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At least 991 records · Page 55

APOLLO: a facility-scale differentiable virtual accelerator at Fermilab FAST/IOTA

As the design complexity of modern accelerators grows, there is more interest in using advanced simulations that have fast execution time or yield additional insights like gradients. The FAST/IOTA facility has been working on implementing and experimentally validating an end-to-end digital twin that is both fast and gradient-aware, allowing for rapid prototyping of new software and experiments with minimal beam time costs. Our framework integrates physics and ML codes for linac and ring simulation through a set of generic interfaces between surrogate and physics-based sections. To reproduce device inputs and outputs, system state is exposed as a deterministic event loop in a specialized discrete event simulator architecture. Because Fermilab is undergoing control system transition, several APIs were implemented as final user interfaces - a fully asynchronous EPICS soft IOC, a gRPC-based Data Pool Manager (DPM), and legacy ACNET protocols. We discuss implementation details as well as challenges handling live data assimilation and future plans to extend modelling to main complex proton accelerators like PIPII and Booster.

Kuklev, Nikita [Fermilab]↗

Mechanisms for the Generation of Complex Fracture Networks: Observations From Slant Core, Analog Models, and Outcrop

We use observations of hydraulic fractures in core, outcrop attributes of natural hydraulic fractures, and analogue models, to address how hydraulic fracture networks evolve. A slant core from the Wolfcamp Formation—an unconventional shale hydrocarbon reservoir in the Permian Basin of West Texas—collected within 18 m and 30 m of two hydraulically stimulated horizontal wells, provided an opportunity to examine hydraulic fractures directly. In approximately 183 m of core, 309 calcite-sealed natural opening-mode fractures and 375 hydraulic fractures were identified. Many hydraulic fractures in the core show complex morphology, including twist-hackle segmentation, diversion, and bifurcation; these structures most commonly develop at lithological bed boundaries and mechanical heterogeneities such as natural fractures and concretions. An outcrop of bed-parallel pavements in the Cretaceous Boquillas Formation in West Texas contains opening-mode fractures that likely formed by natural hydraulic fracturing. Fracture traces provide evidence of twist-hackle segmentation, and are typically associated with bed boundaries and preexisting bed-parallel stylolites. A laboratory study of hydraulic fracturing of 33 synthetic blocks of gypsum and hydrostone revealed fracture steps, diversions, twist hackles, and multiple overlapping fractures together with information on fracture growth directions. These complexities in the fracture network were dominantly nucleated at inclusions used to simulate pre-existing fractures, and as a result of mechanical heterogeneity introduced by the wellbore and perforations. Collectively, our results show that complex fracture networks are produced in hydraulic fracturing of self-sourced reservoir strata. Mechanical stratigraphic boundaries and other heterogeneities are likely to enhance fracture network complexity through the processes of segmentation, diversion, and bifurcation. These processes create multiple fracture strands, resulting in an increased number of hydraulic fractures over those initiated, thereby increasing total fracture surface area. Our study provides insight into hydraulic fracture network propagation, and has applications for evaluation, completion, production, and fracture modeling of unconventional reservoirs.

54 ENVIRONMENTAL SCIENCES↗

Comparison of free vortex wake and blade element momentum results against large-eddy simulation results for highly flexible turbines under challenging inflow conditions

Abstract. Throughout wind energy development, there has been a push to increase wind turbine size due to the substantial economic benefits. However, increasing turbine size presents several challenges, both physically and computationally. Modeling large, highly flexible wind turbines requires highly accurate models to capture the complicated aeroelastic response due to large deflections and nonstraight blade geometries. Additionally, the development of floating offshore wind turbines requires modeling techniques that can predict large rotor and tower motion. Free vortex wake methods model such complex physics while remaining computationally tractable to perform key simulations necessary during the turbine design process. Recently, a free vortex wake model – cOnvecting LAgrangian Filaments (OLAF) – was added to the National Renewable Energy Laboratory's engineering tool OpenFAST to allow for the aerodynamic modeling of highly flexible turbines along with the aero-hydro-servo-elastic response capabilities of OpenFAST. In this work, free vortex wake and low-fidelity blade element momentum (BEM) results are compared to high-fidelity actuator-line computational fluid dynamics simulation results via the Simulator fOr Wind Farm Applications (SOWFA) method for a highly flexible downwind turbine for varying yaw misalignment, shear exponent, and turbulence intensity conditions. Through these comparisons, it was found that for all considered quantities of interest, SOWFA, OLAF, and BEM results compare well for steady inflow conditions with no yaw misalignment. For OLAF results, this strong agreement with the SOWFA results was consistent for all yaw misalignment values. The BEM results, however, deviated significantly more from the SOWFA results with increasing absolute yaw misalignment. Differences between OLAF and BEM results were dominated by the yaw misalignment angle, with varying shear exponent and turbulence intensity leading to more subtle differences. Overall, OLAF results were more consistent than BEM results when compared to SOWFA results under challenging inflow conditions.

