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At least 145 records · Page 8

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DOE OSTI2026

Prediction of Creep-Induced Strain Using a Symbolic Regression-Based Model

Material creep under high-temperature conditions limits the lifetime and safety of structural systems such as advanced nuclear reactors. Conventional creep testing is slow and often produces inconsistent results across nominally identical experiments, making lifetime prediction uncertain. Here, to address these challenges, this work develops a data-driven symbolic regression (SR) model that consolidates results from duplicate creep tests and predicts the remaining strain-time curve of an ongoing experiment. The method uses piece-wise multi-objective SR with physical constraints to generate analytic, interpretable functions describing transient creep strain. Applied to Inconel Alloy 617 data, the approach achieved relative mean absolute errors of 1.0–9.5%, providing closed-form predictions of strain evolution. These results demonstrate a first step toward reducing the duration and cost of long-term creep testing while retaining physically interpretable model forms.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Analytical Identification Method of Generalized Short‐Circuit Ratio Using Phasor Measurement Units

This paper introduces a novel analytical approach for the identification of the admittance matrix and the generalized short-circuit ratio (gSCR) in power systems integrated with renewable energy sources. The proposed method leverages voltage and current measurements from phasor measurement units (PMUs) to construct a least squares objective function, which is then solved using matrix calculus and partial derivatives. Unlike conventional optimization algorithms, this approach provides an analytical solution that substantially reduces data requirements, enabling the efficient and accurate identification of the gSCR with smaller datasets. Additionally, its fixed computational complexity allows for real-time updates as new data are collected, ensuring continuous refinement of the system of equations and enabling rapid, precise gSCR calculations. The method also exhibits strong robustness against measurement noise, making it well-suited for practical applications in dynamic power systems. The combination of reduced data requirements, real-time adaptability, noise robustness and fixed computational load establishes this method as a highly efficient and reliable tool for real-time power system stability analysis. Case studies on an EPRI 36-bus system demonstrate the method's effectiveness, highlighting its accuracy in closely matching true gSCR values, even under diverse disturbances and noisy conditions.

Han, Zelei [Hohai University, Nanjing (China)] (OR↗

DOE OSTI2024

An enrichment wall modeling framework for spectral element methods

In the present work, a first-of-its-kind enrichment wall-model is developed within the spectral element method (SEM) framework for large-eddy simulations (LES) of wall-bounded turbulent flows. The method augments the polynomial solution in the wall-adjacent elements with an analytical law-of-the-wall enrichment function representing the mean velocity near the wall. In the solution representation, this enrichment function captures the large gradients in the boundary layer, which allows the polynomial modes to represent the turbulent fluctuations. The enriched solution is able to resolve the shear stress at the wall without any modification to the no-slip wall boundary conditions, which allows for greater accuracy in the near-wall region compared to traditional methods. The enrichment wall modeling approach is implemented in a high-order SEM computational fluid dynamics solver, Nek5000, and its performance is assessed in turbulent channel flow wall-modeled LES for a range of Reynolds numbers. It is demonstrated that the enrichment wall-model improves solution accuracy on under-resolved near-wall grids as compared to traditional shear stress wall-models.

42 ENGINEERING↗

NASA NTRS1986

Multigrid-sinc methods

A Galerkin method using Whittaker cardinal or 'sinc' functions as basis functions is described for the solution of boundary-value problems. When the solution is analytic in the interior of the domain, the error of approximation using 2N + 1 points is O(e exp /-gamma sq rt N/) even if derivatives of the solution are singular at the boundaries. A multigrid method with overall complexity O(N log N) is used to solve the discrete equations. This paper contains a description of the multigrid-sinc algorithm along with some preliminary numerical results for two-point boundary-value problems.

Schaffer, Steve↗

DOE OSTI2024

A Characteristics Approach to the Finite Element Method

Herein, we present a new method for solving the linear Boltzmann transport equation. Two commonly used and well-understood methods for solving partial differential equations are the method of characteristics (MOC) and the finite element method (FEM). We propose a new method that combines the fundamental concept of the FEM with the analytic solution from the MOC to obtain coefficients for the FEM basis function expansion. Traditionally, coefficients for the FEM basis function expansion are obtained via matrix inversion. Instead, we solve for the coefficients with the MOC and represent the underlying fields with the basis function expansion using these coefficients. We provide a convergence study for our method with results from two sets of FEM basis functions: Gauss-Legendre and Gauss-Lobatto sets. We also compare two different variations of our method categorized as short characteristics and intermediate characteristics.

42 ENGINEERING↗

NASA NTRS1975

High zonal harmonics of rapidly rotating planets

A new perturbation expansion is derived for the structure of rotating bodies in hydrostatic equilibrium. The method uses an expansion of the density on Legendre polynomial functions of angle, and can be developed analytically in a manner analogous to the standard level-surface perturbation theory. The new theory proceeds from a prescribed pressure-density relation rather than from a prescribed density distribution, and is both simpler and more physically transparent than the level-surface approach. High zonal harmonics are shown to arise via a transfer function involving derivatives of the interior sound velocity, and via mixing of multipole density components in the outer shell of the planet. Sample calculations for polytropic sequences are presented, as well as standard gravity models for Jupiter and Saturn. Mathematical subleties of the theory are discussed in an appendix.

