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NASA NTRS1978

Modal confidence factor in vibration testing

The theory and applications of a time domain modal test technique are presented. The method uses free decay of random responses from a structure under test to identify its modal characteristics namely, natural frequencies, damping factors, and mode shapes. The method can identify multimodal (highly coupled) systems and modes that have very small contribution in the responses. A method is presented to decrease the effects of high levels of noise in the data and thus improve the accuracy of identified parameters. This is accomplished using an oversized mathematical model. The concept of modal confidence factor (MCF) is developed. The MCF is a number calculated for every identified mode for a structure under test. The MCF varies from 0.000 for a distorted, nonlinear, or noise mode to 100.0 for a pure structural mode. The theory of the MCF is based on the correlation that exits between the modal deflection at a certain station and the modal deflection at the same station delayed in time. The theory and application of the MCF is illustrated by two experiments. The first experiment deals with simulated responses from a two degree of freedom system with 20 percent, 40 percent, and 100 percent noise added. The second experiment was run on a generalized payload model. The free decay response from the payload model contained about 22 percent noise.

Ibrahim, S. R.↗

DOE OSTI2021

Model Reduction by Generalized Falk Method for Efficient Field-Circuit Simulations

The Generalized Falk Method (GFM) for coordinate transformation, together with two model-reduction strategies based on this method, are presented for efficient coupled field-circuit simulations. Each model-reduction strategy is based on a decision to retain specific linearly-independent vectors, called trial vectors, to construct a vector basis for coordinate transformation. The reduced-order models are guaranteed to be stable and passive since the GFM is a congruence transformation of originally symmetric positive definite systems. We also show that, unlike the Pad´e-via-Lanczos (PVL) method, the GFM does not generate unstable positive poles while reducing the order of circuit problems. Further, the proposed GFM is also faster when compared to methods of the type Lanczos (or Krylov) that are already widely used in circuit simulations for electrothermal and electromagnetic problems. The concept of response participation factors is introduced for the selection of the trial vectors in the proposed model-reduction methods. Further, we present methods to develop simple equivalent circuit networks for the field component of the overall field-circuit system. The implementation of these equivalent circuit networks in circuit simulators is discussed. With the proposed model-reduction strategies, significant improvement on the efficiency of the generalized Falk method is illustrated for coupled field-circuit problems.

42 ENGINEERING↗

DOE OSTI2020

Interface learning in fluid dynamics: Statistical inference of closures within micro–macro-coupling models

Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of the solution is governed by how the information is exchanged between these solvers at the interface and several methods have been devised for such coupling problems. In this article, we construct a data-driven model by spatially coupling a microscale lattice Boltzmann method (LBM) solver and macroscale finite difference method (FDM) solver for reaction-diffusion systems. The coupling between the micro-macro solvers has one to many mapping at the interface leading to the interface closure problem, and we propose a statistical inference method based on neural networks to learn this closure relation. The performance of the proposed framework in a bifidelity setting partitioned between the FDM and LBM domain shows its promise for complex systems where analytical relations between micro-macro solvers are not available.

42 ENGINEERING↗

NASA NTRS1980

A symmetric modal formulation of fluid-structure interaction, including a static approximation to higher order fluid modes

A method of fluid-structure coupling which provides symmetrical matrix equations of standard form solved by existing finite element computer programs is presented. The method postulates that the uncoupled vibration modes of the fluid or the structure be calculated before the coupled analysis. A numerical solution of vibration modes in an axisymmetric container demonstrated that a static approximation to higher order fluid modes can improve the accuracy of dynamic response computations using modal methods.

