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DOE OSTI2024

Comparison of excess free energy at an interface according to the applied interpolation scheme for elasticity: A phase-field method

Phase-field modeling is an effective simulation technique for modeling microstructure evolution of elastically anisotropic systems. To introduce the elastic energy contribution in a phase field model, an interpolation scheme is used to define the mechanical properties within the phases and across the continuous interface. Several existing interpolation schemes introduce a potential excess elastic energy at the interface, which undesirable effect on microstructure evolution needs to be evaluated. In this study, we focused on three interpolation schemes including Khachaturyan’ scheme (KHS), Voigt–Taylor’s scheme (VTS), and Steinbach–Apel’s scheme (SAS). Comparisons of these schemes’ performances were performed in three configuration types using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework: bi-crystal, isotropic particle-matrix and anisotropic particle-matrix. The contribution of excess elastic energy on the interface energy as a function of interface width and the computational time to steady-state were evaluated in these three configurations. SAS introduces the lowest excess elastic energy contribution and the VTS has the biggest contribution amongst the considered schemes. Moreover, when modeling precipitation in an anisotropic elastic material, the SAS approach seems to predict more physical convex shapes during growth, making it preferable to KHS and VTS. Finally, as currently implemented, SAS requires the largest computational time and KHS requires the smallest time to reach steady-state amongst the considered schemes.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Refinements for Bragg coherent X-ray diffraction imaging: electron backscatter diffraction alignment and strain field computation

Bragg coherent X-ray diffraction imaging (BCDI) allows the 3D measurement of lattice strain along the scattering vector for specific microcrystals. If at least three linearly independent reflections are measured, the 3D variation of the full lattice strain tensor within the microcrystal can be recovered. However, this requires knowledge of the crystal orientation, which is typically attained via estimates based on crystal geometry or synchrotron microbeam Laue diffraction measurements. Presented here is an alternative method to determine the crystal orientation for BCDI measurements using electron backscatter diffraction (EBSD) to align Fe–Ni and Co–Fe alloy microcrystals on three different substrates. The orientation matrix is calculated from EBSD Euler angles and compared with the orientation determined using microbeam Laue diffraction. The average angular mismatch between the orientation matrices is less than ∼6°, which is reasonable for the search for Bragg reflections. The use of an orientation matrix derived from EBSD is demonstrated to align and measure five reflections for a single Fe–Ni microcrystal via multi-reflection BCDI. Using this data set, a refined strain field computation based on the gradient of the complex exponential of the phase is developed. This approach is shown to increase accuracy, especially in the presence of dislocations. The results demonstrate the feasibility of using EBSD to pre-align BCDI samples and the application of more efficient approaches to determine the full lattice strain tensor with greater accuracy.

42 ENGINEERING↗

DOE OSTI2025

EOSPAC User's Manual: Version 6.5 Second Edition (Rev. 3)

The EOSPAC utility package is a collection of interface routines, which can be used to access the SESAME data library and perform various data adjustments and interpolations on the SESAME data. The SESAME data library contains both thermodynamic (e.g., equation of state) and transport coefficients (e.g., opacity and conductivity). Note, for simplicity, the term EOS (equation of state) used herein includes both thermodynamic variables and transport coefficients. The EOSPAC utility package is designed to be used by physics codes (henceforth ”host codes”) written in multiple languages and on multiple platforms. The remainder of this manual is organized into several sections. Chapter 2 discusses conventions such as data organization and routine names. Chapter 3 provides a general overview of basic theory and models implemented within EOSPAC. Chapter 4 provides a general overview of how to use the EOSPAC interface library. Chapters 5 to 7 describe the public interfaces of EOSPAC in detail. Chapter 8 provides a brief introduction to some related tools, which may be of use to the user. Chapter 9 provides details related to some selected numerical features of EOSPAC. Chapter 10 gives examples for using the interface routines described in chapters 5 to 7. Chapter 11 provides technical support contact information. Chapter 12 contains a brief set of acknowledgments. Chapter 13 contains a list of referenced documents. Finally, chapter 14 lists the “table types: mnemonic conventions”, “table types: grouped by category, sorted by name”, “table types: eospac version 5 cross reference”, “options: setup phase”, “data information parameters”, “meta-data information parameters”, “options: interpolation phase”, and the “error codes”.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Spectrograph stabilization using a single-delay interferometer on the Hale Telescope

