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Results for “Functional expansion”

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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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1990

A hybrid perturbation-Galerkin technique that combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
DOE OSTI2020

Parton Energy Loss in the Generalized High-Twist Approach

In this work, we calculate the radiative parton energy loss in the deeply inelastic scattering (DIS) off a large nucleus within a generalized high-twist approach. The final gluon radiation spectrum is a convolution of the hard partonic part and the transverse momentum dependent (TMD) quark-gluon correlation function, without the twist expansion in the transverse momentum of the initial gluons used in original high twist approach. The TMD quark-gluon correlation function can be factorized approximately as the product of initial quark distribution and TMD gluon distribution which can be used to define the generalized or TMD jet transport coefficient. The radiation spectrum will recover the Gylassy-Levai-Vitev (GLV) result in the first order of the opacity expansion, under the static scattering center and soft gluon radiation approximation. We also investigate numerically the difference as a result of the soft gluon radiation approximation, under the static scattering center approximation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1990

Solar wind proton velocity distributions - Comparison of the bi-Maxwellian based 16-moment expansion with observations

The purpose of this paper is to study the possible types of velocity distributions that can be obtained from the bi-Maxwellian based 16-moment expansion of the distribution function, assuming macroscopic parameter values characteristic of the range of solar wind conditions. While previous studies also took heat flow into account, the theoretical expansions for f and the definitions of the physical moments adopted in these studies were different from those used in this paper. The choice of the 16-moment expansion and corresponding moment definitions was motivated by the fact that this is the correct generalization of the widely-used Maxwellian-based 13-moment expansion to the case where the zeroth-order distribution is a bi-Maxwellian. It is found that most of the features characteristic of solar wind proton distributions can be reproduced with the 16-moment distribution, including the appearance of secondary peaks. It is also shown how each of the physically significant velocity moments affects the shape of the distribution function.

Demars, H. G.↗
DOE OSTI2025

A generalized and adaptable tensor-contraction-based cluster expansion formalism for multicomponent solids

Density functional theory (DFT)-based simulations of materials have first-principles accuracy, but are very computationally expensive. For simulating various properties of multi-component alloys, the cluster expansion (CE) technique has served as the standard workaround to improve computational efficiency. However, the standard CE technique is difficult to extend to exotic and/or low-symmetry lattices, often implemented via iteration over particular cluster types, which must be enumerated per lattice structure. In this work, we introduce the tensor cluster expansion (TCE), implemented in the open-source code tce-lib, which maps correlation functions to mixed tensor contractions, eliminating the need to iterate over cluster types and additionally making the calculation of correlation functions well-suited for massively parallel architectures like GPUs. We show that local interaction energies are an immediate consequence of the TCE formalism, yielding nearly $\mathcal{O}$(1) energy difference calculations. We then use this formalism to fit CE models for the TaW and CoNiCrFeMn systems, and use these models to respectively compute the enthalpy of mixing curve and Cowley short-range order parameters, showing excellent agreement with ground truth data.

Cluster expansion↗
DOE OSTI2021

Six-point functions and collisions in the black hole interior

In the eternal AdS black hole geometry, we consider two signals sent from the boundaries into the black hole interior shared between the two asymptotic regions. We compute three different out-of-time-order six-point functions to quantify various properties of the collision of these signals behind the horizons: (i) We diagnose the strength of the collision by probing the two-signal state on a late time slice with boundary operators. (ii) We quantify two-sided operator growth, which provides a dual description of the signals meeting in the black hole interior, in terms of the quantum butterfly effect and quantum circuits. (iii) We consider an explicit coupling between the left and right CFTs to make the wormhole traversable and extract information about the collision product from behind the horizon. At a technical level, our results rely on the method of eikonal resummation to obtain the relevant gravitational contributions to Lorentzian six-point functions at all orders in the GN-expansion. We observe that such correlation functions display an intriguing factorization property. We corroborate these results with geodesic computations of six-point functions in two- and three-dimensional gravity.