Macneal, R. H.↗

NASA NTRS1994

A Doubles Correction to Electronic Excited States from Configuration Interaction in the Space of Single Substitutions

A perturbative correction to the method of configuration interaction with single substitutions (CIS) is presented. This CIS(D) correction approximately introduces the effect of double substitutions which are absent in CIS excited states. CIS(D) is a second-order perturbation expansion of the coupled-cluster excited state method, restricted to single and double substitutions, in a series in which CIS is zeroth order, and the first-order correction vanishes. CIS (D) excitation energies are size consistent and the calculational complexity scales with the fifth power of molecular size, akin to second-order Moller-Plesset theory for the ground state. Calculations on singlet excited states of ethylene, formaldehyde, acetaldehyde, butadiene and benzene show that CIS (D) is a uniform improvement over CIS. CIS(D) appears to be a promising method for examining excited states of large molecules, where more accurate methods are not feasible.

Head-Gordon, Martin↗

NASA NTRSDate not supplied

A Nonlinear Schur Complement Solver for CFD-Based Multidisciplinary Models

CFD-based multidisciplinary models are the fundamental building blocks of multidis- ciplinary design optimization frameworks. Linear and nonlinear solutions of these coupled models are difficult, especially when the Jacobian matrices represent a saddle point problem, where a block-diagonal corresponding to a discipline is non-invertible. These scenarios necessitate the use of a coupled solver algorithm such as the Newton’s method instead of the popular block Gauss– Seidel-based methods because of this non-invertible block. To address this challenge, we introduce a nonlinear Schur complement solver suitable for CFD-based multidisciplinary models. The solver leverages the specialized linear and nonlinear solvers of the CFD code, and therefore, does not require the solution of a large coupled linear system as the coupled Newton’s method. Further- more, because the solver primarily uses the specialized linear and nonlinear solvers of the CFD code, it does not suffer from the same robustness limitations as the coupled Newton’s method. In this work, we will implement this solver in NASA’s OpenMDAO framework and demonstrate its effectiveness using a CFD-based aeropropulsive model. The solver will contribute to the develop- ment of aeropropulsive design optimization and CFD-based design optimization methods with the ultimate goal of accelerating the design and integration of advanced propulsion systems.

Nonlinear Solvers↗

DOE OSTI2023

Saddle point search with dynamic active volume

Sampling potential energy surface (PES) is critical for many problems in materials science, chemistry, physics, and biology and requires highly efficient saddle point searches (SPS). In the study, we introduce the concept of dynamic active volume (DAV) in addition to the active volume in self-evolving atomistic kinetic Monte Carlo (SEAKMC). The DAV method has further reduced the dimensionality of the PES at the elevation stage of a SPS. At the subsequent converging stage, the dynamic boundary in DAV is lifted to allow the system to converge to the right location of a saddle point. Coupled with the dimer method, the DAV method not only significantly reduces the time cost for a given search attempt, but also dramatically increases the probability of finding relevant saddle points for PES sampling. Further, a Python software package within the framework SEAKMC (SEAKMC_py) with the DAV method has been developed.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Coherent electrical control of a single high-spin nucleus in silicon

Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, for example, in chemistry, medicine, materials science and mining. Nuclear spins also featured in early proposals for solid-state quantum computers and demonstrations of quantum search and factoring algorithms. Scaling up such concepts requires controlling individual nuclei, which can be detected when coupled to an electron. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multi-spin nanoscale devices, because the field cannot be localized or screened. Control via electric fields would resolve this problem, but previous methods relied on transducing electric signals into magnetic fields via the electron–nuclear hyperfine interaction, which severely affects nuclear coherence. In this work, we demonstrate the coherent quantum control of a single 123 Sb (spin-7/2) nucleus using localized electric fields produced within a silicon nanoelectronic device. The method exploits an idea proposed in 1961 but not previously realized experimentally with a single nucleus. Our results are quantitatively supported by a microscopic theoretical model that reveals how the purely electrical modulation of the nuclear electric quadrupole interaction results in coherent nuclear spin transitions that are uniquely addressable owing to lattice strain. The spin dephasing time, 0.1 seconds, is orders of magnitude longer than those obtained by methods that require a coupled electron spin to achieve electrical driving. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors and hybrid spin-mechanical quantum systems using all-electrical controls. Integrating electrically controllable nuclei with quantum dots could pave the way to scalable, nuclear- and electron-spin-based quantum computers in silicon that operate without the need for oscillating magnetic fields.

