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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Positive ions of the first- and second-row transition metal hydrides

Theoretical dissociation energies for the first- and second-row transition metal hydride positive ions are critically compared against recent experimental values obtained from ion beam reactive scattering methods. Theoretical spectroscopic parameters and dipole moments are presented for the ground and several low-lying excited states. The calculations employ large Gaussian basis sets and account for electron correlation using the single-reference single- and double-excitation configuration interaction and coupled-pair-functional methods. The Darwin and mass-velocity contributions to the relativistic energy are included in the all-electron calculations on the first-row systems using first-order perturbation theory, and in the second-row systems using the Hay and Wadt relativistic effective core potentials. The theoretical D(0) values for the second-row transition metal hydride positive ions should provide a critical measure of the experimental values, which are not as refined as many of those in the first transition row.

Pettersson, Lars G. M.↗
NASA NTRS1972

The stability of motion of satellites with flexible appendages

The mathematical formulation associated with the problem of stability of motion of a satellite consisting of a main rigid body and three (or less) pairs of flexible rods is presented. The rods are capable of flexure in two orthogonal directions. Whereas the rotational motion of the body is described by generalized coordinates depending on time alone, the elastic displacements of the rods depend both on spatial position and time. Assuming no external torques, there exist motion integrals in the form of momentum integrals. These integrals can be regarded as constraint equations relating the system velocities, and used to reduce the number of variables describing the motion. The stability analysis has been carried out by means of an extension of the Liapunov direct method. Since the elastic vibrations result in energy dissipation, it is shown that the equilibrium position is asymptotically stable if the Hamiltonian is positive definite and unstable if it can take negative values in the neighborhood of the equilibrium. Determining the sign definiteness of the Hamiltonian is complicated by the fact that it contains spatial derivatives of the elastic displacements. Two methods are presented to cope with this problem. The first, the standard modal analysis in conjunction with series truncation, develops criteria in terms of infinite series associated with the natural modes and frequencies of the elastic rods. The second, the method of integral coordinates, yields closed-form stability criteria involving the system parameters, such as the body moments of inertia, the length and mass distribution of the rods, the lowest natural frequencies of the rods, and the satellite spin velocity.

Meirovitch, L.↗
NASA NTRS2009

The Principle of Energetic Consistency

A basic result in estimation theory is that the minimum variance estimate of the dynamical state, given the observations, is the conditional mean estimate. This result holds independently of the specifics of any dynamical or observation nonlinearity or stochasticity, requiring only that the probability density function of the state, conditioned on the observations, has two moments. For nonlinear dynamics that conserve a total energy, this general result implies the principle of energetic consistency: if the dynamical variables are taken to be the natural energy variables, then the sum of the total energy of the conditional mean and the trace of the conditional covariance matrix (the total variance) is constant between observations. Ensemble Kalman filtering methods are designed to approximate the evolution of the conditional mean and covariance matrix. For them the principle of energetic consistency holds independently of ensemble size, even with covariance localization. However, full Kalman filter experiments with advection dynamics have shown that a small amount of numerical dissipation can cause a large, state-dependent loss of total variance, to the detriment of filter performance. The principle of energetic consistency offers a simple way to test whether this spurious loss of variance limits ensemble filter performance in full-blown applications. The classical second-moment closure (third-moment discard) equations also satisfy the principle of energetic consistency, independently of the rank of the conditional covariance matrix. Low-rank approximation of these equations offers an energetically consistent, computationally viable alternative to ensemble filtering. Current formulations of long-window, weak-constraint, four-dimensional variational methods are designed to approximate the conditional mode rather than the conditional mean. Thus they neglect the nonlinear bias term in the second-moment closure equation for the conditional mean. The principle of energetic consistency implies that, to precisely the extent that growing modes are important in data assimilation, this term is also important.

