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Results for “subinterval”

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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10 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Optimal subinterval selection approach for power system transient stability simulation

Power system transient stability analysis requires an appropriate integration time step to avoid numerical instability as well as to reduce computational demands. For fast system dynamics, which vary more rapidly than what the time step covers, a fraction of the time step, called a subinterval, is used. However, the optimal value of this subinterval is not easily determined because the analysis of the system dynamics might be required. This selection is usually made from engineering experiences, and perhaps trial and error. This paper proposes an optimal subinterval selection approach for power system transient stability analysis, which is based on modal analysis using a single machine infinite bus (SMIB) system. Fast system dynamics are identified with the modal analysis and the SMIB system is used focusing on fast local modes. An appropriate subinterval time step from the proposed approach can reduce computational burden and achieve accurate simulation responses as well. As a result, the performance of the proposed method is demonstrated with the GSO 37-bus system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Impact of representative ground motion level on seismic PSA with the boundary between overestimation and underestimation

One commonly used approach in seismic probabilistic safety assessment (PSA) is the discrete method. This method follows the standard PSA framework and can be applied to various models, such as multi-unit models, while reducing computational costs using standard software. However, due to the inability to subdivide intervals infinitely, the discrete method approximates with a finite number of subintervals. In practice, different numbers of subintervals are applied, and the representative ground motion level is selected based on expert judgment. When employing a smaller number of subintervals, it is important to take caution to prevent underestimation. This study analyzes the impact of the representative ground motion level on seismic risk. It confirms that underestimation can occur with a small number of subintervals depending on the representative ground motion level. This study also proposes a method for determining the boundary of underestimation and overestimation. The method is demonstrated through examples, providing a mathematical foundation for selecting appropriate representative ground motion levels. By avoiding underestimation, this research helps prevent the oversight of significant risk contributors and enhances the understanding of seismic risk.

99 - GENERAL AND MISCELLANEOUS↗
DOE OSTI2018

Two-Sided Semi-Local Smoothing Splines

A semi-local smoothing spline of degree n and class C{sup p} is a function defined on an interval, having p continuous derivatives on that interval, and coinciding with a polynomial of degree n on the subintervals forming its partition. The domain of each polynomial is a subinterval on which m + 1 values of the approximated function are given, but in order to construct the polynomial, it is necessary to know M ≥ m + 1 values (m and M are determined by the class and the degree of the spline). The additional values can be borrowed from the adjacent subintervals. When constructing an S-spline in the periodic case, the problem of additional values is solved on the basis of periodicity, but in the nonperiodic case, one is expected to define the lacking values of a function beyond the domain. The present paper is aimed at nonperiodic two-sided S-splines whose construction does not require additional data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Entanglement Entropy in Lifshitz Theories

We discuss and compute entanglement entropy (EE) in (1+1)-dimensional free Lifshitz scalar field theories with arbitrary dynamical exponents. We consider both the subinterval and periodic sublattices in the discretized theory as subsystems. In both cases, we are able to analytically demonstrate that the EE grows linearly as a function of the dynamical exponent. Furthermore, for the subinterval case, we determine that as the dynamical exponent increases, there is a crossover from an area law to a volume law. Lastly, we deform Lifshitz field theories with certain relevant operators and show that the EE decreases from the ultraviolet to the infrared fixed point, giving evidence for a possible c c -theorem for deformed Lifshitz theories.

