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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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At least 1,297 records · Page 72
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A variable-order laminated plate theory based on the variational-asymptotical method

The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.

Lee, Bok W.↗
NASA NTRS1998

Applications of Artificial Neural Networks in Structural Engineering with Emphasis on Continuum Models

The use of continuum models for the analysis of discrete built-up complex aerospace structures is an attractive idea especially at the conceptual and preliminary design stages. But the diversity of available continuum models and hard-to-use qualities of these models have prevented them from finding wide applications. In this regard, Artificial Neural Networks (ANN or NN) may have a great potential as these networks are universal approximators that can realize any continuous mapping, and can provide general mechanisms for building models from data whose input-output relationship can be highly nonlinear. The ultimate aim of the present work is to be able to build high fidelity continuum models for complex aerospace structures using the ANN. As a first step, the concepts and features of ANN are familiarized through the MATLAB NN Toolbox by simulating some representative mapping examples, including some problems in structural engineering. Then some further aspects and lessons learned about the NN training are discussed, including the performances of Feed-Forward and Radial Basis Function NN when dealing with noise-polluted data and the technique of cross-validation. Finally, as an example of using NN in continuum models, a lattice structure with repeating cells is represented by a continuum beam whose properties are provided by neural networks.

Kapania, Rakesh K.↗
NASA NTRS2008

Shear Thinning Near the Critical Point of Xenon

We measured shear thinning, a viscosity decrease ordinarily associated with complex liquids, near the critical point of xenon. The data span a wide range of reduced shear rate: 10(exp -3) < gamma-dot tau < 700, where gamma-dot tau is the shear rate scaled by the relaxation time tau of critical fluctuations. The measurements had a temperature resolution of 0.01 mK and were conducted in microgravity aboard the Space Shuttle Columbia to avoid the density stratification caused by Earth's gravity. The viscometer measured the drag on a delicate nickel screen as it oscillated in the xenon at amplitudes 3 mu,m < chi (sub 0) >430 mu, and frequencies 1 Hz < omega/2 pi < 5 Hz. To separate shear thinning from other nonlinearities, we computed the ratio of the viscous force on the screen at gamma-dot tau to the force at gamma-dot tau approximates 0: C(sub gamma) is identical with F(chi(sub 0), omega tau, gamma-dot tau )/F)(chi(sub 0, omega tau, 0). At low frequencies, (omega tau)(exp 2) < gamma-dot tau, C(sub gamma) depends only on gamma-dot tau, as predicted by dynamic critical scaling. At high frequencies, (omega tau)(exp 2) > gamma-dot tau, C(sub gamma) depends also on both x(sub 0) and omega. The data were compared with numerical calculations based on the Carreau-Yasuda relation for complex fluids: eta(gamma-dot)/eta(0)=[1+A(sub gamma)|gamma-dot tau|](exp - chi(sub eta)/3+chi(sub eta)), where chi(sub eta) =0.069 is the critical exponent for viscosity and mode-coupling theory predicts A(sub gamma) =0.121. For xenon we find A(sub gamma) =0.137 +/- 0.029, in agreement with the mode coupling value. Remarkably, the xenon data close to the critical temperature T(sub c) were independent of the cooling rate (both above and below T(sub c) and these data were symmetric about T(sub c) to within a temperature scale factor. The scale factors for the magnitude of the oscillator s response differed from those for the oscillator's phase; this suggests that the surface tension of the two-phase domains affected the drag on the screen below T(sub c).

Zimmerli, Gregory A.↗
DOE OSTI2017

Expansion dynamics of a two-component quasi-one-dimensional Bose–Einstein condensate: Phase diagram, self-similar solutions, and dispersive shock waves