42 ENGINEERING↗

NASA NTRS1983

Numerical solution of a coupled pair of elliptic equations from solid state electronics

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem.

Phillips, T. N.↗

NASA NTRS1984

Numerical solution of a coupled pair of elliptic equations from solid state electronics

Phillips, T. N.↗

NASA NTRS1978

Airfoil design by numerical optimization using a minicomputer

A computer program developed for the automated design of low speed airfoils utilizes a generalized Joukowski method for aerodynamic analysis coupled with a conjugate gradient, penalty function, numerical optimization algorithm to give an efficient calculation technique for use with minicomputers. The program designs airfoils with a prescribed pressure distribution as well as those which minimize or maximize some aerodynamic force coefficient. At present the method is restricted to inviscid, incompressible flow. A typical design problem will execute in 4.5 hr on an HP 9830 minicomputer.

Hicks, R. M.↗

NASA NTRS1996

Overset Grid Methods for Multidisciplinary Applications in Rotorcraft Problems

A methodology for the coupling of an advanced computational fluid dynamics method based on an overset grid flow-solver and an advanced computational structural dynamics method based on a finite element analysis is presented. Various procedures for the fluid-structure interactions modeling along with their limitations are also discussed. The flight test data for the four-bladed UH-60A Blackhawk helicopter rotor is chosen for the validation of the results. Convergence and accuracy are tested by numerical experiments with a single-bladed rotor. A comparison of airload predictions with flight test data as well as with a rigid blade case is presented. Grid and interpolation related issues for this aeroelastic application are described.

Ahmad, J. U.↗

DOE OSTI2025

Quantum Electrodynamics Coupled-Cluster at Scale: High-Performance Implementation for Complex Systems

Coupled-cluster theory (CC) is a highly accurate and versatile method for simulating complex interactions within quantum systems. The extension of CC theory to model mixed electron-photon processes with quantum electrodynamics (QED) has improved our capability to predict cavity-modified chemistry, a field where photons are used as cost-effective and eco-friendly alternatives to catalyze/inhibit chemical reactions. However, calculations with CC methods, even without incorporating QED effects, are often prohibitively expensive. Simulations of larger systems require scalable infrastructures that exist for traditional CC methods but not for QED-CC methods. As such, we present a GPU-enabled, high-performance, open-source implementation of the quantum electrodynamics coupled-cluster method with single and double excitations (QED-CCSD) within the ExaChem quantum chemistry software package. ExaChem relies on the Tensor Algebra for Many-body Methods (TAMM) infrastructure: a parallel heterogeneous tensor library designed to achieve scalable performance on modern heterogeneous supercomputing platforms. Furthermore, we discuss theoretical foundations, algorithmic details, and numerical benchmarks to showcase the larger systems that ExaChem can simulate and how the integration of photonic degrees-of-freedom alters their ground-state properties.

Basis sets↗

DOE OSTI2023

Cascade of vestigial orders in two-component superconductors: Nematic, ferromagnetic, s -wave charge- 4 e , and d -wave charge- 4 e states

