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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials

Abstract The remarkable complexity of a topologically ordered many-body quantum system is encoded in the characteristics of its anyons. Quintessential predictions emanating from this complexity employ the Fibonacci string net condensate (Fib SNC) and its anyons: sampling Fib-SNC would estimate chromatic polynomials while exchanging its anyons would implement universal quantum computation. However, physical realizations remained elusive. We introduce a scalable dynamical string net preparation (DSNP) that constructs Fib SNC and its anyons on reconfigurable graphs suitable for near-term superconducting processors. Coupling the DSNP approach with composite error-mitigation on deep circuits, we create, measure, and braids Fibonacci anyons; charge measurements show 94% accuracy, and exchanging the anyons yields the expected golden ratioϕwith 98% average accuracy. We then sample the Fib SNC to estimate chromatic polynomial atϕ + 2 for several graphs. Our results establish the proof of principle for using Fib-SNC and its anyons for fault-tolerant universal quantum computation and aim at a classically hard problem.

Science & Technology - Other Topics↗
DOE OSTI2026

Scalable quantum computational science: A perspective from block-encodings and polynomial transformations

Significant developments made in quantum hardware and error correction recently have been driving quantum computing toward practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. Recent advancements on these topics are presented, including the construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. The scalability of QSP methods on parallel and distributed quantum architectures is also highlighted. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this perspective serves as a gentle introduction to state-of-the-art quantum algorithms for the computational science community and inspires future development of scalable quantum computational science methodologies that bridge theory and practice.

Bayesian inference↗
DOE OSTI2018

Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials

If the optical system of a telescope is perturbed from rotational symmetry, the Zernike wavefront aberration coefficients describing that system can be expressed as a function of position in the focal plane using spin-weighted Zernike polynomials. Methodologies are presented to derive these polynomials to arbitrary order. This methodology is applied to aberration patterns produced by a misaligned Ritchey Chretian telescope and to distortion patterns at the focal plane of the DESI optical corrector, where it is shown to provide a more efficient description of distortion than conventional expansions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Chiral-odd generalized parton distributions in the large-𝑁 𝑐 limit of QCD: Spin-flavor structure, polynomiality, and sum rules

We study the nonperturbative properties of the nucleon’s chiral-odd generalized parton distributions (transversity GPDs) in the large-𝑁 𝑐 limit of QCD. This includes the parametric ordering of the spin-flavor components, the polynomiality property of the moments, and the sum rules connecting the GPDs with the tensor form factors. A multipole expansion in the transverse momentum transfer is used to enumerate and interpret the structures in the nucleon matrix element of the chiral-odd partonic operator, including monopole, dipole and quadrupole terms. The 1/𝑁 𝑐 expansion of the GPDs is performed using the abstract mean-field picture of baryons in the large-𝑁 𝑐 limit and its symmetries. We derive a large-𝑁 𝑐 relation between the flavor-nonsinglet GPDs 𝐸$^{𝑢−𝑑}_𝑇$ and $\tilde{𝐻}^{𝑢−𝑑}_𝑇$ and test it with recent lattice QCD results. We show that the polynomiality property and sum rules of the GPDs are fulfilled with the restricted realization of translational and rotational invariance in the mean-field picture. The results provide a basis for the phenomenological analysis of chiral-odd GPDs and hard exclusive processes in the large-𝑁 𝑐 limit, and for calculations in specific dynamical models.

generalized parton distributions↗
DOE OSTI2023

Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods

In this paper we generalize the polynomial time integration framework to additively partitioned initial value problems. The framework we present is general and enables the construction of many new families of additive integrators with arbitrary order-of-accuracy and varying degree of implicitness. In this first work, we focus on a new class of implicit-explicit polynomial block methods that are based on fully implicit Runge–Kutta methods with Radau nodes and that possess high stage order. Here, we show that the new fully implicit-explicit (FIMEX) integrators have improved stability compared to existing IMEX Runge–Kutta methods, while also being more computationally efficient due to recent developments in preconditioning techniques for solving the associated systems of nonlinear equations. For PDEs on periodic domains where the implicit component is trivial to invert, we will show how parallelization of the right-hand side evaluations can be exploited to obtain significant speedup compared to existing serial IMEX Runge–Kutta methods. For parallel (in space) finite element discretizations, the new methods can achieve orders of magnitude better accuracy than existing IMEX Runge–Kutta methods and/or achieve a given accuracy several times times faster in terms of computational runtime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Unified Approach to Unimodality of Gaussian Polynomials

In 2013, Pak and Panova proved the strict unimodality property of q-binomial coefficients (as polynomials in q) based on the combinatorics of Young tableaux and the semigroup property of Kronecker coefficients. They showed it to be true for all ℓ, m ≥ 8 and a few other cases. We propose a different approach to this problem based on computer algebra, where we establish a closed form for the coefficients of these polynomials and then use cylindrical algebraic decomposition to identify exactly the range of coefficients where strict unimodality holds. This strategy allows us to tackle generalizations of the problem, e.g., to show unimodality with larger gaps or unimodality of related sequences. In particular, we present proofs of two additional cases of a conjecture by Stanley and Zanello.

