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DOE OSTI2025

Time-resolved chemically-selective spectroscopic investigation of the redox reaction between hematite and aluminium

Thermite reactions –highly energetic redox processes between a metal and an oxide—are used in welding, propulsion, and the fabrication of advanced materials. When reduced to the nanoscale, these reactions exhibit enhanced energetic performance, but their ultrafast dynamics remain poorly understood. Gaining insight into charge transfer during these processes is essential for advancing applications in energy conversion and materials design. Here we show that the reaction between aluminium and hematite, a common iron oxide, can be tracked with femtosecond resolution using extreme ultraviolet (EUV) time-resolved absorption spectroscopy at the Fe M 2,3 and Al L 2,3 edges. By exciting the system with an ultrashort optical pulse and probing element-specific absorption changes, we observe an early spectral shift that reveals the formation of localized charge carriers (polarons). Comparing samples with different supporting substrates highlights ultrafast electron transfer from aluminium to hematite. These results demonstrate an approach to investigating charge flow in energetic materials and provide a basis for studying fast chemical reactions with chemical specificity.

Electron transfer↗

NASA NTRS1995

Numerical simulation of supersonic and hypersonic inlet flow fields

This report summarizes the research performed by North Carolina State University and NASA Ames Research Center under Cooperative Agreement NCA2-719, 'Numerical Simulation of Supersonic and Hypersonic Inlet Flow Fields". Four distinct rotated upwind schemes were developed and investigated to determine accuracy and practicality. The scheme found to have the best combination of attributes, including reduction to grid alignment with no rotation, was the cell centered non-orthogonal (CCNO) scheme. In 2D, the CCNO scheme improved rotation when flux interpolation was extended to second order. In 3D, improvements were less dramatic in all cases, with second order flux interpolation showing the least improvement over grid aligned upwinding. The reduction in improvement is attributed to uncertainty in determining optimum rotation angle and difficulty in performing accurate and efficient interpolation of the angle in 3D. The CCNO rotational technique will prove very useful for increasing accuracy when second order interpolation is not appropriate and will materially improve inlet flow solutions.

Mcrae, D. Scott↗

DOE OSTI2023

Derivation of heterogeneous material distributions and their sensitivity to HM-coupled two-phase flow models exemplified with the LASGIT experiment

Abstract Advective gas transport in bentonite, a possible buffer material in repositories for radioactive materials, is difficult to simulate in numerical continuum models, partly due to the complicated microstructure of bentonite. To generate reliable models of repositories nevertheless, spatially distributed heterogeneous material properties can be used to allow localization of gas flow. In this study, a pore-size-dependent stochastic approach of the gas entry pressure is derived from Mercury Intrusion Porosimetry, which is used to replicate measurements from the LASGIT experiment. In addition, three benchmark tests are simulated to investigate the dependence of heterogeneous distributions of material properties on the mesh discretization, the temporal dependence, and the coupling between the processes influenced by the heterogeneous parameters. The numerical modeling results of the LASGIT experiment show that the onset of gas flow into the system and the subsequent increase in pressure and stress can be well reproduced using heterogeneous distributions. Compared to a model with homogeneous material properties, heterogeneous distributions may allow the generation of dilatancy-controlled microfractures—an important feature with regard to the advective gas flow in bentonites. However, it can be observed that the heterogeneous distributions in LASGIT are less significant, as technical gaps or differences in material types could have a greater impact.

