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DOE OSTI2021

The mechanics of brittle granular materials with coevolving grain size and shape

The influence of particle shape on the mechanics of sand is widely recognized, especially in mineral processing and geomechanics. However, most existing continuum theories for engineering applications do not encompass the morphology of the grains and its evolution during comminution. Similarly, the relatively few engineering models accounting for grain-scale processes tend to idealize particles as spheres, with their diameters considered as the primary and sole geometric descriptor. This paper inspires a new generation of constitutive laws for crushable granular continua with arbitrary, yet evolving, particle morphology. We explore the idea of introducing multiple grain shape descriptors into Continuum Breakage Mechanics (CBM), a theory originally designed to track changes in particle size distributions during confined comminution. We incorporate the influence of these descriptors on the elastic strain energy potential and treat them as dissipative state variables. In analogy with the original CBM, and in light of evidence from extreme fragmentation in nature, the evolution of the additional shape descriptors is postulated to converge towards an attractor. Comparisons with laboratory experiments, discrete element analyses and particle-scale fracture models illustrate the encouraging performance of the theory. The theory provides insights into the feedback among particle shape, compressive yielding and inelastic deformation in crushable granular continua. These results inspire new questions that should guide future research into crushable granular systems using particle-scale imaging and computations.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Differences in water and vapor transport through angstrom-scale pores in atomically thin membranes

Abstract The transport of water through nanoscale capillaries/pores plays a prominent role in biology, ionic/molecular separations, water treatment and protective applications. However, the mechanisms of water and vapor transport through nanoscale confinements remain to be fully understood. Angstrom-scale pores (~2.8–6.6 Å) introduced into the atomically thin graphene lattice represent ideal model systems to probe water transport at the molecular-length scale with short pores (aspect ratio ~1–1.9) i.e., pore diameters approach the pore length (~3.4 Å) at the theoretical limit of material thickness. Here, we report on orders of magnitude differences (~80×) between transport of water vapor (~44.2–52.4 g m −2 day −1 Pa −1 ) and liquid water (0.6–2 g m −2 day −1 Pa −1 ) through nanopores (~2.8–6.6 Å in diameter) in monolayer graphene and rationalize this difference via a flow resistance model in which liquid water permeation occurs near the continuum regime whereas water vapor transport occurs in the free molecular flow regime. We demonstrate centimeter-scale atomically thin graphene membranes with up to an order of magnitude higher water vapor transport rate (~5.4–6.1 × 10 4 g m −2 day −1 ) than most commercially available ultra-breathable protective materials while effectively blocking even sub-nanometer (>0.66 nm) model ions/molecules.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Catalytic resonance of ammonia synthesis by simulated dynamic ruthenium crystal strain

Ammonia affords dense storage for renewable energy as a fungible liquid fuel, provided it can be efficiently synthesized from hydrogen and nitrogen. In this work, the catalysis of ammonia synthesis was computationally explored beyond the Sabatier limit by dynamically straining a ruthenium crystal (±4%) at the resonant frequencies (10 2 to 10 5+ Hz) of N 2 surface dissociation and hydrogenation. Density functional theory calculations at different strain conditions indicated that the energies of NH x surface intermediates and transition states scale linearly, allowing the description of ammonia synthesis at a continuum of strain conditions. A microkinetic model including multiple sites and surface diffusion between step and Ru(0001) terrace sites of varying ratios for nanoparticles of differing size revealed that dynamic strain yields catalytic ammonia synthesis conversion and turnover frequency comparable to industrial reactors (400°C, 200 atm) but at lower temperature (320°C) and an order of magnitude lower pressure (20 atm).

10 SYNTHETIC FUELS↗

DOE OSTI2022

(Invited) Continuum Mathematical Modeling of Water Electrolysis: A Tutorial

Widespread use of hydrogen energy is contingent on the development of reliable and economical sources of hydrogen. Electrolysis from renewably-derived low-carbon electricity is a potentially viable method of hydrogen generation. Prime among the electrolysis technologies are those utilizing ion-conducting polymers (ionomers) including proton-exchange-membrane water electrolyzer (PEMWE). However, these technologies need to exhibit increased efficiency, performance, and durability to become commercially viable. Like most electrochemical devices, PEMWEs involve multiple components (e.g., catalyst, ionomer, transport layers, membrane, plates) and multiple phases, with phenomena occurring across different time and length scales. Furthermore, it is difficult to experimentally probe many of the species and phenomena during operation. Thus, mathematical modeling at the continuum level has been an invaluable aid in exploring, understanding, and optimizing PEMWE cell and components. Furthermore, this is especially true in the highly coupled and complex physics and chemistries that occur with the membrane-electrode assembly (MEA). The physics in a typical volume-averaged non-isothermal model include multiphase transport in porous media, concentrated-solution theory, Ohm's Law, and Butler-Volmer kinetics, and ion, gas, and water transport in the ionomer.