17 WIND ENERGY↗

Constant-depth circuits for dynamic simulations of materials on quantum computers

Abstract Dynamic simulation of materials is a promising application for near-term quantum computers. Current algorithms for Hamiltonian simulation, however, produce circuits that grow in depth with increasing simulation time, limiting feasible simulations to short-time dynamics. Here, we present a method for generating circuits that are constant in depth with increasing simulation time for a specific subset of one-dimensional (1D) materials Hamiltonians, thereby enabling simulations out to arbitrarily long times. Furthermore, by removing the effective limit on the number of feasibly simulatable time-steps, the constant-depth circuits enable Trotter error to be made negligibly small by allowing simulations to be broken into arbitrarily many time-steps. For an N -spin system, the constant-depth circuit contains only $\mathcal {O}(N^{2})$ O ( N 2 ) CNOT gates. Such compact circuits enable us to successfully execute long-time dynamic simulation of ubiquitous models, such as the transverse field Ising and XY models, on current quantum hardware for systems of up to 5 qubits without the need for complex error mitigation techniques. Aside from enabling long-time dynamic simulations with minimal Trotter error for a specific subset of 1D Hamiltonians, our constant-depth circuits can advance materials simulations on quantum computers more broadly in a number of indirect ways.

Materials simulation↗

Unsupervised discovery of nonlinear plasma physics using differentiable kinetic simulations

Plasma supports collective modes and particle–wave interactions that lead to complex behaviour in, for example, inertial fusion energy applications. While plasma can sometimes be modelled as a charged fluid, a kinetic description is often crucial for studying nonlinear effects in the higher-dimensional momentum–position phase space that describes the full complexity of the plasma dynamics. We create a differentiable solver for the three-dimensional partial-differential equation describing the plasma kinetics and introduce a domain-specific objective function. Using this framework, we perform gradient-based optimization of neural networks that provide forcing function parameters to the differentiable solver given a set of initial conditions. We apply this to an inertial-fusion-relevant configuration and find that the optimization process exploits a novel physical effect.

plasma nonlinear phenomena↗

Functional and transcriptional characterization of complex neuronal co-cultures

Brain-on-a-chip systems are designed to simulate brain activity using traditional in vitro cell culture on an engineered platform. It is a noninvasive tool to screen new drugs, evaluate toxicants, and elucidate disease mechanisms. However, successful recapitulation of brain function on these systems is dependent on the complexity of the cell culture. In this study, we increased cellular complexity of traditional (simple) neuronal cultures by co-culturing with astrocytes and oligodendrocyte precursor cells (complex culture). We evaluated and compared neuronal activity (e.g., network formation and maturation), cellular composition in long-term culture, and the transcriptome of the two cultures. Compared to simple cultures, neurons from complex co-cultures exhibited earlier synapse and network development and maturation, which was supported by localized synaptophysin expression, up-regulation of genes involved in mature neuronal processes, and synchronized neural network activity. Also, mature oligodendrocytes and reactive astrocytes were only detected in complex cultures upon transcriptomic analysis of age-matched cultures. Functionally, the GABA antagonist bicuculline had a greater influence on bursting activity in complex versus simple cultures. Collectively, the cellular complexity of brain-on-a-chip systems intrinsically develops cell type-specific phenotypes relevant to the brain while accelerating the maturation of neuronal networks, important features underdeveloped in traditional cultures.

