Search NASA⌕ Search

SEARCH · Search NASA

Results for “second-order methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A Robust Methodology to Elucidate Kinetics of Room Temperature Electrochemical Propane Adsorption on Platinum

Electrocatalytic activation of alkanes can further decarbonize chemical manufacturing by leveraging affordable renewable electricity and readily available shale gas reserves in the United States. Earlier works have identified the unique role of Pt in adsorbing and activating alkanes, like propane, at room temperature in acidic, aqueous electrolytes, revealing spontaneous formation of deeply dehydrogenated propane-derived surface species with an intact C 3 - backbone. Although an adsorption mechanism was hypothesized, it has not been explicitly investigated to date, preventing the quantification of kinetic rate parameters. A robust methodology to investigate and benchmark propane adsorption kinetics on Pt is critical for the rational design of electrocatalysts that exhibit higher selectivity toward desired partially oxidized products. Herein, we analyze an oxidative current transience that appears during the adsorption of propane on Pt in aqueous electrochemical conditions and develop a methodology that elucidates the adsorption mechanism and enables quantification of rate parameters such as order dependences and apparent activation barriers. This method yields an expected first-order dependence with respect to propane concentration at low coverage and reveals a second-order dependence with respect to the concentration of surface active sites. Additionally, the apparent activation barrier for propane adsorption was calculated using an Arrhenius analysis of the current transience under temperature control. The experimentally measured activation barrier of 35 kJ mol –1 is in excellent agreement with the theoretical barrier calculated by density functional theory (DFT). The kinetic analysis was extended, via the use of transition state theory, to extract entropy and enthalpy of activation, yielding consistent results with the proposed two-step adsorption mechanism and DFT calculations. These results demonstrate reliable quantification of kinetic parameters for electrocatalytic activation of C–H bonds in alkanes that can be employed for rational catalyst development for a versatile range of electrocatalytic conditions.

alkane activation↗
DOE OSTI2025

Dark Energy Survey Year 6 Results: Point-Spread Function Modeling

We present the point-spread function (PSF) modeling for weak lensing shear measurement using the full six years of the Dark Energy Survey (DES Y6) data. We review the PSF estimation procedure using the PIFF (PSFs In the Full FOV) software package and describe the key improvements made to PIFF and modeling diagnostics since the DES year three (Y3) analysis: (i) use of external Gaia and infrared photometry catalogs to ensure higher purity of the stellar sample used for model fitting, (ii) addition of color-dependent PSF modeling, the first for any weak lensing analysis, and (iii) inclusion of model diagnostics inspecting fourth-order moments, which can bias weak lensing measurements to a similar degree as second-order modeling errors. Through a comprehensive set of diagnostic tests, we demonstrate the improved accuracy of the Y6 models evident in significantly smaller systematic errors than those of the Y3 analysis, in which all g band data were excluded due to insufficiently accurate PSF models. For the Y6 weak lensing analysis, we include g band photometry data in addition to the riz bands, providing a fourth band for photometric redshift estimation. Looking forward to the next generation of wide-field surveys, we describe several ongoing improvements to PIFF, which will be the default PSF modeling software for weak lensing analyses for the Vera C. Rubin Observatory’s Legacy Survey of Space and Time.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

A robust fourth-order finite-difference discretization for the strongly anisotropic transport equation in magnetized plasmas

We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following Du Toit et al. (2018), the scheme transforms mixed-derivative diffusion fluxes (which are responsible for the lack of a discrete maximum principle) into nonlinear advective fluxes, amenable to nonlinear-solver-friendly monotonicity-preserving limiters. The scheme enables accurate multi-dimensional heat transport simulations with up to seven orders of magnitude of heat-transport-coefficient anisotropies with low cross-field numerical error pollution and excellent algorithmic performance, with the number of linear iterations scaling very weakly with grid resolution and grid anisotropy, and scaling with the square-root of the implicit timestep. We propose a multigrid preconditioning strategy based on a lower-order approximation that renders the scheme efficient and scalable under grid refinement. Several numerical tests are presented that display the expected spatial convergence rates and strong algorithmic performance, including fully nonlinear magnetohydrodynamics simulations of kink instabilities in a Bennett pinch in 2D helical geometry and of ITER in 3D toroidal geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