2D Gravity↗
NASA NTRS1990

Adaptive pattern recognition by mini-max neural networks as a part of an intelligent processor

In this decade and progressing into 21st Century, NASA will have missions including Space Station and the Earth related Planet Sciences. To support these missions, a high degree of sophistication in machine automation and an increasing amount of data processing throughput rate are necessary. Meeting these challenges requires intelligent machines, designed to support the necessary automations in a remote space and hazardous environment. There are two approaches to designing these intelligent machines. One of these is the knowledge-based expert system approach, namely AI. The other is a non-rule approach based on parallel and distributed computing for adaptive fault-tolerances, namely Neural or Natural Intelligence (NI). The union of AI and NI is the solution to the problem stated above. The NI segment of this unit extracts features automatically by applying Cauchy simulated annealing to a mini-max cost energy function. The feature discovered by NI can then be passed to the AI system for future processing, and vice versa. This passing increases reliability, for AI can follow the NI formulated algorithm exactly, and can provide the context knowledge base as the constraints of neurocomputing. The mini-max cost function that solves the unknown feature can furthermore give us a top-down architectural design of neural networks by means of Taylor series expansion of the cost function. A typical mini-max cost function consists of the sample variance of each class in the numerator, and separation of the center of each class in the denominator. Thus, when the total cost energy is minimized, the conflicting goals of intraclass clustering and interclass segregation are achieved simultaneously.

Szu, Harold H.↗
DOE OSTI2021

A Computational Study of the Shear Behavior of Reinforced Concrete Beams Affected from Alkali–Silica Reactivity Damage

In this study, an investigation of the shear behavior of full-scale reinforced concrete (RC) beams affected from alkali–silica reactivity damage is presented. A detailed finite element model (FEM) was developed and validated with data obtained from the experiments using several metrics, including a force–deformation curve, rebar strains, and crack maps and width. The validated FEM was used in a parametric study to investigate the potential impact of alkali–silica reactivity (ASR) degradation on the shear capacity of the beam. Degradations of concrete mechanical properties were correlated with ASR expansion using material test data and implemented in the FEM for different expansions. The finite element (FE) analysis provided a better understanding of the failure mechanism of ASR-affected RC beam and degradation in the capacity as a function of the ASR expansion. The parametric study using the FEM showed 6%, 19%, and 25% reduction in the shear capacity of the beam, respectively, affected from 0.2%, 0.4%, and 0.6% of ASR-induced expansion.

36 MATERIALS SCIENCE↗
DOE OSTI2019

The effect of functional unit and co-product handling methods on life cycle assessment of an algal biorefinery

Microalgae are a promising feedstock for sustainable fuel and nutritional products. To be economically viable, algal biorefineries will need to produce multiple products, such as nutraceuticals and animal feed, in addition to fuel. Life cycle assessment (LCA) has been applied widely to algal biorefineries, but results vary across studies. Here we address two methodological challenges that can lead to variability in LCAs of multi-product algal biorefineries: the choice of functional unit and the method used to handle co-products. LCA was conducted for an algal biorefinery that produces two representative products—fuel and animal feed—using three functional units: (1) 1 MJ fuel, (2) 1 kg animal feed, and (3) 1 ha of production area, coupled with the system expansion method. For the fuel-based functional unit, the system expansion method was compared to impact allocation based on mass, energy, and market value of the biorefinery products. The choice of functional unit affects the results for several environmental indicators. For ecosystem quality, the choice of functional unit can change the overall balance of environmental impacts from harmful to beneficial. The effect of functional unit on climate change depends on the boundary considered in the model—i.e., “well to gate” or “well to wheels”. When a fuel-based functional unit is used, the choice of co-product handling method (i.e., allocation versus the system expansion method) affects environmental impacts, such as ecosystem quality and climate change, differently. For LCAs that use a fuel-based functional unit to compare algal biofuel to other fuels, multiple co-product handling methods should be analyzed and presented to stakeholders. A land based functional unit coupled with the system expansion method can be used to improve LCAs that compare among multi-product algal biorefineries.