59 BASIC BIOLOGICAL SCIENCES↗

Simplified Approximations of Direct Cumulus Entrainment and Detrainment

Abstract In recent years, direct calculations of simulated cumulus entrainment and detrainment have facilitated new physical insights into these highly elusive but critically important processes. However, these calculations require substantial computational resources that may limit their widespread usage. To facilitate such calculations, two simplified approximations of direct cumulus entrainment and detrainment are examined herein. The first approximation, termed the “semidirect” method, follows a standard bulk approach but makes more realistic assumptions about the sources of entrained and detrained air near the cloud edges. In contrast, the second approximation (the “projection” method) uses the governing equations of motion to project whether grid points near the cloud edge will entrain or detrain as the mean cloud ascends by one grid point. Verification exercises using large-eddy simulations reveal that both methods generally agree better with corresponding direct entrainment/detrainment estimates than the traditional bulk formulation, with the projection method outperforming the semidirect method. The two methods can be used in a synergistic fashion, with the semidirect method helping to optimize the projection method, to suit a wide range of applications. Because the latter incorporates the essential dynamics of entrainment and detrainment at the local scale, it can be used to gain physical insight into the causal mechanisms regulating these complex processes.

Meteorology & Atmospheric Sciences↗

Beyond Magic Barrels: Digital manufacturing for crystallization, process development and optimization of explosive materials: Part II Resveratrol Exemplar

This SAND report summarizes work supported by an Engineering Sciences Research Foundation (ESRF) Lab Directed Research and Development (LDRD) project entitled “Beyond Magic Barrels: Digital manufacturing for crystallization, process development and optimization of explosive materials.” This SAND report is written in two parts with Part 1 discusses recrystallization of our explosive exemplar and Part 2 summarizing our work with recrystallization of resveratrol. We have studied resveratrol recrystallization with a multiscale approach combining experiments, modeling and simulation. At the single crystal scale, microscopy experiments illuminate crystal time-dependent growth rates using advanced image analysis. Bench scale experiments were carried out to look at growth of multiple particles in a small reactor creating thousands of particles and analyzing the results with microscopy and μCT. For the modeling we combine kinetic Monte Carlo (kMC) models with subscale information from density functional theory (DFT) or molecular dynamics. This work is discussed in Part 1 and can also be found in a paper from the project discussing a coarse-grained kMC model specifically developed for resveratrol. For well-mixed systems, we have population balance equations (PBE) linked with species mass conservation forming a set of ordinary differential equations that can be solved quickly. For more complicated geometries, such as the vat crystallization used throughout the complex, a coupled computational fluid dynamic (CFD)/PBE method was developed to account for gradients in temperature and concentration and differences in crystallization rates throughout the domain. These simulations are more complex and require high performance computing. We present results for two cases: 5% seed fast cool with parameters fit to the well-mixed case and 5% seed slow cool using the same parameters. We show reasonable agreement with experiments though are particles are significantly larger than the experiments.

36 MATERIALS SCIENCE↗

Tuning aminopolycarboxylate chelators for efficient complexation of trivalent actinides

The complexation of trivalent lanthanides and minor actinides (Am 3+ , Cm 3+ , and Cf 3+ ) by the acyclic aminopolycarboxylate chelators 6,6'-((ethane-1,2-diylbis–((carboxymethyl)azanediyl))bis–(methylene))dipicolinic acid (H 4 octapa) and 6,6'-((((4-(1-(2-(2-(2-hydroxyethoxy)ethoxy)ethyl)-1H-1,2,3-triazol-4-yl)pyridine-2,6-diyl)bis–(methylene))bis–((carboxymethyl)azanediyl))bis–(methylene)) dipicolinic acid (H 4 pypa-peg) were studied using potentiometry, spectroscopy, competitive complexation liquid–liquid extraction, and ab initio molecular dynamics simulations. Two studied reagents are strong multidentate chelators, well-suited for applications seeking radiometal coordination for in-vivo delivery and f-element isolation. The previously reported H 4 octapa forms a compact coordination packet, while H 4 pypa-peg is less sterically constrained due to the presence of central pyridine ring. The solubility of H 4 octapa is limited in a non-complexing high ionic strength perchlorate media. However, the introduction of a polyethylene glycol group in H 4 pypa-peg increased the solubility without influencing its ability to complex the lanthanides and minor actinides in solution.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Thermal and concentration effects on 1 H NMR relaxation of Gd 3+ -aqua using MD simulations and measurements