We investigate the expansion dynamics of a Bose–Einstein condensate that consists of two components and is initially confined in a quasi-one-dimensional trap. We classify the possible initial states of the two-component condensate by taking into account the nonuniformity of the distributions of its components and construct the corresponding phase diagram in the plane of nonlinear interaction constants. The differential equations that describe the condensate evolution are derived by assuming that the condensate density and velocity depend on the spatial coordinate quadratically and linearly, respectively, which reproduces the initial equilibrium distribution of the condensate in the trap in the Thomas–Fermi approximation. We have obtained self-similar solutions of these differential equations for several important special cases and write out asymptotic formulas describing the condensate motion on long time scales, when the condensate density becomes so low that the interaction between atoms may be neglected. The problem on the dynamics of immiscible components with the formation of dispersive shock waves is considered. We compare the numerical solutions of the Gross–Pitaevskii equations with their approximate analytical solutions and numerically study the situations where the analytical method being used admits no exact solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A survey of nonlinear robust optimization

Robust optimization (RO) has attracted great attention from the optimization community over the past decade. RO is dedicated to solving optimization problems subject to uncertainty: design constraints must be satisfied for all the values of the uncertain parameters within a given uncertainty set. Uncertainty sets may be modeled as deterministic sets (boxes, polyhedra, ellipsoids), in which case the RO problem may be reformulated via worst-case analysis, or as families of distributions. The challenge of RO is to reformulate or approximate robust constraints so that the uncertain optimization problem is transformed into a tractable deterministic optimization problem. Most reformulation methods assume linearity of the robust constraints or uncertainty sets of favorable shape, which represents only a fraction of real-world applications. This survey addresses nonlinear RO and includes problem formulations and applications, solution approaches, and available software with code samples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Nonlinear solution of classical three-wave interaction via finite-dimensional quantum model

The quantum three-wave interaction, the lowest-order nonlinear interaction in plasma physics, describes energy–momentum transfer between three resonant waves in the quantum regime. We describe how it may also act as a finite-degree-of-freedom approximation to the classical three-wave interaction in certain circumstances. By promoting the field variables to operators, we quantize the classical system, show that the quantum system has more free parameters than the classical system and explain how these parameters may be selected to optimize either initial or long-term correspondence. We then numerically compare the long-time quantum–classical correspondence far from the fixed point dynamics. We discuss the Poincaré recurrence of the system and the mitigation of quantum scrambling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Pseudodiagonalization Method for Accelerating Nonlinear Subspace Diagonalization in Density Functional Theory

In density functional theory, each self-consistent field (SCF) nonlinear step updates the discretized Kohn-Sham orbitals by solving a linear eigenvalue problem. The concept of pseudodiagonalization is to solve this linear eigenvalue problem approximately, and specifically utilizing a method involving a small number of Jacobi rotations that takes advantage of the good initial guess to the solution given by the approximation to the orbitals from the previous SCF iteration. The approximate solution to the linear eigenvalue problem can be very rapid, particularly for those steps near SCF convergence. Here, we adapt pseudodiagonalization to finite-temperature and metallic systems, where partially-occupied orbitals must be individually resolved with some accuracy. We apply pseudodiagonalization to the subspace eigenvalue problem that arises in Chebyshev-filtered subspace iteration. In tests on metallic and other systems for a range of temperatures, we show that pseudodiagonalization achieves similar rates of SCF convergence to exact diagonalization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Measuring neutrino mass imprinted on the anisotropic galaxy clustering

The anisotropic galaxy clustering of large scale structure observed by the Baryon Oscillation Spectroscopic Survey Data Release 11 is analyzed to probe the sum of neutrino masses in the small m {sub ν} ∼< 1 eV limit in which the early broadband shape determined before the last scattering surface is immune from the variation of m {sub ν}. The signature of m {sub ν} is imprinted on the altered shape of the power spectrum at later epoch, which provides an opportunity to access the non-trivial m {sub ν} through the measured anisotropic correlation function in redshift space (hereafter RSD instead of Redshift Space Distortion). The non-linear RSD corrections with massive neutrinos in the quasi linear regime are approximately estimated using one-loop order terms. We suggest an approach to probe m {sub ν} simultaneously with all other distance measures and coherent growth functions, exploiting this deformation of the early broadband shape of the spectrum at later epoch. If the origin of cosmic acceleration is unknown, m {sub ν} is poorly determined after marginalizing over all other observables. However, we find that the measured distances and coherent growth functions are minimally affected by the presence of mild neutrino mass. Although the standard model of cosmic acceleration is assumed to be the cosmological constant, the constraint on m {sub ν} is little improved. Interestingly, the measured Cosmic Microwave Background (hereafter CMB) distance to the last scattering surface sharply slices the degeneracy between the matter content and m {sub ν}, and the m {sub ν} is observed to be m {sub ν} = 0.19{sup +0.28}{sub −0.17} eV which is different from massless neutrino at 68% confidence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Parallel-in-Time Solution of Scalar Nonlinear Conservation Laws

