Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximation”

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 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

The XPS of pyridine: A combined theoretical and experimental analysis

A detailed analysis of the N(1s) and C(1s) X-Ray Photoelectron Spectroscopy (XPS) is made, where the measured XPS is compared with theoretical Sudden Approximation (SA) intensities and theoretical XPS Binding Energies (BEs). There is remarkably good agreement between the theoretical predictions and the measured XPS; in particular, the different full width at half maximum values for the C(1s) and N(1s) BEs are explained in terms of unresolved C(1s) BEs for the different C atoms in pyridine. Here, this work demonstrates that the combination of theory and XPS measurements can extract analysis of the XPS relevant to the molecular electronic structure. The theory used is based on fully relativistic self-consistent field solutions of the Dirac–Coulomb Hamiltonian, and the SA is used to determine relative XPS intensities.

Binding Energies (BEs)↗
DOE OSTI2025

How the choice of exchange–correlation functional affects DFT-based simulations of the hydrated electron

Hydrated electrons are anionic species that are formed when an excess electron is introduced into liquid water. Building an understanding of how hydrated electrons behave in solution has been a long-standing effort of simulation methods, of which density functional theory (DFT) has come to the fore in recent years. The ability of DFT to model the reactive chemistry of hydrated electrons is an attractive advantage over semi-classical methodologies; however, relatively few density functional approximations (DFAs) have been used for the hydrated electron simulations presented in the literature. Here, we simulate hydrated electron systems using a series of exchange–correlation (XC) functionals spanning Jacob’s ladder. We calculate a variety of experimental and other observables of the hydrated electron and compare the XC functional dependence for each quantity. We find that the formation of a stable localized hydrated electron is not necessarily limited to hybrid XC functionals and that some hybrid functionals produce delocalized hydrated electrons or electrons that react with the surrounding water at an unphysically fast rate. Here, we further characterize how different DFAs impact the solvent structure and predicted spectroscopy of the hydrated electron, considering several methods for calculating the hydrated electron’s absorption spectrum for the best comparison between structures generated using different density functionals. None of the dozen or so DFAs that we investigated are able to correctly predict the hydrated electron’s spectroscopy, vertical detachment energy, or molar solvation volume.

Ab-initio molecular dynamics↗
DOE OSTI2025

Symmetry breaking as predicted by a phase space Hamiltonian with a spin Coriolis potential

Here, we perform electronic structure calculations for a set of molecules with degenerate spin-dependent ground states ( 3 CH 2 , 2 CH$^{•}_{3}$, 3 O 2 ) going beyond the Born–Oppenheimer approximation and accounting for nuclear motion. According to a phase space approach that parameterizes electronic states (|Φ⟩) and electronic energies (E) by nuclear position and momentum [i.e., |Φ(R, P)⟩ and E(R, P)], we find that the presence of degenerate spin degrees of freedom leads to broken symmetry ground states. More precisely, rather than a single degenerate minimum at (R, P) = (R min , 0), the ground state energy has two minima at (R,P)=(R' min ,±P min ) (where R' min is close to R min ), dramatically contradicting the notion that the total energy of the system can be written in separable form as E = $\frac{P^2}{2M}$ + V el . Although we find that the broken symmetry solutions have small barriers between them for the small molecules, we hypothesize that the barriers should be macroscopically large for metallic solids, thus offering up a new phase-space potential energy surface for simulating the Einstein–de Haas effect.

Berry connection↗
DOE OSTI2026

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Derivative-free stochastic optimization via adaptive sampling strategies

In this paper, we present a novel derivative-free framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning to quantum computing involve settings where only stochastic function values are obtained via a zeroth-order oracle, which has no available gradient information and necessitates the usage of derivative-free optimization methodologies. Our approach includes estimating gradients using stochastic function evaluations and integrating adaptive sampling techniques to control the accuracy in these stochastic approximations. Our framework encapsulates several gradient estimation techniques, including standard finite-difference, Gaussian smoothing, sphere smoothing, randomized coordinate finite-difference, and randomized subspace finite-difference methods. We provide theoretical convergence guarantees for our framework and analyze the worst-case iteration and sample complexities associated with each gradient estimation method. Finally, we demonstrate the empirical performance of the methods on logistic regression and nonlinear least squares problems.

