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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

Chebyshev Polynomial↗
NASA NTRSDate not supplied

Field Reconstruction from PIV Measurements Employing Bernstein Polynomial Derived Operators

A fluid-dynamic reconstruction algorithm is presented that generates a least-squares best-fit, two-dimensional density field from a prespecified two-dimensional velocity field. This method recasts the mass-conservation equation as a modified Sylvester equation employing high-order operators derived from modified Bernstein polynomial expansions. To demonstrate its practical utility, this analytic methodology is applied to two canonical cases and a Particle Image Velocimetry dataset obtained from a Mach-2, mechanically back-pressured, isolator experiment. This methodology is envisioned to be used in conjunction with hypersonic-diagnostic techniques to aid in the quantification of isolator flow fields. However, also note that this reconstruction technique is well suited to other applications relevant to fluid dynamics, such as obtaining three-dimensional flow field reconstructions.

Bernstein Polynomials↗
NASA NTRS2023

On Hermite Interpolation using Bernstein Polynomials for Trajectory Generation

This work presents a solution to the two-point Hermite interpolation problem using Bernstein polynomials. The Hermite interpolation problem is of particular interest in aerospace applications where boundary conditions for trajectories often specify derivative constraints. In the examples shown, a trajectory will be generated between an initial condition and a final condition. For example, a trajectory is generated that connects an aircraft’s current position and velocity with a point on the runway at a desired landing velocity. The numerical stability of the proposed algorithms is analyzed empirically.

Bezier curves↗
DOE OSTI2025

Dirac traces and the Tutte polynomial

Perturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has the consequence of replacing 4-dimensional Dirac matrices with d-dimensional counterparts for arbitrary complex values of d. In this work, a connection between traces of d-dimensional Dirac matrices and computations of the Tutte polynomial of associated graphs is proven. The time complexity of computing Dirac traces is analysed by this connection, and improvements to algorithms for computing Dirac traces are proposed.

Renormalization and Regularization↗
DOE OSTI2022

Power counting energy flow polynomials

Power counting is a systematic strategy for organizing collider observables and their associated theoretical calculations. In this paper, we use power counting to characterize a class of jet substructure observables called energy flow polynomials (EFPs). EFPs provide an overcomplete linear basis for infrared-and-collinear safe jet observables, but it is known that in practice, a small subset of EFPs is often sufficient for specific jet analysis tasks. By applying power counting arguments, we obtain linear relationships between EFPs that hold for quark and gluon jets to a specific order in the power counting. We test these relations in the parton shower generator Pythia, finding excellent agreement. Power counting allows us to truncate the basis of EFPs without affecting performance, which we corroborate through a study of quark-gluon tagging and regression.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Data-driven projection pursuit adaptation of polynomial chaos expansions for dependent high-dimensional parameters

Uncertainty quantification (UQ) and inference involving a large number of parameters are valuable tools for problems associated with heterogeneous and non-stationary behaviors. The difficulty with these problems is exacerbated when these parameters are statistically dependent requiring statistical characterization over joint measures. Probabilistic modeling methodologies stand as effective tools in the realms of UQ and inference. Among these, polynomial chaos expansions (PCE), when adapted to low-dimensional quantities of interest (QoI), provide effective yet accurate approximations for these QoI in terms of an adapted orthogonal basis. These adaptation techniques have been cast as projection pursuits in Gaussian Hilbert space in what has been referred to as a projection pursuit adaptation (PPA) by Xiaoshu Zeng and Roger Ghanem (2023). The PPA method efficiently identifies an optimal low-dimensional space for representing the QoI and simultaneously evaluates an optimal PCE within that space. The quality of this approximation clearly depends on the size of the training dataset, which is typically a function of the adapted reduced dimension. Here, the complexity of the problem is thus mediated by the complexity of the low-dimensional quantity of interest and not the complexity of the high-dimensional parameter space.

Data-driven↗
DOE OSTI2022

Model calibration of the liquid mercury spallation target using evolutionary neural networks and sparse polynomial expansions

The mercury constitutive model predicting the strain and stress in the target vessel plays a central role in improving the lifetime prediction and future target designs of the mercury targets at the Spallation Neutron Source. We leverage the experiment strain data collected over multiple years to improve the mercury constitutive model through a combination of large scale simulations of the target behavior and the use of machine learning tools for parameter estimation. We present two interdisciplinary approaches for surrogate-based model calibration of expensive simulations using evolutionary neural networks and sparse polynomial expansions. The newly calibrated simulations achieve 7% average improvement on the prediction accuracy and 8% reduction in mean absolute error compared to previously reported reference parameters, with some individual sensors experiencing up to 30% improvement. The calibrated simulations can aid in fatigue analysis to estimate the mercury target lifetime, which reduces abrupt failure and saves tremendous amount of costs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Dynamic security assessment of systems powered only by grid-forming power plants with uncertain dispatch using polynomial vectors

A modern challenge in power engineering is to perform the dynamic security assessment (DSA) of grids that are 100% powered by inverter-based resources (IBRs). Addressing this challenge is difficult because: (i) the dispatch of IBRs can be uncertain as a result of the variability of renewable resources and (ii) they have hard current control limits that cannot be neglected, contrasting synchronous machines. To address this problem, this paper sets forth a framework to conduct DSA of bulk power systems that are 100% powered by grid-forming IBRs. Furthermore, the framework considers that IBR operational conditions are unknown but bounded by a zonotope which is also expressed as a polynomial vector for uncertainty propagation via Dormand–Prince integration. The framework is applied to modified versions of the WSCC 9-bus and IEEE 39-bus grids.

14 SOLAR ENERGY↗
DOE OSTI2021

Semi-Automated Creation of Density Functional Tight Binding Models through Leveraging Chebyshev Polynomial-Based Force Fields

Density functional tight binding (DFTB) is an attractive method for accelerated quantum simulations of condensed matter due to its enhanced computational efficiency over standard density functional theory (DFT) approaches. However, DFTB models can be challenging to determine for individual systems of interest, especially for metallic and interfacial systems where different bonding arrangements can lead to significant changes in electronic states. In this regard, we have created a rapid-screening approach for determining systematically improvable DFTB interaction potentials that can yield transferable models for a variety of conditions. Our method leverages a recent reactive molecular dynamics force field where many-body interactions are represented by linear combinations of Chebyshev polynomials. This allows for the efficient creation of multi-center representations with relative ease, requiring only a small investment in initial DFT calculations. Here, we have focused our workflow on TiH 2 as a model system and show that a relatively small training set based on unit-cell-sized calculations yields a model accurate for both bulk and surface properties. Our approach is easy to implement and can yield reliable DFTB models over a broad range of thermodynamic conditions, where physical and chemical properties can be difficult to interrogate directly and there is historically a significant reliance on theoretical approaches for interpretation and validation of experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