Here, we consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially nonoscillatory (WENO) reconstructions, and in time with high-order explicit Runge–Kutta methods. The solution of the global, discretized space-time problem is sought via a nonlinear iteration that uses a novel linearization strategy in cases of nondifferentiable equations. Under certain choices of discretization and algorithmic parameters, the nonlinear iteration coincides with Newton’s method, although, more generally, it is a preconditioned residual correction scheme. At each nonlinear iteration, the linearized problem takes the form of a certain discretization of a linear conservation law over the space-time domain in question. An approximate parallel-in-time solution of the linearized problem is computed with a single multigrid reduction-in-time (MGRIT) iteration; however, any other effective parallel-in-time method could be used in its place. The MGRIT iteration employs a novel coarse-grid operator that is a modified conservative semi-Lagrangian discretization and generalizes those we have developed previously for nonconservative scalar linear hyperbolic problems. Numerical tests are performed for the inviscid Burgers and Buckley–Leverett equations. For many test problems, the solver converges in just a handful of iterations with a convergence rate independent of mesh resolution, including problems with (interacting) shocks and rarefactions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Predictions of nucleation theory applied to Ehrenfest thermodynamic transitions

A modified nucleation theory is used to determine a critical nucleus size and a critical activation-energy barrier for second-order Ehrenfest thermodynamic transitions as functions of the degree of undercooling, the interfacial energy, the heat-capacity difference, the specific volume of the transformed phase, and the equilibrium transition temperature. The customary approximations of nucleation theory are avoided by expanding the Gibbs free energy in a Maclaurin series and applying analytical thermodynamic expressions to evaluate the expansion coefficients. Nonlinear correction terms for first-order-transition calculations are derived, and numerical results are presented graphically for water and polystyrene as examples of first-order and quasi-second-order transitions, respectively.

Barker, R. E., Jr.↗
NASA NTRS1986

Ageostrophic motions in the stratosphere from satellite observations

Geopotential height fields, based on high vertical resolution radiometer measurements, have been used to infer the circulation in the stratosphere from 100 to 1 mb, in the Northern Hemisphere, on a daily basis during February and March of 1979. Initial calculations were based on geostrophy in the traditional way. In addition to demonstrating the benefits of high vertical resolution, these calculations show that for the disturbed conditions present at this time, many of the terms in the momentum equation which were neglected would have made nonnegligible contributions to the balance of terms. In particular, the convergence of meridional wave flux can affect the zonally averaged meridional component of the momentum budget. Ageostrophic terms can affect the zonally varying part of the momentum budgets as well, although an accurate assessment of their importance is complicated by nonlinear proceses. These and other results suggest that studies using diagnostically derived winds should include a scale analysis of the momentum budget to verify that the approximations used are valid. Revised estimates have been made of both the zonally averaged and zonally varying components of the wind that include important ageostrophic contributions.

Elson, L. S.↗
NASA NTRS1988

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, Jeffrey M.↗
NASA NTRS1989

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, J. M.↗
NASA NTRS1991

On optimal infinite impulse response edge detection filters

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

Sarkar, Sudeep↗
NASA NTRS1996

Implicit Extrapolation Methods for Variable Coefficient Problems

Implicit extrapolation methods for the solution of partial differential equations are based on applying the extrapolation principle indirectly. Multigrid tau-extrapolation is a special case of this idea. In the context of multilevel finite element methods, an algorithm of this type can be used to raise the approximation order, even when the meshes are nonuniform or locally refined. Here previous results are generalized to the variable coefficient case and thus become applicable for nonlinear problems. The implicit extrapolation multigrid algorithm converges to the solution of a higher order finite element system. This is obtained without explicitly constructing higher order stiffness matrices but by applying extrapolation in a natural form within the algorithm. The algorithm requires only a small change of a basic low order multigrid method.

