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The knowledge of flow hydrodynamics within the next decades is of particular importance in many practical applications. In this study, a methodological improvement has been made to the evaluation of the flow hydrodynamics under climate change. This research, indeed, proposes an approach which includes the methods that can consider the climate change impact on the flow in estuaries, gulfs, etc. It includes downscaling methods to project the required climate variables through the next decades. Here, two statistical downscaling methods, namely, Nearest Neighbouring and Quantile-Quantile techniques, are developed and implemented in order to predict the wind speed over the study area. Wind speed has an essential role in flow field and wave climatology in estuaries and gulfs. In order to make the proposed methodology computationally efficient, the flow in the estuary is simulated by a large-scale model. The finite volume triangular C-grid is analysed and shown to have advantages over the rectangular (finite difference) one. The dispersion relation analysis is performed for both gravity and Rossby waves that have crucial effects in oceanic models. In order to study the unstructured characteristic of the triangular grids, various isosceles triangles with different vertex angles are considered. Moreover, diverse well-known second-order time stepping techniques such as Leap-Frog, Adams-Bashforth and improved Euler are studied in combination with the C-grid semi discrete method. The fully discrete method is examined through several numerical experiments for both linear and non-linear cases. The results of the large-scale model provide the boundary conditions to the local coastal model. In order to model the flow over a local coastal area, a well-balanced positivity preserving central-upwind method is developed for the unstructured quadrilateral grids. The quadrilateral grid can effectively simulate complex domains and is shown to have advantages over the triangular grids. The proposed central-upwind scheme is well-balanced and preserve the positivity. Therefore, it is capable of modelling the wetting and drying processes that may be the case in many local coastal areas. It is also confirmed that the proposed method can well resolve complex flow features. The local model incorporates the outputs of the downscaling and large-scale flow models and evaluates the flow hydrodynamics under changing climate.

In this thesis, we use asymptotic methods to solve problems of wave propagation through infinite and finite (only consider those that are finite in one direction) arrays of scatterers. Both two- and three-dimensional arrays are considered. We always assume the scatterer size is much smaller than both the wavelength and array periodicity. Therefore a small parameter is involved and then the method of matched asymptotic expansions is applicable. When the array is infinite, the elastic wave scattering in doubly-periodic arrays of cavity cylinders and acoustic wave scattering in triply-periodic arrays of arbitrary shape rigid scatterers are considered. In both cases, eigenvalue problems are obtained to give perturbed dispersion approximations explicitly. With the help of the computer-algebra package Mathematica, examples of explicit approximations to the dispersion relation for perturbed waves are given. In the case of finite arrays, we consider the multiple resonant wave scattering problems for both acoustic and elastic waves. We use the methods of multiple scales and matched asymptotic expansions to obtain envelope equations for infinite arrays and then apply them to a strip of doubly or triply periodic arrays of scatterers. Numerical results are given to compare the transmission wave intensity for different shape scatterers for acoustic case. For elastic case, where the strip is an elastic medium with arrays of cavity cylinders bounded by acoustic media on both sides, we first give numerical results when there is one dilatational and one shear wave in the array and then compare the transmission coefficients when one dilatational wave is resonated in the array for normal incidence. Key words: matched asymptotic expansions, multiple scales, acoustic scattering, elastic scattering, periodic structures, dispersion relation.

This work deals with the linear analysis of plasma waves, especially with the methods of solution of a hot plasma dispersion relation. There are cited some results achieved in the space plasma research and mapped current numerical methods of their analysis. Besides, this work introduces a new numeric procedure, computer code PDRS (Plasma Dispersion Relation Solver), which allows finding solution of a dispersion function of a cold or hot plasma with general distribution function. It also demonstrates the usage of the PDRS methods on real examples of waves in space plasma based on the spacecraft Cluster measurement.

We investigate the possibility of measuring and using the phase delay of radio frequency transmissions in the amateur satellite band as a method to determine the distribution of currents systems in the ionosphere. The amateur satellite transmissions at 7MHz, 14M Hz, and 144M Hz are low enough for Faraday rotation to cause a significant phase delay on the propagating signals in addition to the phase delay produced by the total electron content (TEC) in the ionosphere. The ionosphere in the E and F regions is modeled as an equivalent thin planar shell of collision free cold plasma 100 km in thickness located in an altitude range of 100 � 200 km. The earth's magnetic field is superposed with a weaker magnetic field due to a narrow Gaussian strip of current representing an ionospheric electrojet. The prole of the current system is obtained by numerically optimizing the Appleton-Hartree dispersion relation for rays of simulated radio frequency (RF) signals that propagate through the ionosphere shell. The optimization procedure is performed with a differential evolution algorithm. From the optimization procedure, we obtain the ionosphere total electron content (TEC) and the strength, prole, and orientation of the ionospheric current system.

