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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Desmearing small-angle scattering data by central moment expansions of instrument resolution

This study introduces an enhanced numerical technique tailored specifically for refining 1D small-angle scattering (SAS) intensity profiles affected by smearing. Our primary objective is to address the resolution blurring commonly encountered in SAS data, particularly in systems with clearly defined correlation peaks whose spread aligns with the width of the resolution function at corresponding Q positions. Unlike previous approaches that expanded the SAS intensity using central moment expansion, the new method focuses on expanding the resolution function itself, thus eliminating artificial oscillations observed in smeared spectra due to limitations inherent in our earlier algorithm. This method is straightforward to implement, computationally efficient and consistently performs well in numerical benchmarking. To illustrate its effectiveness, we present a case study of a lamellar phase characterized by distinct peaks in its small-angle neutron scattering intensities.

central moment expansions↗
DOE OSTI2022

Synthesis and structural properties of a 2D Zn( II ) dodecahydroxy- closo -dodecaborate coordination polymer

Here, in this work, we discuss the synthesis and characterization of a 2D coordination polymer composed of a dianionic perhydroxylated boron cluster, [B 12 (OH) 12 2– ], coordinated to Zn( II )—the first example of a transition metal-coordinated [B 12 (OH) 12 ] 2– compound. This material was synthesized via cation exchange from the starting cesium salt and then subjected to rigorous characterization prior to and after thermal activation. Numerous techniques, including XRD, FTIR, SEM, TGA, and solid-state NMR revealed a 2D coordination polymer composed of sheets of Zn( II ) ions intercalated between planes of boron clusters. The as-synthesized material was then evacuated of solvent via thermal treatment, and atomic-level changes from this transformation were elucidated through a combination of 1D and 2D solid-state NMR analyses of 11 B and 1 H nuclei, suggesting the full removal of coordinated solvent molecules. Evidence also suggested that [B 12 (OH) 12 2– ] can adjust its coordination to Zn( II ) in the solid-state through hemilability of its numerous –OH ligands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Particle-in-cell Simulations of Relativistic Magnetic Reconnection with Advanced Maxwell Solver Algorithms

Abstract Relativistic magnetic reconnection is a nonideal plasma process that is a source of nonthermal particle acceleration in many high-energy astrophysical systems. Particle-in-cell (PIC) methods are commonly used for simulating reconnection from first principles. While much progress has been made in understanding the physics of reconnection, especially in 2D, the adoption of advanced algorithms and numerical techniques for efficiently modeling such systems has been limited. With the GPU-accelerated PIC code WarpX, we explore the accuracy and potential performance benefits of two advanced Maxwell solver algorithms: a nonstandard finite-difference scheme (CKC) and an ultrahigh-order pseudo-spectral method (PSATD). We find that, for the relativistic reconnection problem, CKC and PSATD qualitatively and quantitatively match the standard Yee-grid finite-difference method. CKC and PSATD both admit a time step that is 40% longer than that of Yee, resulting in a ∼40% faster time to solution for CKC, but no performance benefit for PSATD when using a current deposition scheme that satisfies Gauss’s law. Relaxing this constraint maintains accuracy and yields a 30% speedup. Unlike Yee and CKC, PSATD is numerically stable at any time step, allowing for a larger time step than with the finite-difference methods. We found that increasing the time step 2.4–3 times over the standard Yee step still yields accurate results, but it only translates to modest performance improvements over CKC, due to the current deposition scheme used with PSATD. Further optimization of this scheme will likely improve the effective performance of PSATD.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Distributionally Robust Variational Quantum Algorithms With Shifted Noise

Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant challenge. A practical issue is the high sensitivity of quantum noise to environmental changes, and its propensity to shift in real time. This presents a critical problem as an optimized VQA ansatz may not perform effectively under a different noise environment. For the first time, we explore how to optimize VQA parameters to be robust against unknown shifted noise. We model the noise level as a random variable with an unknown probability density function (PDF), and we assume that the PDF may shift within an uncertainty set. This assumption guides us to formulate a distributionally robust optimization problem, with the goal of finding parameters that maintain effectiveness under shifted noise. We utilize a distributionally robust Bayesian optimization solver for our proposed formulation. This provides numerical evidence in both the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE) with hardware-efficient ansatz, indicating that we can identify parameters that perform more robustly under shifted noise. We regard this work as the first step towards improving the reliability of VQAs influenced by real-time noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Ising meson spectroscopy on a noisy digital quantum simulator