Jung, M.↗
NASA NTRS2014

Quantified Energy Dissipation Rates in the Terrestrial Bow Shock: Waves and Dissipation - 2

We present the first quantified measure of the energy dissipation rates, due to wave-particle interactions, in the transition region of the Earth's collision-less bow shock using data from the Time History of Events and Macro-Scale Interactions during Sub-Storms spacecraft. Our results show that wave-particle interactions can regulate the global structure and dominate the energy dissipation of collision-less shocks. In every bow shock crossing examined, we observed both low-frequency (less than 10 hertz) and high-frequency (approximately or greater than10 hertz) electromagnetic waves throughout the entire transition region and into the magnetosheath. The low-frequency waves were consistent with magnetosonic-whistler waves. The high-frequency waves were combinations of ion-acoustic waves, electron cyclotron drift instability driven waves, electrostatic solitary waves, and whistler mode waves. The high-frequency waves had the following: (1) peak amplitudes exceeding delta B approximately equal to 10 nanoteslas and delta E approximately equal to 300 millivolts per meter, though more typical values were delta B approximately equal to 0.1-1.0 nanoteslas and delta E approximately equal to 10-50 millivolts per meter (2) Poynting fluxes in excess of 2000 microWm(sup −2) (micro-waves per square meter) (typical values were approximately 1-10 microWm(sup −2) (micro-waves per square meter); (3) resistivities greater than 9000 omega meters; and (4) associated energy dissipation rates greater than 10 microWm(sup −3) (micro-waves per cubic meter). The dissipation rates due to wave-particle interactions exceeded rates necessary to explain the increase in entropy across the shock ramps for approximately 90 percent of the wave burst durations. For approximately 22 percent of these times, the wave-particle interactions needed to only be less than or equal to 0.1 percent efficient to balance the nonlinear wave steepening that produced the shock waves. These results show that wave-particle interactions have the capacity to regulate the global structure and dominate the energy dissipation of collision-less shocks.

Terrestrial bow 2↗
NASA NTRS1994

A Galerkin method for linear PDE systems in circular geometries with structural acoustic applications

A Galerkin method for systems of PDE's in circular geometries is presented with motivating problems being drawn from structural, acoustic, and structural acoustic applications. Depending upon the application under consideration, piecewise splines or Legendre polynomials are used when approximating the system dynamics with modifications included to incorporate the analytic solution decay near the coordinate singularity. This provides an efficient method which retains its accuracy throughout the circular domain without degradation at singularity. Because the problems under consideration are linear or weakly nonlinear with constant or piecewise constant coefficients, transform methods for the problems are not investigated. While the specific method is developed for the two dimensional wave equations on a circular domain and the equation of transverse motion for a thin circular plate, examples demonstrating the extension of the techniques to a fully coupled structural acoustic system are used to illustrate the flexibility of the method when approximating the dynamics of more complex systems.

Smith, Ralph C.↗
DOE OSTI2023

Electrostatic modulation of the lateral carrier density profile in field effect devices with nonlinear dielectrics

The properties of two-dimensional (2D) electronic systems are often effectively controlled using electrostatic gating. The geometry of such field effect devices influences the effectiveness of the gate and the carrier density profile in the 2D device. Here, in this work, we analyze the gate-induced spatial variations in the lateral carrier density in patterned LaAlO 3 /SrTiO 3 devices. We model the electrostatics of the 2D interface using the Thomas-Fermi approximation and compute the gate-induced charge distribution at the interface. We show that the electric field lines generated by the gate are focused at the edges of the device, causing an increased depletion near its edges. This effect is accentuated in LaAlO 3 /SrTiO 3 due to the large, nonlinear dielectric constant of the substrate, and the large distance between the gate electrode and the interface. We experimentally demonstrate one consequence of this effect by directly imaging current distributions in gated heterostructures, finding that insulating regions nucleate at the edges of the device due to the gate. Our results suggest that device geometry and choice of dielectric materials control the charge distribution in 2D systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