We describe a technique for spectrograph stabilization useful when conventional mitigation techniques of vacuum tanks, thermal insulation, and laser frequency comb may be impractical, expensive, heavy, or bulky. This includes spectrographs on airborne platforms or mounted on telescopes where they suffer a changing gravity vector or other drifts. Placing a fixed-delay interferometer in series with a spectrograph forms an externally dispersed interferometer (EDI). This produces a uniform sinusoidal comb multiplying input spectrum, creating (through heterodyning) beats (moiré patterns). In Fourier space for low frequencies up to the comb frequency, the moiré generated signal counter-rotates to ordinary spectra under an unknown disperser wavenumber drift Δx. This generates a large negative feedback signal useful in a conceptual control loop, to converge rapidly to a stable spectrum and yield Δx. A modified EDI data analysis algorithm (“crossfading”) combines frequency-weighted moiré with conventional spectrum to cancel net output spectrum reaction to Δx. Needing only a single-delay, this is a practical improvement over prior crossfading analyses requiring multiple delays. We test crossfading on ThAr data near 4850 cm−1 taken on Hale telescope in an earlier project. In a single pass, we reduce drift 20 times. Using seven iterations, we reduce 0.5 cm−1 (31 km/s Doppler equivalent) drift to 4×10−7 cm−1 (2.5 cm/s). The interferometer delay can wander, because linearity of phase versus wavenumber interpolates science features between bracketing calibrating spectral references. Second, mathematically reversing the heterodyning effect doubles effective spectral resolution without changing disperser slit.

Erskine, David J [Lawrence Livermore National Labo↗

DOE OSTI2023

Hierarchical Model Reduction Driven by Machine Learning for Parametric Advection-Diffusion-Reaction Problems in the Presence of Noisy Data

Abstract We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model reduction with a standard Proper Orthogonal Decomposition, according to an offline/online paradigm. In this paper we show that directional HiPOD looses in terms of accuracy when problem data are affected by noise. This is due to the interpolation driving the online phase, since it replicates, by definition, the noise trend. To overcome this limit, we replace interpolation with Machine Learning fitting models which better discriminate relevant physical features in the data from irrelevant unstructured noise. The numerical assessment, although preliminary, confirms the potentialities of the new approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Learning two-phase microstructure evolution using neural operators and autoencoder architectures

Abstract Phase-field modeling is an effective but computationally expensive method for capturing the mesoscale morphological and microstructure evolution in materials. Hence, fast and generalizable surrogate models are needed to alleviate the cost of computationally taxing processes such as in optimization and design of materials. The intrinsic discontinuous nature of the physical phenomena incurred by the presence of sharp phase boundaries makes the training of the surrogate model cumbersome. We develop a framework that integrates a convolutional autoencoder architecture with a deep neural operator (DeepONet) to learn the dynamic evolution of a two-phase mixture and accelerate time-to-solution in predicting the microstructure evolution. We utilize the convolutional autoencoder to provide a compact representation of the microstructure data in a low-dimensional latent space. After DeepONet is trained in the latent space, it can be used to replace the high-fidelity phase-field numerical solver in interpolation tasks or to accelerate the numerical solver in extrapolation tasks.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Size-Dependent Nucleation in Crystal Phase Transition from Machine Learning Metadynamics

