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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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An extensive investigation was conducted to provide realistic error models for Global Positioning System (GPS) related numerical simulation. This study considers most of the important error sources for measurement and dynamic models which are currently being used for GPS geodetic applications. These error models were evaluated by comparing with real GPS data.
Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.
A method for remote sensing of cloud parameters by using infrared sounder data has been developed on the basis of the parameterized infrared transfer equation applicable to cloudy atmospheres. The method is utilized for the retrieval of the cloud height, amount, and emissivity in 11 micro m region. Numerical analyses and retrieval experiments have been carried out by utilizing the synthetic sounder data for the theoretical study. The sensitivity of the numerical procedures to the measurement and instrument errors are also examined. The retrieved results are physically discussed and numerically compared with the model atmospheres. Comparisons reveal that the recovered cloud parameters agree reasonably well with the pre-assumed values. However, for cases when relatively thin clouds and/or small cloud fractional cover within a field of view are present, the recovered cloud parameters show considerable fluctuations. Experiments on the proposed algorithm are carried out utilizing High Resolution Infrared Sounder (HIRS/2) data of NOAA 6 and TIROS-N. Results of experiments show reasonably good comparisons with the surface reports and GOES satellite images.
Geoid undulation computations were performed at 29 laser stations distributed around the world using a combination of terrestrial gravity data within a cap of radius 2 deg and a potential coefficient set up to 180 deg. The traditional methods of Stokes' and Meissl's modification together with the Molodenskii method and the modified Sjoberg method were applied. Performing numerical tests based on global error assumptions regarding the terrestrial data and the geopotential set it was concluded that the modified Sjoberg method is the most accurate and promising technique for geoid undulation computations. The numerical computations for the geoid undulations using all the four methods resulted in agreement with the ellipsoidal minus orthometric value of the undulations on the order of 60 cm or better for most of the laser stations in the eastern United States, Australia, Japan, Bermuda, and Europe. A systematic discrepancy of about 2 meters for most of the western United States stations was detected and verified by using two relatively independent data sets. For oceanic laser stations in the western Atlantic and Pacific oceans that have no terrestrial data available, the adjusted GEOS-3 and SEASAT altimeter data were used for the computation of the geoid undulation in a collocation method.
The First GARP Global Experiment (FGGE) data base has provided the research community with the most complete global coverage of meteorological informaiton since measurements were first taken. It is important to understand the characteristics of the FGGE data base in terms of its accuracy and representativeness compared to the true state of the atmosphere. The uncertainty associated with the initial conditions used in a numerical model plays a significant role in subsequent error growth as shown by predictability theory. The ultimate limit of forecast skill is directly related to the initial uncertainty. The accuracy of analyses using FGGE data base coupled with the errors due to modeling imperfections determines the present skill of numerical models. An estimte of initial uncertainty is determined by examining differences in several FGGE analyses. The estimate is then used to determine an ultimate limit of forecast skill from derived predictability error growth rates. Several different calculations of predictability error growth are also compared. Finally, present-day forecast skill using FGGE analyses is contrasted to the estimates of ultimate skill, and the partition of model error versus initial uncertainty is discussed.
Estimates of the absorption and emission characteristics of molecules required to develop materials for solar-pumped lasers are addressed. These characteristics are described in terms of the Franck Condon factors, which are calculated from the molecular wave functions. Wave functions for vibrational levels in the lower and upper electronic states of I2 and NSe are calculated numerically and methods of checking errors discussed. Errors arise when the vibrational quantum numbers are high; but, using a calculated rather than measured value of the dissociation energy, wave functions up to the fiftieth vibrational level are obtained. A numerical method of evaluating the wave functions is given, which should be more accurate in the region of electronic transitions during absorption. Franck Condon factors, plotted versus the wavelength of the absorbed photons, are shown, and a check on the Franck Condon factors is made using the vibrational sum rule.
