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DOE OSTI2024

Direct numerical simulation of open-channel flow over a heterogeneous particle bed at low relative submergence

In this article, this study investigates turbulent open-channel flows over beds of irregularly arranged particles, using direct numerical simulations at a friction Reynolds number of Re T = 300⁠. Two distinct cases are examined: a polydisperse bed (P800) composed of multiple layers of randomly distributed spheres of varying sizes, and a monodisperse bed (M1015) formed by a random distribution of uniform sized spheres, with a bottommost single layer of varied-sized particles to introduce realistic randomness. Our investigation unveils a rich network of low- and high-speed streaks within the flow field, exhibiting distinctive behaviors in different bed configurations. The P800 case presents a poorly organized flow pattern induced by the varied particle sizes and arrangements, while the M1015 case shows a more regular flow pattern, marked by larger streaks. We also observe that total wall shear stress is substantially influenced by surface roughness-induced drag, extending beyond the effects documented in existing studies of open-channel flows. The present study reveals intricate secondary flow patterns over irregular particle beds. Large-scale circulations are discerned around particle crests in the P800 case and localized circulations with increased turbulence in the M1015 case. Furthermore, analysis of Reynolds stress tensor components indicates that roughness disrupts coherent turbulent eddies, consequently mitigating peak stress. We quantify correlations between drag force and local fluid velocity fluctuations. Notably, a larger deviation in drag is observed in the P800 case compared to M1015, accentuating the influence of particle size and distribution on fluid–particle interactions.

42 ENGINEERING↗

DOE OSTI2024

Modeling the electron cyclotron emission radiation signature from suprathermal electrons in a tokamak

An Electron Cyclotron Emission (ECE) modeling code has been developed to model ECE radiation with an arbitrary electron momentum distribution, a small oblique angle, both ordinary (O-mode) and extraordinary polarizations (X-mode), and multiple cyclotron frequency harmonics. The emission and absorption coefficients are calculated using the Poynting theorem from the cold plasma dispersion and the electron–microwave interaction from the full anti-Hermitian tensor. The modeling shows several ECE radiation signatures that can be used to diagnose the population of suprathermal electrons in a tokamak. First, in an n = 2 X-mode (X2) optically thick plasma and oblique ECE view, the modeling shows that only suprathermal electrons, which reside in a finite region of the velocity and space domains, can effectively generate cyclotron emissions to the ECE receiver. The code also finds that the O1 mode is sensitive to suprathermal electrons of both a high v ⊥ and v || , while the X2 mode is dominantly sensitive to suprathermal electrons of a high v ⊥ . Finally, the modeling shows that an oblique ECE system with both X/O polarization and a broad frequency coverage can be used to effectively yield information of the suprathermal electron population in a tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Harnessing complexity: Nonlinear optical phenomena in L-shapes, nanocrescents, and split-ring resonators

Here, we conduct systematic studies of the optical characteristics of plasmonic nanoparticles that exhibit C 2v symmetry. In particular, we analyze three distinct geometric configurations: an L-type shape, a crescent, and a split-ring resonator shaped like the Greek letter π. Optical properties are examined using the finite-difference time-domain method. It is demonstrated that all three shapes exhibit two prominent plasmon modes associated with the two axes of symmetry. This is in addition to a wide range of resonances observed at high frequencies corresponding to quadrupole modes and peaks due to sharp corners. Next, to facilitate nonlinear analysis, we employ a semiclassical hydrodynamic model, where the electron pressure term is explicitly accounted for. This model goes beyond the standard Drude description and enables capturing nonlocal and nonlinear effects. Employing this model enables us to rigorously examine the second-order angular resolved nonlinear optical response of these nanoparticles in each of the three configurations. Two pumping regimes are considered, namely, continuous wave (CW) and pulsed excitations. For CW pumping, we explore the properties of the second harmonic generation (SHG). Polarization and angle-resolved SHG spectra are obtained, revealing strong dependence on the nanoparticle geometry and incident wave polarization. The C 2v symmetry is shown to play a key role in determining the polarization states and selection rules of the SHG signal. For pulsed excitations, we discuss the phenomenon of broadband terahertz (THz) generation induced by the difference-frequency generation . It is shown that the THz emission spectra exhibit unique features attributed to the plasmonic resonances and symmetry of the nanoparticles. The polarization of the generated THz waves is also examined, revealing interesting patterns tied to the nanoparticle geometry. To gain deeper insight, we propose an analytical theory that agrees very well with the numerical experiments. The theory shows that the physical origin of the THz radiation is the mixing of various frequency components of the fundamental pulse by the second-order nonlinear susceptibility. An expression for the far-field THz intensity is derived in terms of the incident pulse parameters and the nonlinear response tensor of the nanoparticle. The results presented in this work offer new insights into the linear and nonlinear optical properties of nanoparticles with C 2v symmetry. The demonstrated strong SHG response and efficient broadband THz generation hold great promise for applications in nonlinear spectroscopy, nanophotonics, and optoelectronics. The proposed theoretical framework also provides a valuable tool for understanding and predicting the nonlinear behavior of other related nanostructures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Scalable learning of potentials to predict time-dependent Hartree–Fock dynamics

