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NASA NTRS2016

Lidar-Based Estimates of Above-Ground Biomass in the Continental US and Mexico Using Ground, Airborne, and Satellite Observations

Existing national forest inventory plots, an airborne lidar scanning (ALS) system, and a space profiling lidar system (ICESat-GLAS) are used to generate circa 2005 estimates of total aboveground dry biomass (AGB) in forest strata, by state, in the continental United States (CONUS) and Mexico. The airborne lidar is used to link ground observations of AGB to space lidar measurements. Two sets of models are generated, the first relating ground estimates of AGB to airborne laser scanning (ALS) measurements and the second set relating ALS estimates of AGB (generated using the first model set) to GLAS measurements. GLAS then, is used as a sampling tool within a hybrid estimation framework to generate stratum-, state-, and national-level AGB estimates. A two-phase variance estimator is employed to quantify GLAS sampling variability and, additively, ALS-GLAS model variability in this current, three-phase (ground-ALS-space lidar) study. The model variance component characterizes the variability of the regression coefficients used to predict ALS-based estimates of biomass as a function of GLAS measurements. Three different types of predictive models are considered in CONUS to determine which produced biomass totals closest to ground-based national forest inventory estimates - (1) linear (LIN), (2) linear-no-intercept (LNI), and (3) log-linear. For CONUS at the national level, the GLAS LNI model estimate (23.95 +/- 0.45 Gt AGB), agreed most closely with the US national forest inventory ground estimate, 24.17 +/- 0.06 Gt, i.e., within 1%. The national biomass total based on linear ground-ALS and ALS-GLAS models (25.87 +/- 0.49 Gt) overestimated the national ground-based estimate by 7.5%. The comparable log-linear model result (63.29 +/-1.36 Gt) overestimated ground results by 261%. All three national biomass GLAS estimates, LIN, LNI, and log-linear, are based on 241,718 pulses collected on 230 orbits. The US national forest inventory (ground) estimates are based on 119,414 ground plots. At the US state level, the average absolute value of the deviation of LNI GLAS estimates from the comparable ground estimate of total biomass was 18.8% (range: Oregon,−40.8% to North Dakota, 128.6%). Log-linear models produced gross overestimates in the continental US, i.e., N2.6x, and the use of this model to predict regional biomass using GLAS data in temperate, western hemisphere forests is not appropriate. The best model form, LNI, is used to produce biomass estimates in Mexico. The average biomass density in Mexican forests is 53.10 +/- 0.88 t/ha, and the total biomass for the country, given a total forest area of 688,096 sq km, is 3.65 +/- 0.06 Gt. In Mexico, our GLAS biomass total underestimated a 2005 FAO estimate (4.152 Gt) by 12% and overestimated a 2007/8 radar study's figure (3.06 Gt) by 19%.

Hybrid 3-Phase sampling↗
DOE OSTI2021

Detection Limits of Low-mass, Long-period Exoplanets Using Gaussian Processes Applied to HARPS-N Solar Radial Velocities

Radial velocity (RV) searches for Earth-mass exoplanets in the habitable zone around Sun-like stars are limited by the effects of stellar variability on the host star. In particular, suppression of convective blueshift and brightness inhomogeneities due to photospheric faculae/plage and starspots are the dominant contribution to the variability of such stellar RVs. Gaussian process (GP) regression is a powerful tool for statistically modeling these quasi-periodic variations. We investigate the limits of this technique using 800 days of RVs from the solar telescope on the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) spectrograph. These data provide a well-sampled time series of stellar RV variations. Into this data set, we inject Keplerian signals with periods between 100 and 500 days and amplitudes between 0.6 and 2.4 m s{sup −1}. We use GP regression to fit the resulting RVs and determine the statistical significance of recovered periods and amplitudes. We then generate synthetic RVs with the same covariance properties as the solar data to determine a lower bound on the observational baseline necessary to detect low-mass planets in Venus-like orbits around a Sun-like star. Our simulations show that discovering planets with a larger mass (∼0.5 m s{sup −1}) using current-generation spectrographs and GP regression will require more than 12 yr of densely sampled RV observations. Furthermore, even with a perfect model of stellar variability, discovering a true exo-Venus (∼0.1 m s{sup −1}) with current instruments would take over 15 yr. Therefore, next-generation spectrographs and better models of stellar variability are required for detection of such planets.