In this Letter, we present a framework that combines machine learning potential (MLP) and metadynamics to investigate solid-solid phase transition. Here, based on the spectral descriptors and neural networks regression, we develop a scalable MLP model to warrant an accurate interpolation of the energy surface where two phases coexist. Applying it to the simulation of B4–B1 phase transition of GaN under 50 GPa with different model sizes, we observe sequential change of the phase transition mechanism from collective modes to nucleation and growths. When the size is at or below 128 000 atoms, the nucleation and growth appear to follow a preferred direction. At larger sizes, the nuclei occur at multiple sites simultaneously and grow to microstructures by passing the critical size. The observed change of the atomistic mechanism manifests the importance of statistical sampling with large system size in phase transition modeling.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Neural conditional reweighting

There is a growing use of neural network classifiers as unbinned, high-dimensional (and variable-dimensional) reweighting functions. To date, the focus has been on marginal reweighting, where a subset of features are used for reweighting while all other features are integrated over. There are some situations, though, where it is preferable to condition on auxiliary features instead of marginalizing over them. Here, we introduce neural conditional reweighting, which extends neural marginal reweighting to the conditional case. This approach is particularly relevant in high-energy physics experiments for reweighting detector effects conditioned on particle-level truth information. Furthermore we leverage a custom loss function that not only allows us to achieve neural conditional reweighting through a single training procedure, but also yields sensible interpolation even in the presence of phase space holes. As a specific example, we apply neural conditional reweighting to the energy response of high-energy jets, which could be used to improve the modeling of physics objects in parametrized fast simulation packages.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Insulators at fractional fillings in twisted bilayer graphene partially aligned to hexagonal boron nitride

At partial fillings of its flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts a rich variety of competing correlated phases that show sample-to-sample variations. Divergent phase diagrams in MATBG are often attributed to the sublattice polarization energy scale, tuned by the degree of alignment of the hexagonal boron nitride (hBN) substrates typically used in van der Waals devices. Unaligned MATBG exhibits unconventional superconductor and correlated insulator phases, while nearly perfectly aligned MATBG/hBN exhibits zero-field Chern insulating phases and lacks superconductivity. Here we use scanning tunneling microscopy and spectroscopy (STM/STS) to observe gapped phases at partial fillings of the flat bands of MATBG in a new intermediate regime of sublattice polarization, observed when MATBG is only partially aligned (θ Gr-hBN ≈ 1.65°) to the underlying hBN substrate. Under this condition, MATBG hosts not only phenomena that naturally interpolate between the two sublattice potential limits, but also unexpected gapped phases absent in either of these limits. At charge neutrality, we observe an insulating phase with a small energy gap (Δ < 5 meV) likely related to weak sublattice symmetry breaking from the hBN substrate. In addition, we observe new gapped phases near fractional fillings ν = ±1/3 and ν = ±1/6, which have not been previously observed in MATBG. Importantly, energy-resolved STS unambiguously identifies these fractional filling states to be of single-particle origin, possibly a result of the super-superlattice formed by two moiré superlattices. Finally, our observations emphasize the power of STS in distinguishing single-particle gapped phases from many-body gapped phases in situations that could be easily confused in electrical transport measurements, and demonstrate the use of substrate engineering for modifying the electronic structure of a moiré flat-band material.

Physics↗

DOE OSTI2022

Machine learning the metastable phase diagram of covalently bonded carbon

Abstract Conventional phase diagram generation involves experimentation to provide an initial estimate of the set of thermodynamically accessible phases and their boundaries, followed by use of phenomenological models to interpolate between the available experimental data points and extrapolate to experimentally inaccessible regions. Such an approach, combined with high throughput first-principles calculations and data-mining techniques, has led to exhaustive thermodynamic databases (e.g. compatible with the CALPHAD method), albeit focused on the reduced set of phases observed at distinct thermodynamic equilibria. In contrast, materials during their synthesis, operation, or processing, may not reach their thermodynamic equilibrium state but, instead, remain trapped in a local (metastable) free energy minimum, which may exhibit desirable properties. Here, we introduce an automated workflow that integrates first-principles physics and atomistic simulations with machine learning (ML), and high-performance computing to allow rapid exploration of the metastable phases to construct “metastable” phase diagrams for materials far-from-equilibrium. Using carbon as a prototypical system, we demonstrate automated metastable phase diagram construction to map hundreds of metastable states ranging from near equilibrium to far-from-equilibrium (400 meV/atom). We incorporate the free energy calculations into a neural-network-based learning of the equations of state that allows for efficient construction of metastable phase diagrams. We use the metastable phase diagram and identify domains of relative stability and synthesizability of metastable materials. High temperature high pressure experiments using a diamond anvil cell on graphite sample coupled with high-resolution transmission electron microscopy (HRTEM) confirm our metastable phase predictions. In particular, we identify the previously ambiguous structure of n -diamond as a cubic-analog of diaphite-like lonsdaelite phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

