Search NASA⌕ Search

SEARCH · Search NASA

Results for “Corrected equation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Undersizing of aged African biomass burning aerosol by an ultra-high-sensitivity aerosol spectrometer

The ultra-high-sensitivity aerosol spectrometer (UHSAS) differs from most other optical particle spectrometers by using a high-power infrared (IR) laser to detect small particles and reduce the sizing ambiguity due to the non-monotonicity of scattering with particle size. During the NASA ORACLES project (ObseRvations of Aerosols above CLouds and their intEractionS) over the southeast Atlantic Ocean, the UHSAS clearly undersized particles in the biomass burning plume extending from southern Africa. Since the horizontal and vertical extent of the plume was vast, the NASA P-3B research aircraft often flew through a fairly uniform biomass burning plume for periods exceeding 30 min, sufficient time to explore the details of the UHSAS response by selecting single particle sizes with a differential mobility analyzer (DMA) and passing them to the UHSAS. This was essentially an in-flight calibration of the UHSAS using the particles of interest. Two modes of responses appeared. Most particles were undersized by moderate amounts, ranging from not at all for 70 nm aerosols to 15 % for 280 nm particles. Mie scattering calculations show that composition-dependent refractive index of the particles cannot explain the pattern. Heating of brown carbon or tarballs in the beam causing evaporation and shrinking of the particles is the most plausible explanation, though mis-sizing due to non-sphericity cannot be ruled out. A small fraction (10 %–30 %) of the particles were undersized by 25 % to 35 %. Those were apparently the particles containing refractory black carbon. Laboratory calibrations confirm that black carbon is drastically undersized by the UHSAS, because particles heat to their vaporization point and shrink. A simple empirical correction equation was implemented that dramatically improves agreement with DMA distributions between 100 and 500 nm. It raised the median particle diameter by 18 nm, from 163 to 181 nm, during the August 2017 deployment and by smaller amounts during deployments with less intense pollution. Calculated scattering from UHSAS size distributions increased by about 130 %, dramatically improving agreement with scattering measured by nephelometers. The correction is only valid in polluted instances; clean marine boundary layer and free troposphere aerosols behaved more like the calibration spheres. We were unable to directly test the correction between 500 and 1000 nm, though aerodynamic particle sizer (APS) data appear to show that the correction is poor at the largest diameters, which is no surprise as the composition of those particles is likely to be quite different than that of the accumulation mode. This adds to the evidence that UHSAS data must be treated cautiously whenever the aerosol may absorb infrared light. Similar corrections may be required whenever brown carbon aerosol is present.

54 ENVIRONMENTAL SCIENCES↗

An Argument Against Augmenting the Lagrangean for Nonholonomic Systems

Although it is known that correct dynamical equations of motion for a nonholonomic system cannot be obtained from a Lagrangean that has been augmented with a sum of the nonholonomic constraint equations weighted with multipliers, previous publications suggest otherwise. An example has been proposed in support of augmentation and purportedly demonstrates that an accepted method fails to produce correct equations of motion whereas augmentation leads to correct equations; this paper shows that in fact the opposite is true. The correct equations, previously discounted on the basis of a flawed application of the Newton-Euler method, are verified by using Kane's method and a new approach to determining the directions of constraint forces. A correct application of the Newton-Euler method reproduces valid equations.

Roithmayr, Carlos M.↗

Erratum: “Adiabatic matching of particle bunches in a plasma-based accelerator in the presence of ion motion” [Phys. Plasmas 28 , 053102 (2021)]

We would like to correct an error affecting the horizontal scale of panels (c) and (d) of Fig. 4 in Ref. 1. A scale factor of k p was neglected when generating the plots. The correct figure is shown below. Further, the authors would like to thank Yujian Zhao for pointing out this issue. We would also like to correct a typo introduced during the preparation of the proofs and affecting Eq. (25); the correct equation reads. (Formula presented). All the conclusions of the paper are unaffected.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electrolyte concentration changes during operation of the nickel cadmium cell

The concentration and distribution of aqueous potassium hydroxide (KOH) electrolyte in a sealed nickel cadmium cell is considered. The reactions at both electrodes during charge and discharge involve the production or utilization of hydroxyl ion (OH) or water (H2O) which directly affects concentration. Changes in electrolyte concentration relative to the individual electrode reactions is discussed. Quantitative values are provided for the changes in concentration for 6, 12, and 20 ah cells with accepted quantities of precharge and accepted initial quantity of 31% aqueous KOH. Consideration is given to a more correct equation which includes net changes in hydroxyl concentration in addition to water. Also, expected concentrations of electrolyte in cells in the fully charged, 75% charged, 50% charged, 25% charged and discharged condition are calculated. The expected concentration changes for cells in the accelerated tests are also tabulated and compared with measured values. All calculations are made on the assumption that there are no side reactions. Various properties which depend on KOH concentration are listed. The variables include O2, H2, and Cd(OH)2 solubilities in addition to viscosity and conductivity.