Abstract Quantum simulation has the potential to be an indispensable technique for the investigation of non-perturbative phenomena in strongly-interacting quantum field theories (QFTs). In the modern quantum era, with Noisy Intermediate Scale Quantum (NISQ) simulators widely available and larger-scale quantum machines on the horizon, it is natural to ask: what non-perturbative QFT problems can be solved with the existing quantum hardware? We show that existing noisy quantum machines can be used to analyze the energy spectrum of several strongly-interacting 1+1D QFTs, which exhibit non-perturbative effects like ‘quark confinement’ and ‘false vacuum decay’. We perform quench experiments on IBM’s quantum simulators to compute the energy spectrum of 1+1D quantum Ising model with a longitudinal field. Our results demonstrate that digital quantum simulation in the NISQ era has the potential to be a viable alternative to numerical techniques such as density matrix renormalization group or the truncated conformal space methods for analyzing QFTs.

Science & Technology - Other Topics↗
DOE OSTI2022

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗
DOE OSTI2023

Sensitivity analysis of a layered piezoelectric system using ZFEM

The complex variable finite element method (ZFEM) is a numerical technique which aims to find the partial derivatives of the independent variables with respect to variation in dependent parameters declared in the physics. This is done by combining the complex Taylor series expansion within the weak formulation of the governing equation in a coupled system of linear equations forming a complex valued block matrix given by the Cauchy–Riemann matrix representation. In this work, two-dimensional linear first-order elements have been implemented in ZFEM to predict the design derivatives of the mechanical displacement field and the voltage potential field for a layered piezoelectric system in a steady-state study with Dirichlet boundary condition applied at the top and bottom edges of the geometry. This approach allows the standard FEM solution to quantify the sensitivity of the mechanical displacement and voltage potential fields with respect to small variations in the material properties through the information obtained from the computation of the derivatives. The domain is formed by a layered body with PZT-4 and PZT-5 stacked together. For result verification, the numerical solution obtained with ZFEM was compared to results from a commercial FEM package and the solution from the imaginary part was compared to the exact solution of a well-known benchmark problem. In conclusion, comparison of the results showed good agreement for both the real and imaginary parts of the solution and the largest sensitivities were found in PZT-5 specifically in C 13 , C 33 , and ε 33 .

42 ENGINEERING↗
DOE OSTI2022

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The O ( N ) model

The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this approach relies on the derivation of so-called flow equations, which describe the change of the quantum effective action under the variation of a coarse-graining parameter. In the present work, we discuss in detail a novel approach to solve such flow equations. This approach relies on the fact that RG equations can be rewritten such that they exhibit similarities with the conservation laws of fluid dynamics. This observation can be exploited in different ways. First of all, we show that this allows to employ powerful numerical techniques developed in the context of fluid dynamics to solve RG equations. In particular, it allows us to reliably treat the emergence of nonanalytic behavior in the RG flow of the effective action as it is expected to occur in studies of, e.g., spontaneous symmetry breaking. Second, the analogy between RG equations and fluid dynamics offers the opportunity to gain novel insights into RG flows and their interpretation in general, including the irreversibility of RG flows. Further, we work out this connection in practice by applying it to zero-dimensional quantum-field theoretical models. The generalization to higher-dimensional models is also discussed. Our findings are expected to help improving future FRG studies of quantum field theories in higher dimensions both on a qualitative and quantitative level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Simulation Models for Exploring Magnetic Reconnection

Simulations have played a critical role in the advancement of our knowledge of magnetic reconnection. However, due to the inherently multiscale nature of reconnection, it is impossible to simulate all physics at all scales. For this reason, a wide range of simulation methods have been crafted to study particular aspects and consequences of magnetic reconnection. This article reviews many of these methods, laying out critical assumptions, numerical techniques, and giving examples of scientific results. Plasma models described include magnetohydrodynamics (MHD), Hall MHD, Hybrid, kinetic particle-in-cell (PIC), kinetic Vlasov, Fluid models with embedded PIC, Fluid models with direct feedback from energetic populations, and the Rice Convection Model (RCM).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

