Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology

Real-time flutter analysis

The important algorithm issues necessary to achieve a real time flutter monitoring system; namely, the guidelines for choosing appropriate model forms, reduction of the parameter convergence transient, handling multiple modes, the effect of over parameterization, and estimate accuracy predictions, both online and for experiment design are addressed. An approach for efficiently computing continuous-time flutter parameter Cramer-Rao estimate error bounds were developed. This enables a convincing comparison of theoretical and simulation results, as well as offline studies in preparation for a flight test. Theoretical predictions, simulation and flight test results from the NASA Drones for Aerodynamic and Structural Test (DAST) Program are compared

NA

http://archive.org/details/geometricdesignt00zumrNAN

IIR approximation of FIR filters via discrete-time vector fitting

We present a novel technique for approximating finite-impulse-response (FIR) filters with infinite-impulse-response (IIR) structures through extending the vector fitting (VF) algorithm, used extensively for continuous-time frequency-domain rational approximation, to its discrete-time counterpart called VFz. VFz directly computes the candidate filter poles and iteratively relocates them for progressively better approximation. Each VFz iteration consists of the solutions of an overdetermined linear equation and an eigenvalue problem, with real-domain arithmetic to accommodate complex poles. Pole flipping and maximum pole radius constraint guarantee stability and robustness against finite-precision implementation. Comparison against existing algorithms confirms that VFz generally exhibits fast convergence and produces highly accurate IIR approximants. © 2008 IEEE.published_or_final_versio

Stability and Stabilization of the Wave Model.

The stability properties of 2-D systems are an important aspect of the design of acoustic, seismic, image and sonar signal processors. This research utilizes the Wave model format to transport 1-D stability techniques to the 2-D setting. The research studies stability through multistep growth bounds on the Wave state. The use of Lyapunov theory is also considered. The research considers also the problem of stabilizing a 2-D system using state and/or output information feedback to interior and/or boundary controls. Finally the problem of observer design for 2-D systems is considered, with the new stability criteria being used to assure observer/system convergence. New results based on symmetrizability are also discussed. The principal results are illustrated by a number of examples. The results are also interpreted in the context of other contemporary local state models

Measuring aberrations in lithographic projection systems with phase wheel targets

A significant factor in the degradation of nanolithographic image fidelity is optical wavefront aberration. Aerial image sensitivity to aberrations is currently much greater than in earlier lithographic technologies, a consequence of increased resolution requirements. Optical wavefront tolerances are dictated by the dimensional tolerances of features printed, which require lens designs with a high degree of aberration correction. In order to increase lithographic resolution, lens numerical aperture (NA) must continue to increase and imaging wavelength must decrease. Not only do aberration magnitudes scale inversely with wavelength, but high-order aberrations increase at a rate proportional to NA2 or greater, as do aberrations across the image field. Achieving lithographic-quality diffraction limited performance from an optical system, where the relatively low image contrast is further reduced by aberrations, requires the development of highly accurate in situ aberration measurement. In this work, phase wheel targets are used to generate an optical image, which can then be used to both describe and monitor aberrations in lithographic projection systems. The use of lithographic images is critical in this approach, since it ensures that optical system measurements are obtained during the system\u27s standard operation. A mathematical framework is developed that translates image errors into the Zernike polynomial representation, commonly used in the description of optical aberrations. The wavefront is decomposed into a set of orthogonal basis functions, and coefficients for the set are estimated from image-based measurements. A solution is deduced from multiple image measurements by using a combination of different image sets. Correlations between aberrations and phase wheel image characteristics are modeled based on physical simulation and statistical analysis. The approach uses a well-developed rigorous simulation tool to model significant aspects of lithography processes to assess how aberrations affect the final image. The aberration impact on resulting image shapes is then examined and approximations identified so the aberration computation can be made into a fast compact model form. Wavefront reconstruction examples are presented together with corresponding numerical results. The detailed analysis is given along with empirical measurements and a discussion of measurement capabilities. Finally, the impact of systematic errors in exposure tool parameters is measureable from empirical data and can be removed in the calibration stage of wavefront analysis

Skyrmion and other extended solutions of non-linear σ-models in 2 and (2+1) dimensions

Low dimensional models are generally regarded to be a convenient theoretical laboratory for studying various aspects of elementary particle theory. In this thesis, the extended solutions of one particular class of such models, namely the ₵p(^n-1) non-linear a-models in 2 dimensions, are discussed. Special attention is paid to the shape of these extended structures and their dependence on the parameters of the solutions. Time dependence is introduced into the models, and properties of the moving objects in these (2 + l)-dimensional theories are explored. In particular, the Hopf terms of the theories are investigated, and their relation to the spin of the extended solutions is discussed. Also the classical dynamics of these moving objects, and their explanation in terms of the geodesic motions on certain Hermitian and Kāhler manifolds is considered. Finally the embedding of the (₵p(^n-1) solutions into the 2-dimensional U(n) chiral models is studied, paying particular attention to the stability of these embedded solutions in the larger group space, and to the number of independent negative modes of the fluctuation operator around these solutions