Koutschan, Christoph↗
DOE OSTI2017

Polynomial Chaos Characterization of Uncertainty in Multiscale Models and Behavior of Carbon Reinforced Composites

Design of non-crimp fabric (NCF) composites entails major challenges pertaining to (1) the complex fine-scale morphology of the constituents, (2) the manufacturing-produced inconsistency of this morphology spatially, and thus (3) the ability to build reliable, robust, and efficient computational surrogate models to account for this complex nature. Traditional approaches to construct computational surrogate models have been to average over the fluctuations of the material properties at different scale lengths. This fails to account for the fine-scale features and fluctuations in morphology, material properties of the constituents, as well as fine-scale phenomena such as damage and cracks. In addition, it fails to accurately predict the scatter in macroscopic properties, which is vital to the design process and behavior prediction. In this work, funded in part by the Department of Energy, we present an approach for addressing these challenges by relying on polynomial chaos representations of both input parameters and material properties at different scales. Moreover, we emphasize the efficiency and robustness of integrating the polynomial chaos expansion with multiscale tools to perform multiscale assimilation, characterization, propagation, and prediction, all of which are necessary to construct the data-driven surrogate models required to design under the uncertainty of composites. These data-driven constructions provide an accurate map from parameters (and their uncertainties) at all scales and the system-level behavior relevant for design. While this perspective is quite general and applicable to all multiscale systems, NCF composites present a particular hierarchy of scales that permits the efficient implementation of these concepts.

42 ENGINEERING↗
DOE OSTI2023

Use of Sobol’ Variance-Based Global Sensitivity Analysis and Multidimensional Legendre Polynomial Fitting for Reduced Order Modeling

Sandia National Laboratories (SNL) has developed a novel reduced order modeling approach. Prioritization of inputs is accomplished using Sobo' indices obtained through a more efficient variance-based global sensitivity analysis. To determine the Sobo' functions, simulated input values are aligned to collocation points to permit the use of Gauss-Lobatto integration, thereby reducing the number of simulation trials needed by more than an order of magnitude compared to standard Monte Carlo approaches. Furthermore, by leveraging the orthogonality of Legendre polynomials in conjunction with those same simulations at the collocation nodes, an efficient fitting method is developed to represent the Sobo' functions from which a reduced order model (ROM) is constructed. The developed method is both more efficient computationally, and the resulting ROM is more accurate. The efficacy of this technique is demonstrated on a nonlinear polynomial test function as well as the nonlinear Ishigami and Sobo' g functions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1967

Polynomial manipulator AP-168

Linear Systems Design Evaluation Program, AP-168 combines the many different analysis techniques used to evaluate and manipulate polynomials. The single program is a pseudo instruction abstraction. It allows the user to enter polynomials of the laplace operators and to manipulate them freely.

Tutt, G. E.↗
NASA NTRS1969

Root-cubing and general root-powering methods for finding the zeros of polynomials

Mathematical analysis technique generalizes a root squaring and root cubing method into a general root powering method. The introduction of partitioned polynomials into this general root powering method simplifies the coding of the polynomial transformations into input data suitable for processing by computer. The method includes analytic functions.

Bareiss, E. H.↗
NASA NTRS1972

Nth-order flat approximation of the signum function by a polynomial

In the interval studied, the signum function, sgn x, was demonstrated to be uniquely approximated by an odd polynomial f sub n (x) of order 2n-1, for which the approximation is nth order flat with respect to the points (1,1) and (-1,-1). A theorem was proved which states that for even integers n or = 2, the approximating polynomial has a pair of nonzero real roots + or - x sub n such that the x sub n form a monotonically decreasing sequence which converges to the root of 2 as n approaches infinity. For odd n i, f sub n (x) represents a strictly increasing monotonic function for all real x. As n tends to infinity, f sub n (x) converges to sgn x uniformly in two interval ranges.

Hosenthien, H. H.↗
NASA NTRS1972

Roots of polynomials by ratio of successive derivatives

An order of magnitude study of the ratios of successive polynomial derivatives yields information about the number of roots at an approached root point and the approximate location of a root point from a nearby point. The location approximation improves as a root is approached, so a powerful convergence procedure becomes available. These principles are developed into a computer program which finds the roots of polynomials with real number coefficients.

Crouse, J. E.↗
NASA NTRS1972

Generation of the invariant coefficients of the characteristic polynomial for an nxn matrix

In theories of numerical stability, roots to a characteristic polynomial are sought, which, in the case of the predictor with iterative correction method of numerical integration, are eigenvalues of a matrix whose elements depend on the coefficients used in the integration process. The characteristic polynomial is displayed explicitly in terms of the elements of the characteristic matrix.

Beaudet, P. R.↗
NASA NTRS1974

A Monte Carlo investigation of experimental data requirements for fitting polynomial functions

This report examines the extent to which sample size affects the accuracy of a low order polynomial approximation of an experimentally observed quantity and establishes a trend toward improvement in the accuracy of the approximation as a function of sample size. The task is made possible through a simulated analysis carried out by the Monte Carlo method, in which data are generated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to linear quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sample sizes and diminishes drastically for moderate and large amounts of experimental data.

Canavos, G. C.↗
NASA NTRS1974

An empirical analysis of the quantitative effect of data when fitting quadratic and cubic polynomials

A study is made of the extent to which the size of the sample affects the accuracy of a quadratic or a cubic polynomial approximation of an experimentally observed quantity, and the trend with regard to improvement in the accuracy of the approximation as a function of sample size is established. The task is made possible through a simulated analysis carried out by the Monte Carlo method in which data are simulated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to either quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sizes and diminishes drastically for moderate and large amounts of experimental data.

Canavos, G. C.↗