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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Design Optimization for Weighted Conduction Loss Minimization in a Dual-Active-Bridge-Based PV Microinverter

This manuscript presents a harmonic-superposition based frequency-domain approach for analysis and optimal design of a single-stage DAB-based DC-AC converter used in low-voltage DC to high voltage AC applications, such as PV microinverter. Specifically, two topological variations and correspondingly different modulation strategies involving up to four control variables (three phase shifts and switching frequency) are analyzed. Optimal trajectories of control variables are determined that result in minimized transformer RMS current at a given average power, while enforcing near-uniform ZVS. To make the design process holistic, an outer optimization loop is used to determine optimal values for the power transfer inductance (integrated as the transformer’s leakage inductance) and turns ratio, which minimize the weighted-average conduction loss contribution to the microinverter’s CEC efficiency. Based on the optimization analyses, a 400 W microinverter prototype is built and experimental results at one operating point are presented, achieving a measured efficiency of 92.8%.

14 SOLAR ENERGY↗
DOE OSTI2020

Elastic depths for detecting shape anomalies in functional data

This this paper, we propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that have considerably different geometric forms or features from the rest of the data. Identifying them is generally more difficult than identifying magnitude anomalies because shape anomalies are often not distinguishable from the bulk of the data with visualization methods. The proposed elastic depths use the recently developed elastic distances to directly measure the centrality of functions in the amplitude and phase spaces. Measuring shape outlyingness in these spaces provides a rigorous quantification of shape which, in turn, gives the elastic depths a strong theoretical and practical advantage over other methods in detecting shape anomalies. A simple boxplot and thresholding method are introduced to identify shape anomalies using the elastic depths. We assess the elastic depth's detection skill on simulated shape outlier scenarios and compare them against popular shape anomaly detectors. Finally, bond yields, image outlines, and hurricane trajectories are used to demonstrate our method's applicability to functional data observed on three different manifolds.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Pathways of bio-jet adoption in the US aviation industry with implications for the overall transportation and energy sectors: an integrated, multi-sectoral analysis of future scenarios

Bio-jet adoption has emerged as an attractive option to complement and supplement the use of refined fossil liquid fuels in the aviation industry in the US. However, there are significant uncertainties surrounding the costs of bio-jet including but not limited to costs of feedstock, transformation costs and the competition with co-products of bio-jet that may be demanded elsewhere in the transportation or energy sectors. This study models alternative trajectories of bio-jet adoption in the US aviation industry by 2050 through the use of a global integrated multi sector dynamics model. Three bio-jet production and consumption pathways are presented- soybean oil to jet, corn ethanol to jet (ETJ) and Fisher–Tropsch-based bio-jet, with each pathway explicitly considering the co-production of renewable diesel and renewable gasoline alongside the bio-jet. Without explicit actions or technology changes to offset the technology cost of bio-jet, scenarios where bio-jet displaces refined liquids result in higher aviation fuel prices (ranging from a 25% increase to 120% increase by mid-century) and lower demand (ranging from −14% to −43%). Corn ethanol will play an important role in the US if large scale amounts of bio-jet are to be produced with smaller effects on demand and prices. While scenarios with high levels of bio-jet availability without the availability of ETJ in the US can significantly reduce emissions in the aviation sector, these reductions are achieved more through the reduction in overall aviation fuel demand rather than technology adoption.

09 BIOMASS FUELS↗
DOE OSTI2024

Comparative Pore Structure and Dynamics for Bacterial Microcompartment Shell Protein Assemblies in Sheets or Shells

Bacterial microcompartments (BMCs) are protein-bound organelles found in some bacteria that encapsulate enzymes for enhanced catalytic activity. These compartments spatially sequester enzymes within semipermeable shell proteins, analogous to many membrane-bound organelles. The shell proteins assemble into multimeric tiles; hexamers, trimers, and pentamers, and these tiles self-assemble into larger assemblies with icosahedral symmetry. While icosahedral shells are the predominant form in vivo , the tiles can also form nanoscale cylinders or sheets. The individual multimeric tiles feature central pores that are key to regulating transport across the protein shell. Our primary interest is to quantify pore shape changes in response to alternative component morphologies at the nanoscale. We used molecular modeling tools to develop atomically detailed models for both planar sheets of tiles and curved structures representative of the complete shells found in vivo . Subsequently, these models were animated using classical molecular dynamics simulations. From the resulting trajectories, we analyzed the overall structural stability, water accessibility to individual residues, water residence time, and pore geometry for the hexameric and trimeric protein tiles from the Haliangium ochraceu m model BMC shell. These exhaustive analyses suggest no substantial variation in pore structure or solvent accessibility between the flat and curved shell geometries. We additionally compare our analysis to hydroxyl radical footprinting data to serve as a check against our simulation results, highlighting specific residues where water molecules are bound for a long time. Although with little variation in morphology or water interaction, we propose that the planar and capsular morphology can be used interchangeably when studying permeability through BMC pores.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Model for the curvature response of the CDF II drift chamber

