Natural orbitals for H sub 2.
Natural orbital expansion coefficients of LCAO-MO-SCF-CI wave functions for ground state of H molecule
Barker, W. H.↗
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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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Electronic wavefunctions for atoms. III
Electronic wave functions for atoms from atomic configuration-interaction /CI/ expansion for open shell states
Bunge, A.↗
Transient solutions of the Fokker-Planck equation for a class of first-order phase- locked loops
Eigenfunction expansions of reduced nonGaussian phase error transition probability density function for first order tracking loop, analyzing spectral properties of Fokker-Planck equation
La Frieda, J. R.↗
Analytic theory of orbit contraction
The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.
Vinh, N. X.↗
Hybrid perturbation/Bubnov-Galerkin technique for nonlinear thermal analysis
A two step hybrid analysis technique to predict the nonlinear steady state temperature distribution in structures and solids is presented. The technique is based on the regular perturbation expansion and the classical Bubnov-Galerkin approximation. The functions are obtained by using the regular perturbation method. These functions are selected as coordinate functions and the classical Bubnov-Galerkin technique is used to compute their amplitudes. The potential of the proposed hybrid technique for the solution of nonlinear thermal problems is discussed. The effectiveness of this technique is demonstrated by the effects of conduction, convection, and radiation modes of heat transfer. It is indicated that the hybrid technique overcomes the two major drawbacks of the classical techniques: (1) the requirement of using a small parameter in the regular perturbation method; and (2) the arbitrariness in the choice of the coordinate functions in the Bubnov-Galerkin technique. The proposed technique extends the range of applicability of the regular perturbation method and enhances the effectiveness of the Bubnov-Galerkin technique.
Noor, A. K.↗
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.↗
N-point correlations for biased galaxy formation
A general series expansion of arbitrary accuracy is given for the correlation function of the 'biased' regions of galaxy formation in terms of the mass autocorrelations. It is shown how to calculate the N-point correlations to arbitrary accuracy, and the validity of the various approximations is discussed. The asymptotic values of the N-point correlation functions at their highest point at zero spatial separation are given, and the scaling of these values is discussed.
Jensen, L. G.↗
On the efficient calculation of the incomplete Airy function with application to edge diffraction
When the geometrical theory of diffraction (GTD) and its extensions are used to calculate fields across transition regions or in focal areas, various special functions are necessary to create uniform representations. One such transition function is the incomplete Airy function, which is applicable when two reflection points are arbitrarily close to each other and the endpoint of the domain considered. An efficient calculation of the incomplete Airy function is presented and shown to equal known asymptotic expansions when its argument is away from the critical point. By using these expansions, uniform field expressions are found which are consistent with the GTD and maintain its computational efficiency.
Cwik, Tom↗
A simplified wind vector algorithm for satellite scatterometers
A simplified algorithm is derived for retrieving wind vectors from microwave scatterometer observations. The azimuthal dependence of the sea-surface radar cross section is modeled by a double-cosine function, rather than the traditional second-order cosine expansion. The algorithm is tested using the aircraft scatterometer observations obtained during the AAFE-RADSCAT Experiment in 1975 and 1976. There is little difference between the performance of the simplified algorithm and the more involved least-squares searching algorithm. The AAFE-RADSCAT aircraft observations are sampled so as to simulate the three-look satellite scatterometer NSCAT that will be launched on the Japanese Advanced Earth Observing Satellite. The results of the retrievals indicate that it is probably not possible to uniquely determine the wind direction using just NSCAT observations because of a 180 degree ambiguity. However, if forecast models can predict the wind direction to an accuracy of +/- 90 deg, thereby eliminating the ambiguity, then the results indicate that NSCAT can determine the wind direction to an accuracy of about +/- 20 deg. Better performance is obtained when the three observations are the same polarization (either v-pol or h-pol), as compared to using a mix of v-pol and h-pol observations.
Wentz, Frank J.↗
Multi-Beam Approach for Accelerating Alignment and Calibration of HyspIRI-Like Imaging Spectrometers
A paper describes an optical stimulus that produces more consistent results, and can be automated for unattended, routine generation of data analysis products needed by the integration and testing team assembling a high-fidelity imaging spectrometer system. One key attribute of the system is an arrangement of pick-off mirrors that provides multiple input beams (five in this implementation) to simultaneously provide stimulus light to several field angles along the field of view of the sensor under test, allowing one data set to contain all the information that previously required five data sets to be separately collected. This stimulus can also be fed by quickly reconfigured sources that ultimately provide three data set types that would previously be collected separately using three different setups: Spectral Response Function (SRF), Cross-track Response Function (CRF), and Along-track Response Function (ARF), respectively. This method also lends itself to expansion of the number of field points if less interpolation across the field of view is desirable. An absolute minimum of three is required at the beginning stages of imaging spectrometer alignment.
