Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “SERIES EXPANSION”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Taylor-Expansion-Based Robust Power Flow in Unbalanced Distribution Systems: A Hybrid Data-Aided Method

Traditional power flow methods often adopt certain assumptions designed for passive balanced distribution systems, thus lacking practicality for unbalanced operation. moreover, their computation accuracy and efficiency are heavily subject to unknown errors and bad data in measurements or prediction data of distributed energy resources (ders). to address these issues, this paper proposes a hybrid data-aided robust power flow algorithm in unbalanced distribution systems, which combines taylor series expansion knowledge with a data-driven regression technique. the proposed method initiates a linearization power flow model to derive an explicitly analytical solution by modified taylor expansion. to mitigate the approximation loss that surges due to the der integration and bad data, we further develop a data-aided robust support vector regression approach to estimate the errors efficiently. comparative analysis in the 13-bus and 123-bus ieee unbalanced feeders shows that the proposed hybrid algorithm achieves superior computational efficiency, with guaranteed accuracy and robustness against outliers.

data-driven↗
NASA NTRS1977

Vibrations of incompressible liquid-plastic tank combinations using a series representation of the liquid

A series representation is presented of the dynamic behavior of incompressible non-viscous liquids contained in partially filled elastic shells of revolution. Using a series in which each term satisfies exactly Laplace's equation, the liquid portion of the problem becomes an integral equation on the wetted wall of the shell. Physical insight required in selecting the terms of the series is such that selection may be readily programed on a computer. Liquid-shell vibration interaction is investigated by modifying an existing shell of revolution vibration program with the series expansion of the liquid pressure loading on the wetted shell wall. Application of the modified program is demonstrated on a hemispherical tank and a realistic scaled model of a launch vehicle tank having a more complex geometry. Comparison of the present analysis with a NASTRAN finite element analysis for a hemispherical tank, and comparison with test results for a launch vehicle tank shows excellent agreement and rapid convergence of the series representation of the liquid to the true solution.

Housner, J. M.↗
NASA NTRS1990

On the far-field stream function condition for two-dimensional incompressible flows

The present demonstration of the usefulness of the integral series expansion of the stream function as a far-field computational boundary condition shows the method to require only a 10-percent/time-step increase in computational effort over alternative boundary conditions, in the case of implementation of unsteady problems using a direct elliptic solver. So long as the vorticity was encompassed within the computational domain, the method proved sufficiently accurate to yield virtually identical results for two widely different domains. While the integral-series condition yielded the best results for periodic flow, the Neumann condition gave comparable accuracy with less computation time for the steady-flow case despite its inability to treat periodic flow with vortex shedding.

Sa, Jong-Youb↗
NASA NTRS1995

A hybrid neurocomputing/numerical strategy for nonlinear structural analysis

A hybrid neurocomputing/numerical strategy is presented for geometrically nonlinear analysis of structures. The strategy combines model-free data processing capabilities of computational neural networks with a Pade approximants-based perturbation technique to predict partial information about the nonlinear response of structures. In the hybrid strategy, multilayer feedforward neural networks are used to extend the validity of solutions by using training samples produced by Pade approximations to the Taylor series expansion of the response function. The range of validity of the training samples is taken to be the radius of convergence of Pade approximants and is estimated by setting a tolerance on the diverging approximants. The norm of residual vector of unbalanced forces in a given element is used as a measure to assess the quality of network predictions. To further increase the accuracy and the range of network predictions, additional training data are generated by either applying linear regression to weight matrices or expanding the training data by using predicted coefficients in a Taylor series. The effectiveness of the hybrid strategy is assessed by performing large-deflection analysis of a doubly-curved composite panel with a circular cutout, and postbuckling analyses of stiffened composite panels subjected to an in-plane edge shear load. In all the problems considered, the hybrid strategy is used to predict selective information about the structural response, namely the total strain energy and the maximum displacement components only.

Szewczyk, Z. Peter↗
NASA NTRS2011

Validation of Real-Time Data Processing for the Ground and Air-MSPI Systems

JPL is currently developing the multi-angle spectro-polarimetric imager (MSPI), targeted for the Aerosol-Cloud-Ecosystems (ACE) mission, as defined in the National Academies 2007 Decadal Survey. In preparation for the space instrument, the MSPI team has built two incremental camera systems (Ground- and Air-MSPI) to improve understanding of the proposed architecture. Ground-MSPI is a gimballed instrument used primarily for stationary observation and characterization of the imager and optics. The ER-2 based Air-MSPI operates in a step-and-stare mode, providing multi-angle imaging of a static target. This mode-of-operation simulates the observation scenario of the space instrument. Physically, MSPI is a pushbroom camera with a specialized frontend. Before imaging, light entering the camera passes through a pair of photoelastic modulators and a set of pattern polarizers. These optical elements act on the light to make polarimetric extraction computationally feasible. Calculating polarimetric parameters from the imager's data stream requires a real-time least-squares computation that produces coefficients of a truncated time-series expansion of the image. As reported in, the data processing algorithm can operate in real-time on a Xilinx Virtex-5 FPGA. Moving beyond verification with an onboard data source, the algorithm has been validated on a commercial development board interfaced with the ground camera. In addition, the algorithm has been instantiated within the Air-MSPI electronics board's FPGA, and in situ first-light has been achieved.