We propose a framework to learn the time-dependent Hartree–Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Although the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange–correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to 60 × 60 × 60 × 60. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Rovibrationally resolved Rayleigh and Raman scattering cross sections for molecular hydrogen

Accurate Rayleigh and Raman scattering cross sections, tensor components, depolarization ratios, and reversal coefficients for all rovibrational transitions within the X1Σg+ ground electronic state of H2 have been calculated. Raman spectra have been generated using these data. A method for calculating Raman scattering cross sections is formulated that is valid below the ionization threshold and in the region containing resonances, which explicitly accounts for all bound and dissociative vibrational levels of the bound intermediate electronic states and approximately accounts for the ionization continuum. A representative set of cross sections is presented for incident photon energies below 15 eV and compared with existing results in the literature where possible. Convergence of our results with an increasing number of bound intermediate electronic states is demonstrated. The accuracy of the Placzek–Teller approximation is discussed. The effect of accounting for the intermediate ionization continuum is investigated. Local thermal equilibrium cross sections are calculated for Rayleigh and Raman scattering. This work represents the most accurate and complete treatment of Raman scattering for molecular hydrogen to date. A total of 9582 Rayleigh and Raman scattering cross sections have been generated and are openly available on Zenodo under an open-source Creative Commons Attribution license at https://zenodo.org/doi/10.5281/zenodo.13441471.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Extending Badger's rule. I. The relationship between energy and structure in hydrogen bonds

Here, we derive a new expression for the strength of a hydrogen bond (V HB ) in terms of the elongation of the covalent bond of the donor fragment participating in the hydrogen bond (Δr HB ) and the intermolecular coordinates R (separation between the heavy atoms) and θ (deviation of the hydrogen bond from linearity). The expression includes components describing the covalent D–H bond of the hydrogen bond donor via a Morse potential, the Pauli repulsion, and electrostatic interactions between the constituent fragments using a linear expansion of their dipole moment and a quadratic expansion of their polarizability tensor. We fitted the parameters of the model using ab initio electronic structure results for six hydrogen bonded dimers, namely, NH 3 –NH 3 , H 2 O–H 2 O, HF–HF, H 2 O–NH 3 , HF–H 2 O, and HF–NH 3 , and validated its performance for extended parts of their potential energy surfaces, resulting in a mean absolute error ranging from 0.07 to 0.31 kcal/mol. The derived expression describes the energy–structure relationship in terms of a single structural parameter, namely, the elongation of the donor’s covalent bond (Δr HB ), and suggests the novel relationship of 8.0 kcal/mol pm −1 (or 0.8 kcal/mol per 0.001 Å elongation). This structural parameter is easily obtained from theory and can serve as the single descriptor of the strength of individual hydrogen bonds.

Santis, Garrett D. [Univ. of Washington, Seattle, ↗

DOE OSTI2025

The polarized-signal density matrix: A practical way to recover molecular frame information from isotropic samples

We present a novel approach to model ultrafast time-dependent nonlinear optical polarization sensitive signals emitted from randomly oriented molecules. By projecting the laboratory-frame analyzer polarization axis into the molecular-frame and linking that axis with the density matrix through a tensor product, we demonstrate an approach to find a specific molecular orientation that yields a good approximation to simulated four-wave mixing signals produced by the same model but with averaging over molecular orientation.

