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At least 1,243 records · Page 69

Modeling DWPF Hydrogen Gas Retention and Release

Savannah River Remediation (SRR) currently manages the risk for retained hydrogen in the Defense Waste Processing Facility (DWPF) vessels by implementing a Retained Hydrogen Program. The current program conservatively relies on bounding assumptions concerning gas release and retention to develop allowable vessel Q-times. SRR would like to establish more realistic inputs to the Retained Hydrogen Program. To address this need, SRNL conducted a literature search on work investigating the retention and release of gas from DWPF type slurries. The search revealed that the retained hydrogen is not released instantaneously upon the start of agitation, and that hydrogen gas could be released under quiescent, non-agitated, conditions. The literature search also identified a Lattice-Boltzmann computational fluid dynamics (CFD) software that could model and predict hydrogen release from DWPF vessels. SRR requested that Savannah River National Laboratory (SRNL) personnel pursue this software and focus the model for hydrogen gas retention and release to justify relaxing these conservative assumptions. This report documents the refinement of the CFD software model and application to show its ability to describe retained hydrogen release from DWPF vessels and relax the conservativisms in the Retained Hydrogen Program.

08 HYDROGEN↗

Genetically Engineered Elastomeric Polymer Network through Protein Zipper Assembly

The rich palette of chemical and functional diversity found within peptides has driven the recent interest in bottom–up assembly of soft polypeptide–based materials. Herein, we describe the creation of a novel helix–elastin like polymer or HELP. HELP marries the specificity of coiled–coil interactions with the elasticity and stimuli–responsive behavior of elastin, a class of polymers with extraordinary elasticity. We used Rosetta to computationally design highly specific protein helical zippers to connect short elastin segments. As a result, the programmed pairing between the helical blocks of two individual chains produced a genetically encoded material that, when deposited on a substrate, formed a flexible and porous 2D planar network with controllable porosity that responds dynamically upon application of stimuli.

36 MATERIALS SCIENCE↗

Automatic fitting of multiple-field solid-state NMR spectra

The NMR lineshapes produced by half-integer quadrupolar nuclei are sensitive to 11 distinct fit parameters per inequivalent site. To date, automatic fitting routines have failed to replace manual parameter insertion and evaluation due to the importance of local minima and the need for fitting multiple-field magic-angle spinning (MAS) and static spectra simultaneously. Herein we introduce a new tool, AMES-Fit (Automatic Multiple Experiment Simulation and Fitting), to automatically find the global best-fit simulation parameters for a series of multiple-field NMR lineshapes. AMES-Fit uses an adaptive step size random search algorithm to dynamically probe parameter space and requires minimal human input. Importantly, the best fits are obtained in a few minutes of computation time that would otherwise have required several person-hours of work. The program is freely available and open-source.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

phosaa14SB and phosaa19SB: Updated Amber Force Field Parameters for Phosphorylated Amino Acids

Phosphorylated amino acids are involved in many cell regulatory networks; proteins containing these post-translational modifications are widely studied both experimentally and computationally. Simulations are used to investigate a wide range of structural and dynamic properties of biomolecules, such as ligand binding, enzyme-reaction mechanisms, and protein folding. However, the development of force field parameters for the simulation of proteins containing phosphorylated amino acids using the Amber program has not kept pace with the development of parameters for standard amino acids, and it is challenging to model these modified amino acids with accuracy comparable to proteins containing only standard amino acids. In particular, the popular ff14SB and ff19SB models do not contain parameters for phosphorylated amino acids. Here, the dihedral parameters for the side chains of the most common phosphorylated amino acids are trained against reference data from QM calculations adopting the ff14SB approach, followed by validation against experimental data. Finally, library files and corresponding parameter files are provided, with versions that are compatible with both ff14SB and ff19SB.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Preliminary results of the 2023 International Fermilab Booster Studies

Here, an overview is given of the methods and preliminary results from dedicated beam studies on three topics conducted over five days in July 2023. In the first study, the Fermilab Booster magnets were held constant at magnetic fields corresponding to the injection energy. The beam loss and emittance growth were observed under varying intensity, tunes, and sextupole resonances. The corresponding beam conditions were also simulated with the MADX-SC code [1]. In the second study, measurements of the vertical half-integer resonance and correction methods are conducted for high-intensity beams ramping in the Booster. Finally, syncho-betatron instabilities are observed during transition-crossing in the Booster under strong space-charge conditions.

