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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

A variational method for finite element stress recovery: Applications in one-dimension

It is well-known that stresses (and strains) calculated by a displacement-based finite element analysis are generally not as accurate as the displacements. In addition, the calculated stress field is typically discontinuous at element interfaces. Because the stresses are typically of more interest than the displacements, several procedures have been proposed to obtain a smooth stress field, given the finite element stresses, and to improve the accuracy. Hinton and Irons introduced global least squares smoothing of discrete data defined on a plane using a finite element formulation. Tessler and co-workers recently developed a conceptually similar formulation for smoothing of two-dimensional data based on a discrete least square approximation with a penalty constraint. The penalty constraint results in a stress field which is C(exp 1)-continuous, a result not previously obtained. The approach requires additional, 'smoothing' finite element analysis and for their two-dimensional application, they used a conforming C(exp 0)-continuous triangular finite element based on a conforming plate element. This paper presents the results of a detailed investigation into the application of Tessler's smoothing procedure to the smoothing of finite element stresses from one-dimensional problems. Although the one-dimensional formulation has some practical applicability, such as in truss, beam, axisymmetric mechanics, and one-dimensional heat conduction, the primary motivation for developing the one-dimensional smoothing case is to explore the characteristics of the general smoothing strategy. In particular, it is used to describe the behavior of the method and to explore the suitability of criteria proposed for the smoothing analysis. Prior to presenting numerical results, the variational formulation of the smoothing strategy is presented and a criterion for the smoothing analysis is described.

Riggs, H. Ronald↗
DOE OSTI2024

A variational method for the sheath potential of hypersonic leading edges with space-charge limitations

Electron transpiration cooling for the leading edges (LE) of hypersonic aircraft utilizes thermionic emission; however, space-charge effects limit the electron emission rate, potentially diminishing the efficiency of this cooling mechanism. We develop a variational weak form of the Poisson equation that describes the sheath potential and then numerically solve it using the finite element method. This formulation has two main benefits: (1) the space-charge limit condition can be incorporated as a constraint and (2) it allows for the analysis of three-dimensional geometries with complex boundary conditions. We demonstrate that the current emitted from the surface of an LE is generally a small fraction of the Child–Langmuir limit due to space charge. We then propose several methods to enhance the emitted current from the surface and to boost the cooling effect of thermionic emission. These include increasing the plasma density, applying a negative surface potential, and using fringe fields under suitable geometric conditions. For a LaB6 emitting LE, the total emitted current is shown to be minimal and independent of the temperature of a surface with floating potential. However, when a negative potential is applied and the surface is heated, the emitted current follows the Richardson–Dushman relationship up to a critical temperature, beyond which it remains constant. At an applied surface potential of −5 V, the critical temperature is around 1700 K.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Quantum simulations of nuclear resonances with variational methods

Background: The many-body nature of nuclear physics problems poses significant computational challenges. These challenges become even more pronounced when studying the resonance states of nuclear systems, which are governed by the non-Hermitian Hamiltonian. Quantum computing, particularly for quantum many-body systems, offers a promising alternative, especially within the constraints of current noisy intermediate-scale quantum (NISQ) devices. Purpose: This work aims to simulate nuclear resonances using quantum algorithms by developing a variational framework compatible with non-Hermitian Hamiltonians and implementing it fully on a quantum simulator. Methods: We employ the complex scaling technique to extract resonance positions classically and adapt it for quantum simulations using a two-step algorithm. First, we transform the non-Hermitian Hamiltonian into a Hermitian form by using the energy variance as a cost function within a variational framework. Second, we perform 𝜃-trajectory calculations to determine optimal resonance positions in the complex energy plane. To address resource constraints on NISQ devices, we utilize Gray code (GC) encoding to reduce qubit requirements. Results: We first validate our approach using a schematic potential model that mimics a nuclear potential, successfully reproducing known resonance energies with high fidelity. We then extend the method to a more realistic 𝛼−𝛼 nuclear potential and compute the 𝐷- and 𝐺-wave resonance energies with a basis size of 𝑁=16, using only four qubits. The quantum simulation results closely match the classical values, demonstrating the feasibility of our approach. Conclusions: This study demonstrates, for the first time, that the complete 𝜃-trajectory method can be implemented on a quantum computer without relying on any classical input beyond the Hamiltonian. The results establish a scalable and efficient quantum framework for simulating resonance phenomena in nuclear systems. This work represents a significant step toward quantum simulations of open quantum systems and lays the foundation for future investigations into resonance structures in nuclear, atomic, and molecular physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1985

Cross sections for electron impact excitation of the b 3Sigma(+)u state of H2 - An application of the Schwinger multichannel variational method

In this and the two accompanying letters, the results of calculations of the cross sections for electron impact excitation of the b 3Sigma(+)u state of H2, for collision energies from near threshold to 30 eV, are presented. These results are obtained using a multichannel extension of the Schwinger variational principle at the two-state level. The quantitative agreement between the integral cross sections of these three studies is very good. Inclusion of correlation terms in the scattering wavefunctions, which relax the orthogonality between bound and continuum orbitals, is seen to affect the cross sections substantially. Although a comparison of these calculated cross sections with available experimental data is encouraging, some seious discrepancies exist.