Dizon, Arthur↗

DOE OSTI2021

Perspective—Mass Conservation in Models for Electrodeposition/Stripping in Lithium Metal Batteries

25 ENERGY STORAGE↗

DOE OSTI2022

BattPhase—A Convergent, Non-Oscillatory, Efficient Algorithm and Code for Predicting Shape Changes in Lithium Metal Batteries Using Phase-Field Models: Part I. Secondary Current Distribution

Electrochemical models at different scales and varying levels of complexity have been used in the literature to study the evolution of the anode surface in lithium metal batteries. This includes continuum, mesoscale (phase-field approaches), and multiscale models. Thermodynamics-based equations have been used to study phase changes in lithium batteries using phase-field approaches. However, grid convergence studies and the effect of additional parameters needed to simulate these models are not well-documented in the literature. In this paper, using a motivating example of a moving boundary model in one- and two-dimensions, we show how one can formulate phase-field models, implement algorithms for the same and analyze the results. An open-access code with no restrictions is provided as well. This article concludes with some thoughts on the computational efficiency of phase-field models for simulating dendritic growth.

25 ENERGY STORAGE↗

DOE OSTI2021

Data driven learning of robust nonlocal models

Nonlocal models use integral operators that embed length-scales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given physical system, such as laboratory mechanical property tests. In contrast, molecular dynamics (MD) does not require these integrands, but it suffers from computational limitations in the length and time scales it can address. To combine the strengths of both methods and to obtain a coarse-grained, homogenized continuum model that efficiently and accurately captures materials' behavior, we propose a learning framework to extract, from MD data, an optimal nonlocal model as a surrogate for MD displacements. Our framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training. The efficacy of this approach is demonstrated with several numerical tests for single layer graphene both in the case of perfect crystal and in the presence of thermal noise.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Active Galactic Nuclei Continuum Reverberation Mapping Based on Zwicky Transient Facility Light Curves

We perform a systematic survey of active galactic nuclei (AGNs) continuum lags using ~3 days cadence gri-band light curves from the Zwicky Transient Facility. We select a sample of 94 type 1 AGNs at z < 0.8 with significant and consistent inter-band lags based on the interpolated cross-correlation function method and the Bayesian method JAVELIN. Within the framework of the "lamp-post" reprocessing model, our findings are: (1) The continuum emission (CE) sizes inferred from the data are larger than the disk sizes predicted by the standard thin-disk model. (2) For a subset of the sample, the CE size exceeds the theoretical limit of the self-gravity radius (12 lt-days) for geometrically thin disks. (3) The CE size scales with continuum luminosity as R CE ∝ L 0.48±0.04 with a scatter of 0.2 dex, analogous to the well-known radius–luminosity relation of broad Hβ. These findings suggest a significant contribution of diffuse continuum emission from the broad-line region (BLR) to AGN continuum lags. We find that the R CE –L relation can be explained by a photoionization model that assumes ~23% of the total flux comes from the diffuse BLR emission. In addition, the ratio of the CE size and model-predicted disk size anticorrelates with the continuum luminosity, which is indicative of a potential nondisk BLR lag contribution evolving with the luminosity. Finally, a robust positive correlation between the CE size and black hole mass is detected.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Thermal-fluctuation effects on small-scale statistics in turbulent gas flow

Kolmogorov's theory of turbulence assumes that the small-scale turbulent structures in the energy cascade are universal and are determined by the energy dissipation rate and the kinematic viscosity alone. However, thermal fluctuations, absent from the continuum description, terminate the energy cascade near the Kolmogorov length scale. Here, we propose a simple superposition model to account for the effects of thermal fluctuations on small-scale turbulence statistics. Furthermore, for compressible Taylor–Green vortex flow, we demonstrate that the superposition model in conjunction with data from direct numerical simulation of the Navier–Stokes equations yields spectra and structure functions that agree with the corresponding quantities computed from the direct simulation Monte Carlo method of molecular gas dynamics, verifying the importance of thermal fluctuations in the dissipation range.