MFC 5.0: An exascale many-physics flow solver

Many problems of interest in engineering, medicine, and the fundamental sciences rely on high-fidelity flow simulation, making performant computational fluid dynamics solvers a mainstay of the open-source software community. Previous work MFC 3.0 was made a published, documented, and open-source solver via Bryngelson et al. Comp. Phys. Comm. (2021) with numerous physical features, numerical methods, and scalable infrastructure. MFC 5.0 is a significant update to MFC 3.0, featuring a broad set of well-established and novel physical models and numerical methods, as well as the introduction of GPU and APU (or superchip) acceleration. Here, we exhibit state-of-the-art performance and ideal scaling on the first two exascale supercomputers, OLCF Frontier and LLNL El Capitan. Combined with MFC’s single-accelerator performance, MFC achieves exascale computation in practice, and achieved the largest-to-date public CFD simulation at 200 trillion grid points as a 2025 ACM Gordon Bell Prize finalist. New physical features include the immersed boundary method, N-fluid phase change, Euler–Euler and Euler–Lagrange sub-grid bubble models, fluid-structure interaction, hypo- and hyper-elastic materials, chemically reacting flow, two-material surface tension, magnetohydrodynamics (MHD), and more. Numerical techniques now represent the current state-of-the-art, including general relaxation characteristic boundary conditions, WENO variants, Strang splitting for stiff sub-grid flow features, and low Mach number treatments. Weak scaling to tens of thousands of GPUs on OLCF Summit and Frontier and LLNL El Capitan achieves efficiencies within 5% of ideal to over 90% of their respective system sizes. Strong scaling results for a 16-times increase in device count show parallel efficiencies over 90% on OLCF Frontier. MFC’s software stack has undergone further improvements, including continuous integration, which ensures code resilience and correctness through over 300 regression tests; metaprogramming, which reduces code length while maintaining performance portability; and code generation for computing chemical reactions

Computational fluid dynamics↗
DOE OSTI2022

Probabilistic constrained Bayesian inversion for transpiration cooling

Abstract To enable safe operations in applications such as rocket combustion chambers, the materials require cooling to avoid material damage. Here, transpiration cooling is a promising cooling technique. Numerous studies investigate possibilities to simulate and evaluate the complex cooling mechanism. One naturally arising question is the amount of coolant required to ensure a safe operation. To study this, we introduce an approach that determines the posterior probability distribution of the Reynolds number using an inverse problem and constraining the maximum temperature of the system under parameter uncertainties. Mathematically, this chance inequality constraint is dealt with by a generalized polynomial chaos expansion of the system. The posterior distribution will be evaluated by different Markov chain Monte Carlo based methods. A novel method for the constrained case is proposed and tested among others on two‐dimensional transpiration cooling models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An Optothermal Raman Model Accounting for Convection, Radiation, and Substrate Effects for Evaluation of the Thermal Conductivity of Two‐Dimensional Coatings

Thermal conductivity of two‐dimensional (2D) materials is important to characterize as this will govern thermal transport physics in the various thermal and energy applications benefitting from the unique properties of these materials. Here, analytical and numerical techniques are presented to determine the thermal conductivity and interfacial conductance of a 2D material coating using confocal micro‐Raman spectroscopy as a noncontact diagnostic. While several methods have been proposed for calculating the values of thermal conductivity, interfacial conductance, and spatial temperature profile, these models often do not consider effects of radiation, convection, and substrate resistance on the temperature and heat flux profiles. We present a model to calculate the thermal conductivity and interfacial conductance which accounts for convection, radiation, and substrate effects to characterize a variety of 2D material coatings, which is demonstrated using large area graphene transferred onto copper and nickel substrates. Convection and radiation effects are found to have a negligible effect on the temperature profile of supported coatings, while the substrate effects have a considerable effect and therefore impact the quantification of thermal conductivity and interfacial conductance in addition to limiting the spatial resolution of the technique. These findings will allow for more accurate and reproducible extraction of the thermal conductivity of graphene and other 2D material coatings when employing noncontact optothermal Raman spectroscopy methods.

2D coatings↗
DOE OSTI2025

Defect Engineering in Large‐Scale CVD‐Grown Hexagonal Boron Nitride: Formation, Spectroscopy, and Spin Relaxation Dynamics

Recently, numerous techniques have been reported for generating optically active defects in exfoliated hexagonal boron nitride (hBN), which hold transformative potential for quantum photonic devices. However, achieving on-demand generation of desirable defect types in scalable hBN films remains a significant challenge. Here, it is demonstrated that formation of negative boron vacancy defects, V B − , in suspended, large-area CVD-grown hBN is strongly dependent on the type of bombarding particles (ions, neutrons, and electrons) and irradiation conditions. In contrast to suspended hBN, defect formation in substrate-supported hBN is more complex due to the uncontrollable generation of secondary particles from the substrate, and the outcome strongly depends on the thickness of the hBN. Different defect types are identified by correlating spectroscopic and optically detected magnetic resonance features, distinguishing boron vacancies (formed by light ions and neutrons and emitting at 800 nm) from other optically active defects emitting at 650 nm assigned to anti-site nitrogen vacancy (N B V N ) and reveal the presence of additional “dark” paramagnetic defects that influence spin-lattice relaxation time (T 1 ) and zero-field splitting parameters, all of which strongly depend on the defect density. These results underscore the potential for precisely engineered defect formation in large-scale CVD-grown hBN, paving the way for the scalable fabrication of quantum photonic devices.

