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DOE OSTI2021

Inhomogeneous mean-field approach to collective excitations near the superfluid–Mott glass transition

Highlights: • Unconventional collective excitations across the superfluid–Mott glass transition. • Higgs mode localized in superfluid and insulating phases. • Broad uncritical amplitude response function at quantum phase transition. • Goldstone mode delocalizes in the superfluid phase. We develop an inhomogeneous quantum mean-field approach to the behavior of collective excitations across the superfluid–Mott glass quantum phase transition in two dimensions, complementing recent quantum Monte Carlo simulations (Puschmann et al. 2020). In quadratic (Gaussian) approximation, the Goldstone (phase) and Higgs (amplitude) modes completely decouple. Each is described by a disordered Bogoliubov Hamiltonian which can be solved by an inhomogeneous multi-mode Bogoliubov transformation. We find that the Higgs mode is spatially localized in both phases. The corresponding scalar spectral function shows a broad peak that is noncritical in the sense that its peak frequency does not soften but remains nonzero across the quantum phase transition. In contrast, the lowest-energy Goldstone mode delocalizes in the superfluid phase, leading to a zero-frequency spectral peak. We compare these findings to the results of the quantum Monte Carlo simulations. We also relate them to general results on the localization of bosonic excitations, and we discuss the limits and generality of our approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Inference of phase field fracture models

The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). Furthermore, in this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Phasing Magnet for CSX-2 Beamline at NSLS-II

A phasing magnet has been developed at National Synchrotron Light Source II (NSLS-II) for the Coherent Soft X-ray Scattering (CSX) beamline. The phasing magnet will be located at the center of the straight section in between two identical and independent variably polarized APPLE-II devices. Based on Permanent Magnet technology, the phasing magnet has been designed to achieve the required electron beam delay to properly adjust the phase matching of these two consecutive EPUs (Elliptically Polarizing Undulators) and ensure a positive interference between the photon beam emitted in each device. Also this paper will describe the mechanical and magnetic design together with the final field measurements and magnetic tuning results. Also, the spectral performance of the two EPUs and the method used to properly set the field strength of the phasing magnet for any given radiation wavelength and polarization mode will be presented as well.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Data for Propagation Method and Planting Density Influence Canopy Developmental Transition and Biomass Productivity in Miscanthus × giganteus

Understanding how establishment practices influence the mechanisms underlying Miscanthus × giganteus (miscanthus) productivity and canopy development is critical for optimizing management. Data was collected during the juvenile (2011–2013) and mature (2024) phases of a long-term field experiment established in Urbana, Illinois, to evaluate the effects of propagation method (plug propagation [PP] and rhizome propagation [RP]), planting density (1.0, 0.75, and 0.25 plants m⁻²), and nitrogen application (0 and 67 kg N ha⁻¹) on end-of-season biomass yield, tiller mass, tiller density, and tiller height. Linear regression models identified the dominant predictors of yield across stand ages and management regimes. Planting density, nitrogen (N) application, and propagation method significantly influenced early yield and canopy development. During the juvenile phase, biomass yield was driven by tiller density due to canopy expansion; in the mature phase, yield became driven by tiller mass. The PP plots produced higher tiller density than the RP plots, resulting in faster canopy closure and higher juvenile-phase yields. Rhizome-propagated (RP) plots produced lower tiller density, but individual tillers were 3.3–6.4 g tiller−1 heavier than PP tillers. After the canopy reached equilibrium, the PP and RP yields were similar because greater RP tiller mass compensated for its lower tiller density. Higher planting density resulted in greater yield and tiller density during the second year (2012), but this effect was absent from the third year (2013) onward. In the juvenile phase, N fertilization enhanced yield by 1.6–3.4 Mg ha−1. Initiating fertilization in 2013 on unfertilized plots produced biomass similar to that in fertilized plots, suggesting yield recovery in the mature phase. These findings revealed that establishment strategies, including propagation method and planting density, influence juvenile miscanthus canopy development and productivity, transitioning from tiller-density- to mass-dominated yields, but not mature phase productivity.