Thurston, Richard L↗

DOE OSTI2025

Developing reliable machine learning interatomic potential for Fe–Cr–Ni austenitic alloys

Gaining atomistic understanding of mechanical behavior of heat-resistant structural materials such as Fe–Cr–Ni-based alloys requires an approach with an accuracy close to density functional theory (DFT) that considers the intrinsic properties of the bulk lattice and important defects such as stacking faults, grain boundaries, and surfaces. This work aims to develop reliable machine learning interatomic potential (MLIAP) at cross-scale for Fe–Cr–Ni ternary alloys with a focus on the face-centered-cubic (fcc) solid solution structure. Leveraging the advantages of moment tensor potentials, which typically necessitate a relatively small training dataset and enable rapid calculations using the large-scale atomic/molecular massively parallel simulator package, we ensure the stability and accuracy of the trained potentials. Important defects such as stacking faults, grain boundaries, and surfaces for wide-range compositions are investigated. Structural, thermal, elastic, and defect properties are determined from molecular dynamics simulations comprising several thousand atoms, generated via canonical Monte Carlo simulations guided by the trained potential. The trained potential allows efficient atomic simulations of structural, thermal, and mechanical properties of fcc Fe–Cr–Ni solid solution alloys as a function of composition and temperature. Therefore, the MLIAP approach represents a major advancement from DFT calculations that are limited to small simulation sizes and traditional molecular dynamics simulations using relatively low accuracy potentials. Furthermore, this work outlines a practical foundation for further investigating the structural evolution and mechanical behavior of austenitic stainless steel and nickel-based alloys in a wide array of applications in extreme environments.

Crystal structure↗

DOE OSTI2025

Scattering theory in noncanonical phase space: A Drift-Kinetic collision operator for weakly collisional plasmas

After developing a scattering theory for grazing collisions in general noncanonical phase spaces, we introduce a guiding center collision operator in five-dimensional phase space designed for plasma regimes characterized by long wavelengths (relative to the Larmor radius), low frequencies (relative to the cyclotron frequency), and weak collisionality (where repeated Coulomb collisions induce cumulatively small changes in particle magnetic moment). The collision operator is fully determined by the noncanonical Hamiltonian structure of guiding center dynamics and exhibits a metriplectic structure, ensuring the conservation of particle number, momentum, energy, and interior Casimir invariants. It also satisfies an H-theorem, allowing for deviations from an equilibrium Maxwellian distribution due to the nontrivial kernel of the noncanonical guiding center Poisson tensor, spanned by the magnetic moment. We propose that this collision operator and its underlying mathematical structure may offer valuable insight into the study of turbulence, transport, and self-organizing phenomena in both laboratory and astrophysical plasmas.

Hamiltonian mechanics↗

DOE OSTI2025

On the discretization error of the discrete generalized quantum master equation

The transfer tensor method (TTM) [Cerrillo and Cao, Phys. Rev. Lett. 112 , 110401 (2014)] can be considered a discrete-time formulation of the Nakajima–Zwanzig quantum master equation (NZ-QME) for modeling non-Markovian quantum dynamics. A recent paper [Makri, J. Chem. Theory Comput. 21 , 5037 (2025)] raised concerns regarding the consistency of the TTM discretization, particularly a spurious term at the initial time t = 0. Here, this work presents a detailed analysis of the discretization structure of the TTM, clarifying the origin of the initial-time correction and establishing a consistent relationship between the TTM discrete-time memory kernel K N and the continuous-time NZ-QME kernel $\mathscr{K}$( N Δ t ). This relationship is validated numerically using the spin-boson model, demonstrating convergence of reconstructed memory kernels and accurate dynamical evolution as Δ t → 0. While the TTM provides a consistent discretization, we note that alternative schemes are also viable, such as the midpoint derivative/midpoint integral scheme proposed in Makri’s work. The relative performance of various schemes for either computing accurate $\mathscr{K}$( N Δ t ) from exact dynamics or obtaining accurate dynamics from exact $\mathscr{K}$( N Δ t ) warrants further investigation.