47 OTHER INSTRUMENTATION↗
NASA NTRSDate not supplied

Uncertainty Quantification using Deep Ensembles for Decision Making in Cyber-Physical-Human Systems

In this paper and its companion, Differential Equation Approximation Using Gradient-Boosted Quantile Regression, Robison et al., we examine an approach to quantifying model uncertainty with the aim of increasing the trustworthiness of computational models in human-machine interactions. In Differential Equation Approximation Using Gradient-Boosted Quantile Regression, we focus on gradient-boosted decision trees, while in this one, we give more details about deep ensembles. Uncertainty quantification is crucial for building trustworthy autonomous decision-making agents in human-machine teams. There are two types of uncertainties: aleatoric and epistemic. The former is related to the inherent stochasticity (noise) of the process, whereas the latter is associated with the lack of knowledge or representation capability of models, such as neural networks. By lack of knowledge, we mean the model’s inability to accurately predict outputs for all possible inputs. The aleatory uncertainty can be estimated fairly easily with, for example, filters, whereas epistemic uncertainty is challenging to compute. This paper uses deep ensembles to quantify both aleatory and epistemic uncertainty. It can act as an uncertainty-aware surrogate transition model for decision-making frameworks. "Uncertainty-aware" means that the surrogate transition model should make predictions along with confidence in those predictions. In the context of decision-making, the transition models are ordinary differential equations (ODEs). Since ODEs can be simulated to make one-step or multi-step predictions, a good surrogate model for them should perform reasonably well in both modes. In a multi-step approach, the trajectory sampling method TS∞ was used to propagate uncertainty over multiple steps. The cartpole dynamical system was selected to demonstrate the ability of deep ensembles as good surrogate transition models for decision-making frameworks. The deep ensembles modeled the dynamics of cartpole ODEs and made uncertainty-aware predictions in single-step and multi-step transition modes.

CPH systems↗
NASA NTRS2014

Analyzing Source Apportioned Methane in Northern California During DISCOVER-AQ-CA Using Airborne Measurements and Model Simulations

This study analyzes source apportioned methane (CH4) emissions and atmospheric concentrations in northern California during the Discover-AQ-CA field campaign using airborne measurement data and model simulations. Source apportioned CH4 emissions from the Emissions Database for Global Atmospheric Research (EDGAR) version 4.2 were applied in the 3-D chemical transport model GEOS-Chem and analyzed using airborne measurements taken as part of the Alpha Jet Atmospheric eXperiment over the San Francisco Bay Area (SFBA) and northern San Joaquin Valley (SJV). During the time period of the Discover-AQ-CA field campaign EDGAR inventory CH4 emissions were 5.30 Gg/day (Gg 1.0 109 grams) (equating to 1.9 103 Gg/yr) for all of California. According to EDGAR, the SFBA and northern SJV region contributes 30 of total emissions from California. Source apportionment analysis during this study shows that CH4 concentrations over this area of northern California are largely influenced by global emissions from wetlands and local/global emissions from gas and oil production and distribution, waste treatment processes, and livestock management. Model simulations, using EDGAR emissions, suggest that the model under-estimates CH4 concentrations in northern California (average normalized mean bias (NMB) -5 and linear regression slope 0.25). The largest negative biases in the model were calculated on days when hot spots of local emission sources were measured and atmospheric CH4 concentrations reached values 3.0 parts per million (model NMB -10). Sensitivity emission studies conducted during this research suggest that local emissions of CH4 from livestock management processes are likely the primary source of the negative model bias. These results indicate that a variety, and larger quantity, of measurement data needs to be obtained and additional research is necessary to better quantify source apportioned CH4 emissions in California and further the understanding of the physical processes controlling them.

Methane↗
NASA NTRS1986

Satellite scatterometer comparisons with surface measurements: Techniques and Seasat results

A method by which satellite and surface measurements can be compared in order to validate satellite wind observations is presented. The regression method requires knowledge of the expected differences (due to atmospheric variability and differing averaging) between perfect satellite and perfect buoy measurements. A model for estimating these differences is described. The regression method is applied to comparisons between Seasat Scatterometer (SASS) and U.S. National Data Buoy Office buoy data. Comparisons indicating a dependence of SASS accuracy on sea-surface temperature are summarized.