Eastwood, Michael L.↗
Thin, Flexible IMM Solar Array
NASA needs solar arrays that are thin, flexible, and highly efficient; package compactly for launch; and deploy into large, structurally stable high-power generators. Inverted metamorphic multijunction (IMM) solar cells can enable these arrays, but integration of this thin crystalline cell technology presents certain challenges. The Thin Hybrid Interconnected Solar Array (THINS) technology allows robust and reliable integration of IMM cells into a flexible blanket comprising standardized modules engineered for easy production. The modules support the IMM cell by using multifunctional materials for structural stability, shielding, coefficient of thermal expansion (CTE) stress relief, and integrated thermal and electrical functions. The design approach includes total encapsulation, which benefits high voltage as well as electrostatic performance.
Walmsley, Nicholas↗
The Psyche Planning Software Subsystem: Creating a Robust Toolset for a Discovery-class Mission
Psyche is a Discovery-class mission to the small metal-rich asteroid (16) Psyche, and is slated to launch in 2022. Psyche, like many missions, requires low-cost activity planning and sequence generation that serves as the backbone to overall uplink design. Such tools must be maintainable over long periods of operations, and powerful enough to solve complex issues that deep-space one-off missions encounter. In this paper we introduce cost-effective solutions that leverage inner- and open-source principles to meet a variety of common and novel use cases.The uplink process that was designed to meet these challenges is presented, as well as the data-flow through the high-level architecture of the planning software subsystem. The user-facing planning tools are described, particularly the Science Opportunity Analyzer, the Plan Editor, Psyche’s planning automation in the Blackbird framework, and Psyche Simulation Reports. All these applications are either new or have been substantially revamped to meet Psyche’s concept of operations. In particular, ensuring the entire toolchain can correctly process epoch-relative activities is discussed. Underlying the main applications are a common set of dependencies developed and maintained by a new cross-mission association of planning developers. In this way, Psyche can inherit well-tested functionality which saves effort and ensures its developers can focus on solving domain challenges. Quality control of the applications and libraries is ensured with a code-review and unit-test based novel ‘CM lite’ process. Collaboration with international industry and academia using the open-source modules is already occurring.The planning and scheduling software is designed to maximize operator awareness of the integrated plan at every step of the process and use common interfaces and file formats to easily transfer information. Design choices plus the team’s test-driven development process enables more expansive capabilities compared to the decentralized planning and sequence generation functions typical of Discovery-class orbiters without significant development cost increases. Benefits and drawbacks of Psyche’s approach are discussed, including comparison to other missions and tools where appropriate.
Ramanathan, Keshav↗
Higher-Order Approximations for Stabilizing Zero-Energy Modes in Peridynamics Crystal Plasticity Models with Large Horizon Interactions
The non-ordinary state-based peridynamics theory combines non-local dynamic techniques with a desirable correspondence material principle, allowing for the use of continuum mechanics constitutive models. Such an approach presents a unique capability for solving problems involving discontinuities (e.g., strain localization, fracture, and fragmentation). However, the correspondence-based peridynamics models often suffer from zero-energy mode instabilities in numerical implementation, primarily due to the approximations of the non-local deformation gradient tensor. This paper focuses on a computational scheme for eliminating the zero-energy mode oscillations using a choice of influence functions that improve the truncation error in a higher-order Taylor series expansion of the deformation gradient. The novelty here is a tensor-based derivation of the linear constraint equations, which can be used to systematically identify the particle interaction weight functions for various user-specified horizon radii. In this paper, the proposed higher-order stabilization scheme is demonstrated for multi-dimensional examples involving polycrystalline and composite microstructures, along with comparisons against conventional finite element methods. The proposed stabilization scheme is shown to be highly effective in suppressing the spurious zero-energy mode oscillations in all numerical examples while enabling efficient simulations of strain localizations across material interfaces.