The CDF II experiment at the Fermilab Tevatron used a drift chamber to measure the momenta of charged particles. We present a model for the response of the drift chamber to the curvature of a charged particle's trajectory. Constraints on the model parameters are obtained from cosmic-ray data and from information published by CDF in the context of the W boson mass measurement. Implications for the calibration of the drift chamber measurement of momentum are discussed. The robustness of the CDF calibration procedure is demonstrated. The model provides a framework for the analysis of precision magnetic trackers of high-momentum particles. Published by the American Physical Society 2025

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Resolving the Solvation Structure and Transport Properties of Aqueous Zinc Electrolytes from Salt-in-Water to Water-in-Salt Using Neural Network Potential

Zn Cl 2 solutions are promising electrolytes for aqueous zinc-ion batteries. Here, we report a joint computational and experimental study of the structural and dynamic properties of aqueous Zn Cl 2 electrolytes with concentrations ranging from salt-in-water to water-in-salt (WIS). By developing a neural network potential (NNP) model, we perform molecular dynamics (MD) simulations with accuracy but at much larger lengths and longer timescales. The NNP predicted structures are validated by the structure factors measured by X-ray total scattering experiments. The MD trajectories provide a comprehensive and quantitative picture of the Zn 2 + solvation shell structures. Additionally, we find that the O − H covalent bonds in water are strengthened with increasing salt concentration, thus expanding the electrochemical stability window of aqueous electrolytes. In terms of dynamic properties, the calculated and experimentally measured conductivities are in good agreement. Through the analysis of the calculated cation transference number, we propose a three-stage charge carrier transport mechanism with increasing concentration: independent ion transport, strongly correlated ion transport, and small positive charge carrier diffusion through negatively charged polymeric clusters. Our study provides fundamental atomic scale insights into the structure and transport properties of the Zn Cl 2 electrolyte that can aid the optimization and development of WIS electrolytes. Published by the American Physical Society 2025

25 ENERGY STORAGE↗
DOE OSTI2021

High-speed impact of micron-sized diesel drop trains—Splashing dynamics, secondary droplet formation, and effects of pre-existing film thickness

This work investigates surface impingement of monodispersed diesel drop trains using computational simulations. The three-dimensional simulations include high-speed impact of micrometer-sized fuel drops onto initially dry and wetted stainless steel substrates. The drop size and impact velocity are representative of fuel injection conditions in internal combustion engines (ICEs). The drop trains serve as a simplified representation of fuel spray. To accurately capture the film that naturally develops on initially dry substrates, a dynamic diesel-stainless steel contact angle model was developed using experiments of single drop impact under ICE representative temperature. Simulations are presented for a highly splashing case and the effects of a pre-existing film on splashing dynamics were investigated, including the temporal evolution of splashed mass and film thickness. It was concluded that for thin films, the effect of pre-existing film thickness is less significant than in single drop impingement. Secondary droplet characterization was performed on simulation results, leading to instantaneous and time-averaged distributions of secondary droplet size, velocity magnitude, and trajectory angle. It was found that for each drop impingement, approximately 58% of the splashed mass is from the impinging drop itself, while the remainder of the splashed mass is composed of film liquid. From a high resolution case, details of secondary droplet formation are observed and three distinct phases of secondary droplet formation are identified. The detailed analysis of drop train impingement under engine-relevant conditions serves as a first step toward a robust understanding of fuel impingement and the development of cleaner and more efficient ICEs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A coupled human–natural system analysis of freshwater security under climate and population change