real-time data processing↗
DOE OSTI2024

Two-loop master integrals for leading-color $$ pp\to t\overline{t}H $$ amplitudes with a light-quark loop

Abstract We compute the two-loop master integrals for leading-color QCD scattering amplitudes including a closed light-quark loop in$$ t\overline{t}H $$ t t ¯ H production at hadron colliders. Exploiting numerical evaluations in modular arithmetic, we construct a basis of master integrals satisfying a system of differential equations inϵ-factorized form. We present the analytic form of the differential equations in terms of a minimal set of differential one-forms. We explore properties of the function space of analytic solutions to the differential equations in terms of iterative integrals which can be exploited for studying the analytic form of related scattering amplitudes. Finally, we solve the differential equations using generalized series expansions to numerically evaluate the master integrals in physical phase space. As the first computation of a set of two-loop seven-scale master integrals, our results provide valuable input for analytic studies of scattering amplitudes in processes involving massive particles and a large number of kinematic scales.

Physics↗
DOE OSTI2025

Factorization for jet production in heavy-ion collisions

We develop an Effective Field Theory approach for jet observables in heavy-ion collisions, where the jet is treated as an open quantum system interacting with a hot and dense QCD medium. Within this framework, we derive a novel factorization formula for inclusive jet production, expressed as a series expansion with an increasing number of radiating subjet functions that encode forward scattering with the Quark-Gluon Plasma, convolved with perturbative matching coefficients. This work provides a systematic framework for computing jet observables at higher order and understanding their non-perturbative aspects, paving the way for future applications in heavy-ion phenomenology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

A new method for solving the linearized 1D Vlasov–Poisson system yielding a new class of solutions

We describe a new method for solving the linearized 1D Vlasov–Poisson system by using properties of Cauchy-type integrals. Our method remedies critical flaws of the two standard methods, reveals a previously unrecognized Gaussian-in-time-like decay, and can also account for an externally applied electric field. The Landau approximation involves deforming the Bromwich contour around the poles closest to the real axis due to the analytically continued dielectric function, finding the long-time behavior for a stable system: Landau damping. Jackson's generalization encircles all poles while sending the contour to infinity, assuming its contribution vanishes, which is not true in general. This gives incorrect solutions for physically reasonable configurations and can exhibit pathological behavior, of which we show examples. The van Kampen method expresses the solution for a stable equilibrium as a continuous superposition of waves, resulting in an opaque integral. Case's generalization includes unstable systems and predicts a decaying discrete mode for each growing discrete mode, an apparent contradiction to both the Jackson solution and ours. We show, without imposing additional constraints, that the decaying modes are never present in the time evolution due to an exact cancellation with part of the continuum. Our solution is free of integral expressions, is obtained using algebra and Laurent series expansions, does not rely on analytic continuations, and results in a correct asymptotically convergent form in the case of infinite sums. The analysis used can be readily applied in higher-dimensional, electromagnetic systems and also provides a new technique for evaluating certain inverse Laplace transforms.

Physics↗
DOE OSTI2025

Ab-initio simulation of spin-vibronic spectra of methoxy radical

Despite the fact that experimental and theoretical work on the spectrum of methoxy has stretched from the microwave to the ultraviolet and proceeded for nearly 50 years, parts of the spectrum have remained a challenge to simulate theoretically and make reliable line-by-line assignments. The spectral complexity arises because the radical has a non-zero electron spin and significant vibronic coupling between the two elec- tronic components of the ground state due to the presence of a conical intersection. This work describes a completely ab initio effort to understand and assign the spin- vibronic levels of the X 2E state from 0 to above 3000 cm−1, a region that includes the fundamental transitions of the C-H symmetric and asymmetric stretches that have not previously been identified uniquely. A potential energy surface for methoxy was calculated at the EOM-CCSDT/ANO1 level of theory. Subsequently this potential energy surface was fit to a quartic power series expansion of all nine vibrational nor- mal coordinates (as determined at the minimum of the conical intersection) by the use of a machine-learning-based algorithm. After the addition of spin-orbit coupling, the spin-vibronic problem was solved using both the Krylov-Schur and Lanczos algorithms with the SOCJT3 software to converge eigenvalues up to 3500 cm−1 and their eigen- vectors. The latter were used, in conjunction with the calculated dipole moment and its derivatives (calculated using finite differences at EOM-CCSDT/ANO1 level), to determine spectral intensities for the spin-vibronic spectra. The calculated transition frequencies and intensities were used to simulate and assign the observed transitions of the spin-vibronic spectra of the radical. The credibility of the assignments and their significance is discussed in detail.