Non-Ordinary State-Based Peridynamics↗
Sensitivity analysis in multipole-accelerated panel methods for potential flow
In the design of an airframe, the effect of changing the geometry on resulting computations is necessary for design optimization. The geometry is defined in terms of a series of design variables, including design variables to define the wing planform, tail, canard, pylon, and nacelle. Design optimization in this research is based on how these design variable affect the potential flow. The potential flow is computed as a function of the geometry and location of a series of panels describing the airframe, which are in turn a function of the design variables. Multipole accelerated panel methods improve the computational complexity of the problem and thus are an attractive approach. To utilize the methods in design optimization, it was necessary to define the appropriate sensitivity derivatives. The overhead incurred from finding the sensitivity derivatives in conjunction with the original computation should be small. This research developed the background for multipole-accelerated panel methods and the framework for finding sensitivity derivatives in the methods. Potential flow panel codes are commonly used for powered-lift aerodynamic predictions for three dimensional geometries. Given an airframe which has been discretized into a series of panels to define the airframe geometry, potential is computed as a function of the influence of all panels on all other panels. This is a computationally intensive problem for which efficient solutions are desired to improve the computational time and to allow greater resolution by use of more panels. One such solution is the use of hierarchical multipole methods which entail approximations of the effects of far-field terms. Hierarchical multipole methods have become prevalent in molecular dynamics and gravitational physics, and have been introduced into the fields of capacitance calculations, computational fluid dynamics, and electromagnetics. The methods utilize multipole expansions to describe the effect of bodies (i.e. particles, astrophysical bodies, panels, etc.) within a sphere on points distant from the sphere, where the influence diminishes as a function of distance. The expansions are exact with infinite series, however, for practical computations, the series are truncated and accuracy is selected based on the number of terms retained in the expansions. A hierarchical tree structure groups bodies together based on proximity to allow definition of multipole expansions for each group. The multipole expansions are then used to compute the effect of the bodies in a group on distant bodies.
Leathrum, James F., Jr.↗
A Versatile Nonlinear Method for Predictive Modeling
As computational fluid dynamics techniques and tools become widely accepted for realworld practice today, it is intriguing to ask: what areas can it be utilized to its potential in the future. Some promising areas include design optimization and exploration of fluid dynamics phenomena (the concept of numerical wind tunnel), in which both have the common feature where some parameters are varied repeatedly and the computation can be costly. We are especially interested in the need for an accurate and efficient approach for handling these applications: (1) capturing complex nonlinear dynamics inherent in a system under consideration and (2) versatility (robustness) to encompass a range of parametric variations. In our previous paper, we proposed to use first-order Taylor expansion collected at numerous sampling points along a trajectory and assembled together via nonlinear weighting functions. The validity and performance of this approach was demonstrated for a number of problems with a vastly different input functions. In this study, we are especially interested in enhancing the method's accuracy; we extend it to include the second-orer Taylor expansion, which however requires a complicated evaluation of Hessian matrices for a system of equations, like in fluid dynamics. We propose a method to avoid these Hessian matrices, while maintaining the accuracy. Results based on the method are presented to confirm its validity.
nonlinear modeling↗
A non-Gaussian statistical model for surface elevation of nonlinear random wave fields
Probability density function of the surface elevation of a nonlinear random wave field is obtained. The wave model is based on the Stokes expansion carried to the third order for both deep water waves and waves in finite depth. The amplitude and phase of the first-order component of the Stokes wave are assumed to be Rayleigh and uniformly distributed and slowly varying, respectively. The probability density function for the deep water case was found to depend on two parameters: the root-mean-square surface elevation and the significant slope. For water of finite depth, an additional parameter, the nondimensional depth, is also required. An important difference between the present result and the Gram-Charlier representation is that the present probability density functions are always nonnegative. It is also found that the 'constant' term in the Stokes expansion, usually neglected in deterministic studies, plays an important role in determining the details of the density function. The results compare well with laboratory and field experiment data.
Huang, N. E.↗
Large-amplitude inviscid fluid motion in an accelerating container
Study of dynamic behavior of the liquid-vapor interface of an inviscid fluid in an accelerating cylindrical container includes an analytical-numerical method for determining large amplitude motion. The method is based on the expansion of the velocity potential in a series of harmonic functions with time dependent coefficients.
Perko, L. M.↗
Analytical methods for performance evaluation of nonlinear filters.
In the investigation, the filtering problem is considered in the continuous time domain. The postulated simple suboptimal nonlinear filter structure closely parallels the structure of the Kalman-Bucy optimal linear filter algorithm. Two filter performance evaluation methods are developed based on the Kolmogorov equations for the transition density of Markov processes. The expansions in the approximations for the nonlinear system and observation functions are in effect carried out up to second-order terms in both methods. The description of the filter's performance is sought in terms of second-order statistics in both methods.
Bejczy, A. K.↗