We report gadolinium-based contrast agents are key in clinical MRI for enhancing the longitudinal NMR relativity (r 1 ) of hydrogen nuclei ( 1 H) in water and improving the contrast among different tissues. The importance of MRI in clinical practice cannot be gainsaid, yet the interpretation of MRI relies on models with severe assumptions, reflecting a poor understanding of the molecular-scale relaxation processes. In a step towards building a clearer understanding of the relaxation processes, here we investigate thermal and concentration effects on r 1 of the Gd 3+ -aqua complex using both semi-classical molecular dynamics (MD) simulations and measurements. We follow the MD simulation approach recently introduced by [Singer et al., Phys. Chem. Chem. Phys., 2021, 23, 20974], in which no NMR relaxation model or free-parameter is assumed to predict r 1 , thereby bringing new insights into the physics of r 1 on a molecular scale. We expand the autocorrelation function G(t) in terms of molecular modes and determine the thermal activation energies of the two largest modes, both of which are consistent with the range of literature values for rotational diffusion. We also determine the activation energies for translational diffusion and low-field electron-spin relaxation, both of which are consistent with the literature. Furthermore, we validate the MD simulations at human body temperature and concentrations of the paramagnetic ion used in clinical MRI, and we quantify the uncertainties in both simulations and measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multiscale simulation of integrated energy system and electricity market interactions

Accelerating the deep decarbonization of the world's electric grids requires the coordination of complex energy systems and infrastructures across timescales from seconds to decades. Here, we present a new multiscale simulation framework that integrates process- and grid-centric modeling paradigms to better design, operate, and control integrated energy systems (IESs), which combine multiple technologies, in wholesale energy markets. Traditionally, IESs are analyzed with a process-centric paradigm such as levelized cost of electricity (LCOE) or annualized net revenue, ignoring important interactions with electricity markets. This framework explicitly models the complex interactions between an IES's bidding, scheduling, and control decisions and the energy market's clearing and settlement processes, while incorporating operational uncertainties. Through two case studies, we show the importance of understanding and quantifying complex resource-grid interactions. In case study 1, we demonstrate that optimized bidding from one resource shifts the profit distribution for all energy systems in the market. This result suggests new and more flexible IES technologies can disrupt the economics of all market participants, possibly leading to accelerated retirements of less flexible resources. Interestingly, the optimized bidding has little impact on grid-level aggregate statistics, such as total generation costs and renewable penetration rate. While aggregate modeling strategies may remain valid under some IES adoption scenarios for analysis focused on regional outcomes, direct comparisons of IES technologies at specific locations without considering these interactions may lead to misleading or incorrect conclusions. In case study 2, we consider the design and flexible operation of IESs that hybridize conventional generators with energy storage. Through a sensitivity analysis, we find that as the size of the storage system increases, the total number of start-ups for coal- and natural gas-based IESs reduced by 25% and 33.6%, and the total thermal generator ramping (i.e., mileage) reduced by 86.5% and 62.5%, respectively. This shows the primary benefit of storage may not be reduced operational costs (which do not change significantly) but fewer start-ups and less ramping, which may greatly simplify the design, operation, and control of carbon capture systems. The new modeling and optimization capabilities from this work enable the coupling of rigorous, dynamic process models with grid-level production cost models to quantitatively identify the nuanced interdependencies across these vast timescales that must be addressed to realize clean, safe, and secure energy production. Moreover, the proposed general multiscale simulation framework is applicable to all IES technologies and can be easily extended to consider other energy carriers (e.g., hydrogen, ammonia) and energy infrastructures (e.g., natural gas pipelines).

24 POWER TRANSMISSION AND DISTRIBUTION↗

The Straightening of a River Meander Leads to Extensive Losses in Flow Complexity and Ecosystem Services

To assist river restoration efforts we need to slow the rate of river degradation. This study provides a detailed explanation of the hydraulic complexity loss when a meandering river is straightened in order to motivate the protection of river channel curvature. We used computational fluid dynamics (CFD) modeling to document the difference in flow dynamics in nine simulations with channel curvature (C) degrading from a well-established tight meander bend (C = 0.77) to a straight channel without curvature (C = 0). To control for covariates and slow the rate of loss to hydraulic complexity, each of the nine-channel realizations had equivalent bedform topography. The analyzed hydraulic variables included the flow surface elevation, streamwise and transverse unit discharge, flow velocity at streamwise, transverse, and vertical directions, bed shear stress, stream function, and the vertical hyporheic flux rates at the channel bed. The loss of hydraulic complexity occurred gradually when initially straightening the channel from C = 0.77 to C = 0.33 (i.e., the radius of the channel is three-times the channel width), and additional straightening incurred rapid losses to hydraulic complexity. Other studies have shown hydraulic complexity provides important riverine habitat and is positively correlated with biodiversity. This study demonstrates how hydraulic complexity can be gradually and then rapidly lost when unwinding a river, and hopefully will serve as a cautionary tale.

