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NASA NTRS1992

Breccia dikes from the Beaverhead Impact structure, southwest Montana

While shatter cones are generally accepted as indicators of meteorite impact, older petrologic features are not widely recognized in the geologic community. Breccia dikes are one such feature. They are found in many large impact structures occurring over an area at least as extensively as shatter cones. Breccia dikes will survive moderate degrees of metamorphism and tectonism, unlike many other microscopic features (shocked quartz grains, high-pressure polymorphs, etc.) and even large-scale features such as annular or bowl-shaped topographic features. Thus, they are important diagnostic criteria, especially for large, poorly preserved impact structures. The Beaverhead Impact structure is a recently discovered, deeply eroded impact structure in southwestern Montana. The remains of the structure are delineated by the occurrence of shatter cones, found in an area greater than 200 sq km, occurring within the Cabin thrust plate, part of the Cretaceous Sevier fold and thrust system. The distribution of shatter cones is further truncated by Tertiary normal faults. The present remains represent an allochthonous fragment of a larger structure.

Fiske, P. S.↗

NASA NTRS1982

Computer modeling of multiple-channel input signals and intermodulation losses caused by nonlinear traveling wave tube amplifiers

The multiple channel input signal to a soft limiter amplifier as a traveling wave tube is represented as a finite, linear sum of Gaussian functions in the frequency domain. Linear regression is used to fit the channel shapes to a least squares residual error. Distortions in output signal, namely intermodulation products, are produced by the nonlinear gain characteristic of the amplifier and constitute the principal noise analyzed in this study. The signal to noise ratios are calculated for various input powers from saturation to 10 dB below saturation for two specific distributions of channels. A criterion for the truncation of the series expansion of the nonlinear transfer characteristic is given. It is found that he signal to noise ratios are very sensitive to the coefficients used in this expansion. Improper or incorrect truncation of the series leads to ambiguous results in the signal to noise ratios.

Stankiewicz, N.↗

NASA NTRS1993

Development of a recursion RNG-based turbulence model

Reynolds stress closure models based on the recursion renormalization group theory are developed for the prediction of turbulent separated flows. The proposed model uses a finite wavenumber truncation scheme to account for the spectral distribution of energy. In particular, the model incorporates effects of both local and nonlocal interactions. The nonlocal interactions are shown to yield a contribution identical to that from the epsilon-renormalization group (RNG), while the local interactions introduce higher order dispersive effects. A formal analysis of the model is presented and its ability to accurately predict separated flows is analyzed from a combined theoretical and computational stand point. Turbulent flow past a backward facing step is chosen as a test case and the results obtained based on detailed computations demonstrate that the proposed recursion -RNG model with finite cut-off wavenumber can yield very good predictions for the backstep problem.

Zhou, YE↗

NASA NTRS1982

Global-scale weekly and monthly energetics during January and February 1979

Time averages of the latitudinal distribution of kinetic energy and terms of the kinetic energy equation are presented as depicted by analyses of the First GARP Global Experiment during the First Special Observing Period. It is found that the monthly averages exhibit peaks in the stationary wave energy at 30 degrees N and in the tropics, while global decompositions of the streamfunction and velocity potential in spherical harmonics are truncated at the fourth degree. The kinetic energy distribution of the associated wind field displays peaks in the tropics and northern mid-latitudes in January, but only a tropical peak in February. These analyses support the Eliassen-Palm relationship for latitudinal momentum and geopotential wave transport, particularly in the mid-latitudes. However, in the deep tropics, latitudinal convergence of the fully resolved stationary wave momentum transport accompanies latitudinal convergence of stationary wave geopotential flux in westerly flow.

Paegle, J.↗

NASA NTRS1993

Probability of lensing magnification by cosmologically distributed galaxies

We present the analytical formulae for computing the magnification probability caused by cosmologically distributed galaxies. The galaxies are assumed to be singular, truncated-isothermal spheres without both evolution and clustering in redshift. We find that, for a fixed total mass, extended galaxies produce a broader shape in the magnification probability distribution and hence are less efficient as gravitational lenses than compact galaxies. The high-magnification tail caused by large galaxies is well approximated by an A exp -3 form, while the tail by small galaxies is slightly shallower. The mean magnification as a function of redshift is, however, found to be independent of the size of the lensing galaxies. In terms of the flux conservation, our formulae for the isothermal galaxy model predict a mean magnification to within a few percent with the Dyer-Roeder model of a clumpy universe.