The algebraic structure of gravitational scrambling

We introduce a new algebraic framework to describe gravitational scrambling, including the semiclassical limit of any out-of-time-order correlation function that is built out of operator insertions separated by approximately the scrambling time. In two dimensions, the scrambling algebra, which we call a modular-twisted product, is defined in terms of two copies of the Leutheusser-Liu half-sided modular inclusion of von Neumann algebras; these describe early- and late-time operators respectively. In limits where the separation between insertions is taken to be either significantly greater or smaller than the scrambling time, the modular-twisted product reduces, respectively, to free- and tensor-product algebras that were previously studied in [arXiv:2209.10454]. In a sense, the modular-twisted product interpolates between these two products. Including the Hamiltonian in the scrambling algebra leads to a Type II$_\infty$ von Neumann algebra with finite renormalized entropies that interpolate between single-QES and multi-QES phases. We also describe how to generalize the modular-twisted product algebra to higher dimensions, including spatially localized boundary excitations.

FOS: Physical sciences↗

DOE OSTI2022

Strain-tunable metamagnetic critical endpoint in Mott insulating rare-earth titanates

Rare-earth titanates are Mott insulators whose magnetic ground state—antiferromagnetic (AFM) or ferromagnetic (FM)—can be tuned by the radius of the rare-earth element. We combine phenomenology and first-principles calculations to shed light on the generic magnetic phase diagram of a chemically substituted titanate on the rare-earth site that interpolates between an AFM and a FM state. Octahedral rotations present in these perovskites cause the AFM order to acquire a small FM component—and vice-versa—removing any multicritical point from the phase diagram. However, for a wide parameter range, a first-order metamagnetic transition line terminating at a critical endpoint survives inside the magnetically ordered phase. Like the liquid-gas transition, a Widom line emerges from the endpoint, characterized by enhanced fluctuations. In contrast to metallic FMs, this metamagnetic transition involves two symmetry-equivalent and insulating canted spin states. Moreover, instead of a magnetic field, we show that uniaxial strain can be used to tune this transition to zero temperature, inducing a quantum critical endpoint.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Krylov complexity in mixed phase space

We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans two-dimensional random matrix models featuring (I) GOE-Poisson and (II) GUE-Poisson transitions and extends to higher-dimensional cases, including a stringy matrix model (GOE-Poisson) and the mass-deformed SYK model (GUE-Poisson). Krylov complexity consistently emerges as a reliable marker of quantum chaos, displaying a characteristic peak in the chaotic regime that gradually diminishes as the Brody parameter approaches zero, signaling a shift toward integrability. These results establish Krylov complexity as a powerful diagnostic of quantum chaos and highlight its interplay with eigenvalue statistics in mixed phase systems.

chaos & nonlinear dynamics↗

DOE OSTI2023

Refractivity Observations from Radar Phase Measurements: The 22 May 2002 Dryline Case during IHOP Project

