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NASA NTRS1988

Efficient approximation concepts using second order information

The application of second derivative information for solving structural optimization problems is considered. In the present method, rather than building approximate nonlinear forms for the objective function and constraints, only linear approximations are used. A separable quadratic approximation of the Lagrangian function is included in the subproblem statement. The method has been successfully used for simple problems that can be solved in closed form, in addition to the sizing optimization of trusses, and it is shown to converge faster than the convex linearization method or the method of moving asymptotes.

Fleury, Claude↗

NASA NTRS1976

Critical examination of two-equation turbulence closure models

Comparison of the Jones-Launder, Ng-Spalding, Saffman-Wilcox, and Wilcox-Traci two-equation turbulence models has been conducted. It was shown that the Saffman-Wilcox and Wilcox-Traci dissipation-rate formulations admit straightforward integration through the viscous sublayer, whereas integration through the viscous sublayer is a more difficult issue with the Jones-Launder dissipation-function and the Ng-Spalding length-scale formulations. Numerical computations were conducted in which the models were applied to four equilibrium boundary layer flows including adverse, zero, and favorable pressure gradients. Computations of zero pressure gradient flow over a convex wall composed the final part of the comparison.

Chambers, T. L.↗

NASA NTRS1987

Asteroid lightcurve inversion

One of the most fundamental physical properties of any asteroid is its shape. Lightcurves provide the only source of shape information for most asteroids. Unfortunately, the functional form of a lightcurve is determined by the viewing/illumination geometry and the asteroid's light scattering characteristics as well as its shape, and in general it is impossible to determine an asteroid's shape from lightcurves. A technique called convex-profile inversion (CPI) that obtains a convex profile, P, from any lightcurve is introduced. If certain ideal conditions are satisfied, then P is an estimator for the asteroid's mean cross section, C, a convex set defined as the average of all cross sections C(z) cut by planes a distance z above the asteroids's equatorial plane. C is therefore a 2-D average of the asteroid's 3-D shape.

Ostro, Steven J.↗

NASA NTRS2001

Isolating Curvature Effects in Computing Wall-Bounded Turbulent Flows

The flow over the zero-pressure-gradient So-Mellor convex curved wall is simulated using the Navier-Stokes equations. An inviscid effective outer wall shape, undocumented in the experiment, is obtained by using an adjoint optimization method with the desired pressure distribution on the inner wall as the cost function. Using this wall shape with a Navier-Stokes method, the abilities of various turbulence models to simulate the effects of curvature without the complicating factor of streamwise pressure gradient can be evaluated. The one-equation Spalart-Allmaras turbulence model overpredicts eddy viscosity, and its boundary layer profiles are too full. A curvature-corrected version of this model improves results, which are sensitive to the choice of a particular constant. An explicit algebraic stress model does a reasonable job predicting this flow field. However, results can be slightly improved by modifying the assumption on anisotropy equilibrium in the model's derivation. The resulting curvature-corrected explicit algebraic stress model possesses no heuristic functions or additional constants. It lowers slightly the computed skin friction coefficient and the turbulent stress levels for this case (in better agreement with experiment), but the effect on computed velocity profiles is very small.

Rumsey, Christopher L.↗

DOE OSTI2026

An information-matching approach to optimal experimental design and active learning

The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict other quantities of interest (QoI). Because models often contain many unidentifiable (sloppy) parameters, QoIs often depend on a relatively small number of parameter combinations. Therefore, we introduce an information-matching criterion based on the Fisher information matrix to select the most informative training data from a candidate pool. This method ensures that the selected data contain sufficient information to learn only those parameters that are needed to constrain downstream QoIs. It is formulated as a convex optimization problem, making it scalable to large models and datasets. Here, we demonstrate the effectiveness of this approach across various modeling problems in diverse scientific fields, including power systems and underwater acoustics. Finally, we use information-matching as a query function within an active learning (AL) loop for materials science applications. In all these applications, we find that a relatively small set of optimal training data can provide the necessary information for achieving precise predictions. These results are encouraging for diverse future applications, particularly AL in large machine-learning models.

