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Results for “Normal form 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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Bounded motion design in the Earth zonal problem using differential algebra based normal form methods

Establishing long-term relative bounded motion between orbits in perturbed dynamics is a key challenge in astrodynamics to enable cluster flight with minimum propellant expenditure. Herein, we present an approach that allows for the design of long-term relative bounded motion considering a zonal gravitational model. Entire sets of orbits are obtained via high-order Taylor expansions of Poincarè return maps about reference fixed points. The high-order normal form algorithm is used to determine a change in expansion variables of the map into normal form space, in which the phase space behavior is circular and can be easily parameterized by action–angle coordinates. The action–angle representation of the normal form coordinates is then used to parameterize the original Poincarè return map and average it over a full phase space revolution by a path integral along the angle parameterization. As a result, the averaged nodal period and drift in the ascending node are obtained, for which the bounded motion conditions are straightforwardly imposed. Sets of highly accurate bounded orbits are obtained, extending over several thousand kilometers, and valid for decades.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Uniform-in-phase-space data selection with iterative normalizing flows

Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that are routinely generated. In applications that are constrained by memory and computational intensity, excessively large datasets may hinder scientific discovery, making data reduction a critical component of data-driven methods. Datasets are growing in two directions: the number of data points and their dimensionality. Whereas dimension reduction typically aims at describing each data sample on lower-dimensional space, the focus here is on reducing the number of data points. A strategy is proposed to select data points such that they uniformly span the phase-space of the data. The algorithm proposed relies on estimating the probability map of the data and using it to construct an acceptance probability. An iterative method is used to accurately estimate the probability of the rare data points when only a small subset of the dataset is used to construct the probability map. Instead of binning the phase-space to estimate the probability map, its functional form is approximated with a normalizing flow. Therefore, the method naturally extends to high-dimensional datasets. The proposed framework is demonstrated as a viable pathway to enable data-efficient machine learning when abundant data are available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

SDA: a symbolic differential algebra package in C++

Truncated Power Series Algebra (TPSA), or Differential Algebra (DA), is a well-established tool in accelerator physics, commonly used for generating high-order maps of dynamic systems, as well as in symplectic tracking, normal form analysis, verified integration, optimization, and fast multipole methods. This package is the first to perform symbolic DA computations, enabling traceability of initial condition contributions and runtime reduction for repeated DA calculations, potentially expanding DA’s applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Detector alignment for X-ray crystallography using Millepede-II

I describe a method for accurately refining the geometrical parameters of segmented X-ray area detectors on the basis of serial crystallography data, using 'Millepede' – an algorithm created for a very similar problem in high-energy physics. The Millepede method for serial crystallography builds on the approach of Brewster et al. [Acta Cryst. (2018), D74, 877–894], in which the detector parameters are refined simultaneously with the parameters for each individual crystal. This accounts for the mutual dependency between the parameters and thereby avoids the bias and slow convergence problems that have afflicted older approaches in which the deviations between observed and calculated Bragg peak positions were taken directly as the updates for the detector panel positions. The Millepede method uses the special structure of the least-squares normal equations to reduce them to a much smaller form that can be solved very quickly, even compared with the sparse matrix methods used previously. This makes it practical to refine the detector geometry frequently and thereby maintain accurate calibration without specialized alignment campaigns. Tilts of detector panels out of the plane can be reliably refined, as can the overall distance of the detector in the beam direction. With a simulated test case, the new method produced panel shifts within 7% of the correct values with only one iteration, and produced almost exactly correct shifts after a second iteration. A simulated out-of-plane panel rotation was correctly determined to within 0.001°. Applied to experimental data from an X-ray free-electron laser, the method increased the indexable fraction of frames from 30% to 91% in a single iteration, and to 96% after two further iterations. Computing the geometry updates on the basis of 2060 crystals took only 0.819 s on desktop computing hardware, including the time taken to read the required data from disk. The scaling was found to be very close to linear for up to 100 980 sets of crystal parameters, which took only 78.2 s to process under the same conditions. The method has been applied as part of a real-time feedback system at a synchrotron radiation beamline, in which an out-of-plane detector tilt of 0.04° was detected and corrected. Possible further applications are also described here.