Environmental Sciences & Ecology↗

DOE OSTI2022

Relative permeability as a stationary process: Energy fluctuations in immiscible displacement

Relative permeability is commonly used to model immiscible fluid flow through porous materials. In this work, we derive the relative permeability relationship from conservation of energy, assuming that the system to be non-ergodic at large length scales and relying on averaging in both space and time to homogenize the behavior. Explicit criteria are obtained to define stationary conditions: (1) there can be no net change for extensive measures of the system state over the time averaging interval; (2) the net energy inputs into the system are zero, meaning that the net rate of work done on the system must balance with the heat removed; and (3) there is no net work performed due to the contribution of internal energy fluctuations. Results are then evaluated based on direct numerical simulation. Dynamic connectivity is observed during steady-state flow, which is quantitatively assessed based the Euler characteristic. We show that even during steady-state flow at low capillary number ([Formula: see text]), typical flow processes will explore multiple connectivity states. The residence time for each connectivity state is captured based on the time-and-space average. The distribution for energy fluctuations is shown to be multi-modal and non-Gaussian when terms are considered independently. However, we demonstrate that their sum is zero. Given an appropriate choice of the thermodynamic driving force, we show that the conventional relative permeability relationship is sufficient to model the energy dissipation in systems with complex pore-scale dynamics that routinely alter the structure of fluid connected pathways.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2008

Geologic Mapping of Isabella Quadrangle (V-50) and Helen Planitia, Venus

(25-50 S, 180-210 E) is host to numerous coronae and small volcanic centers (paterae and shield fields), focused (Aditi and Sirona Dorsa) and distributed (penetrative north-south trending wrinkle ridges) contractional deformation, and radial and linear extensional structures, all of which contribute materials to and/or deform the expansive surrounding plains (Nsomeka and Wawalag Planitiae). Regional plains, which are a northern extension of regional plains mapped in the Barrymore Quadrangle V-59 [1], dominate the V-50 quadrangle. Previous mapping divided the regional plains into two members: regional plains, members a and b [2]. A re-evaluation of these members has determined that a continuous and consistent unit contact does not exist; however, the majority of this radar unit or surficial unit will still be displayed on the final map as a stipple pattern as it is a prevalent feature of the quadrangle. With minimal tessera or highland material, much of the quadrangle s oldest materials are plains units (the regional plains). Much of these plains are covered with small shield edifices that exhibit a variety of material contributions (or flows). In the northwest, several flows emerge and flow to the southeast from Diana-Dali Chasmata. Local corona- and mons-fed flows superpose the regional plains; however, earlier stages of volcano-tectonic centers marked by arcuate and radial structural elements, including terrain so heavily deformed that it takes on a new appearance, may have developed prior to or concurrently with the region plains. Northtrending deformation belts disrupt the central portion of the map area and wrinkle ridges parallel these larger belts. Isabella crater, in the northeastern quadrant, is highly asymmetric and displays two prominent ejecta blanket morphologies, which generally correlate with distance from the impact structure suggesting that ejecta block size or ejecta blanket thickness may be the cause. The crater floor is very dark and shows no direct connection with the large outflow to the south, which emphasizes the asymmetry observed. Isabella crater ejecta and outflow materials clearly postdate several small craters in the vicinity.

Bleamaster, Leslie F., III↗

DOE OSTI2021

Hyporheic Exchange Driven by Submerged Rigid Vegetation: A Modeling Study

Flow-vegetation interaction affects fluid flow hydraulics and associated material transport in river corridors. Concomitant changes in pressure within the flow field due to the presence of vegetation may act as a driver for the formation of hyporheic flow across the sediment-water interface. This potentially important process, however, has yet to be studied. In order to investigate vegetation-induced hyporheic exchange, a series of numerical models of interlinked surface-subsurface flow modified by plant stems was conducted. Periodically staggered plant stem arrays on a flat sediment bed were considered within a coupled multiphysics computational fluid dynamics approach. Plants were idealized as rigid cylinders and arranged in different streamwise and spanwise spacing distances. Each vegetation array was then subjected to a broad range of flow Reynolds Numbers (Re). The results showed that hyporheic flow occurs in all conditions with the presence of vegetation. The vegetation-induced hyporheic flux is found to be a function of Re via a power law. The flux increases with interstem space until the space reaches the distance that rigid stems no longer affect the flow structures in the vicinity of each other. Larger intervegetation distances lead to a larger hyporheic zone. A direct comparison with bedforminduced hyporheic flow showed that vegetation can induce higher hyporheic flux through relatively shallower exchange zones. The results of all the simulations were synthesized into predictive models for hyporheic flux, bulk residence time and exchange depth based on drag coefficient, vegetation density, and Reynolds Number.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