Freilich, Michael H.↗
DOE OSTI2023

Field-scale dynamics of planting dates in the US Corn Belt from 2000 to 2020

Crop planting dates are a dynamic feature of agricultural systems that respond to short- and long-term climate signals, crop and cultivar selection, and technology changes. Planting date records are essential for yield gap analyses, accurate crop modeling, and tracking farmer adaptations to weather and climate change. Although planting dates have high variation at local scales due to heterogeneity in farm resources and decision-making, available long-term data on planting dates is largely restricted to aggregated regional statistics or, at best, satellite-derived datasets with limited spatiotemporal extent and at resolutions unable to distinguish individual fields (> 250 m). Here, we generated retrospective annual field-scale (30 m) planting date maps for both maize and soybeans spanning 2000-2020 across a 12 state region in the United States Corn Belt based on Landsat satellite data and a large ground sample of over 28,000 maize and soybean fields. Using training data from 2015-2020 for model selection, we found that planting date predictions improved with harmonic regression of Landsat data and additional annual weather covariates. The preferred random forests model approximately doubled performance compared to a null model based on state median planting dates, capturing 47% of field-level variation for maize (mean absolute error, MAE = 7.4 days) and 44% for soybeans (MAE = 7.5 days) against held-out ground truth test data for 2008-2014. We also evaluated the full 2000-2020 dataset with state agricultural statistics, finding strong agreement with median planting dates for maize (R 2 = 0.76, MAE = 4.4 days) and slightly lower agreement for soybeans (R 2 = 0.65, MAE = 5.4 days) when aggregated to the state level. We then used this new dataset to analyze environmental determinants of planting dates at a finer-scale than previously possible, controlling for unobserved variation at the sub-state district level. We found that during 2000-2020, each standard deviation increase in rainfall delayed planting by ~ 2.5 days, and fields with higher soil productivity ratings tended to be planted earlier. We did not find meaningful trends over the last two decades in planting dates for maize or soybeans, in contrast to trends towards earlier planting dates late last century and predicted for this period in climate adaptation studies. We hypothesize increases in early season rainfall may have inhibited these shifts towards earlier planting. Remotely sensed planting dates will be a useful tool for yield gap analyses, crop simulation modeling, and ongoing assessment of climate adaptation.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1990

Constrained optimization using design of experiment surfaces

An algorithm for solving constrained optimization problems is presented. First, design of experiment techniques are used to survey the design space. After evaluating the objective and constraint functions, as specified by Taguchi orthogonal arrays, analytical models of these functions are generated using a least-squares regression analysis. Next, a nonlinear programming package is used to optimize the analytical model. Based on the optimization information, the design space is reduced so as to close in around the minimum, and the entire procedure is repeated until convergence. An important feature of the algorithm is that function gradients are not required; therefore, for problems in which gradients would have to be estimated using finite-differences the number of function evaluations required for the optimization is significantly reduced, when compared with traditional nonlinear programming techniques. In addition, there is no requirement that the gradients must be smooth and continuous.

Bolt, Marvin Vance↗
NASA NTRS2010

Design and Development of a Model to Simulate 0-G Treadmill Running Using the European Space Agency's Subject Loading System

Develop a model that simulates a human running in 0 G using the European Space Agency s (ESA) Subject Loading System (SLS). The model provides ground reaction forces (GRF) based on speed and pull-down forces (PDF). DESIGN The theoretical basis for the Running Model was based on a simple spring-mass model. The dynamic properties of the spring-mass model express theoretical vertical GRF (GRFv) and shear GRF in the posterior-anterior direction (GRFsh) during running gait. ADAMs VIEW software was used to build the model, which has a pelvis, thigh segment, shank segment, and a spring foot (see Figure 1).the model s movement simulates the joint kinematics of a human running at Earth gravity with the aim of generating GRF data. DEVELOPMENT & VERIFICATION ESA provided parabolic flight data of subjects running while using the SLS, for further characterization of the model s GRF. Peak GRF data were fit to a linear regression line dependent on PDF and speed. Interpolation and extrapolation of the regression equation provided a theoretical data matrix, which is used to drive the model s motion equations. Verification of the model was conducted by running the model at 4 different speeds, with each speed accounting for 3 different PDF. The model s GRF data fell within a 1-standard-deviation boundary derived from the empirical ESA data. CONCLUSION The Running Model aids in conducting various simulations (potential scenarios include a fatigued runner or a powerful runner generating high loads at a fast cadence) to determine limitations for the T2 vibration isolation system (VIS) aboard the International Space Station. This model can predict how running with the ESA SLS affects the T2 VIS and may be used for other exercise analyses in the future.