An efficient level set method for tracking many materials

Here, we present an efficient level set method to track an arbitrary number of materials. The algorithm is optimal in the sense that it only needs to store a single unsigned distance-like function and a single integer indicator function, independent of the number of materials or distinct regions being tracked. Furthermore, for smooth velocity fields and smooth interface shape, arbitrarily high order solutions can be demonstrated. For interfaces that are or become kinked, the solution is limited to second-order convergence rates in the L 1 norm and first-order in the L ∞ norm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Determining the complex second-order optical susceptibility in macroscale van der Waals heterobilayers

In this work, we report on the experimental characterization of the second-order susceptibility in MoSe 2 /WS 2 heterobilayers, including their hidden complex phases. To this end, we developed a heterodyne-detection scheme for second-harmonic generation and applied it to macroscale heterobilayer samples prepared using the gold-tape exfoliation method. The heterodyne scheme enabled us to distinguish the relative orientation of the crystal domains, and furthermore, it allowed us to characterize the complex phases of the susceptibility relative to a reference quartz sample. By comparing the results from the monolayer regions and the heterobilayer region over several hundred microns of the sample area, we determined that the contribution of interlayer effects to second-harmonic generation is within the experimental uncertainty arising from the sample inhomogeneity. The results here provide fundamental quantitative information necessary for the precise design of nanophotonic systems based on stacking engineering.

2D materials↗
DOE OSTI2025

Cosmology with second- and third-order shear statistics for the Dark Energy Survey: Methods and simulated analysis

We present a new pipeline designed for the robust inference of cosmological parameters using both second- and third-order shear statistics. We build a theoretical model for rapid evaluation of three-point correlations using our fastnc code and integrate it into the cosmosis framework. We measure the two-point functions 𝜉 ± and the full configuration-dependent three-point shear correlation functions across all auto- and cross-redshift bins. We compress the three-point functions into the mass aperture statistic ⟨ℳ$^{3}_{ap}$⟩ for a set of 796 simulated shear maps designed to model the Dark Energy Survey Year 3 data. We estimate from it the full covariance matrix and model the effects of intrinsic alignments, shear calibration biases and photometric redshift uncertainties. We apply scale cuts to minimize the contamination from the baryonic signal as modeled through hydrodynamical simulations. We find a significant improvement of 83% on the figure of merit in the Ω m − 𝑆 8 plane when we add the ⟨ℳ$^{3}_{ap}$⟩ data to 𝜉 ± . Here, we present our findings for all relevant cosmological and systematic uncertainty parameters and discuss the complementarity of third-order and second-order statistics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Scattering Processes from Quantum Simulation Algorithms for Scalar Field Theories

We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve these improvements through two optimizations. First, we consider a finite volume approach for estimating the elements of the S-matrix. This approach is appropriate in general for 1+1D and for certain low-energy elastic collisions in higher dimensions. Second, we implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians formulated both in the field occupation basis and field amplitude basis. Our algorithms are based on either second-order Trotterization or qubitization. The cost of Trotterization in occupation basis scales as O ( λ N 7 | Ω | 3 / ( M 5 / 2 ϵ 3 / 2 ) ) where λ is the coupling strength, N is the occupation cutoff, | Ω | is the volume of the spatial lattice, M is the mass of the particles and ϵ is the uncertainty in the energy calculation used for the S -matrix determination. Qubitization in the field basis scales as O ( | Ω | 2 ( k 2 Λ + k M 2 ) / ϵ ) , where k is the cutoff in the field and Λ is a scaled coupling constant. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of 4 × 10 6 physical qubits and 10 12 T -gates which corresponds to roughly one day on a superconducting quantum computer with surface code and a cycle time of 100 ns. This places the simulation of scalar field theory within striking distance of the gate counts for the best available chemistry simulation results.

Hardy, Andrew [Toronto U.] (ORCID:0000000235817382↗
DOE OSTI2024

Non-resonant picosecond three-wave mixing in the gas phase

We report on the experimental observation of non-resonant, second-order optical sum-frequency generation (SFG) in five different atomic and molecular gases. The measured signal is attributed to a SFG process by characterizing its intensity scaling and its polarization behavior. We show that the electric quadrupole mechanism cannot explain the observed trends and suggest a mechanism based on symmetry breaking along the incident beam path arising from laser-induced species ground state number density gradients. Our results demonstrate that the SFG is about four orders of magnitude stronger than the third-harmonic generation (THG) and independent from any externally applied electric fields. In conclusion, these features make this method suitable for gas number density measurements at the picosecond time scale in reactive flows and plasmas.