Hubbard, W. B.↗

NASA NTRS1979

A method for correlating performance data of a terrestrial solar cell array

An analytical method was proposed for characterizing array power output, in the region of maximum power, as a function of environmental variables. The correlation provided a way of evaluating the output of an array under environmental conditions that differ from those encountered during testing. Power data obtained at one location was used to predict array performance at other locations.

Simon, F. F.↗

NASA NTRS1989

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Podhorodeski, R. P.↗

DOE OSTI2026

Locally purified maximally mixed states at scale: Entanglement pruning and symmetries

Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states at scale. However, given their non-uniqueness, their representational complexity is generally sub-optimal in practical computations. Here, in this work we perform a comprehensive numerical and analytical analysis and resolve this issue in the experimentally relevant limit where noise depolarizes the density operator into a maximally mixed state. To resolve the sub-optimality issue, we analyze two numerical tools, one analytic method, and detail the relations between them. The numerical tools used are fidelity-preserving truncations and isometric gauge transformations leveraging Riemannian optimizations over entropic objective functions. In addition, by invoking the injectivity and symmetry constraints of the maximally mixed LPDO, we also present analytical closed-form expressions for the disentangler and discuss their relation to numerical optimizers. Further, away from the maximally mixed state, our simulations highlight how the truncation threshold smoothly interpolate, as a function of depolarization, between established matrix product results and our new results. Our work shows how, by minimizing the resources required to represent key states of practical interest in experiment, the efficiency of tensor network algorithms can be substantially increased. This paves the path for uncovering tensor network’s fundamental scalability limits and latent potential in representing the wide locus of mixed quantum states that are accessible on near-term quantum devices.

Gangapuram, Amit Jamadagni [Oak Ridge National Lab↗

NASA NTRS1982

Performance degradation of propeller/rotor systems due to rime ice accretion

A theoretical model has been established which is applicable to both propeller and helicopter systems that determines the effect of rime ice accretion on the thrust coefficient, power coefficient, and efficiency as a function of time in a natural icing condition. Theoretical comparisons have been made with experimentally determined decrease in propeller thrust coefficient and efficiency for five natural icing conditions with good agreement. The present analytical model is also applicable to the helicopter case, where the method predicts radial and azimuthal rotor blade ice shapes in addition to torque rise as a function of time in a natural icing condition.

Korkan, K. D.↗

NASA NTRS1971

Dynamic response of nonuniform structures to classes of pressure fields

A semi-analytical method is developed for the calculation of the response of nonuniform structures to deterministic and random excitation. The method is based on parametric representations of the impulse response and input functions. With these representations, a class of structures of specified geometry and a class of pressure fields of practical concern can be considered simultaneously in a single analytical calculation of structural response. In engineering applications, the parameters in the impulse response function can be fixed once the numerical solution of the associated eigenvalue problem is available; the input function parameters can be specified given a particular input function or pressure field data. This methodology is applied to nonuniform beams and circular cylindrical shells for which parametric response solutions are derived. The computerized version of these solutions is also presented.

Cottis, M. G.↗

NASA NTRS1973

CONMIN: A FORTRAN program for constrained function minimization: User's manual

CONMIN is a FORTRAN program, in subroutine form, for the solution of linear or nonlinear constrained optimization problems. The basic optimization algorithm is the Method of Feasible Directions. The user must provide a main calling program and an external routine to evaluate the objective and constraint functions and to provide gradient information. If analytic gradients of the objective or constraint functions are not available, this information is calculated by finite difference. While the program is intended primarily for efficient solution of constrained problems, unconstrained function minimization problems may also be solved, and the conjugate direction method of Fletcher and Reeves is used for this purpose. This manual describes the use of CONMIN and defines all necessary parameters. Sufficient information is provided so that the program can be used without special knowledge of optimization techniques. Sample problems are included to help the user become familiar with CONMIN and to make the program operational.

Vanderplaats, G. N.↗

DOE OSTI2026

Deep-field analytical calibration

The next generation of imaging surveys, including the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), Euclid, and the Nancy Grace Roman Space Telescope, will provide unprecedented constraints on cosmology using weak gravitational lensing. To fully exploit this statistical power, shear measurement methods must achieve sub- per cent accuracy while mitigating systematic biases from noise, the point-spread function (PSF), blending, and shear-dependent detection. The analytical calibration framework (AnaCal) has demonstrated such accuracy but requires adding noise to images, reducing effective depth. We introduce Deep-Field Analytical Calibration (DEEP-FIELD AnaCal), an extension of AnaCal that uses deep-field images to compute shear responses while preserving the statistical power of wide-field data. We validate DEEP-FIELD AnaCal on isolated and blended galaxy image simulations with LSST-like conditions, finding it meets the stringent requirement of multiplicative bias $|m| < 3\times 10^{-3}$ at 99.7 per cent confidence. Compared to standard AnaCal applied to wide-field images, DEEP-FIELD AnaCal increases the effective galaxy number density from 17 to 30 arcmin$^{-2}$ for simulated 10-yr LSST data. With deep fields $10\times$ longer than the wide field, we find pixel noise variance in shear estimation is reduced by 30 per cent and overall uncertainty by $\sim 25~{{\ \rm per\ cent}}$. Finally, using the LSST Deep Drilling Fields strategy, we assess sample variance and find an equivalent calibration uncertainty of $\lesssim 0.3~{{\ \rm per\ cent}}$. These results demonstrate that DEEP-FIELD AnaCal offers a promising path to achieve the required shear calibration for upcoming weak lensing surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1994