Caldwell, E. C.↗
DOE OSTI2022

Construction of Women’s All-Around Speed Skating Event Performance Prediction Model and Competition Strategy Analysis Based on Machine Learning Algorithms

Introduction Accurately predicting the competitive performance of elite athletes is an essential prerequisite for formulating competitive strategies. Women’s all-around speed skating event consists of four individual subevents, and the competition system is complex and challenging to make accurate predictions on their performance. Objective The present study aims to explore the feasibility and effectiveness of machine learning algorithms for predicting the performance of women’s all-around speed skating event and provide effective training and competition strategies. Methods The data, consisting of 16 seasons of world-class women’s all-around speed skating competition results, used in the present study came from the International Skating Union (ISU). According to the competition rules, distinct features are filtered using lasso regression, and a 5,000 m race model and a medal model are built using a fivefold cross-validation method. Results The results showed that the support vector machine model was the most stable among the 5,000 m race and the medal models, with the highest AUC (0.86, 0.81, respectively). Furthermore, 3,000 m points are the main characteristic factors that decide whether an athlete can qualify for the final. The 11th lap of the 5,000 m, the second lap of the 500 m, and the fourth lap of the 1,500 m are the main characteristic factors that affect the athlete’s ability to win medals. Conclusion Compared with logistic regression, random forest, K-nearest neighbor, naive Bayes, neural network, support vector machine is a more viable algorithm to establish the performance prediction model of women’s all-around speed skating event; excellent performance in the 3,000 m event can facilitate athletes to advance to the final, and athletes with outstanding performance in the 500 m event are more likely competitive for medals.

Liu, Meng↗
DOE OSTI2026

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Hedonic Price Estimates of Lake Water Quality: Valued Attribute, Instrumental Variables, and Ecological-Economic Benefits

We estimate the effect of lake water quality on residential housing prices using cross-sectional data on water clarity from 113 lakes across the United States. An instrumental-variables approach is developed to address potential endogeneity bias in the water-clarity variable. Three lake-based physical variables serve as instrumental variables: total nitrogen concentration in lake water, total phosphorus concentration in lake water, and water temperature near the lake surface. The econometric results include three methodological findings: the instruments are valid and strong; the ordinary-least-squares estimate of the coefficient on the water-clarity variable is unbiased; and water clarity is the attribute of water quality valued in the housing market. The estimated water-clarity effect shows that a one-tenth of a meter change in water clarity leads to a one-percent change in housing price, or an elasticity of 0.20 at mean clarity. Coupling this effect with estimates of an ecological production function, a lake-specific benefit index is developed that shows the effect on housing values of bringing lakes into compliance with the US Environmental Protection Agency's regional recommendations for phosphorous concentration in lake waters.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Development of real-time density feedback control on MAST-U in L-mode

In this paper we report on the development and demonstration of density feedback control for MAST-U. Sinusoidal perturbations are used to measure the frequency response from a deuterium gas valve (actuator) to line-integrated core electron density measured by the interferometer (sensor). In the frequency range relevant for control design, only two system-identification experiments were needed to regress a first-order dynamic model. This control-oriented model informs the offline design of a proportional integral controller with the established loop-shaping controller design method. After offline verification of the controller implementation, control is demonstrated by experimentally tracking a staircase reference for the line-integrated electron density. This paper demonstrates the efficiency of controller design using system-identification and loop-shaping, providing reliable density control for MAST-U.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Analysis of biokinetic parameters reveals patterns in mercury accumulation across aquatic species