He, Temple↗
DOE OSTI2017

NUMERICAL INTEGRAL OF RESISTANCE COEFFICIENTS IN DIFFUSION

The resistance coefficients in the screened Coulomb potential of stellar plasma are evaluated to high accuracy. I have analyzed the possible singularities in the integral of scattering angle. There are possible singularities in the case of an attractive potential. This may result in a problem for the numerical integral. In order to avoid the problem, I have used a proper scheme, e.g., splitting into many subintervals where the width of each subinterval is determined by the variation of the integrand, to calculate the scattering angle. The collision integrals are calculated by using Romberg’s method, therefore the accuracy is high (i.e., ∼10{sup −12}). The results of collision integrals and their derivatives for −7 ≤ ψ ≤ 5 are listed. By using Hermite polynomial interpolation from those data, the collision integrals can be obtained with an accuracy of 10{sup −10}. For very weakly coupled plasma ( ψ ≥ 4.5), analytical fittings for collision integrals are available with an accuracy of 10{sup −11}. I have compared the final results of resistance coefficients with other works and found that, for a repulsive potential, the results are basically the same as others’; for an attractive potential, the results in cases of intermediate and strong coupling show significant differences. The resulting resistance coefficients are tested in the solar model. Comparing with the widely used models of Cox et al. and Thoul et al., the resistance coefficients in the screened Coulomb potential lead to a slightly weaker effect in the solar model, which is contrary to the expectation of attempts to solve the solar abundance problem.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Alternating Sums of Elements of Continued Fractions and the Minkowski Question Mark Function

The paper considers the function A(t) (0 ≤ t ≤ 1), related to the distribution of alternating sums of elements of continued fractions. The function A(t) possesses many properties similar to those of the Minkowski function ?(t). In particular, A(t) is continuous, satisfies similar functional equations, and A′(t) = 0 almost everywhere with respect to the Lebesgue measure. However, unlike ?(t), the function A(t) is not monotonically increasing. Moreover, on any subinterval of [1, 0], it has a sharp extremum.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Results on elastic cross sections in proton–proton collisions at $\sqrt{s}$ = 510 GeV with the STAR detector at RHIC

We report results on an elastic cross section measurement in proton–proton collisions at a center-of-mass energy $\sqrt{s}$ = 510 GeV, obtained with the Roman Pot setup of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The elastic differential cross section is measured in the four-momentum transfer squared range 0.23 ≤ −t ≤ 0.67 GeV 2 . This is the only measurement of the proton-proton elastic cross section in this t range for collision energies above the Intersecting Storage Rings (ISR) and below the Large Hadron Collider (LHC) colliders. We find that a constant slope B does not fit the data in the aforementioned t range, and we obtain a much better fit using a second-order polynomial for B(t). This is the first measurement below the LHC energies for which the non-constant behavior B(t) is observed. The t dependence of B is also determined using six subintervals of t in the STAR measured t range, and is in good agreement with the phenomenological models. The measured elastic differential cross section dσ/dt agrees well with the results obtained at $\sqrt{s}$ = 540 GeV for proton–antiproton collisions by the UA4 experiment. We also determine that the integrated elastic cross section within the STAR t-range is σ$^{fid}_{el}$ = 462.1 ± 0.9(stat.) ± 1.1(syst.) ± 11.6(scale) μb.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a thick-restart version of the Lanczos algorithm with deflation ("locking'') and a new type of polynomial filter obtained from a least-squares technique. Furthermore, the resulting algorithm can be utilized in a “spectrum-slicing” approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different subintervals independently from one another.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Asynchronous Truncated Multigrid-Reduction-in-Time

In this paper, we present the new “asynchronous truncated multigrid-reduction-in-time” (AT-MGRIT) algorithm for introducing time parallelism to the solution of discretized time-dependent problems. The new algorithm is based on the multigrid-reduction-in-time (MGRIT) approach, which, in certain settings, is equivalent to another common multilevel parallel-in-time method, Parareal. In contrast to Parareal and MGRIT that both consider a global temporal grid over the entire time interval on the coarsest level, the AT-MGRIT algorithm uses truncated local time grids on the coarsest level, each grid covering certain temporal subintervals. Further, these local grids can be solved completely in an independent way from each other, which reduces the sequential part of the algorithm and, thus, increases parallelism in the method. Here, we study the effect of using truncated local coarse grids on the convergence of the algorithm, both theoretically and numerically, and show, using challenging nonlinear problems, that the new algorithm consistently outperforms classical Parareal/MGRIT in terms of time to solution.

97 MATHEMATICS AND COMPUTING↗