Pei, Yichuan C.↗

NASA NTRS1974

Approach to the origin of turbulence on the basis of two-point kinetic theory

Equations for the fluctuation correlation in an incompressible shear flow are derived on the basis of kinetic theory, utilizing the two-point distribution function which obeys the BBGKY hierarchy equation truncated with the hypothesis of 'ternary' molecular chaos. The step from the molecular to the hydrodynamic description is accomplished by a moment expansion which is a two-point version of the thirteen-moment method, and which leads to a series of correlation equations, viz., the two-point counterparts of the continuity equation, the Navier-Stokes equation, etc. For almost parallel shearing flows the two-point equation is separable and reduces to two Orr-Sommerfeld equations with different physical implications.

Tsuge, S.↗

NASA NTRS1981

The effects of missing data on global ozone estimates

The effects of missing data and model truncation on estimates of the global mean, zonal distribution, and global distribution of ozone are considered. It is shown that missing data can introduce biased estimates with errors that are not accounted for in the accuracy calculations of empirical modeling techniques. Data-fill techniques are introduced and used for evaluating error bounds and constraining the estimate in areas of sparse and missing data. It is found that the accuracy of the global mean estimate is more dependent on data distribution than model size. Zonal features can be accurately described by 7th order models over regions of adequate data distribution. Data variance accounted for by higher order models appears to represent climatological features of columnar ozone rather than pure error. Data-fill techniques can prevent artificial feature generation in regions of sparse or missing data without degrading high order estimates over dense data regions.

Drewry, J. W.↗

NASA NTRS1992

Microbeam studies of the sensitivity of structures within living cells

Determining the biological effects of low doses of radiation with high linear energy transfer (LET) is complicated by the stochastic nature of charged-particle interactions. Populations of cells exposed to very low radiation doses contain a few cells which have been hit by a charged particle, while the majority of the cells receive no radiation damage. At somewhat higher doses, a few cells receive two or more events. Because the effects of damage produced by separate events can interact in the cell, we have had to make assumptions about the nature of these interactions in order to interpret the results of the experiments. Many of those assumptions can be tested if we can be sure of the number of charged-particle events which occur in individual cells, and correlate this number with the biological effect. We have developed a special irradiation facility at Pacific Northwest Laboratory (PNL) to control the actual number of charged particle tracks that pass through cell nuclei. The beam from a 2 MeV tandem accelerator is collimated to approximately 5 microns. Cells, grown in special dishes with 1.5 microns thick plastic bottoms, are positioned so that the desired portion of the cell aligns with the collimator. A shutter in the beam line is opened and closed after the desired number of particle tracks has been counted. This approach can be used to investigate the effects of the interaction between irradiated and unirradiated cells in an organized system, as well as to study the effects of spatial and temporal distribution of radiation damage within single cells.(ABSTRACT TRUNCATED AT 250 WORDS).

Non-NASA Center↗

NASA NTRS1975

High-beta turbulence in two-dimensional magnetohydrodynamics

Incompressible turbulent flows were investigated in the framework of ideal magnetohydrodynamics. Equilibrium canonical distributions are determined in a phase whose coordinates are the real and imaginary parts of the Fourier coefficients for the field variables. The magnetic field and fluid velocity have variable x and y components, and all field quantities are independent of z. Three constants of the motion are found which survive the truncation in Fourier space and permit the construction of canonical distributions with three independent temperatures. Spectral densities are calculated. One of the more novel physical effects is the appearance of macroscopic structures involving long wavelength, self-generated, magnetic fields ("magnetic islands"). In the presence of finite dissipation, energy cascades to higher wave numbers can be accompanied by vector potential cascades to lower wave numbers, in much the same way that in the fluid dynamic case, energy cascades to lower wave numbers accompany entropy cascades to higher wave numbers.