Cohn, Stephen E.↗
DOE OSTI2021

Correlated Response of Protein Side-Chain Fluctuations and Conformational Entropy to Ligand Binding

The heterogeneous fast side-chain dynamics of proteins plays crucial roles in molecular recognition and binding. Site-specific NMR experiments quantify these motions by measuring the model-free order parameter (O axis 2 ) on a scale of 0 (most flexible) to 1 (least flexible) for each methyl-containing residue of proteins. In this work, we have examined ligand-induced variations in the fast side-chain dynamics and conformational entropy of calmodulin (CaM) using five different CaM–peptide complexes. O axis 2 of CaM in the ligand-free (O axis,U 2 ) and ligand-bound (O axis,B 2 ) states are calculated from molecular dynamics trajectories and conformational energy surfaces obtained using the adaptive biasing force (ABF) method. ΔO axis 2 = O axis,B 2 – O axis,U 2 follows a Gaussian-like unimodal distribution whose second moment is a potential indicator of the binding affinity of these complexes. The probability for the binding-induced O axis,U 2 → O axis,B 2 transition decreases with increasing magnitude of ΔO axis 2 , indicating that large flexibility changes are improbable for side chains of CaM after ligand binding. A linear correlation established between ΔOaxis2 and the conformational entropy change of the protein makes possible the determination of the conformational entropy of binding of protein–ligand complexes. The results not only underscore the functional importance of fast side-chain fluctuations but also highlight key motional and thermodynamic correlates of protein–ligand binding.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1995

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory

The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.

Ristorcelli, J. R.↗
NASA NTRS1995

LES, DNS and RANS for the analysis of high-speed turbulent reacting flows

The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Aug. 1994 - 31 Jul. 1995, we have focused our efforts on two programs: (1) developments of explicit algebraic moment closures for statistical descriptions of compressible reacting flows and (2) development of Monte Carlo numerical methods for LES of chemically reacting flows.

Adumitroaie, V.↗
NASA NTRS2013

Method for Estimating Operational Loads on Aerospace Structures Using Span-Wisely Distributed Surface Strains

This report presents a new method for estimating operational loads (bending moments, shear loads, and torques) acting on slender aerospace structures using distributed surface strains (unidirectional strains). The surface strain-sensing stations are to be evenly distributed along each span-wise strain-sensing line. A depth-wise cross section of the structure along each strain-sensing line can then be considered as an imaginary embedded beam. The embedded beam was first evenly divided into multiple small domains with domain junctures matching the strain-sensing stations. The new method is comprised of two steps. The first step is to determine the structure stiffness (bending or torsion) using surface strains obtained from a simple bending (or torsion) loading case, for which the applied bending moment (or torque) is known. The second step is to use the strain-determined structural stiffness (bending or torsion), and a new set of surface strains induced by any other loading case to calculate the associated operational loads (bending moments, shear loads, or torques). Performance of the new method for estimating operational loads was studied in light of finite-element analyses of several example structures subjected to different loading conditions. The new method for estimating operational loads was found to be fairly accurate, and is very promising for applications to the flight load monitoring of flying vehicles with slender wings.

Ko, William L.↗
NASA NTRS1995

Finding the global minimum: a fuzzy end elimination implementation

The 'fuzzy end elimination theorem' (FEE) is a mathematically proven theorem that identifies rotameric states in proteins which are incompatible with the global minimum energy conformation. While implementing the FEE we noticed two different aspects that directly affected the final results at convergence. First, the identification of a single dead-ending rotameric state can trigger a 'domino effect' that initiates the identification of additional rotameric states which become dead-ending. A recursive check for dead-ending rotameric states is therefore necessary every time a dead-ending rotameric state is identified. It is shown that, if the recursive check is omitted, it is possible to miss the identification of some dead-ending rotameric states causing a premature termination of the elimination process. Second, we examined the effects of removing dead-ending rotameric states from further considerations at different moments of time. Two different methods of rotameric state removal were examined for an order dependence. In one case, each rotamer found to be incompatible with the global minimum energy conformation was removed immediately following its identification. In the other, dead-ending rotamers were marked for deletion but retained during the search, so that they influenced the evaluation of other rotameric states. When the search was completed, all marked rotamers were removed simultaneously. In addition, to expand further the usefulness of the FEE, a novel method is presented that allows for further reduction in the remaining set of conformations at the FEE convergence. In this method, called a tree-based search, each dead-ending pair of rotamers which does not lead to the direct removal of either rotameric state is used to reduce significantly the number of remaining conformations. In the future this method can also be expanded to triplet and quadruplet sets of rotameric states. We tested our implementation of the FEE by exhaustively searching ten protein segments and found that the FEE identified the global minimum every time. For each segment, the global minimum was exhaustively searched in two different environments: (i) the segments were extracted from the protein and exhaustively searched in the absence of the surrounding residues; (ii) the segments were exhaustively searched in the presence of the remaining residues fixed at crystal structure conformations. We also evaluated the performance of the method for accurately predicting side chain conformations. We examined the influence of factors such as type and accuracy of backbone template used, and the restrictions imposed by the choice of potential function, parameterization and rotamer database. Conclusions are drawn on these results and future prospects are given.

