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This is training presentation for REA (Reading Error Analysis) software. REA is designed for analyzing UGT scope reading errors and for developing reading points optimization algorithms.
An analytical transformation method which can map arbitrary physical coordinate grid distribution into desired computational coordinate with uniform grid distribution is derived. The transformation function and its higher derivatives are differentiable. Salient features include; (1) precise control of grid sizes; (2) more than one location of clustered grids; (3) exact positioning of particular computational nodes in the physical plane; and (4) ensuring several patches of uniformly spaced grids in the physical plane for the higher accuracies (such as at the boundaries), etc., while keeping the variation of grid spacing continuous to avoid numerical instability.
We propose a new method to compute magnetic surfaces that are parametrized in Boozer coordinates for vacuum magnetic fields. We also propose a measure for quasisymmetry on the computed surfaces and use it to design coils that generate a magnetic field that is quasisymmetric on those surfaces. The rotational transform of the field and complexity measures for the coils are also controlled in the design problem. Using an adjoint approach, we are able to obtain analytic derivatives for this optimization problem, yielding an efficient gradient-based algorithm. Starting from an initial coil set that presents nested magnetic surfaces for a large fraction of the volume, our method converges rapidly to coil systems generating fields with excellent quasisymmetry and low particle losses. In particular for low complexity coils, we are able to significantly improve the performance compared with coils obtained from the standard two-stage approach, e.g. reduce losses of fusion-produced alpha particles born at half-radius from $17.7\,\%$ to $6.6\,\%$ . We also demonstrate 16-coil configurations with alpha loss ${<}1\,\%$ and neoclassical transport magnitude $\epsilon _{\text {eff}}^{3/2}$ less than approximately $5\times 10^{-9}$ .
The objective of this study is two-fold: to investigate the absorption of hard x rays along a tangential path through the terrestrial atmosphere, and to locate, other than the use of imaging devices, the flare source of x ray emission in the sun. Observational data were taken with the Hard X Ray Burst Spectrometer (HXRBS) on board the Solar Maximum Mission satellite (SMM). The occultation event chosen for investigation is the flare on 14 October 1981. Night fell on SMM during the decaying phase of the flare. In about fifteen seconds, the x ray flux decreased to zero. The model for computing synthetic light curve, which is directly comparable to the observed curve, consists of two computing programs. One is a modified version of an existing code, which compute the coordinates of the tangent points of the SMM-sun lines. The other program computed the atmospheric densities along the angles (N to S and E to W) measured from the center of the sun. The various model also depends on the destination of the terrestrial atmosphere at geocentric positions of SMM and the sun, the mean atmospheric densities at different heights and latitudes, and the x ray absorption cross of nitrogen, oxygen, and argon. The optical length, at a given time and for a x ray energy, is computed with the two angular parameters. The fit of a particular synthetic light, curve, i.e., the exponentials of the optical lengths, to the observed eclipse curve, yields the desired angular parameters.
Coordinates of points on complicated three-dimensional surface of turbo-machine blade computed by method partly simplifying three-dimensional problem to two-dimensional problem. Method implemented in computer program enabling rapid hydrodynamical evaluation and optimization of blade surface prior to definition of final design of, and analysis of stresses in blade. By incorporating program into procedure for designing turbomachine, one reduces time spent on design iterations.
A computer software system has been developed to automatically generate two-dimensional coordinates from algebraic transformations. For topologically complex regions, a smooth assembly of the transformations can be used to automatically produce a composite mesh where a general gridded format is retained. The algebraic mesh generation system consists of a collection of operator subroutines which are applied to an established data structure and which automatically perform the necessary parts of mesh construction from a sequence of multisurface transformations. The system operators are discussed, taking into account the data base, the order of application, direct surface generators, geometric surface operators, surface generators from existing surfaces, transverse operators, mesh operators, assembly operators, and data visualization operators. Attention is given to applications related to airfoils.
The Framework for Interdisciplinary Design Optimization (FIDO) is a general programming environment for automating the distribution of complex computing tasks over a networked system of heterogeneous computers. For example, instead of manually passing a complex design problem between its diverse specialty disciplines, the FIDO system provides for automatic interactions between the discipline tasks and facilitates their communications. The FIDO system networks all the computers involved into a distributed heterogeneous computing system, so they have access to centralized data and can work on their parts of the total computation simultaneously in parallel whenever possible. Thus, each computational task can be done by the most appropriate computer. Results can be viewed as they are produced and variables changed manually for steering the process. The software is modular in order to ease migration to new problems: different codes can be substituted for each of the current code modules with little or no effect on the others. The potential for commercial use of FIDO rests in the capability it provides for automatically coordinating diverse computations on a networked system of workstations and computers. For example, FIDO could provide the coordination required for the design of vehicles or electronics or for modeling complex systems.