High Throughput Discovery of Thermoelectric Materials (Final Report)

New materials form the heart of advances in energy technologies; however, the actual synthesis and characterization of new materials remains an enormous bottleneck. In this award, the research team focused on developing new approaches overcome this bottleneck. The approach involved depositing at high (supersonic) velocity multiple crystalline materials at a substrate while controlling the resulting film composition. The film could then be annealed to create a homogeneous alloy that was suitable for characterization. High throughput characterization tools were developed in parallel. The research focused on thermoelectric materials, which convert the flow of heat into electrical power. The development of new thermoelectric materials with high power conversion efficiency could displace traditional mechanical heat engines (e.g. turbines).

30 DIRECT ENERGY CONVERSION↗

NASA NTRS1993

Explosive mafic volcanism on Earth and Mars

Deposits within Amazonia Planitia, Mars, have been interpreted as ignimbrite plains on the basis of their erosional characteristics. The western flank of Hecates Tholus appears to be mantled by an airfall deposit, which was produced through magma-water interactions or exsolution of magmatic volatiles. Morphologic studies, along with numerical and analytical modeling of Martian plinian columns and pyroclastic flows, suggest that shield materials of Tyrrhena and Hadriaca paterae are composed of welded pyroclastic flows. Terrestrial pyroclastic flows, ignimbrites, and airfall deposits are typically associated with silicic volcanism. Because it is unlikely that large volumes of silicic lavas have been produced on Mars, we seek terrestrial analogs of explosives, mafic volcanism. Plinian basaltic airfall deposits have been well-documented at Masaya, Nicaragua, and basaltic ignimbrite and surge deposits also have been recognized there. Ambrym and Yasour, both in Vanuatu, are mafic stratovolcanioes with large central calderas, and are composed of interbedded basaltic pyrocalstic deposits and lava flows. Zavaritzki, a mafic stratovolcano in the Kurile Islands, may have also produced pyroclastic deposits, although the exact nature of these deposits in unknown. Masaya, Ambrym and Yasour are known to be located above tensional zones. Hadriaca and Tyrrhena Paterae may also be located above zones of tension, resulting from the formation and evolution of Hellas basin, and, thus, may be directly analogous to these terrestrial mafic, explosive volcanoes.

Gregg, Tracy K. P.↗

DOE OSTI2023

Advective gas flow in bentonite: Development and comparison of enhanced multi-phase numerical approaches

Understanding the impact of repository gas, generated from degradation of waste and its interaction with the host rock, is essential when assessing the performance and safety function of long-term disposal systems for radioactive waste. Numerical models based on conventional multi-phase flow theory have historically been applied to predict the outcome and impact of gas flow on different repository components. However, they remain unable to describe the full complexity of the physical processes observed in water-saturated experiments (e.g., creation of dilatant pathways) and thus, the development of novel representations for their description is required when assessing fully saturated clay-based systems. This was the primary focus of Task A within the international cooperative project DECOVALEX-2019 (D-2019) and refinement of these approaches is the primary focus of this study (Task B in the current phase of DECOVALEX-2023). This paper summarises development of enhanced numerical representations of key processes and compares the performance of each model against high-quality laboratory test data. Experimental data reveals that gas percolation in water-saturated compacted bentonite is characterised by four key features: (i) a quiescence phase, followed by (ii) the gas breakthrough, which leads to a (iii) peak value, which is then followed by (iv) a negative decay. Three models based on the multiphase flow theory have been developed. These models can provide good initial values and reasonable responses for gas breakthrough (although some of them still predict a too-smooth response). Peak gas pressure values are in general reasonably well captured, although maximum radial stress differences are observed at 48 mm from the base of the sample. Here, numerical peak values of 12.8 MPa are predicted, whereas experimental values are about 11 MPa. These models are also capable of providing a reasonable representation of the negative pressure decay following peak pressure. However, other key specific features (such as the timing of gas breakthrough) still require a better representation. The model simulations and their comparison with experimental data show that these models need to be further improved with respect to model parameter calibration, the numerical representation of spatial heterogeneities in material properties and flow localisation, and the upscaling of the related physical processes and parameters. To further understand gas flow localisation, a new conceptual model has been developed, which shows that discrete channels can possibly be induced through the instability of gas-bentonite interface during gas injection, thus providing a new perspective for modeling gas percolation in low-permeability deformable media.