42 ENGINEERING↗

DOE OSTI2021

Projecting the number of new HIV infections to formulate the "Getting to Zero" strategy in Illinois, USA

Objectives: Getting to Zero (GTZ) initiatives focus on expanding use of antiretroviral treatment (ART) and pre-exposure prophylaxis (PrEP) to eliminate new HIV infections. Computational models help inform policies for implementation of ART and PrEP continuums. Such models, however, vary in their design, and may yield inconsistent predictions. Using multiple approaches can help assess the consistency in results obtained from varied modeling frameworks, and can inform optimal implementation strategies. Methods: A study using three different modeling approaches is conducted. Two approaches use statistical time series analysis techniques that incorporate temporal HIV incidence data. A third approach uses stochastic stimulation, conducted using an agent-based network model (ABNM). All three approaches are used to project HIV incidence among a key population, young Black MSM (YBMSM), over the course of the GTZ implementation period (2016-2030). Results: All three approaches suggest that simultaneously increasing PrEP and ART uptake is likely to be more effective than increasing only one, but increasing ART and PrEP by 20% points may not eliminate new HIV infections among YBMSM. The results further suggest that a 20% increase in ART is likely to be more effective than a 20% increase in PrEP. All three methods consistently project that increasing ART and PrEP by 30% simultaneously can help reach GTZ goals. Conclusions: Increasing PrEP and ART uptake by about 30% might be necessary to accomplish GTZ goals. Such scale-up may require addressing psychosocial and structural barriers to engagement in HIV and PrEP care continuums. ABNMs and other flexible modeling approaches can be extended to examine specific interventions that address these barriers and may provide important data to guide the successful intervention implementation.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

Phase-field simulations of fission gas bubble growth and interconnection in U-(Pu)-Zr nuclear fuel

Abstract The growth and interconnection of fission gas bubbles in the hotter central regions of U-(Pu)-Zr nuclear fuel has been simulated with a phase-field model. The Cahn-Hilliard equation was used to represent the two-phase microstructure, with a single defect species. The volume fraction of the bubble phase and surface area of the bubble-matrix interface were determined during growth and interconnection. Surface area increased rapidly during the initial stages of growth, then slowed and finally decreased as bubble interconnection began and coarsening acted to reduce surface area. The fraction of the bubbles vented to a simulation domain boundary, f V , was quantified as a measure of the microstructure’s interconnectivity and plotted as a function of porosity p . The defect species diffusivity was varied; although changes in diffusivity significantly affected the microstructure, the plots of f V vs. p did not change significantly. The percolation threshold p c was calculated to be approximately 0.26, depending on the assumed diffusivity and using an initial bubble number density based on experimental observations. This is slightly smaller than the percolation threshold for continuum percolation of overlapping 3D spheres. The simulation results were used to parameterize two different engineering-scale swelling models for U-(Pu)-Zr in the nuclear fuel performance code BISON.

Aagesen, Larry K. (ORCID:000000034936676X)↗

DOE OSTI2024

Accelerating multiscale electronic stopping power predictions with time-dependent density functional theory and machine learning

Knowing the rate at which particle radiation releases energy in a material, the “stopping power,” is key to designing nuclear reactors, medical treatments, semiconductor and quantum materials, and many other technologies. While the nuclear contribution to stopping power, i.e., elastic scattering between atoms, is well understood in the literature, the route for gathering data on the electronic contribution has for decades remained costly and reliant on many simplifying assumptions, including that materials are isotropic. We establish a method that combines time-dependent density functional theory (TDDFT) and machine learning to reduce the time to assess new materials to hours on a supercomputer and provide valuable data on how atomic details influence electronic stopping. Our approach uses TDDFT to compute the electronic stopping from first principles in several directions and then machine learning to interpolate to other directions at a cost of 10 million times fewer core-hours. We demonstrate the combined approach in a study of proton irradiation in aluminum and employ it to predict how the depth of maximum energy deposition, the “Bragg Peak,” varies depending on the incident angle—a quantity otherwise inaccessible to modelers and far outside the scales of quantum mechanical simulations. The lack of any experimental information requirement makes our method applicable to most materials, and its speed makes it a prime candidate for enabling quantum-to-continuum models of radiation damage. The prospect of reusing valuable TDDFT data for training the model makes our approach appealing for applications in the age of materials data science.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Predicting Excitation Energies of Twisted Intramolecular Charge-Transfer States with the Time-Dependent Density Functional Theory: Comparison with Experimental Measurements in the Gas Phase and Solvents Ranging from Hexanes to Acetonitrile