Limited water availability, population growth, and climate change have resulted in freshwater crises in many countries. Jordan’s situation is emblematic, compounded by conflict-induced population shocks. Integrating knowledge across hydrology, climatology, agriculture, political science, geography, and economics, we present the Jordan Water Model, a nationwide coupled human–natural-engineered systems model that is used to evaluate Jordan’s freshwater security under climate and socioeconomic changes. The complex systems model simulates the trajectory of Jordan’s water system, representing dynamic interactions between a hierarchy of actors and the natural and engineered water environment. A multiagent modeling approach enables the quantification of impacts at the level of thousands of representative agents across sectors, allowing for the evaluation of both systemwide and distributional outcomes translated into a suite of water-security metrics (vulnerability, equity, shortage duration, and economic well-being). Model results indicate severe, potentially destabilizing, declines in freshwater security. Per capita water availability decreases by approximately 50% by the end of the century. Without intervening measures, >90% of the low-income household population experiences critical insecurity by the end of the century, receiving <40 L per capita per day. Widening disparity in freshwater use, lengthening shortage durations, and declining economic welfare are prevalent across narratives. To gain a foothold on its freshwater future, Jordan must enact a sweeping portfolio of ambitious interventions that include large-scale desalinization and comprehensive water sector reform, with model results revealing exponential improvements in water security through the coordination of supply- and demand-side measures.

42 ENGINEERING↗
DOE OSTI2026

Implications of climate change impacts for emission and land use scenario development

Scenarios of future emissions and land use produced by integrated assessment models have traditionally been developed without accounting for how climate change impacts could affect the emissions and land use trajectories themselves. This omission risks skewing our assessments of the plausible range of future emission pathways and associated Earth system changes. Beyond the salience for emission scenario development, a better integrated representation of human and Earth system changes and feedbacks would enable better anticipation of the implications of alternative socio-economic development pathways. We use the Global Change Analysis Model to investigate whether endogenizing several impacts when generating its baseline emission scenario is warranted. We do so by comparing the emissions and land use change that result from the baseline scenario with and without impacts, where impacts are implemented as exogenous changes to water availability, crop and labor productivity, and energy demand and supply. Our results indicate that the effect on global emissions leads to less than 0.1 °C increase in warming by 2100 and therefore do not support endogenizing impacts. This conclusion is conditional on our modeling framework and the specific impact channels represented but is consistent with other studies that have addressed the magnitude of feedbacks by implementing a two-way coupling. However, we do find regional impacts indicating that local economies and well-being measures may be affected significantly.

climate impacts↗
DOE OSTI2020

Metagenomic Insight into Environmentally Challenged Methane-Fed Microbial Communities

In this study, we aimed to investigate, through high-resolution metagenomics and metatranscriptomics, the composition and the trajectories of microbial communities originating from a natural sample, fed exclusively with methane, over 14 weeks of laboratory incubation. This study builds on our prior data, suggesting that multiple functional guilds feed on methane, likely through guild-to-guild carbon transfer, and potentially through intraguild and intraspecies interactions. We observed that, under two simulated dioxygen partial pressures—low versus high—community trajectories were different, with considerable variability among the replicates. In all microcosms, four major functional guilds were prominently present, representing Methylococcaceae (the true methanotrophs), Methylophilaceae (the nonmethanotrophic methylotrophs), Burkholderiales, and Bacteroidetes. Additional functional guilds were detected in multiple samples, such as members of Opitutae, as well as the predatory species, suggesting additional complexity for methane-oxidizing communities. Metatranscriptomic analysis suggested simultaneous expression of the two alternative types of methanol dehydrogenases in both Methylococcaceae and Methylophilaceae, while high expression of the oxidative/nitrosative stress response genes suggested competition for dioxygen among the community members. The transcriptomic analysis further suggested that Burkholderiales likely feed on acetate that is produced by Methylococcaceae under hypoxic conditions, while Bacteroidetes likely feed on biopolymers produced by both Methylococcaceae and Methylophilaceae.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Quarterly Research Performance Progress Report (Q8)