Materials science↗

NASA NTRS1984

Boundary-layer linear stability theory

Most fluid flows are turbulent rather than laminar and the reason for this was studied. One of the earliest explanations was that laminar flow is unstable, and the linear instability theory was first developed to explore this possibility. A series of early papers by Rayleigh produced many notable results concerning the instability of inviscid flows, such as the discovery of inflectional instability. Viscosity was commonly thought to act only to stabilize the flow, and flows with convex velocity profiles appeared to be stable. The investigations that led to a viscous theory of boundary layer instability was reported. The earliest application of linear stability theory to transition prediction calculated the amplitude ratio of the most amplified frequency as a function of Reynolds number for a Blasius boundary layer, and found that this quantity had values between five and nine at the observed Ret. The experiment of Schubauer and Skramstad (1947) completely reversed the prevailing option and fully vindicated the Gottingen proponents of the theory. This experiment demonstrated the existence of instability waves in a boundary layer, their connection with transition, and the quantitative description of their behavior by the theory of Tollmien and Schlichting. It is generally accepted that flow parameters such as pressure gradient, suction and heat transfer qualitatively affect transition in the manner predicted by the linear theory, and in particular that a flow predicted to be stable by the theory should remain laminar. The linear theory, in the form of the e9, or N-factor is today in routine use in engineering studies of laminar flow. The stability theory to boundary layers with pressure gradients and suction was applied. The only large body of numerical results for exact boundary layer solutions before the advent of the computer age by calculating the stability characteristics of the Falkner-Skan family of velocity profiles are given. When the digital computer reached a stage of development which permit the direct solution of the primary differential equations, numerical results were obtained from the linear theory during the next 10 years for many different boundary layer flows: three dimensional boundary layers; free convention boundary layers; compressible boundary layers; boundary layers on compliant walls; a recomputation of Falkner-Skan flows; unsteady boundary layers; and heated wall boundary layers.

Leslie M Mack↗

DOE OSTI2020

Effects of surface undulations on asymmetric X-ray diffraction: a rocking-curve topography study

The results are reported of an X-ray diffraction study of an Si crystal designed and fabricated for very asymmetric diffraction from the 333 reflection for X-ray energies of 8.100 and 8.200 keV. A crystal with an asymmetry angle of 46 ± 0.1° between the surface and the (111) planes was studied. The grazing angles of incidence were near 1.08 and 0.33° for these two energies, respectively. Features arising from surface undulations were not observed at 8.100 keV, but were observed at 8.200 keV. The results at 8.100 keV allow an alternative explanation based on strain near the surface to be ruled out. Topographic images were obtained as a function of rocking angle, and in the case of 8.200 keV the surface morphology is evident. Finally, the results are found to be in agreement with dynamical X-ray diffraction calculations made with the Takagi–Taupin equations specialized to a surface having convex or concave features, as reported in the accompanying paper [Macrander (2020). J. Appl. Cryst. 53 , 793–799].

36 MATERIALS SCIENCE↗

NASA NTRS1976

Computer subroutines for the estimation of nuclear reaction effects in proton-tissue-dose calculations

Calculational methods for estimation of dose from external proton exposure of arbitrary convex bodies are briefly reviewed. All the necessary information for the estimation of dose in soft tissue is presented. Special emphasis is placed on retaining the effects of nuclear reaction, especially in relation to the dose equivalent. Computer subroutines to evaluate all of the relevant functions are discussed. Nuclear reaction contributions for standard space radiations are in most cases found to be significant. Many of the existing computer programs for estimating dose in which nuclear reaction effects are neglected can be readily converted to include nuclear reaction effects by use of the subroutines described herein.

Wilson, J. W.↗

NASA NTRS1992

Electromagnetic scattering by coated convex surfaces and wedges simulated by approximate boundary conditions

Asymptotic/high-frequency solutions are developed for analyzing the non-specular scattering mechanisms associated with coated convex surfaces and edges simulated by approximate boundary conditions. In particular, the standard impedance boundary conditions (SIBC's) and the second order generalized impedance boundary conditions (GIBC's) are employed for a characterization of the edge diffraction, creeping wave, and surface diffracted wave contributions. To study the creeping wave and surface diffracted wave mechanisms, rigorous UTD (uniform geometrical theory of diffraction) diffraction coefficients are developed for a convex coated cylinder simulated with SIBC's and GIBC's. The ray solutions obtained remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficient for a convex cylinder are obtained via a generalization of the corresponding ones of the circular cylinder. To validate the asymptotic/high-frequency solution, integral equations are derived for both E and H-polarization and solved numerically using the method of moments. Results are presented for a single and three layered coated convex cylinder. Some insights are also provided on the accuracy of the employed GIBC's versus SIBC's for application to curved surfaces. To characterize the scattering by impedance wedges illuminated at skew incidence, diffraction coefficients are derived from an approximate solution of the governing functional difference equations. This solution exactly recovers the known ones for an impedance half plane or an arbitrary wedge at normal incidence, and to validate it for other wedge angles, a moment method code was used. Finally, to test the usefulness of the approximate skew incidence impedance wedge diffraction coefficient for three dimensional structures, equivalent currents are derived in the context of the physical theory of diffraction (PTD) for a finite length impedance wedge of arbitrary internal angles. These are incorporated in a standard general purpose PTD code and results are presented for a number of different impedance structures.