58 GEOSCIENCES↗

DOE OSTI2020

Shear-Induced Gelation of Self-Yielding Active Networks

An enticing feature of active materials is the possibility of controlling macroscale rheological properties through the activity of the microscopic constituents. Using a unique combination of microscopy and rheology we study three dimensional microtubule-based active materials whose autonomous flows are powered by a continually rearranging connected network. We quantify the relationship between the microscopic dynamics and the bulk mechanical properties of these nonequilibrium networks. Experiments reveal a surprising nonmonotonic viscosity that strongly depends on the relative magnitude of the rate of internally generated activity and the externally applied shear. Here, a simple two-state mechanical model that accounts for both the solidlike and yielded fluidlike elements of the network accurately describes the rheological measurements.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Preparation of 1,3-Dihydroxyphenazine

The ability to effectively store energy produced by intermittent renewable sources is a critical challenge for chemists and materials scientists. Redox flow batteries (RFB), which generate current by the flow of electrons between dissolved redox active compounds in separate solutions, are envisioned as a method to store renewable energy at the electrical grid scale. The best known examples of RFBs are driven by redox active metal or main group complexes. Within the past decade, redox active organic molecules have begun to be used in the construction of RFBs with high cell potential and cycle stability, at economical price points. Of particular interest are substituted dihydroxy phenazines, a class of heterocycles, that have recently been used as an anolyte for aqueous organic RFBs. Recent work indicates that different regioisomers of dihydroxyphenazine show dramatically different solubility and stability under electrochemical cycling conditions. Of particular interest was 1,3-dihydroxyphenazine (1,3-DHP), which showed greater than 1.5 M solubility in 2M KOH and excellent electrochemical stability. Current methods of producing 1,3-DHP, however, are low yielding and cumbersome. In the article proposal that follows, we offer an improved method of producing 1,3-DHP at high purity and moderate yield. The method detailed below was used by the Materials Engineering Research Facility (MERF) at Argonne National Lab to deliver more than 1.5 kg of this compound for use in the construction of aqueous organic RFBs.

Dzwiniel, Trevor [Argonne National Laboratory (ANL↗

DOE OSTI2024

TATB thermal decomposition: Expanding the molecular profile with cryo-focused pyrolysis GC-MS

Understanding the molecular composition of high explosives during thermal decomposition is vital for predicting the sensitivity, safety, and performance of explosive materials. The thermal decomposition of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) has been linked to the formation of furazans through a series of dehydration reactions of the NO2 and NH2 groups on the phenyl ring, along with breakdown into small molecules (≤120 amu). Molecular identification of compounds formed in this transformation of the furazans to light gases has been lacking. To address this, we have applied a pseudo-confined sampling system in a cryo-focused pyrolysis gas chromatography-mass spectrometry (pyGC-MS) system to molecularly identify these intermediates. By design, sublimation of TATB, which has complicated MS analyses of thermal degradation, was significantly reduced and additional compounds were identified with potential structural information. In addition to the known furazan compounds, one of these compounds forms from the loss of oxygen from benzo-trifurazan (F3) and produces an open ring structure that may be the first step in the formation of lower molecular weight furazan breakdown products. The loss of a nitro group from benzo-monofurazan (F1) was also discovered and implicates the formation of oxidizing NO2 gas in the thermal decomposition mechanism. So these findings are vital for understanding the proper heat flow from energetic materials on a molecular level, necessary when measuring enthalpy and developing decomposition models based on kinetic parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2006

