"The most widely used spectral models with the transform method are the de-aliased spectral model in which the de-aliased technique is used in the discrete Fourier transform according to the 3/2-rule. From the viewpoint of the Walsh-Hadamard transform, the multiplications of the values of the variables on the gridpoints do not yield the aliasing terms. In the shallow water equations, we compare the aliased spectral model with the de-aliased spectral model using the initial conditions of the Rossby-Haurwitz wave and the FGGE data. The aliased spectral models are more accurate and more efficient than the de-aliased spectral models. For the same wavenumber truncation, the computational amount of the aliased spectral model is only 60 percent of the de-aliased spectral model. We have not yet discovered the phenomenon of the nonlinear computational instability induced by the aliasing terms in the long time integration of the aliased spectral models. Thus, in the spectral models with the transform method the necessity of using the 3/2-rule in the discrete Fourier transform may be viewed with suspicion"--Abstract. / Typescript. / "Spring Semester, 1991." / "Submitted to the Department of Meteorology in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Richard L. Pfeffer, Professor Directing Thesis. / Includes bibliographical references (leaves 92-95).

During the 1979 Atlantic hurricane season a tropical wave left the west coast of Africa and continued westward where satellite and ship observation indicated strengthening to a tropical depression from which Hurricane Frederic developed. This particular tropical disturbance has an interesting history. In its westward progression it intensified to hurricane strength lasting less than 24 hours followed by a weakening east of the Lesser Antilles. Continuing westward, this disturbance became extratropical over Southeast Cuba, but quickly reintensified to hurricane strength over Northwest Cuba, tracking through the warm Gulf waters and eventually making landfall near Mobile, Alabama. A number of experiments were carried out on a multi-level primitive equation (PE) model, a one-level PE model, and a higher resolution multi-level PE model (T63) in order to simulate the progression and intensification from a wave to a hurricane over a specified limited domain. Although previous experiments using this model with its comprehensive physical processes exhibit a reasonable predictive rate of success, the early experiments during this case study produced poor results. The most successful forecasts will be examined carefully and discussed entirely. There is strong indication that for mesoscale features a higher resolution model would achieve better results. / Typescript. / "Submitted to the Department of Meteorology in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: T. N. Krishnamurti, Professor Directing Thesis. / Includes bibliographical references (leaves 165-167).

Baroclinic tides play a significant role in driving deep-ocean mixing, which not only influences the transport of nutrients and other biological tracers, but also affects the large scale circulations. This thesis combines advanced numerical modeling techniques and available observations to investigate the characteristics of baroclinic tides in the Red Sea, and understand their formation and fate, and their influence on the circulation and ecosystem. Based on a validated 3D, non-hydrostatic and high-resolution MIT General Circulation Model (MITgcm), we first established four potential areas for the generation of baroclinic tide in the Red Sea: the Strait of Bab-el-Mandeb (BAM), the southern Red Sea, the Gulf of Suez, and the Strait of Tiran. These areas are consistently suggested by the spatial distribution of baroclinic tidal kinetic energy and energy fluxes. The majority of the baroclinic energy disappears within the basin; either dissipates due to friction and bottom drag or converts back into barotropic energy due to pressure. We next conducted 2D numerical simulations to investigate the generation mechanism behind the formation of the observed internal solitary waves(ISWs) in the southern Red Sea, revealing the dominant role of tide-topography interactions. Instead of evolving from the disturbed thermocline due to a locally impinging tidal beam ISWs are generated from the depression formed near the shelf. As this depression propagates out of the shelf, it gradually steepens and ultimately breaks into a group of ISWs. To further study the breaking and dissipation processes of the ISWs, we implemented a regional high-resolution MITgcm for the southern Red Sea with a realistic topography revealing that the breaking process is triggered by the fission mechanism. The associated particles transport is further quantitatively analyzed, revealing a significant transport, both vertically and horizontally. The thesis, finally examined the tidal influences on the basin-scale circulation of the Red Sea. Comparison experiments with and without tides show that, the intrusion of the Gulf of Aden Intermediate Water (GAIW) in summer is strongly influenced by the tides. It is suggested that tides enforce more turbulence and mixing at the strait, which significantly increase the diffusivity of heat and salinity.

The aim of this thesis is to implement source terms to numerical model for curent sheet in solar atmosphere. The chapters are structured in the way that can present us with basic knowledge of the Sun and processes in its atmosphere. Than we present important equations for numerical solution and for the initial equilibrium of our simulation. One of the last chapters is dedicated to software we use for our numerical simulations called FLASH. In the end of the thesis we present results of our numerical simulations.