Halpert, G.↗

Influence of stress interaction on the behavior of off-axis unidirectional composites

The yield function for plane stress of a transversely isotropic composite lamina consisting of stiff, linearly elastic fibers and a von Mises matrix material is formulated in terms of Hill's elastic stress concentration factors and a single plastic constraint parameter. The above are subsequently evaluated on the basis of observed average lamina and constituent response for the Avco 5505 boron epoxy system. It is shown that inclusion of residual stresses in the yield function together with the incorporation of Dubey and Hillier's concept of generalized yield stress for anisotropic media in the constitutive equation correctly predicts the trends observed in experiments. The incorporation of the strong axial stress interaction necessary to predict the correct trends in the shear response is directly traced to the high residual axial stresses in the matrix induced during fabrication of the composite.

Pindera, M. J.↗

Bubble migration in a rotating, liquid-filled sphere

Results and analysis of ground-based experiments performed to aid in designing experiments on the behavior of bubbles in a rotating liquid body on board the Shuttle in free fall are presented. Spherical shells filled with silicone oil containing a small gas bubble were spun and filmed by high speed motion picture photography. The rotation of the shell and the trajectory of the bubble motion were recorded and the film was exposed to a motion analyzer connected to a keypunch. The analyzer measured Cartesian coordinates as well as angle, frame number, and rotation rate. Optical correction equations were employed to determine the apparent bubble trajectory relative to an inertial frame of reference. An analytical model for the bubble motion was defined, yielding predictions of velocity and position at different times. Rotation of the fluid container is concluded to aid in centering the bubbles.

Annamalai, P.↗

Remotely sensed sea surface temperature variability off California during a 'Santa Ana' clearing

Multichannel atmospheric correction equations for the NOAA 6 proposed by Bernstein (1982) and by McClain (1981) are evaluated by using satellite and in situ data collected over and in the Southern California Bight. The temporal and spatial variation of sea surface temperature over small scales is estimated from the data, and the effect of this variation in matching satellite and in situ data sets is discussed. Changes in the temperature fields between images are examined for diurnal variation and for surface advection of horizontal temperature gradients.

Lynn, R. J.↗

Flux-limited diffusion in hydrodynamics

The radiation transport equation, correct to order v/c, is used to derive a flux limiter valid in high-velocity hydrodynamic flows. In the limit v = 0 the widely used result of Levermore and Pomraning (LP) (1982) is recovered. In the case of homologous flow (v varies as R) the LP result remains valid, but in the presence of shock waves and other nonhomologous flows differences may be large. We calculate the Eddington factors, which are significantly altered, and discuss the importance of having them possess the correct form in the presence of a shock wave, e.g., on the neutrino transport during the formation of a supernova.

Cooperstein, J.↗

Theoretical rocket performance of JP-4 fuel with mixtures of liquid ozone and fluorine

Data were estimated by means of a heat correction equation using data for JP-4 fuel with mixtures of oxygen and flourine. The estimated data were checked for several cases by direct calculations. The difference in specific impulse between the estimated and directly calculated values was from 0.2 to 0.8 pound-second per pound. The maximum value of specific impulse was 334.9 pound-seconds per pound for a combustion-chamber pressure of 600 pounds per square inch absolute and an exit pressure of 1 atmosphere.

Huff, Vearl N↗

Multiparameter linear least-squares fitting to Poisson data one count at a time

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

Wheaton, Wm. A.↗

Simulation of Acoustic Scattering from a Trailing Edge

Three model problems were examined to assess the difficulties involved in using a hybrid scheme coupling flow computation with the the Ffowcs Williams and Hawkings equation to predict noise generated by vortices passing over a sharp edge. The results indicate that the Ffowcs Williams and Hawkings equation correctly propagates the acoustic signals when provided with accurate flow information on the integration surface. The most difficult of the model problems investigated inviscid flow over a two-dimensional thin NACA airfoil with a blunt-body vortex generator positioned at 98 percent chord. Vortices rolled up downstream of the blunt body. The shed vortices possessed similarities to large coherent eddies in boundary layers. They interacted and occasionally paired as they convected past the sharp trailing edge of the airfoil. The calculations showed acoustic waves emanating from the airfoil trailing edge. Acoustic directivity and Mach number scaling are shown.