Adaptive sampling↗
DOE OSTI2025

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Self-consistent microscopic calculations for electron captures on nuclei in core-collapse supernovae

Calculations for electron capture rates on nuclei with atomic numbers between 𝑍 = 20 and 𝑍 = 52 are performed in a self-consistent finite-temperature covariant energy density functional theory within the relativistic quasiparticle random-phase approximation. Electron captures on these nuclei contribute most to reducing the electron fraction during the collapse phase of core-collapse supernovae. The rates include contributions from allowed (Gamow-Teller) and first-forbidden (FF) transitions, and it is shown that the latter become dominant at high stellar densities and temperatures. Temperature-dependent effects such as Pauli unblocking and transitions from thermally excited states are also included. The new rates are implemented in a spherically symmetric one-dimensional simulation of the core-collapse phase. The results indicate that the increase in electron capture rates, due to inclusion of FF transitions, leads to reductions of the electron fraction at nuclear saturation density, the peak neutrino luminosity, and enclosed mass at core bounce. The new rates reaffirm that the most relevant nuclei for the deleptonization situate around the 𝑁 = 50 and 82 shell closures, but, compared to previous simulations, nuclei are less proton rich. Here, the new rates developed in this work are available, and will be of benefit to improve the accuracy of multidimensional supernova simulations.

Electron & muon capture↗
DOE OSTI2024

Semiclassical theory of bipolaronic superconductivity in a bond-modulated electron-phonon model

We analyze the transition temperature T c of bipolaronic superconductivity in a bond Su-Schrieffer-Heeger (bond-SSH) model—also known as a bond Peierls model—where the electron hoppings are modulated by bond phonons. Using a semiclassical instanton approximation justifiable in the adiabatic limit of slow phonons, we find that the bipolaron mass is only weakly enhanced, in contrast to the typical large mass enhancement found in standard (Holstein) electron-phonon models. Specifically, in the strong coupling limit, the bipolarons can freely slide within a degenerate manifold rather than become self-trapped. A gas of these bipolarons can undergo a superfluid transition at a critical temperature for which we obtain an upper bound. We find that this bound is exponentially larger than that in the Holstein model. In conclusion, our study provides an analytical understanding of the mechanism behind the high-T c bipolaronic superconductivity numerically observed in [Phys. Rev. X 13, 011010 (2023)].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Coupling-dependent antiferromagnetic-ferromagnetic ordering in a pinwheel artificial spin ice

Nanopatterned magnetic thin films offer a platform for exploration of tailored magnetic properties such as emergent long-range order. A prominent example is artificial spin ice (ASI), where an arrangement of nanoscale magnetic elements, acting as macrospins, interact via their dipolar fields. In this study, we discuss the transition from antiferromagnetic (AFM) to ferromagnetic (FM) long-range order in a square lattice ASI as the magnetic elements are gradually rotated through 45⁢° to a “pinwheel” configuration. The AFM-FM transition is observed experimentally using synchrotron radiation x-ray spectromicroscopy and occurs for a certain rotation angle of the nanomagnets, dependent on the dipolar coupling strength determined by the separation of the magnets in the lattice. Large-scale magnetic dipole simulations show that the point-dipole approximation fails to capture the correct AFM-FM transition angle. However, excellent agreement with experimental data is obtained using a dumbbell-dipole model, which better reflects the actual dipolar fields of the magnets. This model also explains the coupling dependence of the transition angle, another feature not captured by the point-dipole model. Our findings resolve a discrepancy between measurement and theory in previous work on “pinwheel” ASIs and establish the coupling dependence of the AFM-FM transition. The revised dipole model, with a more accurate representation of the stray field, offers more precise control of magnetic order in artificial spin systems.