The mathematical framework for a-posteriori error estimation of functionals elucidated by Eriksson et al. [7] and Becker and Rannacher [3] is revisited in a space-time context. Using these theories, a hierarchy of exact and approximate error representation formulas are presented for use in error estimation and mesh adaptivity. Numerical space-time results for simple model problems as well as compressible Navier-Stokes flow at Re = 300 over a 2D circular cylinder are then presented to demonstrate elements of the error representation theory for time-dependent problems.
The simulation of adiabatic evolution has deep connections with adiabatic quantum computation, the quantum approximate optimization algorithm, and adiabatic state preparation. Here we address the error analysis problem in quantum simulation of adiabatic process using Trotter formulas. Here we show that with additional conditions, the circuit depth can be linear in simulation time T. The improvement comes from the observation that the fidelity error here can't be estimated by the norm distance between evolution operators. This phenomenon is termed the robustness of discretization in digital adiabatic simulation. It can be explained in three steps, from analytical and numerical evidence: (1) The fidelity error should be estimated by applying adiabatic theorem on the effective Hamiltonian instead. (2) Because of the specialty of Riemann-Lebesgue lemma, most adiabatic process is naturally robust against discretization. (3) As the Trotter step gets larger, the spectral gap of effective Hamiltonian tends to close, which results in the failure of digital adiabatic simulation.
Abstract One of the most promising routes toward scalable quantum computing is a modular approach. We show that distinct surface code patches can be connected in a fault-tolerant manner even in the presence of substantial noise along their connecting interface. We quantify analytically and numerically the combined effect of errors across the interface and bulk. We show that the system can tolerate 14 times higher noise at the interface compared to the bulk, with only a small effect on the code’s threshold and subthreshold behavior, reaching threshold with ~1% bulk errors and ~10% interface errors. This implies that fault-tolerant scaling of error-corrected modular devices is within reach using existing technology.
Planar supersonic near wake flow field problem with variable viscosity and base injection, investigating boundary errors spatial decay rate
The determination of maximum endpoint tracking error due to uncompensated inertial payload dynamics is investigated. The problem is formulated on the basis of well-known kinetic and kinematic relationships with constraints on maximum joint positions and velocities as well as the generalized force/speed constraint relationship for each actuator. An endpoint tracking error objective function is formed, and numerical optimization is used to determine the maximum. An example computation is presented to show the tracking error under progressively increasing payload using a PUMA 560 manipulator with its first three joints in motion.
The theory of linearized, low-gravity sloshing in axisymmetric tanks is developed in an integral minimization form that permits numerical solutions to be computed easily and that can be modified readily when better knowledge about the important surface physics phenomena becomes available from space experimentation. The slosh force and equivalent mechanical model are also derived, including the correction of errors in previous analyses. Several numerical examples are presented for spherical and cylindrical tanks. The contact angle used in the examples is 5 deg and a 'free' contact line is assumed. The results show that the nondimensional slosh frequency and slosh mass for a spherical tank are smaller for low gravity conditions than for normal gravity conditions, whereas they are larger for cylindrical tank.
Properties of a transformation method, which was developed for solving fluid dynamic problems on general two dimensional regions, are discussed. These include construction error of the transformation and applications to mesh generation. An error and stability analysis for the numerical solution of a model parabolic problem is also presented.
