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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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NASA NTRS2023

Simulations of 7 Be and 10 Be with the GEOS-Chem global model v14.0.2 using state-of-the-art production rates

The cosmogenic radionuclides 7 Be and 10 Be are useful aerosol tracers for atmospheric transport studies. Combining 7 Be and 10 Be measurements with an atmospheric transport model can not only improve our understanding of the radionuclide transport and deposition processes but also provide an evaluation of the transport process in the model. To simulate these aerosol tracers, it is critical to evaluate the influence of radionuclides production uncertainties on simulations. Here we use the GEOS-Chem chemical transport model driven by the MERRA-2 reanalysis to simulate 7 Be and 10 Be with different production scenarios: the default production rate in GEOS-Chem based on an empirical approach (Lal and Peters, 1967; denoted as LP67), and two production rates from the CRAC:Be (Cosmic Ray Atmospheric Cascade: Beryllium; Poluianov et al., 2016) model considering only geomagnetic cut-off rigidities for a geocentric axial dipole (denoted as P16) or realistic spatial geomagnetic cut-off rigidity variations due to non-dipole moments of the geomagnetic field (denoted as P16spa). The model results are comprehensively evaluated with a large number of measurements including surface air concentrations and deposition fluxes. The model with the P16spa production can reproduce the absolute values and temporal variability of 7 Be and 10 Be surface concentrations and deposition fluxes on annual and sub-annual scales, as well as the vertical profiles of air concentrations. Simulations with the LP67 production tend to overestimate the absolute values of 7 Be and 10 Be concentrations. The P16 simulations suggest less than 10% differences compared to P16spa but tend to produce a significant positive bias (>20%) in the 7 Be deposition fluxes over East Asia. We find that the deposition fluxes are more sensitive to the production in the troposphere and downward transport from the stratosphere. Independent of the production models, surface air concentrations and deposition fluxes from all simulations show similar seasonal variations, suggesting a dominant meteorological influence. The model can also simulate reasonably the stratosphere-troposphere exchange process of 7 Be and 10 Be by producing stratospheric contribution and 10 Be/ 7 Be ratio values that agree with measurements. Finally, we illustrate the importance of including the time-varying solar modulation in the production calculation, which can significantly improve the agreement between model results and measurements, especially at mid- and high- latitudes. Reduced uncertainties in the production rates, as demonstrated in this study, improve the utility of 7 Be and 10 Be as aerosol tracers for evaluating and testing transport and scavenging processes in global models.

Minjie Zheng↗
NASA NTRS1972

SYMAT, COVAR: Test Procedures for Matrix Calculations

The FORTRAN subroutine SYMAT and related subroutines are described. In essence SYMAT is an iterative algorithm in which the problem of finding eigenvalues and eigenvectors of a real symmetric matrix is transformed into an equivalent problem of finding eigenvalues and eigenvectors of an infinite sequence of matrices of order two. A DEMO PROGRAM contains a subroutine COVAR which is used to compute the covariance matrix (denoted by A) of a data matrix (denoted by X). Since a covariance matrix is symmetric it can be analyzed by using subroutine SYMAT.

Morris, W. L.↗
NASA NTRS1978

Effects of atmospheric structure on radiative heating for Jupiter entry probe

New estimates of the radiative heat load to a Jupiter entry probe have been obtained for revised models of Jupiter's atmosphere based on the latest data from Pioneer 10 and 11 missions and earth-based experiments. The new estimates of the radiative heat load are compared with results obtained for the previous atmospheric models. The changes in Jupiter's atmospheric models cause a substantial reduction in the radiative heat load for the atmosphere denoted as 'cool', but only moderate reductions for the atmospheres denoted as 'nominal' and 'warm'. Results are also presented showing the effects of inertial entry angle for off-equatorial entries in the revised model atmospheres.

Sutton, K.↗
NASA NTRS1979

The condition of a finite Markov chain and perturbation bounds for the limiting probabilities

The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms.

Meyer, C. D., Jr.↗
NASA NTRS1984

The Laplacian resonance and tidal dissipation

The Laplacian resonance amongst Io, Europa, and Ganymede was examined, taking into account tidal dissipation in Jupiter, Io and Europa. In equilibrium, it is not possible to neglect dissipation in Europa nor the torques of Jupiter on Europa and Ganymede. A formal calculation was made on the assumption that the tidal torques and the torques in orbit-orbit resonance reached an equilibrium such that the rates of decrease of the mean motions of the satellites are in the ratios 4:2:1. Q(j)/k(j)=167 Q(1)/k(1), Q(2)/k(2) = 0.44 Q(1)/K(1), where Q denotes the quality at the body's frequency of rotation, k its second degree Love number and the subscripts J, 1 and 2 denote Jupiter, Io, and Europa. The Q(J) found is at Jupiter's frequency of rotation. The rate of tidal dissipation in Europa comes to 1/5 that of Io. Such a low value of Q(2)/K(2) is plausible if dissipation in both Io and Europa is due to tidal friction in fluid against underlying and overlying solid layers.