Syed, H. H.↗

DOE OSTI2025

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗

NASA NTRS2007

Optical Design of a Compact Imaging Spectrometer for Planetary Mineralogy

We present the design of a compact, wide-angle pushbroom imaging spectrometer suitable for exploration of solar system bodies from low orbit. The spectrometer is based on a single detector array with a broadband response that covers the range 400 to 3000 nm and provides a spectral sampling of 10 nm. The telescope has a 24-deg field of view with 600 spatially resolved elements (detector pixels). A specially designed convex diffraction grating permits optimization of the signal-to-noise ratio through the entire spectral band. Tolerances and design parameters permit the achievement of high uniformity of response through field and wavelength. The spectrometer performance is evaluated in terms of predicted spectral and spatial response functions and from the point of view of minimizing their variation through field and wavelength. The design serves as an example for illustrating the design principles specific to this type of system.

space optics↗

DOE OSTI2026

Data mining the missing ordered phases of Li/Na metal oxides

Data-driven discovery of Li-ion and Na-ion battery materials has been pioneered by generic materials data platforms such as the Materials Project. After decades of progress, it is timely to ask whether there remain underexplored compositional spaces. Here, in this work, we present a systematic data-mining effort to uncover missing ordered binary, ternary and quaternary Li/Na-containing metal oxides using high-throughput density functional theory (DFT). Building on 19,120 stable and metastable oxides entries from the Materials Project, we performed 13,245 additional calculations through isovalent substitutions of known ground states, experimentally reported compounds, and specific prototype structures. Our study identifies 36 new ground states within the GGA/GGA + U convex hull and 45 within the r 2 SCAN convex hull. Additionally, we identified 840 metastable compounds from GGA/GGA + U and 979 from r 2 SCAN that are absent in the present Materials Project databases. Moreover, we have tripled the metastable materials in compositional spaces with a molar ratio of cation/anion >1, highlighting the overlooked opportunities in this compositional space.

25 ENERGY STORAGE↗

NASA NTRS2002

Development of MLPG and LBIE Methods for Nonlinear Problems of Fracture

The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The sub-domains for the shape functions in the MLS approximation are defined only from the primary nodes, and the secondary nodes use the same sub-domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and/or moved without an additional mesh. The essential boundary conditions can be imposed exactly, and non-convex boundaries can be treated without special techniques. Several numerical examples are presented to illustrate the performance of the present method.

Atluri, Satya N.↗

DOE OSTI2021

Effect of workpiece curvature on the tool influence function during hemispherical sub-aperture tool glass polishing

The influence of workpiece curvature on the tool influence function spot during polishing of fused silica glass with cerium oxide slurry, while using a rotating hemispherical pad-foam tool for a wide variety of process conditions (tool displacement, inclination angle, and rotation rate), has been investigated. (Workpiece curvature ranged from 500 mm radius concave to 43 mm radius convex.) The TIF spot decreases in diameter and increases in the peak removal rate on more convex workpieces. In contrast, the TIF spot increases both in diameter and peak removal rate on more concave workpieces. For the range of workpiece curvatures investigated, both the spot size and the peak removal rate changed significantly, as much as 2 times. An elastic sphere–sphere contact mechanics model, which utilizes both a modified displacement (that leads to a change in the applied load) as well as a mismatch factor (that influences the pressure distribution shape), has been developed. Furthermore, the model was validated using both offline load-displacement measurements and finite-element analysis simulations. The model quantitatively describes the measured change in the relative contact diameter and relative pressure distribution, as well as semiquantitively describes the change in the relative volumetric removal rate on a large variety of TIF spots. The change in the volumetric removal rate for convex workpieces is a result of the balance between a decreasing spot size (reducing removal) and an increasing peak pressure (increasing removal), which usually results in relatively small changes in volumetric removal. In the case of concave workpieces, the volumetric removal rate change is also governed by a similar balance, but the spot size increase contribution dominates, resulting in a significant increase in volumetric removal rate. Understanding these trends can enable methods to add greater determinism during the fabrication of freeform optics by adjusting polishing parameters (such as dwell time) while the tool translates along a workpiece surface with different local curvatures.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Formulation and solution approach for calibrating activity-based travel demand model-system via microsimulation