09 BIOMASS FUELS↗
NASA NTRS1995

An efficient algorithm for choosing scattering directions in Monte Carlo work with arbitrary phase functions

This paper describes an efficient Monte Carlo algorithm for choosing a new direction of a photon after a scattering interaction. The algorithm chooses a scattering angle by linear interpolation in a table of the inverse cumulative scattering probability. A Legendre expansion of the phase function makes it easy to apply Clenshaw's algorithm to build the interpolation table. The points in the table are close enough together that linear interpolation is accurate. With a table of 100,000 entries, we can keep the absolute and relative errors in matching the probability distribution below 10(exp -5).

Barkstrom, Bruce R.↗
NASA NTRS2003

Approximating the Helium Wavefunction in Positronium-Helium Scattering

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

DiRienzi, Joseph↗
NASA NTRS1994

Spherical disharmonics in the Earth sciences and the spatial solution: Ridges, hotspots, slabs, geochemistry and tomography correlations

There is increasing use of statistical correlations between geophysical fields and between geochemical and geophysical fields in attempts to understand how the Earth works. Typically, such correlations have been based on spherical harmonic expansions. The expression of functions on the sphere as spherical harmonic series has many pitfalls, especially if the data are nonuniformly and/or sparsely sampled. Many of the difficulties involved in the use of spherical harmonic expansion techniques can be avoided through the use of spatial domain correlations, but this introduces other complications, such as the choice of a sampling lattice. Additionally, many geophysical and geochemical fields fail to satisfy the assumptions of standard statistical significance tests. This is especially problematic when the data values to be correlated with a geophysical field were collected at sample locations which themselves correlate with that field. This paper examines many correlations which have been claimed in the past between geochemistry and mantle tomography and between hotspot, ridge, and slab locations and tomography using both spherical harmonic coefficient correlations and spatial domain correlations. No conclusively significant correlations are found between isotopic geochemistry and mantle tomography. The Crough and Jurdy (short) hotspot location list shows statistically significant correlation with lowermost mantle tomography for degree 2 of the spherical harmonic expansion, but there are no statistically significant correlations in the spatial case. The Vogt (long) hotspot location list does not correlate with tomography anywhere in the mantle using either technique. Both hotspot lists show a strong correlation between hotspot locations and geoid highs when spatially correlated, but no correlations are revealed by spherical harmonic techniques. Ridge locations do not show any statistically significant correlations with tomography, slab locations, or the geoid; the strongest correlation is with lowermost mantle tomography, which is probably spurious. The most striking correlations are between mantle tomography and post-Pangean subducted slabs. The integrated locations of slabs correlate strongly with fast areas near the transition zone and the core-mantle boundary and with slow regions from 1022-1248 km depth. This seems to be consistent with the 'avalanching' downwellings which have been indicated by models of the mantle which include an endothermic phase transition at the 670-km discontinuity, although this is not a unique interpretation. Taken as a whole, these results suggest that slabs and associated cold downwellings are the dominant feature of mantle convection. Hotspot locations are no better correlated with lower mantle tomography than are ridge locations.

Ray, Terrill W.↗
NASA NTRS2011

Underexpanded Supersonic Plume Surface Interactions: Applications for Spacecraft Landings on Planetary Bodies