During the development of flight tests of a spacecraft, heat exchange occurs among the many physically separated subsystem surfaces through the phenomenon of thermal radiation. Considering the increasing complexity of the geometrical forms and shapes in the design of such systems, the monitoring and control of the radiative heat fluxes taking place in the multi-reflecting, absorbing and emitting heat transfer environment are very critical. Because the analytical solution of thermal radiation in such geometrically complex three-dimensional systems is not practical, extensive numerical modelling techniques are widely used to predict radiative heat fluxes on the many thermally active surfaces. From experience, it is found that this can be very difficult and not at all commensurate with fast feedback unless the analysis is from a simple system layout. Considering that a relatively new approach dedicated to the basic analysis of radiative heat flux has been developed by the heat transfer community as a numerical approximation called the Discrete Ordinates Method (DOM), a first question did arise in terms of how well an enhanced and more comprehensive formulation based on this concept would fulfil the task of achieving faster results whilst still accurately predicting radiative heat transfer in three-dimensional, more complex geometries.

by Zheng Yu-kun. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Includes bibliographies.

by Yu Wai Kuen. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 71-76). / Preface --- p.1 / PART I / Chapter Chapter 1 --- Inverse Scattering Method / Chapter §1 --- Introduction --- p.5 / Chapter §2 --- Rapidly decreasing solutions of the GNLSE --- p.6 / Chapter Chapter 2 --- Modified Inverse Scattering Method / Chapter §1 --- Introduction --- p.25 / Chapter §2 --- Singular solutions of the KdV equation --- p.25 / PART II / Chapter Chapter 3 --- Backlund Transformation Method / Chapter §1 --- Introduction --- p.37 / Chapter §2 --- Solution by Backlund transformation --- p.37 / Chapter §3 --- Clairin's method for finding Backlund transformations --- p.46 / Chapter §4 --- Construction of multi-soliton solutions --- p.48 / Chapter Chapter 4 --- Dressing Method And Hirota Direct Method / Chapter §1 --- Introduction --- p.51 / Chapter §2 --- Zakharov-Shabat's dressing method --- p.52 / Chapter §3 --- Hirota direct method --- p.57 / Chapter Chapter 5 --- Group Reduction Method / Chapter §1 --- Introduction --- p.61 / Chapter §2 --- Method of group reduction --- p.61 / Bibliography --- p.71

Chan Yuet Tai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 107-111). / Chapter 1 --- Introduction to Sturm-Liouville Problem --- p.1 / Chapter 1.1 --- What are inverse problems? --- p.1 / Chapter 1.2 --- Introductory background --- p.2 / Chapter 1.3 --- The Liouville transformation --- p.3 / Chapter 1.4 --- The Sturm-Liouville problem 一 A historical look --- p.4 / Chapter 1.5 --- Where Sturm-Liouville problems come from? --- p.6 / Chapter 1.6 --- Inverse problems of interest --- p.8 / Chapter 2 --- Reconstruction Method I --- p.10 / Chapter 2.1 --- Perturbative inversion --- p.10 / Chapter 2.1.1 --- Inversion problem via Fredholm integral equation --- p.10 / Chapter 2.1.2 --- Output least squares method for ill-posed integral equations --- p.15 / Chapter 2.1.3 --- Numerical experiments --- p.17 / Chapter 2.2 --- Total inversion --- p.38 / Chapter 2.3 --- Summary --- p.45 / Chapter 3 --- Reconstruction Method II --- p.46 / Chapter 3.1 --- Computation of q --- p.47 / Chapter 3.2 --- Computation of the Cauchy data --- p.48 / Chapter 3.2.1 --- Recovery of Cauchy data for K --- p.51 / Chapter 3.2.2 --- Numerical implementation for computation of the Cauchy data . --- p.51 / Chapter 3.3 --- Recovery of q from Cauchy data --- p.52 / Chapter 3.4 --- Iterative procedure --- p.53 / Chapter 3.5 --- Numerical experiments --- p.60 / Chapter 3.5.1 --- Eigenvalues without noised data --- p.64 / Chapter 3.5.2 --- Eigenvalues with noised data --- p.69 / Chapter 4 --- Appendices --- p.79 / Chapter A --- Tikhonov regularization --- p.79 / Chapter B --- Basic properties of the Sturm-Liouville operator --- p.80 / Chapter C --- Asymptotic formulas for the eigenvalues --- p.86 / Chapter C.1 --- Case 1: h ≠ ∞ and H ≠ ∞ --- p.87 / Chapter C.2 --- Case 2: h= ∞ and H ≠∞ --- p.90 / Chapter C.3 --- Case 3: h = ∞ and H = ∞ --- p.91 / Chapter D --- Completeness of the eigenvalues --- p.92 / Chapter E --- d'Alembert solution formula for the wave equation --- p.97 / Chapter E.1 --- "The homogeneous solution uH(x,t)" --- p.98 / Chapter E.2 --- "The particular solution up(x, t)" --- p.99 / Chapter E.3 --- "The standard d'Alembert solution u(x,t)" --- p.101 / Chapter E.4 --- Applications to our problem --- p.101 / Chapter F --- Runge-Kutta method for solving eigenvalue problems --- p.104 / Bibliography --- p.107