54 ENVIRONMENTAL SCIENCES↗

Acceleration of Thermochemistry Solves in MOOSE and Pronghorn

This work focuses on the development and implementation of strategies to accelerate thermochemical calculations within MOOSE-based multiphysics simulations, particularly for applications in MSRs. We highlight the inherent complexity of nuclear materials, which require a multiscale approach to accurately model their behavior across various physical domains, including mechanical, chemical, and thermal phenomena. Thermochemical equilibrium calculations are crucial for predicting material properties and enhancing the fidelity of these simulations. The integration of Thermochimica, a Gibbs energy minimizer, into MOOSE allows for the direct minimization of Gibbs energy at every point on the mesh. However, the computational cost of such integration is significant. To address this, we explored acceleration strategies such as multi-threading support and the use of a thermodynamic ValueCache to reduce redundant calculations. Additionally, we investigated modifications to Thermochimica to enable phase constraints and improve its coupling with phase-field models, which are essential for simulating microstructural evolution and corrosion in MSR. These efforts aim to optimize the computational efficiency and accuracy of multiphysics simulations, thereby supporting the development of reliable and efficient nuclear materials for next-generation reactor technologies.

36 - MATERIALS SCIENCE↗

Deep Learning-based Surrogate Model for Efficient Reservoir Simulation in Large-scale Geological Carbon Storage: Application in IBDP Dataset

This project introduces an advanced deep learning (DL)-based surrogate modeling approach to enhance the efficiency and accuracy of large-scale geological carbon storage (GCS) simulations. Using the Illinois Basin Decatur Project (IBDP) dataset as training data, the study employs a residual U-Net architecture to predict critical state variables such as pressure and CO₂ saturation, as well as CO₂ plume migration. By incorporating key geological parameters (e.g., porosity, permeability, and rock facies) and physics-informed inputs like the diffusive time of flight and time step, the DL model effectively reduces computational complexity while maintaining robust physical constraints. Compared to traditional simulators like Eclipse, the DL model achieves remarkable accuracy, with a root mean square error (RMSE) of 1.57 psi for pressure and 0.007 for saturation, and dramatically reduces computational time from hours to just 69.9 seconds for 50-step simulations. These results demonstrate the potential of innovative DL methodologies to improve the predictivity and operational efficiency of GCS simulations, providing a reliable foundation for decision-making in CCS operations. Supported by the SMART initiative, this project underscores the success of leveraging computational innovations to advance CCS technologies.

advanced deep learning↗

Fast Evaluation of Aircraft Icing Severity Using Machine Learning Based on XGBoost

Aircraft icing represents a serious hazard in aviation which has caused a number of fatal accidents over the years. In addition, it can lead to substantial increase in drag and weight, thus reducing the aerodynamics performance of the airplane. The process of ice accretion on a solid surface is a complex interaction of aerodynamic and environmental variables. The complex relationship makes machine learning-based methods an attractive alternative to traditional numerical simulation-based approaches. In this study, we introduce a purely data-driven approach to find the complex pattern between different flight conditions and aircraft icing severity prediction. The supervised learning algorithm Extreme Gradient Boosting (XGBoost) is applied to establish the prediction framework which makes prediction based on any set of observations. The input flight conditions for the proposed prediction framework are liquid water content, droplet diameter and exposure time. The proposed approach is demonstrated in three cases: maximum ice thickness prediction, icing area prediction and icing severity level evaluation. Performance comparison studies and error analysis are also conducted to verify the effectiveness and performance of the proposed method. Results show that the proposed method has reasonable capability in evaluating aircraft icing severity.