A system of computer programs was developed to model general three dimensional surfaces. Surfaces are modeled as sets of parametric bicubic patches. There are also capabilities to transform coordinates, to compute mesh/surface intersection normals, and to format input data for a transonic potential flow analysis. A graphical display of surface models and intersection normals is available. There are additional capabilities to regulate point spacing on input curves and to compute surface/surface intersection curves. Input and output data formats are described; detailed suggestions are given for user input. Instructions for execution are given, and examples are shown.
Appendix 4 of the Study of One- and Two-Dimensional Filtering and Deconvolution Algorithms for a Streaming Array Computer discusses coordinate axes, location of origin, and redundancy for the one- and two-dimensional Fourier transform for complex and real data.
An analytical approach is presented to account for some of the nonlinear characteristics of the transonic flow equation for finite thickness wings undergoing harmonic oscillation at sonic flight speed in an inviscid, shock-free fluid. The thickness effect is accounted for in the analysis through use of the steady local Mach number distribution over the wing at its mean position by employing the local linearization concept and a coordinate transformation. Computed results are compared with that of the linearized theory and experiments. Based on the local linearization concept, an alternate formulation avoiding the limitations of the coordinate transformation method is presented.
A system of computer programs has been developed to model general three-dimensional surfaces. Surfaces are modeled as sets of parametric bicubic patches. There are also capabilities to transform coordinate to compute mesh/surface intersection normals, and to format input data for a transonic potential flow analysis. A graphical display of surface models and intersection normals is available. There are additional capabilities to regulate point spacing on input curves and to compute surface intersection curves. Internal details of the implementation of this system are explained, and maintenance procedures are specified.
A numerical method, which is simpler and more efficient than others currently in use, is proposed for the computation of the full viscous flow over an aerobrake body in hypersonic stream at high altitude. It treats the shock layer surrounding the blunt forebody and the near wake behind the base simultaneously by formulating the Navier-Stokes equations in conformal and azimuthal-angle coordinates. The computational domain is confined by the body wall, outflow surface and the shock, which is adjusted along the coordinate normal to the wall in the course of iterations. Because of the optimal grid and a well developed alternating direction implicit factorization technique for the governing equations, reasonably accurate results can be obtained with a 28 x 36 x 7 grid and 400 time-marching iterations. Excellent agreement of shock location is found between the present result and the schlieren photograph. Details of the base flow and shear layer impingement on the cylindrical aft body are presented for an adiabatic wall case.
To examine ion solvation, exchange, and speciation for minority components in molten salts (MS) typically found as corrosion products, we propose a multimodal approach combining extended X-ray absorption fine structure (EXAFS) spectroscopy, optical spectroscopy, ab initio molecular dynamics (AIMD) simulations, and rate theory of ion exchange. Going beyond conventional EXAFS analysis, our method can accurately quantify populations of different coordination states of ions with highly disordered coordination environments via linear combination fitting of the EXAFS spectra of these coordination states computed from AIMD to the experimental EXAFS spectrum. In a case study of dilute Ni(II) dissolved in the ZnCl 2 +KCl melts, our method reveals heterogeneous distributions of coordination states of Ni(II) that are sensitive to variations in temperature and melt composition. These results are fully explained by the difference in the chloride exchange dynamics at varied temperatures and melt compositions. Finally, this insight will enable a better understanding and control of ion solubility and transport in MS.
A combined Eulerian-Lagrangian analysis, which combines a linearized block implicit Navier-Stokes analysis for the continuous phase with a Lagrangian analysis for the motion of the droplet phase to simulate evaporating two-phase flows, has been developed. A unique aspect of this analysis is that the Lagrangian equations for the droplet motion have been transformed into the Eulerian computational space using coordinate transformation resulting in better computational efficiency. Use of the present implicit procedure for the continuous phase makes it possible to efficiently use a locally highly refined mesh. The coupling of the continuous phase and the droplet phase analyses is such that it allows the use of convergence acceleration techniques for steady-state problems, as well as making it possible to simulate transient flows. A rapidly evaporating two-phase flow caused by spray of liquid nitrogen in gaseous nitrogen has been used as a test problem to demonstrate the computer code using this analysis.