NASA Program Exobiology↗
NASA NTRS1992

Maxwell's second- and third-order equations of transfer for non-Maxwellian gases

Condensed algebraic forms for Maxwell's second- and third-order equations of transfer are developed for the case of molecules described by either elastic hard spheres, inverse-power potentials, or by Bird's variable hard-sphere model. These hardly reduced, yet exact, equations provide a new point of origin, when using the moment method, in seeking approximate solutions in the kinetic theory of gases for molecular models that are physically more realistic than that provided by the Maxwell model. An important by-product of the analysis when using these second- and third-order relations is that a clear mathematical connection develops between Bird's variable hard-sphere model and that for the inverse-power potential.

Baganoff, D.↗
NASA NTRS1994

Advanced data assimilation in strongly nonlinear dynamical systems

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Miller, Robert N.↗
NASA NTRSDate not supplied

Snow Depth from AMSR-2 Using Multispectral Satellite Data in an Artificial Neural Network

By using diffusion theory and Monte Carlo lidar radiative transfer simulations, Hu et al. (2022b) has derived snow depth from the first-, second- and third-order moments of the lidar backscattering pathlength distribution. Lu et al. (2022) calculated the snow depth by applying the methods to the satellite ICESat-2 lidar measurements over the Arctic sea ice, as well as land surfaces of Northern Hemisphere. In this paper, an artificial neural network (ANN) algorithm, employing several channels from Advanced Microwave Scanning Radiometer 2 (AMSR-2) and the humidity vertical profiles from Global Modeling and Assimilation Office (GMAO) Goddard Earth Observing System for Instrument Teams (GEOS-IT) product, is trained to determine snow depth identified by time and geolocation matched 2019 ICESat-2 snow-depth data during winter months over the Arctic sea ice. The trained ANN snow-depth was applied to 2018 AMSR-2 clear pixel data, although the algorithms perform reasonably well in thinner clouds. The validation data (different from the training set) of ANN snow depth from AMSR-2 showed a good agreement with time matched and co-located snow-depth values from ICESat-2. The bias was near zero, with mean absolute error (MAE) 0.05 cm and a root-mean-square-error (RMSE) 0.08 cm. Prior applying the trained ANN snow depth to AMSR-2 data, a cloud screening algorithm was developed with a similar approach. A separate ANN cloud mask was trained to determine an AMSR-2 pixel is clear or cloudy with time and geolocation matched 2015 CALIOP Vertical Feature Mask (VFM) over Arctic sea ice. The ANN cloud mask from AMSR-2 under-estimated cloud fraction by 3-6% compared to CALIOP . The additional research is needed to conclusively evaluate the ANN cloud mask accuracy. Finally, this paper will lay the foundation for a sustained long-term snowfall and snow-storm monitoring system. The future Cloud Aerosol LIdar for Global scale Observations of the ocean-Land Atmosphere system (CALIGOLA) mission will provide a means to calculate snow depth from the lidar backscattering pathlength distribution, benefiting from the UV, visible and infrared pulses. With the calculated snow depth as the truth one could develop a machine learning algorithm, as it was done in this paper, using a passive microwave instrument available at that time to generate a wide range of snow depth data, covering extensive spatial areas in the cross-orbit direction.

Neural Network↗
NASA NTRS1994

LES, DNS and RANS for the analysis of high-speed turbulent reacting flows

The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Sep. 1993 - 1 Sep. 1994, we have focused our efforts on two research problems: (1) developments of 'algebraic' moment closures for statistical descriptions of nonpremixed reacting systems, and (2) assessments of the Dirichlet frequency in presumed scalar probability density function (PDF) methods in stochastic description of turbulent reacting flows. This report provides a complete description of our efforts during this past year as supported by the NASA Langley Research Center under Grant NAG1-1122.

Givi, Peyman↗
NASA NTRS1993

A theory of nonlocal mixing-length convection. I - The moment formalism

A flexible and potentially powerful theory of convection, based on the mixing length picture, is developed to make unbiased self-consistent predictions about overshooting and other complicated phenomena in convection. The basic formalism is set up, and the method's power is demonstrated by showing that a simplified version of the theory reproduces all the standard results of local convection. The second-order equations of the theory are considered in the limit of a steady state and vanishing third moments, and it is shown that they reproduce all the standard results of local mixing-length convection. There is a particular value of the superadiabatic gradient, below which the only possible steady state of a fluid is nonconvecting. Above this critical value, a fluid is convectively unstable. Two distinct regimes of convection, which are identified as efficient and inefficient convection, are determined.