Electronically excited states characterized by intramolecular charge transfer play an essential role in many biological processes and optical devices. The ability to make quantitative ab initio predictions of the relative energetics involved is a challenging yet desirable goal, especially for large molecules in solution. In this work, we present a data set of 61 experimental measurements of absorption and emission processes, both in the gas phase and in solvents representing a broad range of polarities, which involve intramolecular charge transfer mediated by a nonzero, "twisted" dihedral angle between one or more donor and acceptor subunits. Among a variety of density functionals investigated within the framework of linear-response theory, the "optimally tuned" LRC-ωPBE functional, which utilizes a system-specific yet nonempirical procedure to specify the range-separation parameter, emerges as the preferred choice. For the entire set of excitation energies, involving changes in dipole moment ranging from 4 to >20 Debye, the mean signed and absolute errors are 0.02 and 0.18 eV, respectively (compared, e.g., to -0.30 and 0.30 for PBE0, 0.44 and 0.47 for LRC-ωPBEh, 0.83 and 0.83 for ωB97X-V). We analyze the performance of polarizable continuum solvation models available in Q-Chem that partition the solvent response into fast and slow time scales, and clear trends emerge when measurements corresponding to the four small 4-(dimethylamino)benzonitrile (DMABN)-like molecules and a charged species are excluded. We make the case that the large errors found only for small molecules in the gas phase and weak solvents cannot be expected to improve via the optimal tuning procedure, which enforces a condition that is exact only in the well-separated donor-acceptor limit, and present empirical evidence implicating the outsized importance for small donor-acceptor systems of relaxation effects that cannot be accounted for by the linear-response time-dependent density functional theory within the adiabatic approximation. Finally, we demonstrate the utility of the optimally tuned density functional approach by targeting the charge-transfer states of a large biomimetic model system for light-harvesting structures in Photosystem II.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

On the mechanism of ionization oscillations in Hall thrusters

Low-frequency ionization oscillations involving plasma and neutral density (breathing modes) are the most violent perturbations in Hall thrusters for electric propulsion. Because of its simplicity, the zero-dimensional (0D) predator–prey model of two nonlinearly coupled ordinary differential equations for plasma and neutral density has often been used for the characterization of such oscillations and scaling estimates. In this work, we investigate the properties of its continuum analog, the one-dimensional (1D) system of two nonlinearly coupled equations in partial derivatives (PDEs) for plasma and neutral density. This is a more general model, of which the standard 0D predator–prey model is a special limit case. We show that the 1D model is stable and does not show any oscillations for the boundary conditions relevant to Hall thrusters and the uniform ion velocity. We then propose a reduced 1D model based on two coupled PDEs for plasma and neutral densities that is unstable and exhibit oscillations if the ion velocity profile with the near-the-anode back-flow (toward the anode) region is used. Comparisons of the reduced model with the predictions of the full model that takes into account the self-consistent plasma response show that the main properties of the breathing mode are well captured. In particular, it is shown that the frequency of the breathing mode oscillations is weakly dependent on the final ion velocity but shows a strong correlation with the width of the ion back-flow region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Spatiotemporal Variability in Transport and Reactive Processes Across a First- to Fifth-Order Fluvial Network

Fluvial networks integrate and transport constituents from terrestrial and aquatic ecosystems. To date, most research on water quality dynamics has focused on process understanding at individual streams and, as a result, there is a lack of studies analyzing how small-scale, physical and biogeochemical drivers scale across fluvial networks. We performed tracer tests in five stream orders of the Jemez River continuum in New Mexico, USA, to quantify reach-scale hyporheic exchange during two different seasonal periods to address: how do hyporheic zone contributions to riverine processing change with space and time? And does the spatiotemporal variability of hyporheic exchange scale across fluvial networks? Combining conservative (i.e., bromide) and reactive (i.e., resazurin) tracer analyses with solute transport modeling, we found a dominance of reaction-limited transport conditions in space (for all stream orders) and time (two contrasting flow regimes). Moreover, we found a trend toward more reaction-limited conditions with increasing discharge across all stream orders. While our studied fluvial network did not consistently follow the expectations of decreasing hyporheic exchange contributions with increasing stream order, as it has been previously suggested from modeling studies, we found that processing rate coefficients and Damköhler numbers consistently decreased along the continuum with increasing discharge. Our findings suggest that knowledge transferability of hyporheic zone processing along fluvial networks may be possible if the scaling patterns that we found hold true in other catchments. Thus, more research on scaling patterns along fluvial networks is highly needed.