A numerical method, which is simpler than others currently in use, is proposed for determining the full viscous flow over a finite body in hypersonic stream at high altitude. It treats the shock layer surrounding the blunt foebody and the near wake behind the base simultaneously by formulating the Navier-Stokes equations in conformal and azimuthal-angle coordinates. The computational domain is confined to the body wall, outflow surface and the bow shock, which is adjusted along the coordinate normal to the wall in the course of iterations. Because of the optimal grid and a well developed alternating direction implicit factorization technique for the governing equations, reasonably accurate results can be obtained on a 30 by 36 by 6 grid with 400 time-marching iterations. Results for body shapes belonging to the ellipsoid-cone family are compared with the experimental data for the Apollo command module and the Viking aeroshell. Validation of the method based on self-consistency is also discussed.
Detailed descriptions are given of the theoretical methods and associated computer codes of a program to smooth and a program to scale arbitrary airfoil coordinates. The smoothing program utilizes both least-squares polynomial and least-squares cubic spline techniques to smooth interatively the second derivatives of the y-axis airfoil coordinates with respect to a transformed x-axis system which unwraps the airfoil and stretches the nose and trailing-edge regions. The corresponding smooth airfoil coordinates are then determined by solving a tridiagonal matrix of simultaneous cubic-spline equations relating the y-axis coordinates and their corresponding second derivatives. A technique for computing the camber and thickness distribution of the smoothed airfoil is also discussed. The scaling program can then be used to scale the thickness distribution generated by the smoothing program to a specific maximum thickness which is then combined with the camber distribution to obtain the final scaled airfoil contour. Computer listings of the smoothing and scaling programs are included.
A three-dimensional elliptic solver technique is utilized to generate surface-fitted coordinates about wing/wing-tip configurations. The method is applicable to wings of arbitrary section profile and camber, leading-edge sweep, taper ratio, and spanwise thickness variation. The basic theory of three-dimensional elliptic mappings is developed along with a method to compute interior coordinate control functions. Examples of grids generated about several wing/wing-tip geometries are given. A 49 x 33 x 17 grid requires about 3 minutes of CPU time on a CYBER 203 computer.
Correction to: Naturehttps://doi.org/10.1038/s41586-024-07117-5 Published online 13 March 2024 In the version of the article initially published, several errors were present and have been corrected in the HTML and PDF versions of the article and Supplementary Information. The main results, conclusions, and our interpretations of the data remain unchanged. See the new Supplementary Information Section S15 for a more detailed description of the errors corrected and the resulting effects on the analysis. Data processing and methods corrections Overflight count correction: We previously used pre-computed source coverage data for some Carbon Mapper campaigns that was computed differently than was required for our analysis. We have re-computed Carbon Mapper source coverage based on flightline polygons and source coordinates. Transition point computation, well sites: The updated version now correctly compares the cumulative emissions distribution of simulated well site emissions with that of aerially detected sources (rather than plumes) when computing the transition point. Transition point computation, midstream: Additionally, the transition point calculation has been corrected to exclude aerially detected midstream emissions below the transition point, which was previously leading to double counting of these emissions. This error was not present for upstream (well site) emissions. Calculation errors Unit error: We corrected a specific unit conversion error affecting well site emissions in the Kairos Fort Worth dataset. Across all datasets, we also correct the conversion factor for converting from standard volume to mass for midstream emissions. Sorting error: We correct code that was applying incorrect sorting when computing correction factors to account for partial detection at well sites. Small typographical corrections were made in Fig. 1b and SI Section S4.1. Data processing and methods corrections Overflight count correction: We previously used pre-computed source coverage data for some Carbon Mapper campaigns that was computed differently than was required for our analysis. We have re-computed Carbon Mapper source coverage based on flightline polygons and source coordinates. Transition point computation, well sites: The updated version now correctly compares the cumulative emissions distribution of simulated well site emissions with that of aerially detected sources (rather than plumes) when computing the transition point. Transition point computation, midstream: Additionally, the transition point calculation has been corrected to exclude aerially detected midstream emissions below the transition point, which was previously leading to double counting of these emissions. This error was not present for upstream (well site) emissions. Calculation errors Unit error: We corrected a specific unit conversion error affecting well site emissions in the Kairos Fort Worth dataset. Across all datasets, we also correct the conversion factor for converting from standard volume to mass for midstream emissions. Sorting error: We correct code that was applying incorrect sorting when computing correction factors to account for partial detection at well sites. Small typographical corrections were made in Fig. 1b and SI Section S4.1. The following practices may help researchers conducting similar analyses avoid making similar errors: 1, Clear, accessible documentation explaining the interpretation of all columns in data input tables and all internal variables within the model, 2, Simple cross-check calculations computed before and after unit conversions.