Lima, M. A. P.↗
DOE OSTI2026

A scalable variational method for estimating the latent infection-rate field of an outbreak

In this paper, we explore whether the infection-rate of a disease can serve as a robust monitoring variable in epidemiological surveillance algorithms. The infection-rate is dependent on population mixing patterns that do not vary erratically day-to-day; in contrast, daily case-counts used in contemporary surveillance algorithms are corrupted by reporting errors. The technical challenge lies in estimating the latent infection-rate from case-counts. Here we devise a Bayesian method to estimate the infection-rate across multiple adjoining areal units, and then use it, via an anomaly detector, to discern a change in epidemiological dynamics. We extend an existing model for estimating the infection-rate in an areal unit by incorporating a Markov random field model, so that we may estimate infection-rates across multiple areal units, while preserving spatial correlations observed in the epidemiological dynamics. To carry out the high-dimensional Bayesian inverse problem, we develop an implementation of mean-field variational inference specific to the infection model and integrate it with the random field model to incorporate correlations across counties. The method is tested on estimating the COVID-19 infection-rates across all 33 counties in New Mexico using data from the summer of 2020, and then employing them to detect the arrival of the Fall 2020 COVID-19 wave. We perform the detection using a temporal algorithm that is applied county-by-county. We also show how the infection-rate field can be used to cluster counties with similar epidemiological dynamics.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

A Variational Method for Analyzing Vortex Flows in Radar-Scanned Tornadic Mesocyclones. Part III: Sensitivities to Vortex Center Location Errors

Abstract When the vortex center location is estimated from a radar-scanned tornadic mesocyclone, the estimated location is not error-free. This raises an important issue concerning the sensitivities of analyzed vortex flow (VF) fields by the VF-Var (formulated in Part I of this paper series and tested in Part II) to vortex center location errors, denoted by Δ x c . Numerical experiments are performed to address this issue with the following findings: The increase of |Δ x c | from zero to a half of vortex core radius causes large analysis error increases in the vortex core but the increased analysis errors decrease rapidly away from the vortex core especially for dual-Doppler analyses. The increased horizontal-velocity errors in the vortex core are mainly in the Δ x c -normal component, because this component varies much more rapidly than the other component along the Δ x c direction in the vortex core. The vertical variations of Δ x c distort the vertical correlation structure of Δ x c -dislocated VF-dependent background error covariance, which can increase the analysis errors in the vortex core. The dual-Doppler analyses have adequate accuracies outside the vortex core even when |Δ x c | increases to a half of vortex core radius, while single-Doppler analyses can also have adequate accuracies outside the vortex core mainly for the single-Doppler-observed velocity component. The sensitivities to Δ x c are largely unaffected by the vortex slanting. The above findings are important and useful for assessing the accuracies of analyzed VFs for real radar-observed tornadic mesocyclones. Significance Statement When the vortex center location is estimated from a radar-scanned tornadic mesocyclone, the estimated location is not error-free. This raises an issue concerning the sensitivity of analyzed vortex flow (VF) by the VF-Var (formulated in Part I of this paper series and tested with simulated radar observations in Part II) to vortex center location error. This issue and its required investigations are very important for the VF-Var to be applied to real radar-observed tornadic mesocyclones, especially in an operational setting with the WSR-88Ds. Numerical experiments are performed to address this issue. The findings from these experiments are important and useful for assessing the accuracies of VF-Var analyzed VF fields for real radar-observed tornadic mesocyclones.

Xu, Qin↗
NASA NTRS1984

A variational method for the calculation of dynamic polarizabilities and two-photon transition moments - The dressed molecule approach

The solution of the time-dependent Schroedinger equation of the molecule + radiation field system is analyzed. A quantized radiation field is used. The relationship between the oscillatory wave function and the dressed state wave function is established, the oscillatory wave function being the solution if the radiation field is turned on at t = 0 and the dressed state being the stationary solution satisfying the boundary condition only if the field is present at t = negative infinity. In general, the oscillatory wave function can be expressed using a complete set of dressed states. However, in the presence of a nonresonant radiation field, the system is well represented by a single dressed state. Molecular properties such as dynamic polarizabilities and two-photon transition moments can be deduced from the dressed state wave function instead of the oscillatory wave function as in previous methods. Because of its stationary character, the dressed state is more amenable to approximate calculations. A CI method is developed for this purpose. The CI matrix is simple in form and can be readily constructed using existing computer codes. The present method can also be adapted to calculate other optical properties.

Huo, W. M.↗