Sharma, Ketan [University of Florida, Gainesville,↗
DOE OSTI2024

Measurements of the branching fractions of semileptonic D s + decays via e + e − → D s * + D s * −

We measure the absolute branching fractions of semileptonic D s + decays via the e + e − → D s * + D s * − process using e + e − collision data corresponding to an integrated luminosity of 10.64 fb − 1 collected by the BESIII detector at center-of-mass energies between 4.237 and 4.699 GeV. The branching fractions are B ( D s + → η e + ν e ) = ( 2.35 ± 0.11 stat ± 0.10 syst ) % , B ( D s + → η ′ e + ν e ) = ( 0.82 ± 0.09 stat ± 0.04 syst ) % , B ( D s + → ϕ e + ν e ) = ( 2.21 ± 0.16 stat ± 0.11 syst ) % , B ( D s + → f 0 ( 980 ) e + ν e , f 0 ( 980 ) → π + π − ) = ( 0.15 ± 0.02 stat ± 0.01 syst ) % , B ( D s + → K 0 e + ν e ) = ( 0.24 ± 0.0 4 stat ± 0.0 1 syst ) % , and B ( D s + → K * 0 e + ν e ) = ( 0.19 ± 0.0 3 stat ± 0.0 1 syst ) % . These results are consistent with those measured via the e + e − → D s * ± D s ∓ process by BESIII and CLEO. Using two-parameter series expansion, the hadronic transition form factors of D s + → η e + ν e , D s + → η ′ e + ν e , and D s + → K 0 e + ν e are determined to be f + η ( 0 ) = 0.442 ± 0.02 2 stat ± 0.01 7 syst , f + η ′ ( 0 ) = 0.557 ± 0.06 2 stat ± 0.02 4 syst , and f + K 0 ( 0 ) = 0.677 ± 0.09 8 stat ± 0.02 3 syst . Published by the American Physical Society 2024

Ablikim, M.↗
DOE OSTI2025

Almost strong zero modes at finite temperature

Interacting fermionic chains exhibit extended regions of topological degeneracy of their ground states as a result of the presence of Majorana or parafermionic zero modes localized at the edges. In the opposite limit of infinite temperature, the corresponding nonintegrable spin chains, obtained via generalized Jordan-Wigner mapping, are known to host so-called almost strong zero modes, which are long-lived with respect to any bulk excitations. Here we study the fairly unexplored territory that bridges these two extreme cases of zero and infinite temperature. We blend two established techniques for states, the Lanczos series expansion and a tensor network ansatz, uplifting them to the level of operator algebra. This allows us to efficiently simulate large system sizes for arbitrarily long timescales and to extract the temperature-dependent decay rates. We observe that for the Kitaev-Hubbard model, the decay rate of the edge mode depends exponentially on the inverse temperature 𝛽, and on an effective energy scale Δ eff that is greater than the thermodynamic gap of the system Δ.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Study of Quadrupole Fringe Fields in the Interaction Region of the Hadron Storage Ring of the Electron Ion Collider

Fringe fields in quadrupole magnets are usually neglected in studies of beam dynamics at accelerators. However, the extreme optical parameters present in the final focus of a collider such as the Electron–Ion Collider (EIC) may give rise to effects that should not be overlooked. The calculation of quadrupole fringe fields presented in this study follows the procedure outlined in Ref. [1], specialized to the case of a straight reference orbit (i.e., with no dipole field component). A right-handed Cartesian coordinate system is employed, with the $z$-axis aligned with the quadrupole axis and $x$ and $y$ denoting the horizontal and vertical transverse coordinates, respectively. The magnetic quadrupole field gradient, $G = \partial B_y / \partial x$, transitions from its peak value inside the quadrupole—where it is nearly independent of the longitudinal coordinate $z$—to zero at some distance beyond the magnet edge. Consequently, $G$ is treated as a function of $z$. The region over which this variation occurs is defined as the quadrupole fringe field region. The study begins with the development of a description of the magnetic field in the fringe region using a power-series expansion in the transverse coordinates $x$and $y$, consistent with the longitudinally varying gradient. A model for the $z$-dependence of the gradient is then proposed and adjusted to reproduce magnetic field data obtained from three-dimensional field calculations. To evaluate the impact of the fringe fields on beam dynamics, the corresponding vector potential is derived and incorporated into a Hamiltonian formulation of particle motion. The significance of the fringe fields is quantified by calculating the amplitude-dependent tune shift from the Hamiltonian. Using linear beam optics parameters of the Hadron Storage Ring (HSR) of the EIC, the tune shift due to the fringe fields of all quadrupole magnets in the IR-6 interaction region is evaluated. Finally, the resulting tune shifts are compared with those arising from other nonlinear field components present in the HSR.

43 PARTICLE ACCELERATORS↗
NASA NTRS1962

One-Dimensional Heat Conduction Through the Skin of a Vehicle upon Entering a Planetary Atmosphere at Constant Velocity and Entry Angle

Closed-form solutions of the one-dimensional heat-conduction equations for the flow of heat into a plate with a laminar boundary layer have been obtained for a configuration entering a planetary atmosphere with constant velocity and negative entry angle. The atmospheric density was assumed to obey an exponential law and the temperature was assumed constant initially. The solution is in the form of a Fourier series expansion which, for most practical applications, can be approximated by retaining only one term of the expression. The solution applies to the initial part of the entry before the maximum heating conditions are encountered.

SKIN TEMPERATURE↗