Density-matrix↗

DOE OSTI2025

Machine learning interatomic potential for predicting the thermal properties of uranium nitride

We present a combined computational and experimental investigation of the thermal properties of uranium nitride (UN), focusing on the development of a machine learning interatomic potential (MLIP) using the moment tensor potential framework. The MLIP was trained on density functional theory (DFT) data and validated against various quantities including energies, forces, elastic constants, phonon dispersion, and defect formation energies, achieving excellent agreement with DFT calculations, prior experimental results, and our thermal conductivity measurement. The potential was then employed in molecular dynamics simulations to predict key thermal properties such as melting point, thermal expansion, specific heat, and lattice thermal conductivity. To further assess model accuracy, we fabricated a UN sample and performed new thermal conductivity measurements representative of single-crystal properties, which showed strong agreement with the MLIP predictions. This work confirms the reliability and predictive capability of the developed potential for determining the thermal properties of UN.

36 - MATERIALS SCIENCE↗

DOE OSTI2026

Non-resonant Raman optical activity from phase-space electronic structure theory

In order to model experimental non-resonant Raman optical activity, chemists must compute a host of second-order response tensors (e.g., the electric-dipole–magnetic-dipole polarizability) and their nuclear derivatives along a set of vibrational modes. While these response functions are almost always computed within a Born–Oppenheimer (BO) framework, here we provide a natural interpretation of the electric-dipole–magnetic-dipole polarizability within phase space electronic structure theory, a beyond-BO model whereby the electronic structure depends on nuclear momentum (P) in addition to nuclear position (R). By coupling to nuclear momentum, phase space electronic structure theory is able to capture the asymmetric response of the electronic properties to an external field, in so far as for a vibrating (non-stationary) molecule, $\frac{∂μ}{∂B}$≠$\frac{∂m}{∂F}$, where μ and m are the electrical linear and magnetic dipoles, and F and B are electric and magnetic fields. As an example, for a prototypical methyloxirane molecule, we show that phase space electronic structure theory is able to deliver a reasonably good match with experimental results in a manner that is formally invariant to gauge origin G 0 —provided that one uses a complete basis or, alternatively, gauge invariant atomic orbitals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Phase field dislocation dynamics formulation coupled with Fourier based micromechanics solver and its application to grain boundary–dislocation interactions

A new phase field dislocation dynamics (PFDD) formulation for homogeneous and heterogeneous materials is presented, which couples micromechanical solvers and the time-dependent Ginzburg–Landau equation. The strain fields are obtained from the micromechanical solver by solving the Lippmann–Schwinger equation and then used to define energy terms to model the evolution of the dislocations. Grain boundary (GB)–dislocation interactions are studied using the coupled PFDD formulation and by describing GBs as inclusions. GB energy and stiffness tensors are computed from molecular statics simulations, and a newly proposed lattice energy term that is dependent on the GB energy is considered in the calculations. Interaction of a screw dislocation with minimum energy and metastable states of low and high angle ⟨110⟩ symmetric tilt grain boundaries are studied. We show good agreement between predictions from our PFDD formulation and molecular dynamics simulations of grain boundary–dislocation interactions.

36 MATERIALS SCIENCE↗

DOE OSTI2026

An algebraic convolution formulation for multiple-scattering correction in small-angle neutron scattering

Multiple scattering in small-angle neutron scattering (SANS) redistributes spectral weight and distorts structural interpretation, particularly for thick or strongly scattering samples. We develop a finite-dimensional spectral desmearing framework that corrects multiple scattering without resorting to integral transforms or model-dependent extrapolation. The primary intensity is expanded in an orthonormal basis adapted to the isotropic transverse-momentum measure, under which convolution reduces to a recursive tensor contraction, allowing the Poisson-weighted multiple-scattering series to be evaluated directly in a finite-dimensional basis representation. This formulation yields a stable forward–inverse mapping between apparent and primary spectra. Numerical tests demonstrate convergence under repeated convolution and accurate recovery of the single-scattering intensity. Application to SANS measurements collected at multiple neutron facilities, including the Spallation Neutron Source, the High Flux Isotope Reactor, and the Institut Laue-Langevin, shows the quantitative reconstruction of the underlying primary spectrum across a wide range of transmission conditions, including strongly attenuating samples. Here, the method provides a stable, model-agnostic framework for multiple-scattering correction in SANS and enables consistent structural interpretation across instruments and scattering regimes.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗

