Approved for public release, distribution is unlimited / A study of the performance of the Coupled Ocean Atmosphere Mesoscale Prediction System (COAMPS) was performed based on collected METOC properties affecting radar propagation during the Roughness and Evaporation Duct (RED) experiment conducted off the windward coast of Oahu, HI. The measured refractivity influencing parameters (SST, air temperature, humidity, and wind speed) were compared to COAMPS predicted values. Using the NPS bulk evaporation duct model, profiles of the modified refractivity were computed from the buoy data and compared to profiles computed from the COAMPS data. The profiles were obtained concurrently with S-Band propagation measurements along a 26-km path. The radar propagation predictions created by APM from the modified refractivity profiles, derived from the measured METOC values and COAMPS modeled values, were compared to the in situ measured propagation losses. The mean RMS error of the prop loss predictions derived from the COAMPS forecasted METOC values was <4 dB compared to a mean RMS error of <3 dB from the in situ measurement derived prop loss predictions. Significantly larger errors occurred at the COAMPS analysis times. Overall, the results are very promising for this trade wind region, where the air is cooler than the relatively warm sea surface. / Lieutenant, United States Navy

Wang Jing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 55-59). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Formulation of the Problem --- p.10 / Chapter 1.1 --- Reformulated Navier-Stokes Equations --- p.10 / Chapter 1.2 --- Linearized Problems --- p.15 / Chapter 2 --- Construction of the Approximate Solution --- p.19 / Chapter 2.1 --- Two-scale Asymptotic Expansions --- p.19 / Chapter 2.2 --- Determination of Each Inner and Boundary Terms --- p.22 / Chapter 2.3 --- Truncation Terms --- p.31 / Chapter 3 --- Estimates of the Error Term of the Approximate Solution and Main Results --- p.33 / Chapter 3.1 --- Error Equations --- p.33 / Chapter 3.2 --- Energy Estimates --- p.36 / Chapter 3.2.1 --- BasicL2 Estimates --- p.36 / Chapter 3.2.2 --- Tangential Derivatives Estimates --- p.38 / Chapter 3.2.3 --- Normal Derivatives Estimates --- p.49 / Chapter 3.3 --- Pointwise Estimates --- p.52 / Bibliography --- p.55

The heat affected zone (HAZ) of friction stir welded Al 7075 T7 shows diminished corrosion resistance properties when compared with the parent material. Corrosion attack in this region of the weld is primarily intergranular and is associated with the presence of precipitate free zones. Current TEM research conducted at Brigham Young University by Dr. Bin Cai finds a correlation between precipitate free zone (PFZ) width and grain boundary geometry. As both grain boundary geometry and the PFZ are associated with modes of failure in 7XXX aluminum, this paper makes a comparison of grain boundary character distributions (GBCD) in the HAZ and the parent metal via multi-section plane five-parameter stereology. The stereology is conducted in a convenient macroscopic coordinate frame, associated with the HAZ. This is the first investigation to determine the GBCD in the HAZ of friction-stirred weld material and requires multiple section plane sampling. It is discovered that aluminum here exhibits the property of non-sidedness, a long assumed but unproven characteristic. Further comparisons between the two microstructures are conducted relative to (2-dimensional) grain boundary network connectivity, recovered from EBSD data in each section plane. It is shown that the relative fraction of grain boundaries of misorientation character associated with smaller PFZ size is larger in the HAZ as compared to the parent material. A commensurate decrease in the connectivity (radius of gyration) of grain boundaries of character conducive to larger PFZ size is also found in the HAZ, relative to the parent material. Distribution of inclinations changes as a function of grain boundary geometry. Surface area per unit volume of CSL and low angle random (LAR) misorientations increases in the HAZ, while high angle random (HAR) boundaries decrease. In the case of LAR and some CSL boundaries, a reorientation occurs in which macroscopic normals of these interfaces rotate. It is anticipated that these significant changes in the GBCD within the HAZ could be important in terms of understanding the post-weld mechanical and physical properties in friction-stirred materials.