This study addresses the problem of calibrating utility-maximizing nested logit activity-based travel demand model-systems. After estimation, it is common practice to use aggregate measurements to calibrate the estimated model-system’s parameters prior to their application in transportation planning, policy making, and operations. However, calibration of activity-based model-systems has received much less attention. Existing calibration approaches are myopic heuristics in the sense that they do not consider the fundamental inter-dependencies among choice-models and do not have a systematic way to adjust model parameters. Also, other purely simulation-based approaches do not perform well in large-scale applications. In this study, we focus on utility-maximizing nested logit activity-based model-systems and calibrating aggregate statistics such as activity shares, mode shares, time-dependent & mode-specific OD flows, and time-dependent & mode-specific sensor counts. We formulate the calibration problem as a simulation-based optimization problem and propose a stochastic gradient-based solution procedure to solve it. The solution procedure relies on microsimulation to calculate expectations of the aggregate statistics of interest to the calibration problem. Additionally, we derive approximate analytical expressions for the gradient of the objective function —that are evaluated through microsimulation on mini-batches of the population. The proposed solution procedure is sensitive to the fundamental structure of the activity-based model-system and is non-myopic in considering the dependencies across its model components. The formulated optimization problem is non-convex, highly nonlinear, and potentially has multiple-minima. Lastly, we show —through a real-world application— that the proposed solution procedure outperforms other state-of-the-art purely simulation-based optimization approaches in terms of computational efficiency, stability, and convergence. We also compare various gradient-based solution algorithms to determine the best algorithm to update the parameters. This work has the potential to facilitate wider and easier application of activity-based model-systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

ZEUS: An Efficient GPU Optimization Method Integrating PSO, BFGS, and Automatic Differentiation

We introduce a novel, efficient computational method, ZEUS, for numerical optimization, and provide an open-source implementation. It has four key ingredients: (1) particle swarm optimization (PSO), (2) the use of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, (3) automatic differentiation (AD), and (4) GPUs. Our approach addresses the computational challenges inherent in high-dimensional, non-convex optimization problems. In the first phase of the algorithm, we get a potentially good set of starting points using PSO. Thereafter, we run BFGS independently in parallel from these starting points. BFGS is one of the best-performing algorithms for numerical optimization. However, it requires the gradient of the function being optimized. ZEUS integrates automatic differentiation into BFGS thus avoiding the need for the user to calculate derivatives explicitly. The use of GPUs allows ZEUS to speed up the calculations substantially. We carry out systematic studies to explore the trade-offs between the number of PSO iterations taken, starting points, and BFGS iteration depth. We show that a handful of iterations of PSO can improve global convergence when combined with BFGS. We also present performance studies using common test functions. The source code can be found at https://github.com/fnal-numerics/global-optimizer-gpu.

Soos, Dominik [Old Dominion U.]↗

NASA NTRS2000

Distribution of expansins in graviresponding maize roots

To test if expansins, wall loosening proteins that disrupt binding between microfibrils and cell wall matrix, participate in the differential elongation of graviresponding roots, Zea mays L. cv. Merit roots were gravistimulated and used for immunolocalization with anti-expansin. Western blots showed cross-reaction with two proteins of maize, one of the same mass as cucumber expansin (29 kDa), the second slightly larger (32 kDa). Maize roots contained mainly the larger protein, but both were found in coleoptiles. The expansin distribution in cucumber roots and hypocotyls was similar to the distribution in maize. Roots showed stronger expansin signals on the expanding convex side than the concave flank as early as 30 min after gravistimulation. Treatment with brefeldin A, a vesicle transport inhibitor, or the auxin transport inhibitor, naphthylphthalamic acid, showed delayed graviresponse and the appearance of differential staining. Our results indicate that expansins may be transported and secreted to cell walls via vesicles and function in wall expansion.

Non-NASA Center↗

DOE OSTI2024

Comparison of excess free energy at an interface according to the applied interpolation scheme for elasticity: A phase-field method

Phase-field modeling is an effective simulation technique for modeling microstructure evolution of elastically anisotropic systems. To introduce the elastic energy contribution in a phase field model, an interpolation scheme is used to define the mechanical properties within the phases and across the continuous interface. Several existing interpolation schemes introduce a potential excess elastic energy at the interface, which undesirable effect on microstructure evolution needs to be evaluated. In this study, we focused on three interpolation schemes including Khachaturyan’ scheme (KHS), Voigt–Taylor’s scheme (VTS), and Steinbach–Apel’s scheme (SAS). Comparisons of these schemes’ performances were performed in three configuration types using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework: bi-crystal, isotropic particle-matrix and anisotropic particle-matrix. The contribution of excess elastic energy on the interface energy as a function of interface width and the computational time to steady-state were evaluated in these three configurations. SAS introduces the lowest excess elastic energy contribution and the VTS has the biggest contribution amongst the considered schemes. Moreover, when modeling precipitation in an anisotropic elastic material, the SAS approach seems to predict more physical convex shapes during growth, making it preferable to KHS and VTS. Finally, as currently implemented, SAS requires the largest computational time and KHS requires the smallest time to reach steady-state amongst the considered schemes.

36 MATERIALS SCIENCE↗