited to the periventricular region. Venous fluid content is heavily influenced by the Biot-Willis constant, whilst both the venous and CSF/ISF compartments show to be strongly influenced by breakdown in the blood-CSF barrier. Increasing the venous compliance effects the arterial, capillary and venous compartments. Decreasing the venous compliance shows an accumulation of fluid, possibly helping to explain why the ventricles can be induced to compress rather than expand under decreased compliance. Finally, a successful application of the 3D-MPET template is shown for simple geometries. It is envisaged that future observations into the biology of cerebral fluid flow (such as perivascular CSF-ISF fluid exchange) and its interaction with the surrounding parenchyma, will demand the evolution of the MPET model to reach a level of complexity that could allow for an experimentally guided exploration of areas that would otherwise prove too intricate and intertwined under conventional settings.

L'objectif de cette thèse dans le domaine de la nanoélectronique est de contribuer à l'analyse des phénomènes de transport électronique quantique dans les nanostructures. Nous développons ainsi spécifiquement la théorie de raccordement des champs de phase (PFMT). Cette approche algébrique décrit les propriétés électroniques du système par les liaisons fortes, mais repose fondamentalement sur la technique de raccordement de phase des états électroniques des électrodes avec ceux sur les nanojonctions moléculaires. En comparant certains de nos résultats avec ceux des méthodes de principes premiers, nous avons montré la justesse et fonctionnalité de notre approche. Une alternative pratique et générale aux nombreuses techniques basées sur la fonction de Green, elle est appliquée dans ce travail de thèse pour modéliser le transport électronique à travers de nanojonctions sous forme de fils mono et diatomiques, constitués d'éléments de Na, Cu, Co, C, Si, Ga et As, mono et multivalents. / The aim of this thesis in the nanoelectronics domain is to present a contribution to the analysis of the quantum electronic transport phenomena in nanostructures. For this purpose, we specifically develop the phase field matching theory (PFMT). Within this algebraic approach the electronic properties of the system are described by the tight-binding formalism, whereas the analysis of the transport properties based on the phase matching of the electronic states of the leads to the states of the molecular nanojunctions. By comparing some of our results with those of the first principles methods, we have shown the correctness and fonctionality of our approach. Moreover, our method can be considered as a practical and general alternative to the Green’s function-based techniques, and is applied in this work to model the electronic transport across mono and diatomic nanojunctions, consisting of mono and multivalent Na, Cu, Co, C, Si, Ga and As elements.

In this dissertation, the evolution of a pressure wave driven by a harmonic signal on the boundary during gas combustion is studied. The problem is modeled by a nonlinear, hyperbolic partial differential equation. Steady-state behavior is investigated using the perturbation method to ensure that enough time has passed for any transient effects to have dissipated. The zeroth, first and second-order perturbation solutions are obtained and their moduli are plotted against frequency. It is seen that the first and second-order corrections have unique maxima that shift to the right as the frequency decreases and to the left as the frequency increases. Dispersion relations are determined and their limiting behavior investigated in the low and high frequency regimes. It is seen that for low frequencies, the medium assumes a diffusive-like nature. However, for high frequencies the medium behaves similarly to one exhibiting relaxation. The phase speed is determined and its limiting behavior examined. For low frequencies, the phase speed is approximately equal to sqrt[ω/(n+1)] and for high frequencies, it behaves as 1/(n+1), where n is the mode number. Additionally, a maximum allowable value of the perturbation parameter, ε = 0.8, is determined that ensures boundedness of the solution. The location of the peak of the first-order correction, xmax, as a function of frequency is determined and is seen to approach the limiting value of 0.828/sqrt(ω) as the frequency tends to zero and the constant value of 2 ln 2 as the frequency tends to infinity. Analytic expressions are obtained for the approximate general perturbation solution in the low and high-frequency regimes and are plotted together with the perturbation solution in the corresponding frequency regimes, where the agreement is seen to be excellent. Finally, the solution obtained from the perturbation method is compared with the long-time solution obtained by the finite-difference scheme; again, ensuring that the transient effects have dissipated. Since the finite-difference scheme requires a right boundary, its location is chosen so that the wave dissipates in amplitude enough so that any reflections from the boundary will be negligible. The perturbation solution and the finite-difference solution are found to be in excellent agreement. Thus, the validity of the perturbation method is established.