Electronically ordered states that break multiple symmetries can melt in multiple stages, similarly to liquid crystals. In a partially melted phase, known as vestigial phase, a bilinear made out of combinations of the multiple components of the primary order parameter condenses. Multicomponent superconductors are thus natural candidates for vestigial order since they break both the U⁡(1)-gauge and also time-reversal or lattice symmetries. Here, we use group theory to classify all possible real-valued and complex-valued bilinears of a generic two-component superconductor on a tetragonal or hexagonal lattice. While the more widely investigated real-valued bilinears correspond to vestigial nematic or ferromagnetic order, the little explored complex-valued bilinears correspond to a vestigial charge-4e condensate, which itself can have an underlying s-wave, d x 2 –y 2 -wave, or d xy -wave symmetry. To properly describe the fluctuating regime of the superconducting Ginzburg-Landau action and thus access these competing vestigial phases, we employ both a large-N and a variational method. We show that while vestigial order can be understood as a weak-coupling effect in the large-N approach, it is akin to a moderate-coupling effect in the variational method. Despite these distinctions, both methods yield similar results in wide regions of the parameter space spanned by the quartic Landau coefficients. Specifically, we find that the nematic and ferromagnetic phases are the leading vestigial instabilities, whereas the various types of charge-4⁢e order are attractive albeit subleading vestigial channels. The only exception is for the hexagonal case, in which the nematic and s-wave charge-4e vestigial states are degenerate. Finally, we discuss the limitations of our approach, as well as the implications of our results for the realization of exotic charge-4⁢e states in material candidates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1979

A scheme for computing surface fluxes from mean flow observations

A computational method for estimating turbulent surface stress, sensible heat flux, and humidity flux from mean velocity, temperature, and humidity at a single height in the atmospheric surface layer is presented. The method is based on coupling a Monin-Obukhov similarity profile to a 'force-restore' formulation for the evolution of surface soil temperature to yield the local values of shear stress, heat flux, and surface temperature. In addition to reference-level mean flow properties, the parameters required to implement this method are the thermal heat capacity of the soil, the surface aerodynamic roughness, latitude, solar declination, surface albedo, surface emissivity, and atmospheric transmissivity. Sample calculations are presented for (1) constant atmospheric forcing at the reference level, and (2) variable atmospheric forcing corresponding to Kahle's (1977) measurements of windspeed, air temperature, and radiometer soil surface temperature under dry vegetatively sparse conditions in the Mohave Desert, Calif.

Hoffert, M. I.↗

DOE OSTI2025

Advancing material modeling in hydrocodes using a concurrent finite-element and molecular dynamics multiscale framework

We present a multiscale simulation framework that couples the finite-element method with molecular dynamics. Bypassing traditional equations of state (EOS) by using in-line atomistic simulations, the method offers the advantage of incorporating detailed microscale physics not easily represented with coarse-grained models. Coupling consistency with the continuum code is ensured through the use of lifting and restriction operators, in line with heterogeneous multiscale methods. The concurrent continuum-atomistic framework is validated through comparison with experimental results and conventional EOS models, and demonstrated in a shock-driven hydrodynamic flow simulation under extreme conditions. We further evaluate the framework's usability by comparing it to state-of-the-art EOS models of deuterium. A computational performance study reveals that the atomistic EOS evaluation is a feasible alternative to conventional approaches, and demonstrates a weak scaling of 99% efficiency. These results highlight the framework's potential for large-scale multiscale modeling across a broad range of materials and conditions.

Computer science↗

DOE OSTI2026

Bootstrap embedding for interacting electrons in phonon coherent-state mean field

Here, we develop a Fermi–Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron–phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard–Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.

Islam, Shariful [North Carolina State University, ↗

DOE OSTI2022

Complex paths around the sign problem

The Monte Carlo evaluation of path integrals is one of a few general purpose methods to approach strongly coupled systems. It is used in all branches of physics, from QCD and nuclear physics to the correlated electron systems. However, many systems of great importance (dense matter inside neutron stars, the repulsive Hubbard model away from half filling, and dynamical and nonequilibrium observables) are not amenable to the Monte Carlo method as it currently stands due to the so-called sign problem. Here, a new set of ideas recently developed to tackle the sign problem based on the complexification of field space and the Picard-Lefshetz theory accompanying it is reviewed. The mathematical ideas underpinning this approach, as well as the algorithms developed thus far, are described together with nontrivial examples where the method has already been proved successful. Directions of future work, including the burgeoning use of machine learning techniques, are delineated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