The dryline, often associated with the development of severe storms in the Southern Great Plains of the United States of America, is a boundary layer phenomenon that occurs when a warm and moist air mass from the Gulf of Mexico meets a hot and dry air mass from the southwest desert area. An accurate knowledge of the water vapor spatio-temporal variability in the lower part of the atmosphere is crucial for a better understanding of the evolution of the dryline. The tropospheric refractivity, directly related to water vapor content, is a proxy for the water vapor content of the troposphere. It has already been demonstrated that the refractivity and the refractivity vertical gradient can be jointly estimated from radar phase measurements. In fact, it has been shown that using kriging interpolation techniques, accurate refractivity maps within the coverage area of the radar can be obtained with high temporal resolution. In this paper, a detailed analysis of the time series of radar-based refractivity maps obtained during a dryline that occurred on the afternoon of 22 May 2002 during the International H 2 O Project is presented. Comparisons between the time series of radar refractivity maps, obtained with the NCAR S-Pol radar, and the refractivity measurements derived from automatic ground-based weather stations and the AERI instrument, placed at different locations within the coverage area of the NCAR S-Pol radar, demonstrate the accuracy of radar refractivity estimates even for highly variable conditions, both in time and space, in the troposphere. Correlation coefficients higher than 0.95 are obtained in all weather station locations. Regarding the RMSE, errors less than 6 N-units are obtained for all cases, being even as low as 2.92 N-units at some locations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Cascading from $\mathscr{N}$ = 2 supersymmetric Yang–Mills theory to confinement and chiral symmetry breaking in adjoint QCD

We argue that adjoint QCD in 3 + 1 dimensions, with any SU(N) gauge group and two Weyl fermion flavors (i.e. one adjoint Dirac fermion), confines and spontaneously breaks its chiral symmetries via the condensation of a fermion bilinear. We flow to this theory from pure $\mathscr{N}$ = 2 SUSY Yang–Mills theory with the same gauge group, by giving a SUSY-breaking mass M to the scalars in the $\mathscr{N}$ = 2 vector multiplet. This flow can be analyzed rigorously at small M, where it leads to a deconfined vacuum at the origin of the $\mathscr{N}$ = 2 Coulomb branch. The analysis can be extended to all M using an Abelian dual description that arises from the N multi-monopole points of the $\mathscr{N}$ = 2 theory. At each such point, there are N −1 hypermultiplet Higgs fields h$^{i=1,2}_m$, which are SU(2) R doublets. We provide a detailed study of the phase diagram as a function of M, by analyzing the semi-classical phases of the dual using a combination of analytic and numerical techniques. The result is a cascade of first-order phase transitions, along which the Higgs fields h i m successively turn on, and which interpolates between the Coulomb branch at small M, where all h$^{i}_m$ = 0, and a maximal Higgs branch, where all h$^{i}_m$ ≠ 0, at sufficiently large M. We show that this maximal Higgs branch precisely matches the confining and chiral symmetry breaking phase of two-flavor adjoint QCD, including its broken and unbroken symmetries, its massless spectrum, and the expected large-N scaling of various observables. The spontaneous breaking pattern SU(2) R → U(1) R , consistent with the Vafa–Witten theorem, is ensured by an intricate alignment mechanism for the h$^{i}_m$ in the dual, and leads to a CP 1 sigma model of increasing radius along the cascade.

D’Hoker, Eric [Univ. of California, Los Angeles, C↗

DOE OSTI2023

A phased workflow to define permit‐ready locations for large volume CO 2 injection and storage