As part of Task 1, we have started by testing our modeling capabilities by reproducing isothermal DFIT simulations presented in the literature. Once satisfied with the results we have started by targeting the modeling of the DFITs at conducted at well 58-32. We have a identified a specific test (cycle 4 in zone 2) as the most interesting to be model with GEOS hydraulic fracturing module. Thus, we have first produced results with an isothermal model and adjusted model parameters to get a satisfying match with field pressure data. The, we have added thermal effects and compared the modeling results with and without thermal effects to estimate how thermal effects may influence test interpretation. Models seem to suggest that, for small volumes of fluid, thermal effects are moderate. In Task 2, we have adapted GEOS phase-field formulation to be able to simulate near-wellbore hydraulic fracture nucleation and propagation. We have devised a novel formulation that, compared to other existing ones, incorporates rock strengths. We have submitted a journal publication about our work. We are currently employing this phase-field formulation to model the experiments taking place at U Pitt and help us understand the effect of various parameters. In Task 3, we have built a model of the region surround well 16A and have started modeling stage 3 stimulation because of its simpler planar geometry. After calibrating simulation parameters using known analytical solutions, we have simulated the stage 3 stimulation using our isothermal hydraulic fracturing module, varying the permeability field, the stress conditions including different physics to get a better understanding of the numerical challenges and of the effects of varying these parameters on the simulation results. In Task 4 laboratory experimentation, a set of specialized drilling and injection tools has been customized and constructed to accommodate an inclined well with an orientation of up to 30 degrees relative to material anisotropy or principal stress axes. These inclined samples have also undergone thermal stress and hydraulic fracturing at a temperature of 190 degrees Celsius. Furthermore, both vertical and deviated sampling testing setups enable an extended analysis of post-peak pressure behaviors, facilitating post-test pressure analyses such as the G-function, step rate, and fracture reopening measurements. Thus, the key components of in-situ stress estimation can be extracted and validated through our experiment, providing a solid foundation for validating existing in-situ stress estimation theories or proposing new ones. Simultaneously, we are integrating computer vision techniques with traditional experimental fracture observation methods such as multi-overcore/slicing and water-penetration fracture observation. This combination will prove beneficial in populating the hydraulic fracture patterns database, generated under challenging EGS conditions. This approach aims to deepen our understanding of the complexities in EGS reservoirs and pave the way for future data-driven investigations. Additionally, PITT has also equipped the ELE International compression machine, which is now prepared for conducting indirect tensile and fracture toughness tests. These tests will aid in characterizing how rock fabrics influence the resulting fracture patterns. Additionally, we have completed the required personnel training and gained access to Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) for conducting more detailed characterization and analysis of rock fabrics, as well as the examination of thermal and hydraulically induced fracture patterns. Thus, the PITT team has effectively demonstrated the capabilities of our experimental apparatuses in exploring the thermal effects, well deviation angles, material anisotropy, and operational choices (such as circulation rate, injection fluid viscosity, and injection rate) and their impact on pressure responses and fracture trajectories under the Utah FORGE conditions.

15 GEOTHERMAL ENERGY↗
DOE OSTI2020

Why Interstellar Ice Dust Grains Should Be Elongated

Models of interstellar dust alignment assume that dust grains are elongated, but none of these models explain why dust grains should be elongated. On the other hand, models of interstellar dust grain growth assume that dust grains are spherical and not elongated. We show that when dusty plasma effects and the dipole moment of water molecules are together taken into account, ice grains in interstellar space should be prolate ellipsoids and not spheres. Dusty plasma analysis shows that an ice grain is charged to a negative potential that has magnitude nearly equal to that of the electron temperature. Several different mechanisms causing deviation from sphericity are identified; these mechanisms involve the interaction of the dipole moment of water molecules with electric fields associated with ice grain charging. These mechanisms include the focusing of water molecule trajectories, the migration of water molecules in a quasi-liquid layer on the grain surface toward regions where the electric field is strongest, the enhancement of this migration by the bombardment of energetic protons that gain energy upon falling into the ice grain negative potential, and mutual repulsion by electric charges having the same sign. Furthermore, the aspect ratio is established shortly after the ice grain is formed, and then is maintained as the grain grows.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Notes on Asay Foil Analysis

As is the norm for momentum diagnostic analyses (i.e., both piezopin and Asay foil measurements), we begin by assuming all particles are created instantaneously at the moment of shock breakout; that all particles move collinearly through a perfect vacuum from source to sensor with a long mean free path to scattering (i.e., so that particle velocities and areal masses do not change in flight); and that the particles collide perfectly inelastically with the sensor. We also assume the foil supports have a negligible effect on the trajectory, as has been demonstrated experimentally, and the foil is sufficiently thin that corrections for thick-plate effects (e.g., time delays between particle impacts on the collecting side and velocity changes on the probe side) can be disregarded. We seek an exact analytic treatment of an ideal system that perfectly embodies these characteristics.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Second-generation downscaled earth system model data using generative machine learning