Artificial spin ice↗
DOE OSTI2024

Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates La 3 ⁢Ni 2 ⁢O 7

Motivated by the recently proposed alternating single-layer trilayer stacking structure for the nickelate La 3 ⁢Ni 2 ⁢O 7 , we comprehensively study this system using ab initio and random-phase approximation techniques. Here, our analysis unveils similarities between this novel La 3⁢ Ni 2 ⁢O 7 structure and other Ruddlesden-Popper nickelate superconductors, such as a similar charge-transfer gap value and orbital-selective behavior of the eg orbitals. Pressure primarily increases the bandwidths of the Ni e g bands, suggesting an enhancement of the itinerant properties of those e g states. By changing the cell volume ratio V/V 0 from 0.9 to 1.10, we found that the bilayer structure in La 3 ⁢Ni 2 ⁢O 7 always has lower energy than the single-layer trilayer stacking La 3 ⁢Ni 2 ⁢O 7 . In addition, we observe a “self-doping” effect (compared to the average 1.5 electrons per eg orbital per site of the entire structure) from the trilayer to the single-layer sublattices and this effect will be enhanced by overall electron doping. Moreover, we find a leading d x 2 -y 2 -wave pairing state that is restricted to the single layer. Because the effective coupling between the single layers is very weak, due to the nonsuperconducting trilayer in-between, this suggests that the superconducting transition temperature T c in this structure should be much lower than in the bilayer structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Weak decays in superheavy nuclei

Superheavy nuclei represent the extreme atoms and nuclides known at the limit of mass and charge. The observed superheavy nuclei are all proton-rich; they decay primarily by emitting 𝛼 particles and by fission with a possible small electron capture (EC) branch. Here, due to the huge atomic numbers and associated relativistic effects, EC decays of superheavy systems are expected to differ from what is known in lighter nuclei. In this letter, using the quantified relativistic nuclear density functional theory and the quasiparticle random-phase approximation with the interaction optimized to experimental EC/𝛽 ± -decay half-lives, and Gamow-Teller resonance energies, we study the EC/𝛽 ± -decays in 𝑍=101–118 nuclei. Both allowed (1 + ) and first-forbidden (0 − ,1 − and 2 − ) transitions are considered. We show that the first-forbidden 1 − transitions dominate the decay rates in almost all studied nuclei. For proton-rich nuclei, EC dominates over 𝛽 + decay. Based on calculations with two relativistic energy density functionals, we identify 45 candidate nuclei in which a competition between weak decays and 𝛼 decay and spontaneous fission is expected.

A ≥ 220↗
DOE OSTI2024

Prediction of s ± -Wave Superconductivity Enhanced by Electronic Doping in Trilayer Nickelates La 4 Ni 3 O 10 under Pressure

Motivated by the recently reported signatures of superconductivity in trilayer La 4 ⁢Ni 3 ⁢O 10 under pressure, here we comprehensively study this system using ab initio and random-phase approximation techniques. Without electronic interactions, the Ni d 3z 2 –r 2 orbitals show a bonding-antibonding and nonbonding splitting behavior via the O p z orbitals inducing a “trimer” lattice in La 4⁢ Ni 3 ⁢O 10 , analogous to the dimers of La 3 ⁢Ni 2 ⁢O 7 . The Fermi surface consists of three electron sheets with mixed e g orbitals, and a hole and an electron pocket made up of the d 3⁢z 2 –r 2 orbital, suggesting a Ni two-orbital minimum model. In addition, we find that superconducting pairing is induced in the s ± -wave channel due to partial nesting between the M = (π,π) centered pockets and portions of the Fermi surface centered at the Γ = (0,0) point. With changing electronic density n, the s ± instability remains leading and its pairing strength shows a domelike behavior with a maximum around n = 4.2 ( ~6.7% electron doping). The superconducting instability disappears at the same electronic density as that in the new 1313 stacking La 3 ⁢Ni 2 ⁢O 7 , correlated with the vanishing of the hole pocket that arises from the trilayer sublattice, suggesting that the high-T c superconductivity of La 3⁢ Ni 2 ⁢O 7 does not originate from a trilayer and monolayer structure. Furthermore, we confirm the experimentally proposed spin state in La 4 ⁢Ni 3 ⁢O 10 with an in-plane (π, π) order and antiferromagnetic coupling between the top and bottom Ni layers, and spin zero in the middle layer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Nonresonant two-photon x-ray absorption in Cu