DOE OSTI2020

The influence of packing structure and interparticle forces on ultrasound transmission in granular media

Ultrasound propagation through externally stressed, disordered granular materials was experimentally and numerically investigated. Experiments employed piezoelectric transducers to excite and detect longitudinal ultrasound waves of various frequencies traveling through randomly packed sapphire spheres subjected to uniaxial compression. The experiments featured in situ X-ray tomography and diffraction measurements of contact fabric, particle kinematics, average per-particle stress tensors, and interparticle forces. The experimentally measured packing configuration and inferred interparticle forces at different sample stresses were used to construct spring networks characterized by Hessian and damping matrices. The ultrasound responses of these network were simulated to investigate the origins of wave velocity, acoustic paths, dispersion, and attenuation. Results revealed that both packing structure and interparticle force heterogeneity played an important role in controlling wave velocity and dispersion, while packing structure alone quantitatively explained most of the observed wave attenuation. This research provides insight into time- and frequency-domain features of wave propagation in randomly packed granular materials, shedding light on the fundamental mechanisms controlling wave velocities, dispersion, and attenuation in such systems.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Mapping the intrinsic photocurrent streamlines through micromagnetic heterostructure devices

Photocurrent in quantum materials is often collected at global contacts far away from the initial photoexcitation. This collection process is highly nonlocal. It involves an intricate spatial pattern of photocurrent flow (streamlines) away from its primary photoexcitation that depends sensitively on the configuration of current collecting contacts as well as the spatial nonuniformity and tensor structure of conductivity. Direct imaging to track photocurrent streamlines is challenging. Here, we demonstrate a microscopy method to image photocurrent streamlines through ultrathin heterostructure devices comprising platinum on yttrium iron garnet (YIG). We accomplish this by combining scanning photovoltage microscopy with a uniform rotating magnetic field. Here, local photocurrent is generated through a photo-Nernst type effect with its direction controlled by the external magnetic field. This enables the mapping of photocurrent streamlines in a variety of geometries that include conventional Hall bar-type devices, but also unconventional wing-shaped devices called electrofoils. In these, we find that photocurrent streamlines display contortion, compression, and expansion behavior depending on the shape and angle of attack of the electrofoil devices, much in the same way as tracers in a wind tunnel map the flow of air around an aerodynamic airfoil. This affords a powerful tool to visualize and characterize charge flow in optoelectronic devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Scientific machine learning for modeling and simulating complex fluids

The formulation of rheological constitutive equations—models that relate internal stresses and deformations in complex fluids—is a critical step in the engineering of systems involving soft materials. While data-driven models provide accessible alternatives to expensive first-principles models and less accurate empirical models in many engineering disciplines, the development of similar models for complex fluids has lagged. The diversity of techniques for characterizing non-Newtonian fluid dynamics creates a challenge for classical machine learning approaches, which require uniformly structured training data. Consequently, early machine-learning based constitutive equations have not been portable between different deformation protocols or mechanical observables. Here, we present a data-driven framework that resolves such issues, allowing rheologists to construct learnable models that incorporate essential physical information, while remaining agnostic to details regarding particular experimental protocols or flow kinematics. These scientific machine learning models incorporate a universal approximator within a materially objective tensorial constitutive framework. By construction, these models respect physical constraints, such as frame-invariance and tensor symmetry, required by continuum mechanics. We demonstrate that this framework facilitates the rapid discovery of accurate constitutive equations from limited data and that the learned models may be used to describe more kinematically complex flows. This inherent flexibility admits the application of these “digital fluid twins” to a range of material systems and engineering problems. We illustrate this flexibility by deploying a trained model within a multidimensional computational fluid dynamics simulation—a task that is not achievable using any previously developed data-driven rheological equation of state.

Science & Technology - Other Topics↗

DOE OSTI2024

Sprain energy consequences for damage localization and fracture mechanics

The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the “sprain,” as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ( C 0 ) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.

Science & Technology - Other Topics↗