Fyfe, D.↗

NASA NTRS1985

Finite Control in Underdamped Distributed Parameter Systems

Specifically, a class of distributed parameter systems is defined using Hilbert space methods based on a partial differential equation model of a structure. In this space a simple, easy to check definition of underdamping is constructed based on the well known single degree of freedom concept of critical damping. It is then shown that if a given distributed parameter system satisfies this definition, each mode of the modal expansion of the solution is in fact an underdamped function of time. It is noted that a distributed parameter system which is underdamped is also uniformly exponentially stable. By appealing to the work of Gibson, a finite dimensional model of the system will yield satisfactory control laws. Furthermore, it is shown that the assumption of the underdamping also allows straightforward computation of rough bounds on the magnitude of the unmodeled or residual modes for a modal truncation scheme. Hence, underdamped systems are precisely that class of distributed parameter systems which are not likely to have spillover problems and which will yield convergence of finite dimensional control laws to control laws which are optimal for the full distributed parameter model of the system.

Inman, D. J.↗

NASA NTRS2014

Water Delivery and Giant Impacts in the 'Grand Tack' Scenario

A new model for terrestrial planet formation has explored accretion in a truncated protoplanetary disk, and found that such a configuration is able to reproduce the distribution of mass among the planets in the Solar System, especially the Earth/Mars mass ratio, which earlier simulations have generally not been able to match. Walsh et al. tested a possible mechanism to truncate the disk-a two-stage, inward-then-outward migration of Jupiter and Saturn, as found in numerous hydrodynamical simulations of giant planet formation. In addition to truncating the disk and producing a more realistic Earth/Mars mass ratio, the migration of the giant planets also populates the asteroid belt with two distinct populations of bodies-the inner belt is filled by bodies originating inside of 3 AU, and the outer belt is filled with bodies originating from between and beyond the giant planets (which are hereafter referred to as 'primitive' bodies). One implication of the truncation mechanism proposed in Walsh et al. is the scattering of primitive planetesimals onto planet-crossing orbits during the formation of the planets. We find here that the planets will accrete on order 1-2% of their total mass from these bodies. For an assumed value of 10% for the water mass fraction of the primitive planetesimals, this model delivers a total amount of water comparable to that estimated to be on the Earth today. The radial distribution of the planetary masses and the dynamical excitation of their orbits are a good match to the observed system. However, we find that a truncated disk leads to formation timescales more rapid than suggested by radiometric chronometers. In particular, the last giant impact is typically earlier than 20 Myr, and a substantial amount of mass is accreted after that event. This is at odds with the dating of the Moon-forming impact and the estimated amount of mass accreted by Earth following that event. However, 5 of the 27 planets larger than half an Earth mass formed in all simulations do experience large late impacts and subsequent accretion consistent with those constraints.

Planetary dynamics↗

NASA NTRS1983

Scattering of electromagnetic waves from a half space of densely distributed dielectric scatterers

The scattering of a plane wave obliquely incident on a half space of densely distributed spherical dielectric scatterers is studied. The quasi-crystalline approximation is applied to truncate the hierarchy of multiple scattering equations, and the Percus-Yevick and the Verlet-Weis results are used to represent the pair distribution function. The coherent reflected wave is studied with these approximations. The incoherent scattered wave is calculated with the distorted Born approximation. In the low-frequency limit, closed-form expressions are obtained for the effective propagation constants, the coherent reflected wave, and the bistatic scattering coeficients. Results at higher frequencies are calculated numerically. The advantage of the present approach is that, in the low-frequency limit, it reproduces the effects of specular reflection, Fresnel reflection coefficient, Brewster angle, and Clausius-Mosotti relation. In addition to the classical results, the bistatic scattering coefficients are also calculated. The theory is also applied to match backscattering data from dry snow at microwave frequencies.

Tsang, L.↗

NASA NTRS1977

Orbiting molecular-beam laboratory

The composition of the atmosphere within the planned orbital envelope of the Space Shuttle and the velocity necessary to maintain a stable orbit within that envelope provide unique conditions for forming a high-purity, moderate energy beam (about 5 eV) of atomic oxygen. At 500 km, for example, atomic oxygen comprises approximately 90% of the atmosphere. Since the mean thermal speed of the ambient atomic oxygen is substantially less than the orbital speed, a high-purity beam can be generated by sweeping through the gas with a series of beam-forming truncated conical shells. Characteristics of the beam, including energy distribution, flux, and purity variation with orbital altitude and methods for lowering the mean energy, are presented. Gas-surface interaction experiments that have been proposed for this laboratory are also discussed.