Millepede-II↗
DOE OSTI2025

Using DAPPER to extract the photon strength function of 58 Fe using the inverse Oslo and shape methods

The photon strength function of 58 Fe has been extracted using both the Oslo and Shape methods from particle–γ coincidence data measured using the Detector Array for Photons, Protons, and Exotic Residues, which probes nuclei utilizing (d,p) reactions in inverse kinematics. Four particle–γ coincidence matrices, each constructed with different treatments of the γ–ray energies, are explored in order to observe the impact on the resulting nuclear level density and photon strength. The final photon strength function reported is found to agree well with previous Oslo measurements of other iron isotopes. Systematic uncertainties are included, using different model parameters and their reported errors to perform the Oslo method normalization. The model-independent Shape method is explored and the functional form of the photon strength function obtained is in agreement with the Oslo method results. A low-energy enhancement is not reported for 58 Fe in this work given possible subtraction issues originating from strongly populated states.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Using DAPPER to extract the photon strength function of 58Fe using the inverse Oslo and shape methods

The photon strength function of 58 Fe has been extracted using both the Oslo and Shape methods from particle-γ coincidence data measured using the Detector Array for Photons, Protons, and Exotic Residues, which probes nuclei utilizing (d,p) reactions in inverse kinematics. Four particle-γ coincidence matrices, each constructed with different treatments of the γ-ray energies, are explored in order to observe the impact on the resulting nuclear level density and photon strength. The final photon strength function reported is found to agree well with previous Oslo measurements of other iron isotopes. Systematic uncertainties are included, using different model parameters and their reported errors to perform the Oslo method normalization. The model-independent Shape method is explored and the functional form of the photon strength function obtained is in agreement with the Oslo method results. A low-energy enhancement is not reported for 58 Fe in this work given possible subtraction issues originating from strongly populated states.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Numerical algorithms for water waves with background flow over obstacles and topography

Abstract We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface, are compatible with arbitrary parameterizations of the free surface and boundaries, and allow for circulation around each obstacle, which leads to multiple-valued velocity potentials but single-valued stream functions. We prove that the resulting second-kind Fredholm integral equations are invertible, possibly after a physically motivated finite-rank correction. In an angle-arclength setting, we show how to avoid curve reconstruction errors that are incompatible with spatial periodicity. We use the proposed methods to study gravity-capillary waves generated by flow around several elliptical obstacles above a flat or variable bottom boundary. In each case, the free surface eventually self-intersects in a splash singularity or collides with a boundary. We also show how to evaluate the velocity and pressure with spectral accuracy throughout the fluid, including near the free surface and solid boundaries. To assess the accuracy of the time evolution, we monitor energy conservation and the decay of Fourier modes and compare the numerical results of the two methods to each other. We implement several solvers for the discretized linear systems and compare their performance. The fastest approach employs a graphics processing unit (GPU) to construct the matrices and carry out iterations of the generalized minimal residual method (GMRES).

Ambrose, David M.↗
DOE OSTI2021

Independent normalization for γ -ray strength functions: The shape method

Here, the shape method, a novel approach to obtain the functional form of the γ-ray strength function (γSF), is introduced. In connection with the Oslo method the slope of the nuclear level density (NLD) and γSF can be obtained simultaneously even in the absence of neutron resonance spacing data. The foundation of the shape method lies in the primary γ-ray transitions which preserve information on the functional form of the γSF. The shape method has been applied to 56 Fe, 92 Zr, and 164 Dy, which are representative cases for the variety of situations encountered in typical NLD and γSF studies. The comparisons of results from the shape method to those from the Oslo method demonstrate that the functional form of the γSF is retained regardless of nuclear structure details or J π values of the states fed by the primary transitions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Extracting Topological Orders of Generalized Pauli Stabilizer Codes in Two Dimensions

In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The algorithm applies to Z d qudits, including instances where d is a nonprime number. This capability allows the identification of topological orders that differ from the Z d toric codes. It extends our understanding beyond the established theorem that Pauli stabilizer codes for Z p qudits (with p being a prime) are equivalent to finite copies of Z p toric codes and trivial stabilizers. The algorithm is designed to determine all anyons and their string operators, enabling the computation of their fusion rules, topological spins, and braiding statistics. The method converts the identification of topological orders into computational tasks, including Gaussian elimination, the Hermite normal form, and the Smith normal form of truncated Laurent polynomials. Furthermore, the algorithm provides a systematic approach for studying quantum error-correcting codes. We apply it to various codes, such as self-dual CSS quantum codes modified from the two-dimensional honeycomb color code and non-CSS quantum codes that contain the double semion topological order or the six-semion topological order. Published by the American Physical Society 2024