Cook, A. F.↗
NASA NTRS1985

The natural angular momentum distribution in the study of thick disks around black holes

The thick-disk model is reviewed with an angular momentum distribution chosen to have a power-law relation with the von Zeipel parameter lambda = sq rt(l/Omega), where l denotes the specific angular momentum and Omega denotes the angular velocity. This choice permits the integration of the relativistic Euler equation independent of the background geometry. The consequences with regard to the Schwarzschild and Kerr black-hole geometries are briefly investigated.

Chakrabarti, S. K.↗
NASA NTRS1985

Solar activity and modulation of the cosmic ray intensity

Since its discovery by Forbush (1954), the 11-year cycle modulation of the cosmic ray intensity has been studied extensively. Bowe and Hatton (1982) obtained a well-behaved transfer function F between the solar activity S and the cosmic ray intensity modulation Io-I. They suggested that the 11-year variation for sunspot cycle 20 can be attributed to the modulating effect of solar flare-induced shocks propagating through the heliosphere. The cosmic ray intensity in the absence of solar activity is denoted by Io, while I denotes the observed intensity. Bowe and Hatton infer that the boundary of the heliosphere is located at a distance of 70-90 AU. Since their conclusion is of great importance in understanding the mechanism of the 11-year modulation, the present investigation is concerned with a repetition of their study for two cycles, taking into account the use of a slightly modified method. The obtained results confirm the conclusions reached by Bowe and Hatton that there is a well-behaved transfer function for solar flares.

Akasofu, S.-I.↗
NASA NTRS1988

Rational-Spline Subroutines

Smooth curves drawn among plotted data easily. Rational-Spline Approximation with Automatic Tension Adjustment algorithm leads to flexible, smooth representation of experimental data. "Tension" denotes mathematical analog of mechanical tension in spline or other mechanical curve-fitting tool, and "spline" as denotes mathematical generalization of tool. Program differs from usual spline under tension, allows user to specify different values of tension between adjacent pairs of knots rather than constant tension over entire range of data. Subroutines use automatic adjustment scheme that varies tension parameter for each interval until maximum deviation of spline from line joining knots less than or equal to amount specified by user. Procedure frees user from drudgery of adjusting individual tension parameters while still giving control over local behavior of spline.

Schiess, James R.↗
NASA NTRS1987

Third and higher harmonic plasma emission due to Raman scattering

The theory for third and higher harmonic plasma emission by the weak turbulence (or random phase) process L + T prime to T (where L denotes a Langmuir wave, and T and T prime denote transverse waves) is developed. Kinematic constraints on the characteristics and growth lengths of waves participating in the wave processes are identified. The cases of L waves produced either directly by a streaming instability, or by the decay L to L prime + S (S is an ion sound wave) of L waves generated by a streaming instability, are considered. Limits on the brightness temperature of the radiation are determined, and expressions for the growth rate and path-integrated wave temperatures are derived.

Cairns, Iver H.↗
NASA NTRS1989

Querying databases of trajectories of differential equations: Data structures for trajectories

One approach to qualitative reasoning about dynamical systems is to extract qualitative information by searching or making queries on databases containing very large numbers of trajectories. The efficiency of such queries depends crucially upon finding an appropriate data structure for trajectories of dynamical systems. Suppose that a large number of parameterized trajectories gamma of a dynamical system evolving in R sup N are stored in a database. Let Eta is contained in set R sup N denote a parameterized path in Euclidean Space, and let the Euclidean Norm denote a norm on the space of paths. A data structure is defined to represent trajectories of dynamical systems, and an algorithm is sketched which answers queries.

Grossman, Robert↗
NASA NTRS1989

Optimal trajectories for the aeroassisted flight experiment

The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. The intent of this experiment is to simulate a GEO-to-LEO transfer, where GEO denotes a geosynchronous earth orbit and LEO denotes a low earth orbit. The trajectories of an AFE spacecraft are analyzed in a 3D-space, employing the full system of 6 ordinary differential equations (ODEs) describing the atmospheric pass. The atmospheric entry conditions are given, and the atmospheric exit conditions are adjusted. Two possible transfers are considered: (1) indirect ascent to a 178 NM perigee via a 197 NM apogee; and (2) direct ascent to a 178 NM apogee.

Miele, A.↗
NASA NTRS1989

Optimal trajectories for the aeroassisted flight experiment. Part 3: Formulation, results, and analysis

The determination of optimal trajectories for the aero-assisted flight experiment (AFE) is investigated. The intent of this experiment is to simulate a GEO-to-LEO transfer, where GEO denotes a geosynchronous Earth orbit and LEO denotes a low Earth orbit. The trajectories of an AFE spacecraft are analyzed in a 3D-space, employing the full system of 6 ODEs describing the atmospheric pass. The atmospheric entry conditions are given, and the atmospheric exit conditions are adjusted in such a way that the following conditions are satisfied: (1) the atmospheric velocity depletion is such that, after exiting, the AFE spacecraft first ascends to a specified apogee and then descends to a specified perigee; and (2) the exit orbital plane is identical with the entry orbital plane. The final maneuver, not analyzed here, includes the rendezvous with and the capture by the space shuttle.