Concentrating Solar Power (CSP) provides firm and dispatchable electricity due to its thermal storage and hybridization capabilities, which supports the decarbonization of our energy supply. Of the various CSP technologies, parabolic trough collectors are the most mature, with over 500 MW operating worldwide. The optical performance of parabolic trough systems is sensitive to tracking error, which is defined as the angular offset of a collector away from the sun position in the transversal plane. Tracking error commonly occurs due to non-continuous adjustment of the trough angle to point toward the sun, but other factors such as gravity, heating, and wind loading can also contribute to tracking error. Researchers have explored the impact of tracking error on optical performance both numerically and experimentally, but existing studies do not include measurements from operational utility-scale power plants. Tilt angle measurements of parabolic troughs at operational utility-scale power plants illustrate spatial variations in optical performance and include various sources of tracking error such as gravity, heating, and wind loading. To fully characterize wind driven loads on parabolic troughs, we are conducting a long-term field measurement campaign at the Nevada Solar One CSP plant located in Boulder City, NV, which has a nominal capacity of 72 MW and 0.5 hours of full-load storage. We record load measurements on four outer trough rows, collecting support structure bending moments, drive torque moments, dynamic accelerations of the spaceframe, mirror displacement, and tilt angles. Using the tilt measurements acquired at 20 Hz frequency, we calculate the deviation between the nominal sun position and the tracker angle. Using a Monte-Carlo ray-tracing simulation software, we assess the impact of the tracker angle deviation on optical performance throughout the diurnal cycle at various spatial locations within the CSP plant. In our view, this first-of-a-kind study will provide important guidance for future trough designs that reduce the impact of various sources of tracking error on performance.
Jet impingement cooling of a hypersonic airfoil leading edge is experimentally investigated using thermochromic liquid crystals (TLCS) to measure surface temperature. The experiment uses computer data acquisition with digital imaging of the TLCs to determine heat transfer coefficients during a transient experiment. The data reduction relies on analysis of a coupled transient conduction - convection heat transfer problem that characterizes the experiment. The recovery temperature of the jet is accounted for by running two experiments with different heating rates, thereby generating a second equation that is used to solve for the recovery temperature. The resulting solution requires a complicated numerical iteration that is handled by a computer. Because the computational data reduction method is complex, special attention is paid to error assessment. The error analysis considers random and systematic errors generated by the instrumentation along with errors generated by the approximate nature of the numerical methods. Results of the error analysis show that the experimentally determined heat transfer coefficients are accurate to within 15%. The error analysis also shows that the recovery temperature data may be in error by more than 50%. The results show that the recovery temperature data is only reliable when the recovery temperature of the jet is greater than 5 C, i.e. the jet velocity is in excess of 100 m/s. Parameters that were investigated include nozzle width, distance from the nozzle exit to the airfoil surface, and jet velocity. Heat transfer data is presented in graphical and tabular forms. An engineering analysis of hypersonic airfoil leading edge cooling is performed using the results from these experiments. Several suggestions for the improvement of the experimental technique are discussed.
A prescription is given for conservatively integrating generalized hydromagnetic equations using flux-corrected transport (FCT) techniques. By placing the magnetic-field components at the interface locations of the finite-difference grid, the field is kept divergence-free to within machine roundoff error. The use of FCT techniques allows an integration scheme of high accuracy to be employed, while the numerical ripples associated with large dispersion errors are avoided. The method is particularly well suited for problems involving magnetohydrodynamic shocks and other discontinuities.
In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.
In many situations, the dual-purpose heater/thermometer wires used in the three-omega method – one of the most precise and sensitive techniques for measuring the thermal conductivity of thin films and interfaces – must include bends and curves to avoid obstructions on the surface of a sample. Although the three-omega analysis assumes that the heating wire is infinitely long and straight, recent experimental work has demonstrated that in some cases curved-wire geometries can be used without introducing detectable systematic error. We describe a general numerical method that can be used to calculate the temperature of three-omega heating wires with arbitrary wire geometries. Furthermore, this method provides experimentalists with a simple quantitative procedure for calculating how large the systematic error caused by a particular wire asymmetry will be. We show calculations of two useful cases: a straight wire with a single bend of arbitrary angle and a wire that forms a circle. We find that the amplitude of the in-phase temperature oscillations near a wire that forms a circle differs from the prediction using the analytic straight-line source solution by <12%, provided that the thermal penetration depth is less than ten times the radius of curvature of the wire path. The in-phase temperature amplitude 1.5 wire widths away from a 90° bend in a wire is within 11% of the straight-line source prediction for all penetration depths greater than the wire width. Our calculations indicate that the straight-line source solution breaks down significantly when the wire bend angle is less than 45°.