43 PARTICLE ACCELERATORS↗

Tagging efficiency study of incoherent diffractive vector meson production at the second interaction region at the Electron-Ion Collider

The Electron-Ion Collider (EIC) is an upcoming accelerator facility aimed at exploring the properties of quarks and gluons in nucleons and nuclei, shedding light on their structure and dynamics. The inaugural experimental apparatus, ePIC (electron-Proton and Ion Collider), is designed as a general-purpose detector to address the National Academy of Sciences and the Nuclear Science Advisory Committee physics program at the EIC. The wider EIC community is strongly supporting a second interaction region and an associated second detector to enhance the full science program. In this study, we evaluate how this second interaction region and detector can be complementary to ePIC. The layout of an interaction region for the second detector offers a secondary focus that provides better forward detector acceptance at scattering angles near θ ~ 0 mrad, which can specifically enhance the exclusive, tagging, and diffractive physics program. Here, this article presents an analysis of a tagging program using the second interaction region layout with incoherent diffractive vector meson production. The current design of the second EIC interaction region is evaluated for its vetoing capabilities of incoherent events required for the study of coherent diffractive measurements. We find an increased vetoing performance compared to the ePIC interaction region, thus improving measurements which are important for the spatial imaging of nucleons and nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

SU-F-J-158: Respiratory Motion Resolved, Self-Gated 4D-MRI Using Rotating Cartesian K-Space Sampling

Purpose: Dynamic MRI has been used to quantify respiratory motion of abdominal organs in radiation treatment planning. Many existing 4D-MRI methods based on 2D acquisitions suffer from limited slice resolution and additional stitching artifacts when evaluated in 3D{sup 1}. To address these issues, we developed a 4D-MRI (3D dynamic) technique with true 3D k-space encoding and respiratory motion self-gating. Methods: The 3D k-space was acquired using a Rotating Cartesian K-space (ROCK) pattern, where the Cartesian grid was reordered in a quasi-spiral fashion with each spiral arm rotated using golden angle{sup 2}. Each quasi-spiral arm started with the k-space center-line, which were used as self-gating{sup 3} signal for respiratory motion estimation. The acquired k-space data was then binned into 8 respiratory phases and the golden angle ensures a near-uniform k-space sampling in each phase. Finally, dynamic 3D images were reconstructed using the ESPIRiT technique{sup 4}. 4D-MRI was performed on 6 healthy volunteers, using the following parameters (bSSFP, Fat-Sat, TE/TR=2ms/4ms, matrix size=500×350×120, resolution=1×1×1.2mm, TA=5min, 8 respiratory phases). Supplemental 2D real-time images were acquired in 9 different planes. Dynamic locations of the diaphragm dome and left kidney were measured from both 4D and 2D images. The same protocol was also performed on a MRI-compatible motion phantom where the motion was programmed with different amplitude (10–30mm) and frequency (3–10/min). Results: High resolution 4D-MRI were obtained successfully in 5 minutes. Quantitative motion measurements from 4D-MRI agree with the ones from 2D CINE (<5% error). The 4D images are free of the stitching artifacts and their near-isotropic resolution facilitates 3D visualization and segmentation of abdominal organs such as the liver, kidney and pancreas. Conclusion: Our preliminary studies demonstrated a novel ROCK 4D-MRI technique with true 3D k-space encoding and respiratory motion self-gating. The technique leads to high-resolution and artifacts-free 4D images for improved abdominal organ motion studies. K.S acknowledges funding support from NIH R01CA188300.