Grossman, Scott A.↗
NASA NTRS1924

The Influence of the Form of a Wooden Beam on Its Stiffness and Strength I : Deflection of Beams with Special Reference to Shear Deformations

The purpose of this investigation was to determine to what extent ordinary deflection formulas, which neglect shear deformations, are in error when applied to beams of various sections, and to develop reasonably accurate yet comparatively simple formulas which take into account such deformations. A great many tests were made to determine the amount of shear deformation for beams of various sections tested over many different spans. As the span over which the beam is tested is increased the error introduced by neglecting shear deformations becomes less, and the values obtained by substituting measured deflections in the ordinary formulas approach more nearly the modulus of elasticity in tension and compression. For short spans the error is considerable and increases rapidly as the span is reduced. Two formulas were developed for estimating the magnitude of shear deformations, both of which have been verified by tests. The first assumes the parabolic distribution of shear on a cross section of a beam and, starting with a differential volume, the distortion due to shear is determined by the ordinary methods of summarizing the work. The second assumes that the deflections due to shear in any two beams of the same length, height, and moment of inertia, which are similarly loaded, are proportional to the summations of the shear stresses on their respective vertical sections. Both formulas check experimental results very closely when the calculations are made with great refinement.

Newlin, J A↗
NASA NTRS1982

Static calibration for measurement of loads in wind tunnel tests on Shuttle surface tiles

A description is given of the procedures used for the static calibrations of the Coe (1981) sensor array to determine normal force, pitching moment, and rolling moment from the ensemble of sensor outputs. The use of independent data to confirm the validity of the calibration is also described. Two methods are used in calibrating the Coe sensors. In the first, calibration loads and readings are arranged in matrix form and are assumed to be related in a linear fashion. In the second, each Coe sensor reading is regarded as a sum of contributions from each of the calibration loads. It is shown that the Coe load sensors, in conjunction with either of two data analysis methods, can be used to determine the forces and moments experienced by a Shuttle TPS tile.

Rummler, D. R.↗
NASA NTRSDate not supplied

AMSR-2 Daily Snow Depth Data Product Using a Neural Network Algorithm Trained by Collocated ICESat-2 Measurements

By using diffusion theory and Monte Carlo lidar radiative transfer simulations, Hu 1 et al. (2022b) has derived snow depth from the first-, second- and third-order moments of the lidar backscattering pathlength distribution. Lu 2 et al. (2022,2024) calculated the snow depth by applying the methods to the satellite ICESat-2 lidar measurements over the Arctic sea ice, as well as land surfaces of Northern Hemisphere. In this paper, a neural network (NN) algorithm, employing several channels from AMSR-2 and the humidity vertical profiles GMAO GEOS-IT, is trained to determine snow depth identified by time and geolocation matched 2019 ICESat-2 snow-depth data during winter months over the Arctic sea ice. The trained NN snow-depth was applied to 2014-2020 AMSR-2 clear pixel data, although the algorithms perform reasonably well in thinner clouds. This paper used AMSR-2 data, a passive microwave instrument to generate a wide range of snow depth data, covering extensive spatial areas in the cross-orbit direction.

Neural Network↗
DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗
NASA NTRS1989

Nonprincipal-plane scattering from flat plates: Second-order and corner diffraction and pattern control of horn antennas

Several high-frequency models for nonprincipal-plane scattering from a rectangular, perfectly conducting plate are examined. Two methods, the Method of Equivalent Currents and corner diffraction coefficients, are considered. Formulations for second-order Physical Theory of Diffraction equivalent currents and for corner diffracted fields are presented. Comparisons are made among plate models. Results away from grazing are accurate using only first-order terms. Near grazing, second-order and corner diffraction terms improve the results for many cases. The pattern control of horn antennas using lossy materials to coat the inner walls of the horn is also investigated. Integral Equation and Moment Method techniques are used to formulate the problem. It is clearly demonstrated that side lobe level reduction can be achieved using impedance surfaces on the inner walls of the horn.

Balanis, Constantine A.↗