Doctor of Philosophy (PhD) / For many practitioners and market participants, the valuation of financial derivatives is considered of very high importance as its uses range from a risk management tool, to a speculative investment strategy or capital enhancement. A developing market requires efficient but accurate methods for valuing financial derivatives such as American options. A closed form analytical solution for American options has been very difficult to obtain due to the different boundary conditions imposed on the valuation problem. Following the method of solving the American option as a free boundary problem in the spirit of the "no-arbitrage" pricing framework of Black-Scholes, the option price and hedging parameters can be represented as an integral equation consisting of the European option value and an early exercise value dependent upon the optimal free boundary. Such methods exist in the literature and along with risk-neutral pricing methods have been implemented in practice. Yet existing methods are accurate but inefficient, or accuracy has been compensated for computational speed. A new numerical approach to the valuation of American options by cubic splines is proposed which is proven to be accurate and efficient when compared to existing option pricing methods. Further comparison is made to the behaviour of the American option's early exercise boundary with other pricing models.

Boundary-layer flows near leading edges of generally curved obstacles have been studied for a long time. Apart from having many practical applications, the theory and approaches prevailing in this area stimulate development of a variety of computational tools and form a ground for testing them. The specific aim of this work is to study two-dimensional laminar boundary layer flows near the leading edges of airfoils and other elongated bodies, and to explore geometries for which boundary layer separation can be avoided. This class of problems is relevant to optimal design of wings, aircraft and projectile noses, laminar flow control methods and adaptive wing technology. One of the findings of this work suggests that local modifications to parabolic wing noses can yield up to 11% increase in the unseparated angle of attack. Another result obtained here is the set of shortest possible generalised elliptic noses of long symmetric bodies which allow unseparated flow. Methods adopted in this work are based on the combined use of numerically solved Prandtl equations written in Gortler variables, and inviscid solutions obtained semi-analytically by the conformal mapping method. The resulting technique being reliable, fast and computationally inexpensive, can complement or test the results obtained using a comprehensive CFD approach. / Thesis (Ph.D.)--School of Mathematical Sciences, 2002.

This thesis consists of three papers concerning problems related to plurisubharmonic functions on bounded hyperconvex domains, in particular boundary values of such functions. The papers summarized in this thesis are:* Paper I Urban Cegrell and Berit Kemppe, Monge-Ampère boundary measures, Ann. Polon. Math. 96 (2009), 175-196.* Paper II Berit Kemppe, An ordering of measures induced by plurisubharmonic functions, manuscript (2009).* Paper III Berit Kemppe, On boundary values of plurisubharmonic functions, manuscript (2009).In the first paper we study a procedure for sweeping out Monge-Ampère measures to the boundary of the domain. The boundary measures thus obtained generalize measures studied by Demailly. A number of properties of the boundary measures are proved, and we describe how boundary values of bounded plurisubharmonic functions can be associated to the boundary measures.In the second paper, we study an ordering of measures induced by plurisubharmonic functions. This ordering arises naturally in connection with problems related to negative plurisubharmonic functions. We study maximality with respect to the ordering and a related notion of minimality for certain plurisubharmonic functions. The ordering is then applied to problems of weak*-convergence of measures, in particular Monge-Ampère measures.In the third paper we continue the work on boundary values in a more general setting than in Paper I. We approximate measures living on the boundary with measures on the interior of the domain, and present conditions on the approximation which makes the procedure suitable for defining boundary values of certain plurisubharmonic functions.

The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.