60 APPLIED LIFE SCIENCES↗

General Line Ampacity State Solver

INL’s General Line Ampacity State Solver (GLASS) is a high performance software platform that enables advanced grid system operations and planning efforts to be computed in real time. It enables the combination of advanced sensors and sensor networks, communication and data transfer channels, secure and reliable data management, and real-time processing through a flexible system architecture, with the ability to support and integrate with any utility enterprise system. GLASS is designed to help resolve the problems associated with thermally limited transmission and distribution networks, namely bare overhead power transmission lines. GLASS enables the methodology of Concurrent Cooling (Dynamic Line Rating) by reducing the need of using a cost-prohibited number of weather stations (reduce the number of weather stations per mile of overhead power line) to achieve the resolution necessary for individual electric transmission line span capacity calculations. GLASS achieves this by coupling real-time grid operations data and infrastructure architecture information with real-time field deployed weather station measurements and pre-computed Computational Fluid Dynamics (CFD)-based wind modeling interpolation parameters (look-up tables). GLASS uses mathematical models based on the IEEE 738 standard and builds off of the provided iterative solution using modern software paradigms and programming styles to provide a more robust and modular software system. GLASS also interfaces in real-time with utility companies using known transmission line spans and structures. GLASS provides real-time ampacity calculations based on recent weather station data as well as transmission line specifications. GLASS also allows the user to interact graphically with internal databases, which include information such as transmission line conductor types and thermal rating limits, weather station names and locations, specific transmission line span and structure locations, as well as recent ampacity calculations.

Gentle, Jake↗

Computation Annual Report (2013)

Computation provides the intellectual electricity that helps make Lawrence Livermore National Laboratory (LLNL) a thriving and innovative research and development (R&D) institution. Our hardware, software, and discipline experts are integrated into almost every field of research at LLNL. Our in-house programs, software applications, and support initiatives help achieve mission-critical national-security objectives for the U.S. Departments of Energy, Homeland Security, and Defense, as well as other federal and state agencies. We deliver comprehensive support to a wide set of scientific disciplines that include physical sciences (materials modeling, fluid dynamics), biology (genomic sequencing), mathematics (scalable algorithms), and computer sciences (parallel processing, real-time control systems). This year, we have expanded our outreach with high performance computing (HPC) collaborations and made great strides in our capabilities related to mathematical computation, control systems, and computation infrastructure, many of them in concert with partners in industry and academia. The Computation workforce remains highly motivated and passionate about melding computational expertise with cutting-edge science and technology to enable breakthroughs. 2013 has once again proven that Computation provides the foundation and support that are essential for productivity at LLNL. Every scientific discipline and program leverages the tools and expertise provided by our staff. We remain at the forefront of HPC moving towards exascale and have developed the infrastructure and proficiency to make this an achievable goal. Our researchers repeatedly deliver outstanding research, attracting collaborations with the biggest names in academia and industry, while joining forces with other national laboratories to further push the bounds of what is scientifically possible. Computation’s mission is echoed by the President of the United States in his assertion that “our future depends on reaffirming America’s role as the world’s engine of scientific discovery and technological innovation.” Driven by this lofty goal, we employ our state-of-the-art computational capabilities to ensure LLNL’s position as a global science and technology leader.

97 MATHEMATICS AND COMPUTING↗

Hawaiian Electric Advanced Inverter Grid Support Function Laboratory Validation and Analysis

The objective for this test plan was to better understand how to utilize the performance capabilities of advanced inverter functions to allow the interconnection of distributed energy resource (DER) systems to support the new Customer Self-Supply, Customer Grid-Supply, and other future DER programs. The purpose of this project was: 1) to characterize how the tested grid supportive inverters performed the functions of interest, 2) to evaluate the grid supportive inverters in an environment that emulates the dynamics of O'ahu's electrical distribution system, and 3) to gain insight into the benefits of the grid support functions on selected O'ahu island distribution feeders. These goals were achieved through laboratory testing of photovoltaic inverters, including power hardware-in-the-loop testing.

14 SOLAR ENERGY↗

Data-Model Needs for Belowground Ecology. A Summary Report from the Terrestrial Ecosystem Science (TES) Mini-Workshop, May 8, 2014