Minnowbrook V: 2006 Workshop on Unsteady Flows in Turbomachinery

This volume contains materials presented at the Minnowbrook V 2006 Workshop on Unsteady Flows in Turbomachinery, held at the Syracuse University Minnowbrook Conference Center, New York, on August 20-23, 2006. The workshop organizers were John E. LaGraff (Syracuse University), Martin L.G. Oldfield (Oxford University), and J. Paul Gostelow (University of Leicester). The workshop followed the theme, venue, and informal format of four earlier workshops: Minnowbrook I (1993), Minnowbrook II (1997), Minnowbrook III (2000), and Minnowbrook IV (2003). The workshop was focused on physical understanding of unsteady flows in turbomachinery, with the specific goal of contributing to engineering application of improving design codes for turbomachinery. The workshop participants included academic researchers from the United States and abroad and representatives from the gas-turbine industry and U.S. Government laboratories. The physical mechanisms discussed were related to unsteady wakes, active flow control, turbulence, bypass and natural transition, separation bubbles and turbulent spots, modeling of turbulence and transition, heat transfer and cooling, surface roughness, unsteady CFD, and DNS. The workshop summary and the plenary discussion transcripts clearly highlight the need for continued vigorous research in the technologically important area of unsteady flows in turbomachines. This volume contains abstracts and copies of select viewgraphs organized according to the workshop sessions. Full-color viewgraphs and animations are included in the CD-ROM version only (Doc.ID 20070024781).

LaGraff, John E.↗

DOE OSTI2023

Colocalized Raman spectroscopy – scanning electrochemical microscopy investigation of redox flow battery dialkoxybenzene redoxmer degradation pathways

Non-aqueous redox flow batteries offer high voltages for grid-level energy storage technologies. However, decomposition of the redoxmers - redox-active molecules that make up the anolyte and catholyte in the negative and positive cell compartments - is an important challenge to overcome for long-term storage. Here, we present a spectroelectrochemical study of the catholyte candidate 2,3-dimethyl-1,4-dialkoxybenzene (C7) and its decomposition mechanisms in the presence of a model nucleophilic base, pyridine. We utilize colocalized Raman microscopy and scanning electrochemical microscopy (Raman-SECM) to quantify the chemical rates of decom-position and qualitatively identify the reaction intermediates and products. A detailed study on how the Raman-SECM parameters (electrode distance, substrate electrode, and laser focal height) influence the Raman signal of the charged catholyte C7 ∙+ is presented. Using optimized conditions, we monitored the deprotonation of C7 ∙+ via Raman spectroscopy and the subsequent hydrogen abstraction from solvent molecules to regenerate C7 via electrochemistry. Finite element modeling was used to fit electrochemical and spectroscopic data, quantifying the deprotonation rates as k dep = 2000 and 700 L mol -1 s -1 and abstraction rates as k abs = 0.5 and 0.2 s - 1 in propylene carbonate and acetonitrile solvents, respectively. Our results show the value of spatiotemporal reso-lution in evaluating the chemical and electrochemical behavior of materials for redox flow batteries.

25 ENERGY STORAGE↗

DOE OSTI2020

Transient Microstructure Evolutions and Local Properties of Dual-Phase 980 MPa Grade Steel Via Friction Stir Spot Processing