Computation of turbulent boundary layers employing the defect wall-function method

In order to decrease overall computational time requirements of spatially-marching parabolized Navier-Stokes finite-difference computer code when applied to turbulent fluid flow, a wall-function methodology, originally proposed by R. Barnwell, was implemented. This numerical effort increases computational speed and calculates reasonably accurate wall shear stress spatial distributions and boundary-layer profiles. Since the wall shear stress is analytically determined from the wall-function model, the computational grid near the wall is not required to spatially resolve the laminar-viscous sublayer. Consequently, a substantially increased computational integration step size is achieved resulting in a considerable decrease in net computational time. This wall-function technique is demonstrated for adiabatic flat plate test cases from Mach 2 to Mach 8. These test cases are analytically verified employing: (1) Eckert reference method solutions, (2) experimental turbulent boundary-layer data of Mabey, and (3) finite-difference computational code solutions with fully resolved laminar-viscous sublayers. Additionally, results have been obtained for two pressure-gradient cases: (1) an adiabatic expansion corner and (2) an adiabatic compression corner.

Brown, Douglas L.↗

NASA NTRS1989

Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

The theoretical basis of flexible-aircraft modeling techniques encompassing aerodynamic, control, and elastic-structure effects is investigated analytically, with a focus on methods which employ minimum-state approximations for the unsteady aerodynamics. Rational-function approximations to generalized aerodynamic forces are reviewed; constraints and lag-coefficient optimization are explained; the problem of physical weighting in the minimum-state equations of motion is examined; and results of typical analyses from the NASA Active Flexible Wing project (Perry et al., 1988) are presented in extensive tables and graphs and discussed in detail. The minimum-state approach is shown to produce accurate models at significantly reduced computation costs.

Tiffany, Sherwood H.↗

NASA NTRS1993

An approach for finding long period elliptical orbits for precursor SEI missions

Precursors for Solar System Exploration Initiative (SEI) missions may require long period elliptical orbits about a planet. These orbits will typically have periods on the order of tens to hundreds of days. Some potential uses for these orbits may include the following: studying the effects of galactic cosmic radiation, parking orbits for engineering and operational test of systems, and ferrying orbits between libration points and low altitude orbits. This report presents an approach that can be used to find these orbits. The approach consists of three major steps. First, it uses a restricted three-body targeting algorithm to determine the initial conditions which satisfy certain desired final conditions in a system of two massive primaries. Then the initial conditions are transformed to an inertial coordinate system for use by a special perturbation method. Finally, using the special perturbation method, other perturbations (e.g., sun third body and solar radiation pressure) can be easily incorporated to determine their effects on the nominal trajectory. An algorithm potentially suitable for on-board guidance will also be discussed. This algorithm uses an analytic method relying on Chebyshev polynomials to compute the desired position and velocity of the satellite as a function of time. Together with navigation updates, this algorithm can be implemented to predict the size and timing for AV corrections.

Fraietta, Michael F.↗

NASA NTRS1994

Azimuthally-dependent Finite Element Solution to the Cylindrical Resonator

The cylindrical cavity resonator loaded with an anisotropic dielectric is analyzed as a two-dimensional problem using a finite element approach that assumes sinusoidal dependence in azimuth. This methodology allows the first finite element treatment of the technically important case of a resonator containing a sapphire element with a cylindrically aligned c axis. Second order trial functions together with quadrilateral elements are adopted in the calculations. The method was validated through comparisons with the analytical solutions for the hollow metal cavity and a coaxial cavity, as well as through measurements on a shielded sapphire resonator.

cylindrical resonator two-dimensional finite eleme↗

NASA NTRS2007

Coupling of Multiple Coulomb Scattering with Energy Loss and Straggling in HZETRN

The new version of the HZETRN deterministic transport code based on Green's function methods, and the incorporation of ground-based laboratory boundary conditions, has lead to the development of analytical and numerical procedures to include off-axis dispersion of primary ion beams due to small-angle multiple Coulomb scattering. In this paper we present the theoretical formulation and computational procedures to compute ion beam broadening and a methodology towards achieving a self-consistent approach to coupling multiple scattering interactions with ionization energy loss and straggling. Our initial benchmark case is a 60 MeV proton beam on muscle tissue, for which we can compare various attributes of beam broadening with Monte Carlo simulations reported in the open literature.

Mertens, Christopher J.↗