Terrestrial life on Earth depends on belowground cycling and storage of a significant portion of the planet’s biologically-active carbon. The interplay among organic inputs by primary producers, soil organic matter stabilization, and assimilation and mineralization by soil organisms drives belowground ecology. Understanding belowground carbon dynamics, including the stability and vulnerability of soil organic carbon stocks, is necessary to project the responses and feedbacks of terrestrial ecosystems to a changing climate. Although conceptually understood, belowground hydrobiogeochemical systems are not well characterized with quantitative and mechanistic representations of critical functions. As a result, these systems are inadequately represented in modeling efforts, limiting our ability to understand and project terrestrial carbon source/sink relationships at various temporal and spatial scales. The belowground science community lacks robust databases and data libraries against which model sensitivities and performance can be tested and enhanced. Improved understanding of belowground ecosystems, including biotic and abiotic interactions, is needed to ensure that model structures include and provide adequate representations of critical belowground processes, functions, and dynamics. A one-day workshop brought together experimental and modeling representatives from the four Department of Energy (DOE) National Laboratories where the Office of Biological and Environmental Research (BER) Terrestrial Ecosystem Science (TES) program has investments in belowground ecology. The group focused on identifying and characterizing (1) critical experimental and observational datasets for testing and developing existing and future belowground-process models and land models; (2) the limitations and needs for modeling belowground processes within ecosystem models; and (3) key areas for leveraging current research activities across the National Laboratories and BER-funded projects. Discussion results are organized in this report as: (I) over-arching data requirements for advancing understanding of belowground ecosystems; (II) efforts that could rapidly improve understanding and model representations of belowground components of terrestrial ecosystems; and (III) longer-term research needs that would benefit from greater and more sustained support.

54 ENVIRONMENTAL SCIENCES↗

Cooperative Research and Development Agreement between National Energy Technology Laboratory and University of Kentucky (Abstract)

The National Energy Technology Laboratory (NETL) and University of Kentucky (Participant) will collaborate in the development of “Deep Learning Potential-based Molecular Dynamics Simulation Investigation of Chemical Conversion-Absorption Coupling of CO 2 at Air-Reactive Deep Eutectic Solvent Interface.” This project is supported by DOE-Office of Science Graduate Student Research (SCGSR) program and managed by Oak Ridge Institute for Science and Education (ORISE). Deep eutectic solvents (DESs) are promising alternative sorbents for direct air capture (DAC) CO 2 due to their low vapor pressure, low corrosion, non-toxicity, relatively low cost, and biodegradable nature. Understanding the CO 2 reaction-transport mechanisms at the interface can help develop cost-effective DAC by DESs with high capacity and stability. The collaboration will investigate the absorption and chemical conversion of CO 2 at the air-DES interface to facilitate the development of novel DAC technology using reactive DESs. The anticipated results will make DAC more efficient, allow more sustainable use of our Nation’s fossil energy resources, and advance NETL’s ongoing CO 2 capture efforts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Active Asteroids Citizen Science Program: Overview and First Results

Abstract We present the Citizen Science program Active Asteroids and describe discoveries stemming from our ongoing project. Our NASA Partner program is hosted on the Zooniverse online platform and launched on 2021 August 31, with the goal of engaging the community in the search for active asteroids—asteroids with comet-like tails or comae. We also set out to identify other unusual active solar system objects, such as active Centaurs, active quasi-Hilda asteroids (QHAs), and Jupiter-family comets (JFCs). Active objects are rare in large part because they are difficult to identify, so we ask volunteers to assist us in searching for active bodies in our collection of millions of images of known minor planets. We produced these cutout images with our project pipeline that makes use of publicly available Dark Energy Camera data. Since the project launch, roughly 8300 volunteers have scrutinized some 430,000 images to great effect, which we describe in this work. In total, we have identified previously unknown activity on 15 asteroids, plus one Centaur, that were thought to be asteroidal (i.e., inactive). Of the asteroids, we classify four as active QHAs, seven as JFCs, and four as active asteroids, consisting of one main-belt comet (MBC) and three MBC candidates. We also include our findings concerning known active objects that our program facilitated, an unanticipated avenue of scientific discovery. These include discovering activity occurring during an orbital epoch for which objects were not known to be active, and the reclassification of objects based on our dynamical analyses.