Singer, Bart A.↗

Cerium Stable Isotope Analysis of Synthetic and Terrestrial Rock Reference Materials by MC-ICPMS

Cerium is the most abundant rare earth element (REE) in the solar photosphere, CI chondrites, and the Earth. It has four main stable isotopes (masses: 136,138,140, and 142), with 138Ce being the most studied species, used in geochronology and petrogenesis. In addition, more abundant 140Ce and 142Ce are suggested to be potentially applicable in geochemical investigations. In this work, we developed a modified four-step ion chromatography procedure for Ce chemical separation. Using a MC-ICPMS, we designed a cup configuration to measure 142Ce/140Ce ratio of the samples with an optimized Nd correction equation. A 0.03‰ (2SD) reproducibility was obtained for Ce Ames metal standard. We analyzed ten different igneous and one sedimentary geochemical reference materials. Mean δ142Ce range from −0.07 to 0.32‰. Most of the samples show a heavier Ce isotopic composition than the Ce Ames standard. The majority of rocks have a homogenous δ142Ce. The δ142Ce does not show any correlation with rock chemical composition including their Ce content or rock types. A carbonatite (SARM 40) has a mean δ142Ce of −0.07 ± 0.13‰ (2SD), lower than the other rocks, suggesting the possibility of a pronounced isotopic fractionation. Our work demonstrates the applicability of the developed methodology and the potential of Ce stable isotopes for future geochemical studies. Production of a larger database of δ142Ce values is required to obtain a clearer view on the similarities and differences between different geological material and explaining Ce stable isotope dynamics.

Cerium↗

Correction function in the Lidar equation and the solution techniques for CO2 Lidar date reduction

For lidar systems with long laser pulses the unusual behavior of the near-range signals causes serious difficulties and large errors in reduction. The commonly used lidar equation is no longer applicable since the convolution of the laser pulse with the atmospheric parameter distributions should be taken into account. It is important to give more insight into this problem and find the solution techniques. Starting from the original equation, a general form is suggested for the single scattering lidar equation where a correction function Cr is introduced. The correction Function Cr(R) derived from the original equation indicates the departure from the normal lidar equation. Examples of Cr(R) for a coaxial CO2 lidar system are presented. The Differential Absorption Lidar (DIAL) errors caused by the differences of Cr(R) for H2O measurements are plotted against height.

Zhao, Y.↗

An O(Nm(sup 2)) Plane Solver for the Compressible Navier-Stokes Equations

A hierarchical multigrid algorithm for efficient steady solutions to the two-dimensional compressible Navier-Stokes equations is developed and demonstrated. The algorithm applies multigrid in two ways: a Full Approximation Scheme (FAS) for a nonlinear residual equation and a Correction Scheme (CS) for a linearized defect correction implicit equation. Multigrid analyses which include the effect of boundary conditions in one direction are used to estimate the convergence rate of the algorithm for a model convection equation. Three alternating-line- implicit algorithms are compared in terms of efficiency. The analyses indicate that full multigrid efficiency is not attained in the general case; the number of cycles to attain convergence is dependent on the mesh density for high-frequency cross-stream variations. However, the dependence is reasonably small and fast convergence is eventually attained for any given frequency with either the FAS or the CS scheme alone. The paper summarizes numerical computations for which convergence has been attained to within truncation error in a few multigrid cycles for both inviscid and viscous ow simulations on highly stretched meshes.

Thomas, J. L.↗

Leptodermic corrections to the TOV equations and nuclear astrophysics within the effective surface approximation

The macroscopic model for a neutron star (NS) as a liquid drop at the equilibrium is used to extend the Tolman-Oppenheimer-Volkoff (TOV) equations taking into account the gradient terms responsible for the system surface. The parameters of the Schwarzschild metric in the spherical case are found with these surface corrections to the known leading (zero) order of the leptodermic approximation a/R << 1, where a is the NS effective-surface (ES) thickness, and R is the effective NS radius. The energy density $\mathscr{E}$ is considered in a general form including the functions of the particle number density and of its gradient terms. The macroscopic gravitational component $Φ$(ρ) of the energy density is taken into account in the simplest form as expansion in powers of $ρ$ – $\overline{ρ}$, where $\overline{ρ}$ is the saturation density, up to second order, in terms of its contributions to the separation particle energy and incompressibility. Density distributions ρ across the NS ES in the normal direction to the ES, which are derived in the simple analytical form at the same leading approximation, was used for the derivation of the modified TOV (MTOV) equations by accounting for their NS surface corrections. As a result, the MTOV equations are analytically solved at first order and the results are compared with the standard TOV approach of the zero order.

Magner, A. G. [Institute for Nuclear Research, Kyi↗

A simple improved low temperature correction for the hierarchical equations of motion

The study of open system quantum dynamics has been transformed by the hierarchical equations of motion (HEOM) method, which gives the exact dynamics for a system coupled to a harmonic bath at arbitrary temperature and system–bath coupling strength. However, in its standard form, this method is only consistent with the weak-coupling quantum master equation at all temperatures when many auxiliary density operators are included in the hierarchy, even when low temperature corrections are included. Here, we propose a new low temperature correction scheme for the termination of the hierarchy based on Zwanzig projection, which alleviates this problem and restores consistency with the weak-coupling master equation with a minimal hierarchy. The utility of the new correction scheme is demonstrated on a range of model systems, including the Fenna–Matthews–Olson complex. The new closure is found to improve convergence of the HEOM even beyond the weak-coupling limit and is very straightforward to implement in existing HEOM codes.

Fay, Thomas P. (ORCID:000000030625731X)↗