CVD↗
DOE OSTI2023

Calculation of Dynamical Response Functions Using a Bound-State Method

Abstract We investigate a method to extract response functions (dynamical polarisabilities) directly from a bound-state approach applied to calculations of perturbation-induced reactions. The use of a square-integrable basis leads to a response in the form of a sum of $$\delta $$ δ functions. We integrate this over energy and fit a smooth function to the resulting stepwise-continuous one. Its derivative gives the final approximation to the physical response function. We show that the method reproduces analytical results where known, and analyse the details for a variety of models. We apply it to some simple models, using the stochastic variational method as the numerical method. Albeit we find that this approach, and other numerical techniques, have some difficulties with the threshold behavior in coupled-channel problems with multiple thresholds, its stochastic nature allows us to extract robust results even for such cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Origin of the background absorption in carbon nanotubes: Phonon-assisted excitonic continuum

Excitonic effects in 1D semiconductors can be qualitatively different from those in higher dimensions. In particular, the Sommerfeld factor, the ratio of the above-band-edge excitonic continuum absorption to free electron-hole pair generation, has been shown to be less than 1 (suppressed) in 1D systems while it is larger than 1 (enhanced) in 2D and 3D systems. Strong continuum suppression indeed exists in semiconducting single-wall carbon nanotubes, a prototypical 1D semiconductor. However, absorption spectra for carbon nanotubes are typically fit with a combination of Lorentzians and a polynomial background baseline with little physical meaning. We performed absorption measurements in aligned single-chirality (6,5) carbon nanotube films. The obtained spectra were fit with our theoretical model obtained by solving the Boltzmann scattering equation involving fifty-nine different types of transitions among three different types of quasiparticles. Specifically, we took into account microscopic interactions between photons, phonons, and excitons, including their dispersions, which unambiguously demonstrated that the background absorption is due to phonon-assisted transitions from the semiconductor vacuum to finite-momentum continuum states of excitons. The excellent agreement we obtained between experiment and theory suggests that our numerical technique can be seamlessly extended to compute strongly out-of-equilibrium many-body dynamics and time-resolved spectra in low-dimensional materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Recent progress in the phase-field dislocation dynamics method

The phase-field dislocation dynamics (PFDD) method, originated in 2002, is a continuum dislocation model that uses order parameters to describe dislocation slips in crystalline materials. In the past two decades, and especially since it was last reviewed in 2016, PFDD was advanced significantly in terms of the mathematical formulation, numerical implementation, and applicability. The main purpose of this short review is to summarize recent progress made to improve the energy functional formulation and numerical techniques of PFDD as well as its recent applications. Additionally, some recommendations for future work to further extend the PFDD method are presented.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A predictive strain-gradient model with no undetermined constants or length scales

A general meso–scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. As a result, GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Emergence of 4 H $J^π$ = 1 - resonance in contact theories

We obtain the s- and p-wave low-energy scattering parameters for n 3 H elastic scattering and the position of the 4 H J π = 1 - resonance using the pionless effective field theory at leading order. Results are extracted with three numerical techniques: confining the system in a harmonic oscillator trap, solving the Faddeev-Yakubovsky equations in configuration space, and using an effective two-body cluster approach. The renormalization of the theory for the relevant amplitudes is assessed in a cutoff-regulator range between 1 fm -1 and 10 fm -1 . Most remarkably, we find a cutoff-stable/RG-invariant resonance in the 4 H J π = 1 - system. This p-wave resonance is a universal consequence of a shallow two-body state and the introduction of a three-body s-wave scale set by the triton binding energy. The stabilization of a resonant state in a few-fermion system through pure contact interactions has a significant consequence for the powercounting of the pionless theory. Specifically, it suggests the appearance of similar resonant states also in larger nuclei, like 16-oxygen, in which the theory’s leading order does not predict stable states. Those resonances would provide a starting state to be moved to the correct physical position by the perturbative insertion of sub-leading orders, possibly resolving the discrepancy between data and contact EFT.

79 ASTRONOMY AND ASTROPHYSICS↗