Li, Sibo (ORCID:000000021705844X)↗

Prediction of alkaline earth metal ion adsorption on goethite for various background electrolytes with the CD-MUSIC model

As water scarcity drives the use of more saline water sources, contaminant fate and transport models must capture the impact of high concentrations of alkaline earth metal ions (AEMs) and background electrolytes in these more complex waters. By utilizing macroscopic adsorption data from various electrolyte systems, a Charge Distribution – Multisite Complexation (CD-MUSIC) model, capable of incorporating electrolyte adsorption, was able to accurately simulate the adsorption behavior of alkaline earth metal ions onto goethite. The modeling effort was guided by previous spectroscopic and surface complexation modeling of alkaline earth metal adsorption and built on previous CD-MUSIC modeling that accounted for changes in crystal face contributions to the surface site density as a function of specific surface area. Further, the model was constrained to consider only two dominant surface complex species for each metal ion adsorption reaction. These two species were selected from 44 possible species through objective curve fitting of single-solute macroscopic adsorption data. While most of the alkaline earth metal surface complexes formed outer-sphere complexes at the goethite surface, an inner-sphere species was utilized for Mg 2+ . With the surface complex species and equilibrium constants obtained from this study, the calibrated model successfully predicted alkaline earth metal ion adsorption over a wide range of solution and surface conditions; the model predictions encompassed a wide range of pH (5–11), solute/solid ratio (1.37 × 10 -5 – 8.33 × 10 -4 mol -solute /g -solid ), ionic strengths (0.01 M – 0.7 M), and background electrolytes (Na + , Cs + , Rb + , Cl - , and NO 3 - ) using the same crystal face contribution methodology for site density, capacitance values, and surface acidity constants adopted for proton and cadmium adsorption in previous work (Han and Katz, 2019). Model simulations for a range of background water chemistries demonstrated the potential for Mg 2+ to reduce Cd 2+ adsorption to goethite in model seawater and oil- and gas-produced waters.

42 ENGINEERING↗

BASIN-3D: A brokering framework to integrate diverse environmental data

Diverse observational and simulation datasets are needed to understand and predict complex ecosystem behavior over seasonal to decadal and century time-scales. Integration of these datasets poses a major barrier towards advancing environmental science, particularly due to differences in the structure and formats of data provided by various sources. Here, we describe BASIN-3D (Broker for Assimilation, Synthesis and Integration of eNvironmental Diverse, Distributed Datasets), a data integration framework designed to dynamically retrieve and transform heterogeneous data from different sources into a common format to provide an integrated view. BASIN-3D enables users to adopt a standardized approach for data retrieval and avoid customizations for the data type or source. We demonstrate the value of BASIN-3D with two use cases that require integration of data from regional to watershed spatial scales. The first application uses the BASIN-3D Python library to integrate time-series hydrological and meteorological data to provide standardized inputs to analytical and machine learning codes in order to predict the impacts of hydrological disturbances on large river corridors of the United States. The second application uses the BASIN-3D Django framework to integrate diverse time-series data in a mountainous watershed in East River, Colorado, United States to enable scientific researchers to explore and download data through an interactive web portal. Thus, BASIN-3D can be used to support data integration for both web-based tools, as well as data analytics using Python scripting and extensions like Jupyter notebooks. The framework is expected to be transferable to and useful for many other field and modeling studies.

Varadharajan, C↗

Assessment of reverse gun taylor cylinder experimental configuration

Experimental efforts for Taylor-anvil impact tests have often been limited to near room temperature. The ‘Reverse Gun’ method proposed by Gust in 1982 allows for the Taylor impact specimen to be uniformly heated without temperature losses before impact. Through the use of finite element analysis, we explore two topics in this work. First, we examine whether the reverse gun experimental configuration is comparable to the traditional Taylor-anvil setup. Second, we assess the accuracy of several commonly employed flow strength models in terms of their ability to predict the reverse gun experimental results which involve dynamic loading conditions and complex thermo-mechanical coupling. The reverse gun simulations are performed for tantalum targets at initial temperatures in the range 295 K to 1295 K and velocities from 135 m/s to 242 m/s. We show that with suitable care in the modeling of the preheated reverse gun experiments one can make valuable assessments of flow strength models. Given the conditions explored, these observations probe the thermal softening, strain hardening, and strain rate sensitivity of the material.

42 ENGINEERING↗