Miscanthus↗

DOE OSTI2022

A phase-field model for quasi-dynamic nucleation, growth, and propagation of rate-and-state faults

Despite its critical role in the study of earthquake processes, numerical simulation of the entire stages of fault rupture remains a formidable task. The main challenges in simulating a fault rupture process include the complex evolution of fault geometry, frictional contact, and off-fault damage over a wide range of spatial and temporal scales. Here, in this paper, we develop a phase-field model for quasi-dynamic fault nucleation, growth, and propagation, which features two standout advantages: (i) it does not require any sophisticated algorithms to represent fault geometry and its evolution; and (ii) it allows for modeling fault nucleation, propagation, and off-fault damage processes with a single formulation. Built on a recently developed phase-field framework for shear fractures with frictional contact, the proposed formulation incorporates rate- and state-dependent friction, radiation damping, and their impacts on fault mechanics and off-fault damage. We show that the numerical results of the phase-field model are consistent with those obtained from well-verified approaches that model the fault as a surface of discontinuity, without suffering from the mesh convergence issue in the existing continuous approaches to fault rupture (e.g., the stress glut method). Further, through numerical examples of fault propagation in various settings, we demonstrate that the phase-field approach may open new opportunities for investigating complex earthquake processes that have remained overly challenging for the existing numerical methods.

58 GEOSCIENCES↗

DOE OSTI2024

Identifying Topological Defects in Lamellar Phases through Contour Analysis of Complex Wave Fields

Lamellar phases frequently contain structural imperfections that significantly affect their behaviors and properties. Our previous research successfully reconstructed real-space configurations of defective lamellar phases from diffuse scattering patterns, indicating the presence of phase vortices as a potential method for identifying topological defects disrupting the smectic ordering. Here, this report presents a mathematical framework using regularized wave fields to represent defective lamellar structures in real space. Phase singularities, resulting from the interference of random waves and indicating lamellar order disruption, are identified through a contour integral. These wave fields, derived from coherent scattering in reciprocal space, were validated via computational benchmarks analyzing small-angle neutron scattering data from AOT surfactant solutions, facilitating further statistical analysis of the defects. Our study highlights the potential to extract meaningful information about topological defects in lyotropic phases by inversely analyzing experimentally measured two-point static correlations. Our method allows for detailed structural analysis of various lyotropic phases, both particulate and nonparticulate, in their quiescent states and facilitates quantitative investigation of defects’ role in phase transitions. By integrating small-angle scattering, deep learning, and vortex tangle analysis, our comprehensive approach shows promise in addressing complex challenges in the structural analysis of soft matter systems.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Detecting Quantum Critical Points of Correlated Systems by Quantum Convolutional Neural Network Using Data from Variational Quantum Eigensolver

Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable accuracy. The QCNN can be trained to predict the corresponding ‘phase’ of wavefunctions around the putative quantum critical point even though it is trained by wavefunctions far away. The paper provides a basis for exploiting the QCNN to identify the quantum critical point.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗

DOE OSTI2020

Thermodynamic signatures of an antiferromagnetic quantum critical point inside a superconducting dome

Recent experiments in unconventional superconductors, and in particular iron-based materials, have reported evidence of an antiferromagnetic quantum critical point (AFM-QCP) emerging inside the superconducting dome of the phase diagram. Fluctuations associated with such an AFM-QCP are expected to promote unusual temperature dependencies of thermodynamic quantities. Here, we compute the T dependence of the specific heat C(T) deep inside a fully gapped s +– superconducting state as the AFM-QCP is approached. We find that at the AFM-QCP, the specific heat C(T) vanishes quadratically with temperature, as opposed to the typical exponential suppression seen in fully gapped BCS superconductors. This robust result is due to a nonanalytic contribution to the free energy arising from the general form of the bosonic (AFM) propagator in the SC state. Away from the AFM-QCP, as temperature is lowered, C(T) shows a crossover from a T2 behavior to an exponential behavior, with the crossover temperature scale set by the value of the superconducting gap and the distance to the QCP. As a result, we argue that these features in the specific heat can be used to unambiguously determine the existence of AFM-QCPs inside the superconducting domes of iron-based and other fully gapped unconventional superconductors.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Microstructural pattern formation during liquid metal dealloying: Phase-field simulations and theoretical analyses