Gootman, Kaylyn S.↗

DOE OSTI2020

Modeling Single and Two-Phase Transport in Thin Porous Layers Using a Composite Continuum-Pore Network Formulation

In this work, a composite continuum-pore network formulation is presented to model single and two-phase transport thin porous layers, such as gas diffusion layers in polymer electrolyte fuel cells (PEFCs) and active electrodes in redox flow batteries (RFBs). The formulation can be integrated into CFD codes, thus combining the ease of implementation of continuum-based modeling and the computational power of pore-network modeling. The composite model includes a control volume (CV) mesh at the layer scale, which embeds a cubic pore network [1,2]. The pore-network model is used to determine analytically local anisotropic effective transport properties (local effective diffusivity and permeability), which are mapped onto the CV mesh to simulate transport in the porous transport layer [3,4]. Good agreement is found between the predicted global effective transport properties (global effective diffusivity and permeability) under dry and wet conditions and previous experimental data reported in the literature for Toray TGP-H series carbon paper. Water saturation distributions are also compared with results obtained using X-ray computed tomography [4]. [1] P.A. García-Salaberri, I.V. Zenyuk, J.T. Gostick, A.Z. Weber, Modeling Gas Diffusion Layer in Polymer Electrolyte Fuel Cells Using a Continuum-Based Pore-Network Formulation, ECS Trans. 97 (2020) 615. [2] P.A. García-Salaberri, Modeling diffusion and convection in thin porous transport layers using a composite continuum-network model: Application to gas diffusion layers in polymer electrolyte fuel cells, Int J. Heat Mass Transf. (2020), submitted. [3] P.A. García-Salaberri, J.T. Gostick, G. Hwang, A.Z. Weber, M. Vera, Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: Effect of local saturation and application to macroscopic continuum models, J. Power Sources 296 (2015) 440–453. [4] P.A. García-Salaberri, G. Hwang, M. Vera, A.Z. Weber, J.T. Gostick, Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: Effect of through-plane saturation distribution, Int. J. Heat Mass Transf. 86 (2015) 319–333.

Garcia-Salaberri, Pablo↗

DOE OSTI2026

Instabilities and phase transitions in architected metamaterials: a gradient-enhanced continuum approach

Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transitions. Their macroscopic response–including energy dissipation during impact, large recoverable deformations, morphing between configurations, and auxetic behavior–remains difficult to capture with conventional continuum models, which often rely on discrete approaches that limit scalability. In this work, we propose a nonlocal continuum formulation that captures both stable and unstable responses of elastic architected metamaterials. The framework extends anisotropic hyperelasticity by introducing nonlocal variables and internal length scales reflective of microstructural features. Local polyconvex free-energy models are systematically augmented with two families of non-(poly)convex energies, enabling both metastable and bistable responses. Implementation in a finite element framework enables solution using a hybrid monolithic–staggered strategy. Simulations capture densification fronts, forward and reverse transitions, hysteresis loops, imperfection sensitivity, and globally coordinated auxetic modes. Overall, this framework provides a robust foundation for accelerated modeling of instability-driven phenomena in architected metamaterials, while enabling extensions to anisotropic, dissipative, and active systems as well as integration with data-driven and machine learning approaches.

42 ENGINEERING↗

DOE OSTI2021

Continuum gyrokinetic simulations of edge plasmas in single-null geometries

The first continuum gyrokinetic calculations of electrostatic ion scale turbulence are presented for the case of a diverted tokamak geometry. The simulation model solves the long-wavelength limit of the full-F gyrokinetic equation for ion species coupled to the quasi-neutrality equation for electrostatic potential variations, where a fluid model is used for an electron response. Furthermore, in order to facilitate simulations of highly-anisotropic microturbulence in the presence of strong magnetic shear and a magnetic X-point, a numerical algorithm utilizing a locally field-aligned multiblock coordinate system has been developed and implemented in the 5D finite-volume code COGENT. In this approach, the toroidal direction is divided into blocks, such that within each block, the cells are field-aligned and a non-matching grid interface is allowed at block boundaries. The toroidal angle corresponds to the “coarse” field-aligned coordinate, whereas the poloidal cross section, comprised of the radial and poloidal directions, is finely gridded to resolve short-scale perpendicular turbulence structures and to support accurate re-mapping (interpolation) at block boundaries. The 5D simulations explore cross-separatrix ion scale turbulence in the presence of a self-consistent radial electric field and address the effects of magnetic-shear stabilization in the X-point region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