The second-generation Sup3rCC dataset provides high-resolution meteorological data generated through the downscaling of multiple earth system models (ESMs) from the Coupled Model Intercomparison Project Phase 6 (CMIP6). This downscaling is performed through application of a generative machine learning approach called Super-Resolution for Renewable Resource Data (sup3r). This dataset builds on the first-generation Sup3rCC data by applying improved bias correction methods and adding downscaled precipitation to the output variables. As with the first Sup3rCC version, the data still include temperature, wind speed and direction at multiple heights, pressure, three components of downwelling solar radiation, and relative humidity—all at 4-kilometer (km) hourly resolution over the contiguous United States. This is a 25x spatial enhancement and 24x temporal enhancement of the source 100-km daily-average ESM data. This extension of the Sup3rCC dataset includes data from six ESMs from two shared socioeconomic pathways (SSPs) totaling 400 years of data with multiple future projections of changing meteorological conditions. The scenario selection was based on a structured evaluation of historical ESM skill and comprehensive representation of possible trajectories of future climate change in temperature, humidity, precipitation, solar irradiance, and near-surface wind speeds. The inclusion of multiple future projections is intended to enable users to assess key drivers of un 36 certainty and variability. All data are double-bias corrected, resulting in a product that can be used out-of-the-box for energy system analysis with minimal historical bias. The potential applications of Sup3rCC data extend to various topics in renewable energy resource assessment, energy systems modeling, and grid resilience studies. High-resolution future meteorological projections are critical for evaluating the effects of changing meteorological conditions on renewable energy generation, energy demand, and for optimizing energy storage and grid infrastructure. The 4-km hourly resolution of the downscaled data enables understanding of spatial and temporal variability at the scales necessary for energy system operational planning. In addition, the dataset can support risk assessments by providing detailed information on possible future extreme weather events and long-term meteorological variability at scales relevant to energy infrastructure. By offering an enhanced representation of possible future meteorological conditions, the second-generation Sup3rCC dataset enables more precise modeling of energy resilience and adaptation strategies in response to changing meteorological conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Tune compensation in nearly scaling fixed field alternating gradient accelerators

In this paper, we investigate the stability of the particle trajectories in fixed field alternating gradient accelerators (FFAs) in the presence of field errors. The emphasis is on the scaling radial sector FFA type: A collaboration work is ongoing in view of better understanding the properties of the 150 MeV scaling FFA at Kyoto University Institute for Integrated Radiation and Nuclear Science in Japan and progress toward high-intensity operation. Analysis of certain types of field imperfections revealed some interesting features that required the development of an analytical model based on the scalloping angle of the orbits. This helped explain some of the experimental results as well as generalize the concept of a scaling FFA to a nonscaling one for which the tune variations obey a well-defined law. Based on this, a compensation scheme of tune variations in imperfect scaling FFAs is presented. This is the cornerstone of a novel concept of a fixed tune FFA in which the scaling is not achieved at every azimuthal position of the ring but rather in an average sense.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Large eddy simulation of a pressurized reactive fluid–particle system: single-particle dynamics analysis

Pressurized oxy-combustion (POC) is a promising candidate to reduce carbon emissions in power generation. Designing an effective burner plays a vital role in developing new combustion technologies. Because of the high pressure, the volume fraction of particles in a pressurized oxy-combustor could be higher than that in the conventional combustor, therefore, the particle dynamics in the pressurized vessel need to be evaluated accordingly. The present computational work is to predict the influence of the particle size and particle injection location on the particle trajectory. The Stokes number based on turbulence fluctuation, St, is adopted to evaluate the impact of the gas phase on the particulate phase. A large eddy simulation (LES) with the environment pressure of 15 bar and the thermal input of the fuel particle of 100 kWth has been performed by means of the commercial CFD package. It is shown that that in this pressurized environment St << 1 for the 25 µm particles, St ~ 1 for the 100 µm particles, while for the particles exceeding 200 µm St >> 1. The trajectories of the sampling particles from the LES results support this conclusion: the particles less than 100 µm tend to be uniformly distributed in the space while the particles exceeding 200 µm tend to concentrate in the combustor.

Li, Lei↗
DOE OSTI2024

A model for oblique impacts on material surfaces

Many practical situations of material damage, wear, and erosion involve collisions between small particles and surfaces at inclined angles. While there are many well-validated models of normal incidence impact situations, elastic-plastic models for oblique incidence impact events are lacking. Here the finite element method is used to predict the normal and tangential coefficient of restitution in oblique impacts for hard, elastic spheres impacting an elastic-perfectly plastic material surface. The proposed model covers various impact angles ranging from 0° to 45°, within a limiting impact velocity below which the effects of heating are negligible. The normal coefficient of restitution follows power-laws with respect to normalized values of the impact velocity. Interestingly, the tangential coefficient of restitution follows a linear relationship with impact velocity. Together, these results provide a semi-empirical set of equations predicting oblique impact rebounds (both velocity and trajectory) for a wide range of conditions and material properties, with which experimental results can be rapidly interpreted. As a result, Laser-Induced Particle Impact Test (LIPIT) data are also presented for aluminum particles impacting aluminum substrates, at impact angles of 25° and 40°; the results compare favorably with the model and validate the general use of such models for the analysis of experimental data.

Coefficient of restitution↗