Physics↗
DOE OSTI2020

Theoretical Development of Controller Transfer applied to Dynamical Systems

Data-driven control strategies suffer from the necessity of training and its associated computational time and cost. This motivates the continuous increase of popularity of transfer learning based methods. In this paper, we have investigated transfer learning in the context of controller for dynamical systems. First, we have derived conditions under which controller can be transferred between two linear dynamical systems. Furthermore, we have introduced a novel algorithm to design the transferable and non-transferable control components for linear systems. Secondly, we have derived conditions under which a stabilizing controller can be transferred between two different nonlinear dynamical systems. Furthermore, we have used the notion of zero dynamics to transform the nonlinear dynamics into global normal form, to derive the transferability conditions on the controller. Finally, we have numerically evaluated the performance of our transfer learning based methods for two sets of example linear and nonlinear dynamical systems.

Chakraborty, Indrasis↗
DOE OSTI2023

Wassersplines for Neural Vector Field-Controlled Animation

Much of computer-generated animation is created by manipulating meshes with rigs. While this approach works well for animating articulated objects like animals, it has limited flexibility for animating less structured free-form objects. Here we introduce Wassersplines, a novel trajectory inference method for animating unstructured densities based on recent advances in continuous normalizing flows and optimal transport. The key idea is to train a neurally-parameterized velocity field that represents the motion between keyframes. Trajectories are then computed by advecting keyframes through the velocity field. We solve an additional Wasserstein barycenter interpolation problem to guarantee strict adherence to keyframes. Our tool can stylize trajectories through a variety of PDE-based regularizers to create different visual effects. We demonstrate our tool on various keyframe interpolation problems to produce temporally-coherent animations without meshing or rigging.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A 2D/3D Heterostructure Perovskite Solar Cell with a Phase‐Pure and Pristine 2D Layer

Abstract Interface engineering plays a critical role in advancing the performance of perovskite solar cells. As such, 2D/3D perovskite heterostructures are of particular interest due to their optoelectrical properties and their further potential improvements. However, for conventional solution‐processed 2D perovskites grown on an underlying 3D perovskite, the reaction stoichiometry is normally unbalanced with excess precursors. Moreover, the formed 2D perovskite is impure, leading to unfavorable energy band alignment at the interface. Here a simple method is presented that solves both issues simultaneously. The 2D formation reaction is taken first to completion, fully consuming excess PbI 2 . Then, isopropanol is utilized to remove excess organic ligands, control the 2D perovskite thickness, and obtain a phase‐pure, n = 2, 2D perovskite. The outcome is a pristine (without residual 2D precursors) and phase‐pure 2D perovskite heterostructure with improved surface passivation and charge carrier extraction compared to the conventional solution process. PSCs incorporating this treatment demonstrate a notable improvement in both stability and power conversion efficiency, with negligible hysteresis, compared to the conventional process.

14 SOLAR ENERGY↗
DOE OSTI2025

Rolling Behavior of Surface Tagged Aluminum 6061 using Photoluminescent Oxides

Physical tagging of nuclear fuel is potentially one way of tracking throughout the fuel lifecycle. The process of tagging can take many forms, but one promising method is to embed a small amount of photoluminescent particles in the surface of a material which are not detectable under normal illumination but are readily visible under excitation by ultraviolet light. The goal of this project was to explore the potential to tag simulated nuclear fuel cladding with small ceramic particles, via laser beam welding or gas tungsten arc welding, and measure the photoluminescent response. Surface tagging using this method has demonstrated viability and detectability throughout this project; work in FY24 focused on the survivability of these tags through subsequent deformation processing similar to what taggants in a fuel manufacturing environment would be subjected to. This work demonstrated that particles are readily visible in the as-welded state (i.e., before subsequent rolling treatment to represent mechanical processing of a fuel material), but visibility is reduced as the deformation is induced. Despite the reduction in photoluminescence, the taggants are still visible after rolling processes are performed, making this surface tagging technique a promising candidate for nuclear fuel cladding tagging. This work demonstrated, though, that targeted optimization work would be necessary to develop a robust taggant depending on the fidelity and luminescent properties required.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Correlations between thermal history and keyhole porosity in laser powder bed fusion