Abstract To‐date, only two UIC Class VI permits have been issued by the US Environmental Protection Agency. We illustrate a four‐phase workflow to first identify regional storage resources and then down‐select sites to yield permit‐ready locations that can accept and store large volumes of CO 2 . Specific permit requirements should guide objectives and define deliverables of respective workflow phases. In the first phase we used available regional data and screened structure and injection zones to locate resources that match CO 2 volumes planned to be captured. Available data were also used to assess presence and depth of usable groundwater, the key resource being protected via permitting. We then used advanced, closed‐form, analytical solutions (EASiTool) to estimate CO 2 injectivity into each hydrologically connected injection compartment. In the second phase we acquired and conditioned additional wireline logs and leased available seismic datasets. We interpreted the depositional systems from wireline well‐log character and mapped sandbody geometry to interpolate injection and confining‐zone distribution. Using available data, we mapped faults and locations of freshwater and overpressure (or other capacity‐limiting geologic parameters) in more detail. In the third phase, we used the augmented geologic data to develop a static model for the selected area, extracted the areas of highest interest, and generated and ran dynamic (flow) models. In a fourth phase, we reduced major uncertainties identified in earlier phases. Our case study indicates that to complete preparation of a permit application requires (1) improved lithologic characterization information (thicknesses and horizontal and vertical connectivity) and (2) better definition of poorly defined local faults. © 2023 The Authors. Greenhouse Gases: Science and Technology published by Society of Chemical Industry and John Wiley & Sons Ltd.

58 GEOSCIENCES↗

DOE OSTI2024

GX: a GPU-native gyrokinetic turbulence code for tokamak and stellarator design

GX is a code designed to solve the nonlinear gyrokinetic system for low-frequency turbulence in magnetized plasmas, particularly tokamaks and stellarators. In GX, our primary motivation and target is a fast gyrokinetic solver that can be used for fusion reactor design and optimization along with wide-ranging physics exploration. Here, this has led to several code and algorithm design decisions, specifically chosen to prioritize time to solution. First, we have used a discretization algorithm that is pseudospectral in the entire phase space, including a Laguerre–Hermite pseudospectral formulation of velocity space, which allows for smooth interpolation between coarse gyrofluid-like resolutions and finer conventional gyrokinetic resolutions and efficient evaluation of a model collision operator. Additionally, we have built GX to natively target graphics processors (GPUs), which are among the fastest computational platforms available today. Finally, we have taken advantage of the reactor-relevant limit of small $\rho _*$ by using the radially local flux-tube approach. In this paper we present details about the gyrokinetic system and the numerical algorithms used in GX to solve the system. We then present several numerical benchmarks against established gyrokinetic codes in both tokamak and stellarator magnetic geometries to verify that GX correctly simulates gyrokinetic turbulence in the small $\rho _*$. Moreover, we show that the convergence properties of the Laguerre–Hermite spectral velocity formulation are quite favourable for nonlinear problems of interest. Coupled with GPU acceleration, which we also investigate with scaling studies, this enables GX to be able to produce useful turbulence simulations in minutes on one (or a few) GPUs and higher fidelity results in a few hours using several GPUs. GX is open-source software that is ready for fusion reactor design studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Timing based clustering of childhood BMI trajectories reveals differential maturational patterns; Study in the Northern Finland Birth Cohorts 1966 and 1986

Children’s biological age does not always correspond to their chronological age. In the case of BMI trajectories, this can appear as phase variation, which can be seen as shift, stretch, or shrinking between trajectories. With maturation thought of as a process moving towards the final state - adult BMI, we assessed whether children can be divided into latent groups reflecting similar maturational age of BMI. The groups were characterised by early factors and time-related features of the trajectories. We used data from two general population birth cohort studies, Northern Finland Birth Cohorts 1966 and 1986 (NFBC1966 and NFBC1986). Height (n = 6329) and weight (n = 6568) measurements were interpolated in 34 shared time points using B-splines, and BMI values were calculated between 3 months to 16 years. Pairwise phase distances of 2999 females and 3163 males were used as a similarity measure in k-medoids clustering. We identified three clusters of trajectories in females and males (Type 1: females, n = 1566, males, n = 1669; Type 2: females, n = 1028, males, n = 973; Type 3: females, n = 405, males, n = 521). Similar distinct timing patterns were identified in males and females. The clusters did not differ by sex, or early growth determinants studied. Trajectory cluster Type 1 reflected to the shape of what is typically illustrated as the childhood BMI trajectory in literature. However, the other two have not been identified previously. Type 2 pattern was more common in the NFBC1966 suggesting a generational shift in BMI maturational patterns.

60 APPLIED LIFE SCIENCES↗