Astronomy & Astrophysics↗

An Advanced Extreme-Environment Wireless Telemetry System for Turbine Blade Instrumentation

As advanced natural gas power generation systems evolve, the thrust for increased efficiencies and reduced emissions results in increasingly harsh conditions inside the turbine environment. These high temperatures, pressures, and corrosive atmospheres result in accelerated rates of degradation, leading to failure of turbine materials and components. Wolfspeed, A Cree Company, Siemens Energy, and Siemens Corporate Technology, in collaboration with the Department of Energy (DOE)'s National Energy Technology Laboratory, are developing a reliable and long-term monitoring capability in the turbine hot gas path in the form of novel ceramic-based thermocouples and wide bandgap instrumentation electronics that will contribute to the overall reliability of gas turbines. When equipped with better monitoring and controls, power plants can operate with increased fuel-burning efficiency, improved process dynamics and gas concentrations, and increased overall longevity of the power plant components. This will result in increased turbine availability and a reduction in outages and maintenance costs. The technology being developed in this program is based on advanced techniques and innovations in nearly every aspect of high-temperature electronics, including materials, semiconductor devices, subcomponents, electronic packaging, and system integration. The environment in which this wireless system must operate has continuous centrifugal loads with a gravitation force on the order of 16,000 times the force of gravity (16,000 g) and temperatures exceeding 400°C. This article will specifically discuss the background and motivation for the high-temperature instrumentation system and will explain the high-level electrical system, the construction of the instrumentation package, the techniques used for integration onto rotating components, as well as the wireless power and data transmission systems. In addition to the electrical and mechanical design, this article will also discuss results from laboratory bench testing as well as heated spin rig testing. Lastly, this article will highlight the future direction of the instrumentation system evolution, with a final objective of insertion into Siemens natural gas turbine power plants.

47 OTHER INSTRUMENTATION↗

Vehicle-to-manufacturing (V2M) system: A novel approach to improve energy demand flexibility for demand response towards sustainable manufacturing

The U.S. manufacturing sector accounts for 77% of the industrial energy consumption, but its participation in demand response (DR) programs is largely lagged behind. The limited flexibility in production scheduling under high capacity utilization and the lack of DR schemes that incorporate energy demand flexibility measures are deemed as major barriers. In this study, a framework of the interactive vehicles-to-manufacturing (V2M) energy sharing system is proposed to improve the energy demand flexibility of the aggregated system and enhance the DR effectiveness for manufacturers. The V2M-based DR scheme aims to reduce the energy cost by load shifting through joint production and energy sharing control, which can eventually promote manufacturing DR implementation even under high capacity utilization requirements and dynamic real-time electricity prices. The V2M system is modeled based on a discrete-Markov chain considering the complex interconnections among various manufacturing resources and multi-directional energy flows among manufacturing facilities, electric vehicles, and the power grid. Based on the system model, a mixed-integer nonlinear programming (MINLP) problem is formulated to identify the optimal DR scheme. The effectiveness of the proposed approach is validated through comparisons with traditional manufacturing DR schemes. Finally, the results show that a 2.1 to 6.5 times energy demand flexibility improvement and an additional 4.7% to 6.9% energy cost reduction can be achieved by the proposed approach.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A experimental research program on chirality at the LHC

Heavy-ion collisions provide a unique opportunity to investigate the fundamental laws of physics of the strong force. The extreme conditions created by the collisions within a finite volume are akin to the properties of the deconfined partonic state which existed very shortly after the Big Bang and just prior to visible matter formation in the Universe. In this state massless quarks and gluons (partons) are ``quasi free" particles, the so-called Quark Gluon Plasma (QGP). By following the expansion and cooling of this state, we will map out the process of nucleonic matter formation, which occurs during the phase transition. The fundamental properties of this early partonic phase of matter are not well understood, but they are essential for confirming QCD (Quantum Chromo-Dynamics) and the Standard Model. The specific topic, chiral symmetry restoration, has been called ``the remaining puzzle of QCD.'' This puzzle can only be studied in the dense partonic medium generated in heavy-ion collisions. The research objectives of this proposal are the development and application of new analysis strategies to study chirality and the properties of the medium above the QGP phase transition using hadronic resonances detected with the ALICE experiment at the Large Hadron Collider (LHC) at the CERN research laboratory in Switzerland. This grant funded a new effort at the University of Texas at Austin (UT Austin) to investigate the Quark Gluon Plasma (QGP) at the highest possible energy of 2.76 TeV per nucleon at the Large Hadron Collider (LHC) at CERN via the ALICE experiment. The findings added to our knowledge of the dynamical evolution and the properties of the hot, dense matter produced in heavy-ion collisions, and provided a deeper understanding of multi-hadron interactions in these extreme nuclear matter systems. Our group contributed as well to the hardware and software for the ALICE USA-funded Calorimeter Detector (EMCal). The LHC research program and its connection to fundamental questions in high energy, nuclear and astrophysics has triggered the imagination of many young students worldwide. The studies also promoted the early involvement of students and young postdocs in a large, multi-national research effort abroad, which provided them with substantial experience and skills prior to choosing their career path. The undergraduate program, in conjunction with the Freshman Research Initiative at UT Austin, allowed the students to complete a research project within the field of Nuclear Physics.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Quantum Computing Strategy 2026