Additive manufacturing has the potential to revolutionize the production of metallic components as it yields near net shape parts with complex geometries and minimizes waste. At the present day, additively manufactured components face qualification and certification challenges due to the difficulty in controlling defects. This has driven a significant research effort aimed at better understanding and improving processing controls – yielding a plethora of in-situ measurements aimed at correlating defects with material quality metrics of interest. In this work, we develop machine-learning methods to learn correlations between thermal history and subsurface porosity for a variety of print conditions in laser powder bed fusion. Un-normalized surface temperatures (in the form of black-body radiances) are obtained using high-speed infrared imaging and porosity formation is observed in the sample cross-section through synchrotron x-ray imaging. To demonstrate the predictive power of these features, we present four statistical machine-learning models that correlate temperature histories to subsurface porosity formation in laser fused Ti-6Al4V powder.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Long–short-term memory encoder–decoder with regularized hidden dynamics for fault detection in industrial processes

The ability of recurrent neural networks (RNN) to model nonlinear dynamics of high dimensional process data has enabled data-driven RNN-based fault detection algorithms. Previous studies have focused on detecting faults by identifying the discrepancies in data distribution between the faulty and normal data, as reflected in prediction errors generated by RNN models. However, in industrial processes, variations in data distribution can also result from changes in normal control setpoints and compensatory control adjustments in response to disturbances, making it hard to differentiate between normal and faulty conditions. This paper proposes a fault detection method utilizing a long short-term memory (LSTM) encoder–decoder structure with regularized hidden dynamics and reversible instance normalization (RevIN) to compactly represent high-dimensional measurements for effective monitoring. During training, the hidden states of the model are regularized to form a low-dimensional latent space representation of the original multivariate time series data. As a result, the prediction errors of the latent states can be used to monitor the abnormal dynamic variations, while the reconstruction errors of the measured variables are used to monitor the abnormal static variations. Furthermore, the proposed indices can reflect operating conditions, even when the distribution of test data changes, which helps distinguish faults from normal adjustments and disturbances that controllers can settle. Here, data from numerical simulation and the Tennessee Eastman process are used to illustrate the effectiveness of the proposed fault detection method.

42 ENGINEERING↗
DOE OSTI2022

Oxidation Resistance in 1200°C Steam of a FeCrAl Alloy Fabricated by Three Metallurgical Processes

Abstract FeCrAl alloys are a leading candidate material for accident tolerant fuel cladding due to their good performance in both normal light-water reactor operating conditions as well as their resilience to high-temperature accident scenarios. For commercial-scale production, new fabrication techniques need to be investigated. In this study, the effects of fabrication methods on the high-temperature steam oxidation performance of C26M (Fe12Cr6Al2Mo in wt.%) were investigated. Three variants of C26M were manufactured: wrought (cast and forged) (WC26M), powder metallurgy hot isostatic pressing (PMC26M), and laser powder bed fusion additive manufacturing (AMC26M). All three variants were exposed to steam at 1200°C for 2 h. Results showed no significant variation in mass change between the variants after steam exposure. All three variants effectively formed stable protective alumina films with ~0.6–1.3 µ m thickness. This study suggests FeCrAl alloys have excellent resilience to high-temperature steam in nuclear reactor accident scenarios regardless of the fabrication method.

Materials Science↗
DOE OSTI2024

Putative rhamnogalacturonan-II glycosyltransferase identified through callus gene editing bypasses embryo lethality

Rhamnogalacturonan II (RG-II) is a structurally complex and conserved domain of the pectin present in the primary cell walls of vascular plants. Borate crosslinking of RG-II is required for plants to grow and develop normally. Mutations that alter RG-II structure also affect crosslinking and are lethal or severely impair growth. Thus, few genes involved in RG-II synthesis have been identified. Here we developed a method to generate viable loss-of-function Arabidopsis (Arabidopsis thaliana) mutants in callus tissue via CRISPR/Cas9-mediated gene editing. We combined this with a candidate gene approach to characterize the male gametophyte defective 2 (MPG2) gene that encodes a putative family GT29 glycosyltransferase. Plants homozygous for this mutation do not survive. We showed that in the callus mutant cell walls, RG-II does not crosslink normally because it lacks 3-deoxy-D-manno-octulosonic acid (Kdo) and thus cannot form the α-L-Rhap-(1→5)-α-D-kdop-(1→ sidechain. We suggest that MGP2 encodes an inverting RG-II CMP-β-Kdo transferase (RCKT1). Our discovery provides further insight into the role of sidechains in RG-II dimerization. Our method also provides a viable strategy for further identifying proteins involved in the biosynthesis of RG-II.

59 BASIC BIOLOGICAL SCIENCES↗