We investigate the possibility of measuring and using the phase delay of radio frequency transmissions in the amateur satellite band as a method to determine the distribution of currents systems in the ionosphere. The amateur satellite transmissions at 7MHz, 14M Hz, and 144M Hz are low enough for Faraday rotation to cause a significant phase delay on the propagating signals in addition to the phase delay produced by the total electron content (TEC) in the ionosphere. The ionosphere in the E and F regions is modeled as an equivalent thin planar shell of collision free cold plasma 100 km in thickness located in an altitude range of 100 􀀀 200 km. The earth's magnetic field is superposed with a weaker magnetic field due to a narrow Gaussian strip of current representing an ionospheric electrojet. The prole of the current system is obtained by numerically optimizing the Appleton-Hartree dispersion relation for rays of simulated radio frequency (RF) signals that propagate through the ionosphere shell. The optimization procedure is performed with a differential evolution algorithm. From the optimization procedure, we obtain the ionosphere total electron content (TEC) and the strength, prole, and orientation of the ionospheric current system.

In this thesis a model involving two coupled nonlinear PDEs is developed to study instability of a two-component metal film due to horizontal electric field and in a high-temperature environment similar to operational conditions of integrated circuits. The proposed model assumes the anisotropies of the diffusional mobilities for two atomic species, and negligible stresses in the film. The purpose of the modeling is to describe and understand the time-evolution of the shape of the film surface. Toward this end, the linear stability analysis (LSA) of the initially planar film surface with respect to small shape perturbations is performed. Such characteristics of the instability as the perturbation growth rate omega and the cut-off wave number are studied as functions of key physical parameters.

Derivation of an electromagnetic model, regarding the wave propagation in a very long (10 km or more) High Voltage Direct Current (HVDC) power cable, is the central part of this thesis. With an existing “perfect” electromagnetic model there are potentially a wide range of applications.The electromagnetic model is focused on frequencies between 0 and 100 kHz since higher frequencies essentially will be attenuated. An exact dispersion relation is formulated and the propagation constant is computed numerically. The dominating mode is the first Transversal Magnetic (TM) mode of order zero, denoted TM01, which is also referred to as the quasi-TEM mode. A comparison is made with the second propagating TM mode of order zero denoted TM02. The electromagnetic model is verified against real time data from Time Domain Reflection (TDR) measurements on a HVDC power cable. A mismatch calibration procedure is performed due to matching difficulties between the TDR measurement equipment and the power cable regarding the single-mode transmission line model.An example of power cable length measurements is addressed, which reveals that with a “perfect” model the length of an 80 km long power cable could be estimated to an accuracy of a few centimeters. With the present model the accuracy can be estimated to approximately 100 m.In order to understand the low-frequency wave propagation characteristics, an exact asymptotic analysis is performed. It is shown that the behavior of the propagation constant is governed by a square root of the complex frequency in the lowfrequency domain. This thesis also focuses on an analysis regarding the sensitivity of the propagation constant with respect to some of the electric parameters in the model. Variables of interest when performing the parameter sensitivity study are the real relative permittivityand the conductivity.

The quantal Boltzmann&ndash / Langevin equation is used to obtain a dispersion relation for the growth rates of instabilities in infinite nuclear matter. The dispersion relation is solved numerically for three different potentials. The quantal results are compared with the semi-classical solutions. It is seen that with the inclusion of the quantal effects the growth rates of the fastest growing modes in the system are reduced and these modes have the tendency to occur at longer wavelengths for all the potentials considered. Furthermore, the boundaries of the spinodal region is determined by the phase diagrams using the same three potentials and it is observed that the expanding nuclear matter undergoes liquid-gas phase transition at reduced temperatures when the quantum effects are included.

Monte Carlo based statistical approach to solve Boltzmann Transport Equation (BTE) has become a norm to investigate heat transport in semiconductors at sub-micron regime, owing mainly to its ability to characterize realistically sized device geometries qualitatively. One of the primary issues with this technique is that the approach predominantly uses empirically fitted phonon dispersion relations as input to determine the properties of phonons so as to predict the thermal conductivity of specified material geometry. The empirically fitted dispersion relations assume harmonic approximation thereby failing to account for thermal expansion, interaction of lattice waves, effect of strain on spring stiffness, and accurate phonon-phonon interaction. To circumvent this problem, in this work, a coupled molecular mechanics-Monte Carlo (MM-MC) platform has been developed and used to solve the phonon Boltzmann Transport Equation (BTE) for the calculation of thermal conductivity of several novel and emerging nanostructures. The use of the quasi-anharmonic MM approach (as implemented in the open source NEMO 3-D software toolkit) not only allows one to capture the true atomicity of the underlying lattice but also enables the simulation of realistically-sized structures containing millions of atoms. As compared to the approach using an empirically fitted phonon dispersion relation, here, a 17% increase in the thermal conductivity for a silicon nanowire due to the incorporation of atomistic corrections in the LA (longitudinal acoustic) branch alone has been reported. The atomistically derived thermal conductivity as calculated from the MM-MC framework is then used in the modular design and analysis of (i) a silicon nanowire based thermoelectric cooler (TEC) unit, and (ii) a GaN/InN based nanostructured light emitting device (LED). It is demonstrated that the use of empirically fitted phonon bandstructure parameters overestimates the temperature difference between the hot and the cold sides and the overall cooling efficiency of the system, thereby, demanding the use of the BTE derived thermal conductivity in the calculation of thermal conductivity. In case of the light-emitting device, the microscopically derived material parameters, as compared to their bulk and fitted counterparts, yielded ~3% correction (increase) in optical efficiency. A non-deterministic approach adopted in this work, therefore, provides satisfactory results in what concerns phonons transport in both ballistic and diffusive regimes to understand and/predict the heat transport phenomena in nanostructures.