We present a real-space Green's function theory and calculations of two-photon x-ray absorption (TPA). Our focus is on nonresonant 𝐾-shell TPA in metallic Cu, which has been observed experimentally at intense x-ray free electron laser (XFEL) sources. The theory is based on an independent particle Green's function treatment of the Kramers-Heisenberg equation and an approximation for the sum over nonresonant intermediate states in terms of a static quadrupole transition operator. XFEL effects are modeled by a partially depleted 𝑑 band. This approach is shown to give results for 𝐾-shell TPA in quantitative agreement with XFEL experiment and with a Bethe-Salpeter equation approach. Furthermore, we also briefly discuss many-body corrections and TPA sum rules.

Approximation methods for many-body systems↗
DOE OSTI2025

Surrogate models for linear response

Linear response theory is a well-established method in physics and chemistry for exploring excitations of many-body systems. In particular, the quasiparticle random-phase approximation (QRPA) provides a powerful microscopic framework by building excitations on top of the mean-field vacuum; however, its high computational cost limits model calibration and uncertainty quantification studies. Here, we present two complementary QRPA surrogate models and apply them to study response functions of finite nuclei. One is a reduced-order model that exploits the underlying QRPA structure, while the other utilizes the recently developed parametric matrix model algorithm to construct a map between the system’s Hamiltonian and observables. Our benchmark applications, the calculation of the electric dipole polarizability of 180 Yb and the 𝛽-decay half-life of 80 Ni, show that both emulators can achieve 0.1%–1% accuracy while offering a 6–7 orders of magnitude speedup compared to state-of-the-art QRPA solvers. These results demonstrate that the developed QRPA emulators are well positioned to enable Bayesian calibration and large-scale studies of computationally expensive physics models describing the properties of many-body systems.

Beta decay↗
DOE OSTI2025

Strategic Placement and Sizing of Distributed Generation for Resilience Enhancement of Distribution Grids With Microgrid Formation

The rise in frequency and severity of extreme weather events highlights the need for resilient power distribution networks. Microgrids can help improve the resilience of distribution grids by providing continuous power supply using local distribution generation (DG) when the distribution grid fails. In this paper, we propose an approach for optimal placement and sizing of DG to form multiple microgrids throughout the distribution network by restoration actions such as switching operations in case of distribution grid outages caused by extreme weather events. Considering the randomness of damaged distribution lines, the DG placement and sizing problem is formulated as a two-stage stochastic mixed-integer program, with the first stage determining the placement and size of DG, and the second stage focusing on minimizing the amount of load shedding through network restoration and microgrid formations for each scenario. Due to the large number of scenarios, the sample average approximation (SAA) method is employed to solve the problem. The results of case studies on a modified IEEE 33 bus distribution grid demonstrate the effectiveness of the proposed DG placement and sizing strategy in improving the resilience of distribution grids by allowing the formation of multiple microgrids. In addition, the robustness and accuracy of the SAA method are validated through various case studies.

Distributed generation planning↗
DOE OSTI2024

A Data-Driven Approach for High-Impedance Fault Localization in Distribution Systems

Accurate and quick identification of high-impedance faults (HIFs) is critical for the reliable operation of distribution systems. Unlike other faults in power grids, HIFs are very difficult to detect by conventional overcurrent relays due to the low fault current. Although HIFs can be affected by various factors, the voltage-current characteristics can substantially imply how the system responds to the disturbance and thus provides opportunities to effectively localize HIFs. In this work, we propose a data-driven approach for the identification of HIF events. To tackle the nonlinearity of the voltage-current trajectory, first, we formulate optimization problems to approximate the trajectory with piecewise functions. Then we collect the function features of all segments as inputs and use the support vector machine approach to efficiently identify HIFs at different locations. Numerical studies on the IEEE 123-node test feeder demonstrate the validity and accuracy of the proposed approach for real-time HIF identification.

explainable artificial intelligence↗
DOE OSTI2024

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗
DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