by Chan Kam Wai Clifford. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 105-108). / Text in English; abstracts in English and Chinese. / by Chan Kam Wai Clifford. / Abstract --- p.i / Acknowledgements --- p.iii / Contents --- p.iv / List of Figures --- p.vii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Motivations of the Project --- p.1 / Chapter 1.2 --- Historical Background --- p.1 / Chapter 1.3 --- Objective and Outline of Thesis --- p.3 / Chapter Chapter 2. --- Reviews on One-dimensional Dynamical Cavity --- p.4 / Chapter 2.1 --- Formalism --- p.4 / Chapter 2.2 --- Methods of Solution --- p.6 / Chapter 2.2.1 --- Phase Construction (R function) --- p.6 / Chapter 2.2.2 --- Instantaneous Mode Expansion --- p.12 / Chapter 2.2.3 --- Transformation Method --- p.15 / Chapter 2.3 --- Numerical Results --- p.15 / Chapter 2.3.1 --- Some Results using R function --- p.16 / Chapter 2.3.2 --- Some Results using Instantaneous Mode Decomposition --- p.24 / Chapter 2.3.3 --- Remarks on the Numerical Scheme used in Transformation Method --- p.28 / Chapter 2.3.4 --- "Comparisons of Results obtained by Phase Construction, In- stantaneous Mode Decomposition and Transformation" --- p.28 / Chapter 2.4 --- Conclusion --- p.30 / Chapter Chapter 3. --- Fixed-point Analysis for the One-dimensional Cavity --- p.31 / Chapter 3.1 --- Introduction --- p.31 / Chapter 3.2 --- What are the fixed-points? --- p.32 / Chapter 3.3 --- Characteristics of Fixed-points --- p.36 / Chapter 3.4 --- Fixed-points and Geometric Resonance --- p.39 / Chapter Chapter 4. --- Electromagnetic Field in an Undulating Spherical Cavity --- p.44 / Chapter 4.1 --- Classical Electromagnetic field theory --- p.44 / Chapter 4.2 --- Boundary Conditions --- p.46 / Chapter 4.3 --- The Motion of Cavity Surface --- p.47 / Chapter Chapter 5. --- Methods of Solution and Results to the Spherical Cavity --- p.48 / Chapter 5.1 --- Introduction --- p.48 / Chapter 5.2 --- Mode Decomposition and Transformation Method revisited --- p.49 / Chapter 5.2.1 --- Mode Decomposition --- p.49 / Chapter 5.2.2 --- Transformation Method --- p.50 / Chapter 5.2.3 --- Remarks on the use of Instantaneous Mode Expansion and Transformation Method --- p.51 / Chapter 5.3 --- The Ge(z) function --- p.52 / Chapter 5.3.1 --- The Ge(z) function as a solution of the scalar wave equation --- p.52 / Chapter 5.3.2 --- Numerical Results --- p.54 / Chapter 5.4 --- The Me(z) function --- p.60 / Chapter 5.4.1 --- Formalism --- p.60 / Chapter 5.4.2 --- Comparison of Me(z) with Ge(z) --- p.62 / Chapter 5.4.3 --- Numerical Results --- p.63 / Chapter 5.5 --- Conclusions and Discussions --- p.93 / Chapter 5.5.1 --- Geometric Resonances --- p.93 / Chapter 5.5.2 --- Harmonic Resonances --- p.94 / Chapter Chapter 6. --- Conclusion --- p.95 / Appendix A. Electromagnetic Field in Spherical Cavity --- p.97 / Chapter A.1 --- Field Strength --- p.97 / Chapter A.2 --- Field Energy --- p.98 / "Appendix B. Construction of Ψe(r,t) by G(z)" --- p.100 / Appendix C. The Arbitrary Part GH(z) of Ψe(r，t) --- p.103 / Bibliography --- p.105

Modeling of the electromagnetic, structural, thermal, or acoustic response of the human body to various external and internal stimuli is limited by the availability of anatomically accurate and numerically efficient computational models. The models currently approved for use are generally of proprietary or fixed format, preventing new model construction or customization. 1. This dissertation develops a new Visible Human Project - Female (VHP-F) computational phantom, constructed via segmentation of anatomical cryosection images taken in the axial plane of the human body. Its unique property is superior resolution on human head. In its current form, the VHP-F model contains 33 separate objects describing a variety of human tissues within the head and torso. Each obejct is a non-intersecting 2-manifold model composed of contiguous surface triangular elements making the VHP-F model compatible with major commercial and academic numerical simulators employing the Finite Element Method (FEM), Boundary Element Method (BEM), Finite Volume Method (FVM), and Finite-Difference Time-Domain (FDTD) Method. 2. This dissertation develops a new workflow used to construct the VHP-F model that may be utilized to build accessible custom models from any medical image data source. The workflow is customizable and flexible, enabling the creation of standard and parametrically varying models facilitating research on impacts associated with fluctuation of body characteristics (for example, skin thickness) and dynamic processes such as fluid pulsation. 3. This dissertation identifies, enables, and quantifies three new specific computational bioelectromagnetic problems, each of which is solved with the help of the developed VHP-F model: I. Transcranial Direct Current Stimulation (tDCS) of human brain motor cortex with extracephalic versus cephalic electrodes; II. RF channel characterization within cerebral cortex with novel small on-body directional antennas; III. Body Area Network (BAN) characterization and RF localization within the human body using the FDTD method and small antenna models with coincident phase centers. Each of those problems has been (or will be) the subject of a separate dedicated MS thesis.