In recent years, liquid metal dealloying has emerged as a promising material processing method to generate micro- and nanoscale bicontinuous or porous structures. Most previous studies focused on the experimental characterization of the dealloying process and on the properties of the dealloyed materials, leaving the theoretical study incomplete to fully understand the fundamental mechanisms of the liquid metal dealloying process. In this paper, we use theoretical models and phase-field simulations to clarify the kinetics and pattern formation during liquid metal dealloying. Our investigation starts from a theoretical analysis of the 1D dissolution of a binary precursor alloy, which reveals that the 1D dissolution process involves two regimes. In the first regime, due to the low solubility of one of the elements in the melt, it accumulates at the solid-liquid interface, which reduces the dissolution kinetics. In the second regime, the interface kinetics reaches a stationary regime where both elements of the precursor alloy dissolve into the melt. Previous works revealed that in the early dealloying stage, the dealloying front is destabilized by an interfacial spinodal decomposition, which triggers the formation of interconnected ligaments. Here we extend this line of work by proposing a linear stability analysis able to predict the initial length scale of the ligaments formed in the initial stage of the dealloying. Combining this analysis with the 1D dissolution model proposed here enables us to better understand the initial conditions (composition of the precursor alloy and the melt) leading to a planar dissolution without interface destabilization. Finally, we report a strong influence of solid-state diffusion on dealloying. Although the solid-state diffusivity is four to five orders of magnitude smaller than in the liquid phase, it is found to affect both dissolution kinetics and ligament morphologies.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Scale-bridging with the extended/generalized finite element method for linear elastodynamics

This paper presents an extended/generalized finite element method for bridging scales in linear elastodynamics in the absence of scale separation. More precisely, the GFEMgl framework is expanded to enable the numerical solution of multiscale problems through the automated construction of specially-tailored shape functions, thereby enabling high-fidelity finite element modeling on simple, fixed finite element meshes. Furthermore, this introduces time-dependencies in the shape functions in that they are subject to continuous adaptation with time. The temporal aspects of the formulation are investigated by considering the Newmark-β time integration scheme, and the efficacy of mass lumping strategies is explored in an explicit time-stepping scheme. This method is demonstrated on representative wave propagation examples as well as a dynamic fracture problem to assess its accuracy and flexibility.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Classical analog of quantum models in synthetic dimensions

We introduce a classical analog of quantum matter in ultracold molecule-synthetic or Rydberg atom-synthetic dimensions, by extending the Potts model to include interactions J 1 between atoms adjacent in both real and synthetic space and studying its finite-temperature properties. For intermediate values of J 1 , the resulting phases and phase diagrams are similar to those of the clock and Villain models, in which three phases emerge. There exists a sheet phase analogous to that found in quantum synthetic dimension models between the high-temperature disordered phase and the low-temperature ferromagnetic phase. Furthermore, we also employ machine learning to uncover nontrivial features of the phase diagram using the learning by confusion approach, which is able to discern several successive phase transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Solid phase sampling device and methods for point-source sampling of polar organic analytes

Sampling devices for sampling an aqueous source (e.g., field testing of ground water) for multiple different analytes are described. Devices include a solid phase extraction component for retention of a wide variety of targeted analytes. Devices include analyte derivatization capability for improved extraction of targeted analytes. Thus, a single device can be utilized to examine a sample source for a wide variety of analytes. Devices also include an isotope dilution capability that can prevent error introduction to the sample analysis and can correct for sample loss and degradation from the point of sampling until analysis as well as correction for incomplete or poor derivatization reactions. The devices can be field-deployable and rechargeable.