LaCombe, Grayson↗
NASA NTRS1972

Navigation strategy and filter design for solar electric missions

Methods which have been proposed to improve the navigation accuracy for the low-thrust space vehicle include modifications to the standard Sequential- and Batch-type orbit determination procedures and the use of inertial measuring units (IMU) which measures directly the acceleration applied to the vehicle. The navigation accuracy obtained using one of the more promising modifications to the orbit determination procedures is compared with a combined IMU-Standard. The unknown accelerations are approximated as both first-order and second-order Gauss-Markov processes. The comparison is based on numerical results obtained in a study of the navigation requirements of a numerically simulated 152-day low-thrust mission to the asteroid Eros. The results obtained in the simulation indicate that the DMC algorithm will yield a significant improvement over the navigation accuracies achieved with previous estimation algorithms. In addition, the DMC algorithms will yield better navigation accuracies than the IMU-Standard Orbit Determination algorithm, except for extremely precise IMU measurements, i.e., gyroplatform alignment .01 deg and accelerometer signal-to-noise ratio .07. Unless these accuracies are achieved, the IMU navigation accuracies are generally unacceptable.

Tapley, B. D.↗
NASA NTRS1972

Displacement interaction and surface curvature effects on hypersonic boundary layers.

The title problem was studied employing implicit finite-difference methods to obtain numerical solutions to a composite set of boundary-layer equations valid to second order. Results are given for flow up a two-dimensional cubic compression ramp for free-stream Mach numbers of 6, 8, and 12.25 and for free-stream Re/inch equal to 85,800 and 25,800 at a wall-to-stagnation temperature ratio of 0.223. Comparisons with independent theories and experimental results are given. Nonsingular separation was produced at a free-stream Mach number of 12.25. For all cases considered, displacement and curvature effects canceled one another when a consistent treatment of inviscid and viscous curvature corrections was employed - the second-order theory virtually reproducing the first-order results.

Wornom, S. F.↗
NASA NTRS1973

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

Lancaster, J. E.↗
NASA NTRS1974

On the accuracy of Whitham's method

The steady flow of an ideal gas past a conical body is studied by the method of matched asymptotic expansions and by Whitham's method in order to assess the accuracy of the latter. It is found that while Whitham's method does not yield a correct asymptotic representation of the perturbation field to second order in regions where the flow ahead of the Mach cone of the apex is disturbed, it does correctly predict the changes of the second-order perturbation quantities across a shock (the first-order shock strength). The results of the analysis are illustrated by a special case of a flat, rectangular plate at incidence.

Zahalak, G. I.↗
NASA NTRS1977

Polynomial interpolation methods for viscous flow calculations

Higher-order collocation procedures which result in block-tridiagonal matrix systems are derived from (1) Taylor series expansions and from (2) polynomial interpolation, and the relationships between the two formulations, called respectively Hermite and spline collocation, are investigated. A Hermite block-tridiagonal system for a nonuniform mesh is derived, and the Hermite approach is extended in order to develop a variable-mesh sixth-order block-tridiagonal procedure. It is shown that all results obtained by Hermite development can be recovered by appropriate spline polynomial interpolation. The additional boundary conditions required for these higher-order procedures are also given. Comparative solutions using second-order accurate finite difference and spline and Hermite formulations are presented for the boundary layer on a flat plate, boundary layers with uniform and variable mass transfer, and the viscous incompressible Navier-Stokes equations describing flow in a driven cavity.

Rubin, S. G.↗
NASA NTRS1978

Marching methods for elliptic problems. II, III

Higher-order operators for marching methods for elliptic equations are considered. Higher-order is understood in the sense of higher-order accuracy solutions to second-order Poisson equations, and in the sense of higher-order elliptic equations such as the biharmonic equation. The use of deferred corrections for overcoming stability problems is illustrated. Direct and iterative methods of extending the mesh size are considered. Multiple marching, patching, and influence extending techniques are described.

Roache, P. J.↗
NASA NTRS1976

Polynominal Interpolation Methods for Viscous Flow Calculations

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.

Rubin, S. G.↗
NASA NTRS1951

On the particular integrals of the Prandtl-Busemann iteration equations for the flow of a compressible fluid

The particular integrals of the second-order and third-order Prandtl-Busemann iteration equations for the flow of a compressible fluid are obtained by means of the method in which the complex conjugate variables are utilized as the independent variables of the analysis. The assumption is made that the Prandtl-Glauert solution of the linearized or first-order iteration equation for the two-dimensional flow of a compressible fluid is known. The forms of the particular integrals, derived for subsonic flow, are readily adapted to supersonic flows with only a change in sign of one of the parameters of the problem.

Kaplan, Carl↗