Friction stir processing is a novel solid-state process to modify microstructures and their properties by intense, localized plastic deformation. However, little research has been reported for microstructure evolutions of advanced high-strength steels during the process. The present work focuses on the study of transient microstructure changes and local mechanical properties for friction stir spot processed dual-phase (DP) 980 MPa grade steel (DP980) under different peak temperatures. A pinless silicon nitride ceramic tool was used to produce relatively simple material deformation and flow near the tool. Friction stir spot processed steel samples were characterized by optical and electron microscopies. Furthermore, Vickers microhardness and nano-indentation measurements were used to study local mechanical properties for correlation with microstructures. A swallow layer of refined grains (<0.6 µm) was obtained with a low peak temperature (under 400 °C), whereas higher peak temperatures (>Ac 1 ) led to a change in grain size with different microstructures (fine-grained DP or martensite). Electron back-scattered diffraction characterizations revealed a large deformation in the as-received microstructures (mixture of ferrite and tempered martensite) induced by friction stir spot processing, leading to recrystallization and grain refinement around the stirred zone. Also, nano-indentation measurements showed a higher hardness than the hardness of the as-received DP980. Friction stir processing with different process conditions effectively changed microstructures and local mechanical properties.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Beyond conventional batteries: a review on semi-solid and redox targeting flow batteries-LiFePO{sub 4} as a case study.

Clean and sustainable energy is becoming increasingly crucial to tackle the current energy crisis. However, the intermittent nature of renewable energy sources presents a challenge for their effective implementation. Redox flow batteries (RFBs) have emerged as a promising solution to this problem, as they can help enhance the stability of grid networks and promote the use of renewable energy sources. RFBs are highly modular and scalable systems that can be customized to meet the power and energy requirements of different renewable energy plants. Moreover, they offer several advantages over conventional battery technologies, including cost and safety concerns. However, conventional RFBs have limited energy densities due to the low solubility of their active species in electrolyte. To overcome this limitation, semi-solid (SSRFBs) and redox targeting (RTFBs) flow batteries have been proposed. These systems feature high concentrations of active species and impressive energy densities, making them highly attractive for renewable energy applications. LiFePO4 (LFP) is a highly promising active material for semi-solid and targeting flow batteries. One of the key advantages of LFP is its low raw materials cost, as it is composed of Earth-abundant elements such as iron and phosphorus. This makes it an attractive option for large-scale battery production. The recent developments in SSRFBs and RTFBs using LFP as catholyte hold great promise for the future of sustainable energy storage. The combination of LFP's low cost, safety, durability, and high energy density with the modularity and scalability of flow battery systems make for a compelling solution to the challenges of intermittent renewable energy sources. Ongoing research and development in this area will likely yield even further improvements in the performance and efficiency of LFP-based flow batteries, opening exciting new possibilities for sustainable energy storage.

El Halya, Nabil↗

DOE OSTI2025

The molten salt tritium transport experiment: A pumped fluoride salt loop for hydrogen isotope experimentation

Molten salt reactors (MSRs) and fusion reactors propose to use molten salts as coolants and breeder blanket materials, respectively. Tritium, however, poses safety concerns in both reactor types due to its ability to permeate through reactor materials and potential for environmental release. This manuscript addresses the tritium transport phenomena in molten salts and presents the design and analysis of the Molten Salt Tritium Transport Experiment (MSTTE). MSTTE is a forced-convection fluoride salt loop intended to measure hydrogen isotope permeation through structural materials in a flowing salt system. In the first phase, MSTTE will use FLiNaK salt and deuterium as surrogates for FLiBe and tritium, with future plans to utilize tritium and FLiBe. MSTTE couples a Copenhagen Atomics pumped salt loop with an external test section that introduces hydrogen isotopes into the loop and measures transport phenomena. The Hydrogen Injection System (HIS) controls hydrogen isotope introduction into the molten salt loop. Here, the permeation test section measures the permeation rate through stainless steel tubing in contact with flowing salt. Computational fluid dynamics (CFD) analysis ensures fully developed salt flow in the permeation test section. MSTTE is modeled with MELCOR-TMAP to predict the permeation rate as a function of experimental variables such as source term, salt flow rate, and salt temperature. Results indicate that the source term is the only parameter with a significant effect on the permeation rate. Pressure drop analysis suggests that the loop should operate below 200 LPM to maintain a pressure drop below 200 kPa. Additionally, finite-element analysis assesses thermal stress during loop operation to ensure the experiment's safe design. MSTTE will provide semi-integral data on tritium transport phenomena in molten salts and serve as a testbed for advancing molten salt technology.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE↗