Miele, A.↗
NASA NTRS1990

Trees, bialgebras and intrinsic numerical algorithms

Preliminary work about intrinsic numerical integrators evolving on groups is described. Fix a finite dimensional Lie group G; let g denote its Lie algebra, and let Y(sub 1),...,Y(sub N) denote a basis of g. A class of numerical algorithms is presented that approximate solutions to differential equations evolving on G of the form: dot-x(t) = F(x(t)), x(0) = p is an element of G. The algorithms depend upon constants c(sub i) and c(sub ij), for i = 1,...,k and j is less than i. The algorithms have the property that if the algorithm starts on the group, then it remains on the group. In addition, they also have the property that if G is the abelian group R(N), then the algorithm becomes the classical Runge-Kutta algorithm. The Cayley algebra generated by labeled, ordered trees is used to generate the equations that the coefficients c(sub i) and c(sub ij) must satisfy in order for the algorithm to yield an rth order numerical integrator and to analyze the resulting algorithms.

Crouch, Peter↗
NASA NTRS1991

Querying databases of trajectories of differential equations 2: Index functions

Suppose that a large number of parameterized trajectories (gamma) of a dynamical system evolving in R sup N are stored in a database. Let eta is contained R sup N denote a parameterized path in Euclidean space, and let parallel to center dot parallel to denote a norm on the space of paths. A data structures and indices for trajectories are defined and algorithms are given to answer queries of the following forms: Query 1. Given a path eta, determine whether eta occurs as a subtrajectory of any trajectory gamma from the database. If so, return the trajectory; otherwise, return null. Query 2. Given a path eta, return the trajectory gamma from the database which minimizes the norm parallel to eta - gamma parallel.

Grossman, Robert↗
NASA NTRS1990

Evaluating the effect of accuracy ratios on the percent of calibrations which are out of tolerance

The standard practice in calibration laboratories across the country, including the Measurement Standards and Calibration Laboratory (MSCL) at the Johnson Space Center, is to use accuracy ratios to determine if instruments are in-tolerance rather than computing the actual uncertainty associated with the instruments. In the past, the accepted practice was to use an accuracy ratio of 10:1, but then state of the art advanced to the point where the 10:1 ratio could no longer be maintained, and the ratio was arbitrarily lowered to 4:1. It is now becoming increasingly difficult to maintain the 4:1 accuracy ratio, and in some cases 1:1 is the best that can be achieved. However, the effect of using these small accuracy ratios on the number of mistakes made in classifying instruments as in or out of tolerance is completely unknown. In order to assess the effect of using accuracy ratios in calibration, a simulation program was written to compute the proportion of instruments determined to be out of tolerance which were actually in, denoted by alpha, and the proportion of instruments determined to be in-tolerance which were actually out, denoted by beta. This was done for accuracy ratios of 1:1 and 10:1, for one to five progressive calibrations, under varying standard and instrument conditions. Selected results are presented and explained.

Navard, Sharon E.↗
NASA NTRS1991

Bialgebra deformations and algebras of trees

Let A denote a bialgebra over a field k and let A sub t = A((t)) denote the ring of formal power series with coefficients in A. Assume that A is also isomorphic to a free, associative algebra over k. A simple construction is given which makes A sub t a bialgebra deformation of A. In typical applications, A sub t is neither commutative nor cocommutative. In the terminology of Drinfeld, (1987), A sub t is a quantum group. This construction yields quantum groups associated with families of trees.

Grossman, Robert↗
NASA NTRS1993

Study Of Compressibility Corrections To Turbulence Models

Effects on shear layers in simulated confined and unconfined flows studied. Report presents comparative study of some terms that correct for effects of compressibility in standard k-epsilon mathematical model of turbulence where k denotes turbulence kinetic energy and epsilon denotes rate of dissipation of turbulence kenetic energy. Involved simulation of flows by numerical solution of Reynolds-averaged Navier-Stokes equations.

Viegas, J. R.↗
NASA NTRS1924

Tests on a model of the D.F.W. airplane T-29 of the "Deutsche Flugzeug derke" (German airplane works)

Experiments similar to those carried out with the A.E.G (Allgemeine Elektrizitats-Gesellschaft) were made in the small wind tunnel of the Gottingen laboratory on a model of the D.F.W. airplane T-29. Three series of tests were carried out on the model with a velocity head (or dynamic pressure) of 5 kg/sq m (1.02 lb/sq ft), during which one of the movable surfaces was deflected at various angles, while both the others were retained in their central positions. Of special interest among the results of the tests is the different run of the elevating moments. The curves for the A.E.G. model, rising to the right, denote stability with the elevator locked, while the slight inclination to the left with the D.F.W model denotes a slight instability. For the maximum C(sub L) values, the stability of A.E.G. model continues to increase and the instability of the D.F.W. model is converted into stability. The rolling moments shown when the angular deflection of the ailerons is 0 degrees are due, in both series of tests, to the unequal distribution of the air velocity over the cross section of the wind tunnel, rather than to a lack of symmetry in the model.

Molthan, Wilhelm↗