Laminar flow control holds major promise for increasing aircraft efficiency and increasing laminar flow over aerodynamic surfaces could decrease drag by up to 30 percent. The Flight Research Lab at Texas A&M University has studied laminar flow over a wing with 30 degrees of leading edge sweep with Discrete Roughness Elements (DREs) installed and has indicated that DREs can be used to increase laminar flow at Reynolds numbers up to 7.5 million at Mach 0.3. A new project, termed SARGE, has been commissioned in conjunction with NASA for studying DREs on a swept wing glove at conditions relevant to jet transports. The SARGE project must have an instrumentation system capable of accurately measuring flow conditions and transition location on the suction side of the glove. Infrared (IR) thermography has been selected as the primary transition detection tool. A heat transfer analysis has shown that solar radiation will warm the surface of the glove above the adiabatic wall temperature and therefore the laminar region will appear to be warmer. The FLIR SC8000 IR camera has been selected for this application due to its ability to produce high-resolution images in the appropriate IR band. High quality air data is also required for the experiment. A five-hole probe will be used to measure flow angle and velocity near the glove. This instrument will provide meanflow conditions due to its limited frequency response. High quality pressure transducers coupled with careful probe calibration will allow for differential measurements to be made with an uncertainty of +/- 0.03 degrees. Static pressure ports and high frequency response Kulite transducers will also be employed. Hotfilm sensors will be used to verify the state of the boundary layer on the glove through spectral analysis. A unique hotfilm array has been proposed that will enable the measurement of traveling wave vectors through a spectral technique. An experiment on the Flight Research Lab's Cessna O-2 to investigate the veracity of this technique has also been suggested. Thermocouples will also be installed on the glove's surface to monitor temperatures and verify transition location. The layout of the hotfilms and thermocouples is also detailed.

In this dissertation, we introduce and analyse a scheme for the fast evaluation of integrals stemming from boundary element methods including discretisations of the classical single and double layer potential operators. Our method is based on the parametrisation of boundary elements in terms of a d-dimensional parameter tuple. We interpret the integral as a real-valued function f depending on d parameters and show that f is smooth in a d-dimensional box. A standard interpolation of f by polynomials leads to a d-dimensional tensor which is given by the values of f at the interpolation points. This tensor may be approximated in a low rank tensor format like the canonical format or the hierarchical format. The tensor approximation has to be done only once and allows us to evaluate interpolants in O(dr(m+1)) operations in the canonical format, or O(dk³ + dk(m + 1)) operations in the hierarchical format, where m denotes the interpolation order and the ranks r, k are small integers. In particular, we apply an efficient black box scheme in the hierarchical tensor format in order to adaptively approximate tensors even in high dimensions d with a prescribed (but heuristic) target accuracy. By means of detailed numerical experiments, we demonstrate that highly accurate integral values can be obtained at very moderate costs.

Efficiency is one of the key issues in numerical simulation of large-scale problems with complex 3-D geometry. Traditional domain based methods, such as finite element methods, may not be suitable for these problems due to, for example, the complexity of mesh generation. The Boundary Element Method (BEM), based on boundary integral formulations (BIE), offers one possible solution to this issue by discretizing only the surface of the domain. However, to date, successful applications of the BEM are mostly limited to linear and continuum problems. The challenges in the extension of the BEM to nonlinear problems or problems with non-continuum boundary conditions (BC) include, but are not limited to, the lack of appropriate BIE and the difficulties in the treatment of the volume integrals that result from the nonlinear terms. In this thesis work, new approaches and techniques based on the BEM have been developed for 3-D nonlinear problems and Stokes problems with slip BC. For nonlinear problems, a major difficulty in applying the BEM is the treatment of the volume integrals in the BIE. An efficient approach, based on the precorrected-FFT technique, is developed to evaluate the volume integrals. In this approach, the 3-D uniform grid constructed initially to accelerate surface integration is used as the baseline mesh to evaluate volume integrals. The cubes enclosing part of the boundary are partitioned using surface panels. No volume discretization of the interior cubes is necessary. This grid is also used to accelerate volume integration. Based on this approach, accelerated BEM solvers for non-homogeneous and nonlinear problems are developed and tested. Good agreement is achieved between simulation results and analytical results. Qualitative comparison is made with current approaches. Stokes problems with slip BC are of particular importance in micro gas flows such as those encountered in MEMS devices. An efficient approach based on the BEM combined with the precorrected-FFT technique has been proposed and various techniques have been developed to solve these problems. As the applications of the developed method, drag forces on oscillating objects immersed in an unbounded slip flow are calculated and validated with either analytic solutions or experimental results.