Boggess, Andrew J.↗

DOE OSTI2023

Solid-phase sampling device and methods for point-source sampling of polar organic analytes

Boggess, Andrew J.↗

DOE OSTI2021

Differential programming enabled functional imaging with Lorentz transmission electron microscopy

Abstract Lorentz transmission electron microscopy is an advanced characterization technique that enables the simultaneous imaging of both the microstructure and functional properties of materials. Information such as magnetization and electric potentials is carried by the phase of the electron wave, and is lost during image acquisition. Various methods have been proposed to retrieve the phase of the electron wavefunction using intensities of the acquired images, most of which work only in the small defocus limit. Imaging at strong defoci not only carries more quantitative phase information, but is essential to the study of weak magnetic and electrostatic fields at the nanoscale. In this work we develop a method based on differentiable programming to solve the inverse problem of phase retrieval. We show that our method maintains a high spatial resolution and robustness against noise even at the upper defocus limit of the microscope. More importantly, our proposed method can go beyond recovering just the phase information. We demonstrate this by retrieving the electron-optical parameters of the contrast transfer function alongside the electron exit wavefunction.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Spectroscopic signatures and oxidation characteristics of nanosecond laser-induced cerium plasmas

Improving technologies related to the wide area environmental sampling of nuclear materials supports the nuclear nonproliferation mission of preventing the proliferation of nuclear weapons by monitoring nuclear weapons tests and detecting undeclared nuclear fuel cycle activities. Standoff, laser-based detection techniques such as laser-induced breakdown spectroscopy have the potential to offer robust, field-deployable methods that provide rapid element-specific and phase identifiable measurements over a wide range of materials. This work aims to elucidate the effects of atmospheric conditions and oxidation reactions on the highly complex and transient spectroscopic signatures of laser-induced plutonium surrogate plasmas. Time-resolved spectra of nanosecond laser ablation cerium plasmas were measured using laser-induced breakdown spectroscopy in a range of atmospheres containing low to high concentrations of oxygen. Here, the growth of strong CeO molecular emission bands was observed in the visible spectrum, where it was shown that the persistence of CeO is reduced from around 60 μs to 50 μs in oxygen rich atmospheric environments. To further investigate the growth and depletion of CeO in the laser-produced plasma, ratios of CeO-to-Ce emission were generated using integrated intensities corresponding to the Q-branch of the CeO D 1 -X 1 transitions and numerous strong atomic Ce peaks. It was determined that the fastest rate of formation of CeO in argon occurred for moderate oxygen mass fractions between 0.10 and 0.15 while the ratios were reduced at higher oxygen mass fractions (i.e., Y O 2 = 0.20) due to competing oxidation reactions and lower plasma temperatures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Referenceless, grating-based, single shot X-ray phase contrast imaging with optimized laser-driven K-α sources

With its ability to efficiently probe low-Z materials, X-ray phase imaging methods have recently raised high interest in multiple fields from biology and medical applications to high energy density (HED) physics. Initially developed with synchrotron light and X-ray tubes, we present a novel grating based Talbot X-ray deflectometer (TXD) diagnostic that was coupled with laser-generated K-α X-ray sources. The multi-terawatt laser (I > 1 × 10 14 W cm -2 ) was used as a testbed for diagnostic development. It was found that X-ray source chromaticity plays an important role in TXD. Indeed, the broadband spectrum of laser-generated X-ray sources may strongly impact image quality and thus diagnostic performance. We qualified X-ray emission from different laser-produced sources and determined laser, target, and deflectometer parameters that optimize TXD performance. We present the first results of referenceless grating-based X-ray imaging at high-power laser facilities and discuss the implications of this new development in HED research.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

CPU and memory efficient coherent mode decomposition for the partially coherent x-ray simulations

In this work, the method of the Coherent Mode Decomposition (CMD) is applied to numerical wave propagation calculations for partially-coherent X-rays, using the Fourier optics and compatible methods. Its CPU and memory efficiency is discussed in various cases of the wavefront at the source and the beam waist. With the absence of the quadratic phase terms, the required sampling density of the electric fields is effectively reduced. The problem size is thus moderate and the method is feasible to be implemented on a single-node CPU server. In other cases, the same argument holds with proper treatments of the quadratic phase terms. Tests on CMD and the modes propagation are done for the case of the Coherent Hard X-ray beamline of the National Synchrotron Light Source II, using the Synchrotron Radiation Workshop software. We observe a few hundred or less dominant decomposed modes that resemble the electric fields converge to the wavefront intensity at a high accuracy of over 99%.

36 MATERIALS SCIENCE↗