Outlaw, R. A.↗

NASA NTRS1985

Parameterization in Grid Generation

The distribution of grid points for calculating the solution of partial differential equations is chosen so as to include consideration of truncation error, stability, and the resolution of the solution near boundary layers and shocks. It is important to specify the distribution of points along a grid line. The problem of distributing points along a curve is considered. It is assumed that the curve is defined parametrically. The objective is to select a set of parameter values so that the corresponding points on the curves are properly distributed. The distribution is based on some intrinsic property of the curve such as arc length or curvature.

Mastin, C. W.↗

NASA NTRS1985

Composition of cosmic-ray nuclei from boron to nickel for 1200 to 2400 MeV per nucleon

Balloon-borne measurements of cosmic-ray nuclear abundances for Z = 5-28 and energies 1.2-1.4 GeV/nucleon, obtained using the scintillation/Cerenkov-counter telescope and multiwire proportional counter described by Dwyer et al. (1984) on four flights from Texas and Oklahoma during 1973-1975, are reported. The data are presented in tables and graphs and compared with published observations. Charge separation (sigma = 0.2 units for Fe) and exposure factor (38 sq m sr h) are attained, and the findings are found to be in good agreement with the predictions of a simple leaky-box model of the Galaxy and a pure exponential path-length distribution, although a nested-leaky-box model with some truncation is possible. The delay between e-process nucleosynthesis and cosmic-ray acceleration is estimated on the basis of the Co abundance at greater than 100 d and probably greater than 100,000 yr.

Dwyer, R.↗

NASA NTRS2021

Truncated ARQ Statistical Link Analysis for Dynamic Links

The future deep space links are migrating towards higher frequency bands such as Ka band and optical. These links are susceptible to non Gaussian and non linear effects such as atmospheric turbulence, scintillation, antenna mis-pointing, jitter, etc. These dynamic links thus will experience various degrees of fading loss, and some of these link disruptions cannot be effectively mitigated by forward error correction coding and/or interleaving. One effective way to ensure reliable communication is by using Automatic Repeat Request (ARQ) protocol, where the receiver acknowledges to the transmitter whether or not a data unit is successfully received. If a data unit is not successfully received (such as after a pre-set time-out), the transmitter would then re-transmit the lost data unit to the receiver. In a previous paper, we derived a statistical link analysis method of finding the optimal operating Signal-to-Noise Ratio (SNR) and estimating the latency of an ARQ scheme. In a more recent paper, we demonstrated the above method using the SNR distribution constructed from the Ka-band (32 GHz) flight data. To simplify the discussion, we considered the academic approach that the ARQ scheme allows for an infinite number of retransmissions. In this paper, we consider the more practical case of a truncated ARQ scheme, where there is a limit on the number of retransmissions. We derive the error probability, the optimal SNR setting, and the latency statistics of the correctly received frames of the truncated ARQ schemes. We first discuss the truncated ARQ link analysis principles using the Gaussian assumption for SNR distribution with a large variance. Next, we demonstrate the statistical truncated ARQ link analysis using the SNR distribution constructed from the Ka-band flight data. The results in this paper can be applied in the design of reliable communication systems such as the Consultative Committee for Space Data System (CCSDS) File Transfer Protocol (CFTP) and the Delay Tolerant Network (DTN).

Morabito, David↗

NASA NTRS1989

Application of a self-adaptive grid method to complex flows

A directional-split modular user-friendly grid-point distribution code is applied to several test problems. Grid-point spacing is determined by user-specified constants denoting maximum and minimum grid spacings and relating the relative influence of smoothness and orthogonality. Estimates of truncation error, in terms of flowfield gradients and/or geometric features, are used to determine the point distribution.

Deiwert, G. S.↗

NASA NTRS1992

An efficient HZETRN (a galactic cosmic ray transport code)

An accurate and efficient engineering code for analyzing the shielding requirements against the high-energy galactic heavy ions is needed. The HZETRN is a deterministic code developed at Langley Research Center that is constantly under improvement both in physics and numerical computation and is targeted for such use. One problem area connected with the space-marching technique used in this code is the propagation of the local truncation error. By improving the numerical algorithms for interpolation, integration, and grid distribution formula, the efficiency of the code is increased by a factor of eight as the number of energy grid points is reduced. The numerical accuracy of better than 2 percent for a shield thickness of 150 g/cm(exp 2) is found when a 45 point energy grid is used. The propagating step size, which is related to the perturbation theory, is also reevaluated.

Shinn, Judy L.↗