Numerical and experimental investigations of both far-field and near-field supersonic steady jet interactions with a flat surface at various atmospheric pressures are presented in this paper. These studies were done in assessing the landing hazards of both the NASA Mars Science Laboratory and Phoenix Mars spacecrafts. Temporal and spatial ground pressure measurements in conjunction with numerical solutions at altitudes of approx.35 nozzle exit diameters and jet expansion ratios (e) between 0.02 and 100 are used. Data from steady nitrogen jets are compared to both pulsed jets and rocket exhaust plumes at Mach approx.5. Due to engine cycling, overpressures and the plate shock dynamics are different between pulsed and steady supersonic impinging jets. In contrast to highly over-expanded (e <1) and underexpanded exhaust plumes, results show that there is a relative ground pressure load maximum for moderately underexpanded (e approx.2-5) jets which demonstrate a long collimated plume shock structure. For plumes with e much >5 (lunar atmospheric regime), the ground pressure is minimal due to the development of a highly expansive shock structure. We show this is dependent on the stability of the plate shock, the length of the supersonic core and plume decay due to shear layer instability which are all a function of the jet expansion ratio. Asymmetry and large gradients in the spatial ground pressure profile and large transient overpressures are predominantly linked to the dynamics of the plate shock. More importantly, this study shows that thruster plumes exhausting into martian environments possess the largest surface pressure loads and can occur at high spacecraft altitudes in contrast to the jet interactions at terrestrial and lunar atmospheres. Theoretical and analytical results also show that subscale supersonic cold gas jets adequately simulate the flow field and loads due to rocket plume impingement provided important scaling parameters are in agreement. These studies indicate the critical importance of testing and modeling plume-surface interactions for descent and ascent of spacecraft and launch vehicles.

Mehta, M.↗
NASA NTRS1993

Efficient and accurate computation of the incomplete Airy functions

The incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high-frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals with such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. In this paper a convergent series solution for the incomplete Airy functions is derived. Asymptotic expansions involving several terms are also developed and serve as large argument approximations. The combination of the series solution with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration data.

Constantinides, E. D.↗
NASA NTRS1992

Numerical evaluation of the incomplete airy functions and their application to high frequency scattering and diffraction

The incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals of such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. Here, a convergent series solution form for the incomplete Airy functions is derived. Asymptotic expansions involving several terms were also developed and serve as large argument approximations. The combination of the series solution form with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration data.

Constantinides, E. D.↗
DOE OSTI2021

Calculating elements of matrix functions using divided differences

In this work, we introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We showcase our approach by calculating the matrix elements of the exponential of a transverse-field Ising model and evaluating quantum transition amplitudes for large many-body Hamiltonians of sizes up to 2 64 x 2 64 on a single workstation. We also discuss the application of the method to matrix inverses. We relate and compare our method to the state-of-the-art and demonstrate its advantages. We also discuss practical applications of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Phenotypic and functional characterization of corneal endothelial cells during in vitro expansion

The advent of cell culture-based methods for the establishment and expansion of human corneal endothelial cells (CEnC) has provided a source of transplantable corneal endothelium, with a significant potential to challenge the one donor-one recipient paradigm. However, concerns over cell identity remain, and a comprehensive characterization of the cultured CEnC across serial passages has not been performed. To this end, we compared two established CEnC culture methods by assessing the transcriptomic changes that occur during in vitro expansion. In confluent monolayers, low mitogenic culture conditions preserved corneal endothelial cell state identity better than culture in high mitogenic conditions. Expansion by continuous passaging induced replicative cell senescence. Transcriptomic analysis of the senescent phenotype identified a cell senescence signature distinct for CEnC. We identified activation of both classic and new cell signaling pathways that may be targeted to prevent senescence, a significant barrier to realizing the potential clinical utility of in vitro expansion.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1974

Electromagnetic and scalar diffraction by a right-angled wedge with a uniform surface impedance

The diffraction of an electromagnetic wave by a perfectly-conducting right-angled wedge with one surface covered by a dielectric slab or absorber is considered. The effect of the coated surface is approximated by a uniform surface impedance. The solution of the normally incident electromagnetic problem is facilitated by introducing two scalar fields which satisfy a mixed boundary condition on one surface of the wedge and a Neumann of Dirichlet boundary condition on the other. A functional transformation is employed to simplify the boundary conditions so that eigenfunction expansions can be obtained for the resulting Green's functions. The eigenfunction expansions are transformed into the integral representations which then are evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. A far zone approximation is made to obtain the scattered field from which the diffraction coefficient is found for scalar plane, cylindrical or sperical wave incident on the edge. With the introduction of a ray-fixed coordinate system, the dyadic diffraction coefficient for plane or cylindrical EM waves normally indicent on the edge is reduced to the sum of two dyads which can be written alternatively as a 2 X 2 diagonal matrix.

Hwang, Y. M.↗