Quantum computing (QC) is a rapidly maturing technology with the potential for revolutionary impacts on stockpile stewardship science and national security. Recent developments in fault-tolerant architectures have compressed vendor roadmaps, and predictions of a production-ready quantum computer by the mid-2030s are becoming increasingly credible. This strategy provides a roadmap for integrating QC into the Advanced Simulation and Computing (ASC) program by investing in four strategic focus areas: 1. Develop Capabilities in Mission-Relevant Quantum Applications: ASC will prioritize developing quantum-ready applications in mission areas that have shown significant promise for quantum advantage, including simulations of materials in extreme environments, nuclear dynamics, solving linear and nonlinear partial differential equations, and uncertainty quantification. These applications directly support stockpile stewardship science and modernization objectives. 2. Conduct R&D in Algorithms, Software, and Hardware: Sustained research into quantum algorithms, robust software tools, and quantum hardware is essential. ASC will develop efficient quantum algorithms; invest in quantum compilers, debuggers, and performance tools; and explore specialized quantum hardware tailored to NNSA’s unique requirements. 3. Engage with Vendors and Partners: Early and active collaboration with commercial quantum hardware vendors and academic partners is critical. Through testbeds, co-design agreements, and quantum demonstration facilities, ASC will influence hardware design, gain early access to emerging technologies, and ensure that quantum platforms evolve to meet mission needs. 4. Build Knowledge, Experience, and Workforce: Expanding and upskilling the quantum-trained workforce is essential to long-term success. This includes hiring, internal training, university outreach, and postdoctoral support to ensure ASC maintains the expertise required to operate, program, and integrate quantum systems as they become available. While quantum computing will never replace classical computing, it has the potential to solve certain problems with speed and accuracy that would be unachievable using any conceivable classical high-performance computing (HPC) system. By investing strategically in QC, ASC will help propel the emergent QC industry, maintain U.S. technological leadership, ensure mission readiness, and position itself to rapidly adopt quantum technologies as they mature.

97 MATHEMATICS AND COMPUTING↗

Studying performance portability of LAMMPS across diverse GPU-based platforms

The molecular dynamics simulation software, LAMMPS, utilizes the Kokkos acceleration library to port computation to a diverse set of architectures including those based on GPU accelerators. In addition to Kokkos, LAMMPS contains a vast code base that leverages the CUDA application programming interface using library functions such as cuFFT, CUDA's fast-fourier transform (FFT) library, and, more recently, also support for AMD's Heterogeneous Interface for Portability (HIP) that is rapidly growing. While preparing LAMMPS tests for the AMD GPU-based test system precursors to Frontier, we investigated several strategies for accelerating LAMMPS on AMD GPUs, using the AMD Instinct MI100 and MI250X. In this work, we integrated the HIP FFT library, hipFFT, into the particle-particle particle-mesh (PPPM) long-range solver, which allowed the porting of PPPM calculations to the GPUs. Kokkos behavior on the MI100 and MI250X was also investigated through the package kokkos command of LAMMPS, targeting communication, memory usage, and particle grid decomposition. The Tersoff, Reax, Lennard-Jones (LJ), EAM, Granular, and PPPM potentials were investigated in this effort, and results from these experiments are provided. In conclusion, the selected potentials were run on Spock (AMD Instinct MI100), Crusher (AMD Instinct MI250X), AFW HPC11 (NVIDIA A100) and Summit (NVIDIA V100), for comparison. Operational roofline models were constructed and analyzed for the Tersoff, Reax, and Lennard–Jones potentials on Crusher and Summit.

97 MATHEMATICS AND COMPUTING↗