Mercury (Hg) is a potent neurotoxicant and poses a risk to human health through the ingestion of Hg-contaminated fish. Mercury, especially in its organic form methylmercury (MeHg), biomagnifies up food chains such that even small aqueous concentrations of Hg can result in significant concentrations of total Hg in fish. Understanding the ecological and human health risks associated with Hg and MeHg exposure requires an understanding of the factors that affect its bioaccumulation in aquatic species. We compiled estimates of three biokinetic parameters: uptake rate (k u ), assimilation efficiency (AE), and efflux rate (k e ). These parameters describe contaminant uptake from aqueous (k u ) and dietary (AE) exposure and the rate of excretion (k e ). We found parameter values for 38 and 34 different species of fish and aquatic invertebrates, respectively, and collected 502 parameter values in total. Here, we used a machine learning technique to establish the relationships between experimental and physiological variables and these parameter values. We found differences in which variables were associated with biokinetic parameter values for fish and aquatic invertebrates. The form of Hg was the most impactful variable, influencing values of all parameters except k u for invertebrates, for which aqueous exposure time was the only significant predicator variable. The parameter k e were the only values significantly influenced by more than one variable, with water type (freshwater, brackish, or marine), organism weight, and form of Hg significantly impacting parameter values for fish and/or invertebrates. To our knowledge, this study represents the most extensive review of biokinetic parameters of Hg and MeHg accumulation in aquatic organisms. Environmental parameters found to significantly impact Hg and MeHg bioaccumulation in past studies were not identified as important in our analyses across aquatic ecosystems and species. Our dataset and analysis reveal novel patterns that may help us better understand and manage Hg bioaccumulation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Discovery of Pyridopyrimidinones that Selectively Inhibit the H1047R PI3Kα Mutant Protein

The H1047R mutation of PIK3CA is highly prevalent in breast cancers and other solid tumors. Selectively targeting PI3Kα H1047R over PI3Kα WT is crucial due to the role that PI3Kα WT plays in normal cellular processes, including glucose homeostasis. Currently, only one PI3Kα H1047R -selective inhibitor has progressed into clinical trials, while three pan mutant (H1047R, H1047L, H1047Y, E542K, and E545K) selective PI3Kα inhibitors have also reached the clinical stage. Herein, we report the design and discovery of a series of pyridopyrimidinones that inhibit PI3Kα H1047R with high selectivity over PI3Kα WT , resulting in the discovery of compound 17. When dosed in the HCC1954 tumor model in mice, 17 provided tumor regressions and a clear pharmacodynamic response. X-ray cocrystal structures from several PI3Kα inhibitors were obtained, revealing three distinct binding modes within PI3Kα H1047R including a previously reported cryptic pocket in the C-terminus of the kinase domain wherein we observe a ligand-induced interaction with Arg1047.

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

Rapid quantitative analysis of trace elements in plutonium alloys using a handheld laser-induced breakdown spectroscopy (LIBS) device coupled with chemometrics and machine learning

Here, we present the first reported quantification of trace elements in plutonium via a portable laser-induced breakdown spectroscopy (LIBS) device and demonstrate the use of chemometric analysis to enhance the handheld device's sensitivity and precision. Quantification of trace elements such as iron and nickel in plutonium metal via LIBS is a challenging problem due to the complex nature of the plutonium optical emission spectra. While rapid analysis of plutonium alloys has been demonstrated using portable LIBS devices, such as the SciAps Z300, their detection limits for trace elements are severely constrained by their achievable pulse power and length, light collection optics, and detectors. In this paper, analytical methods are evaluated as a means to circumvent the detection constraints. Three chemometric methods often used in analytical spectroscopy are evaluated; principal component regression, partial least-squares regression, and artificial neural networks. These models are evaluated based on goodness-of-fit metrics, root mean-squared error, and their achievable limits of detection (LoDs). Partial least squares proved superior for determining content of iron and nickel in plutonium metal, yielding LoDs of 15 and 20 ppm, respectively. These results of identifying the undesirable trace elements in plutonium components are critical for applications such as fabricating radioisotope thermoelectric generators or nuclear fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Guiding the design of oxidation-resistant Fe-based single atom alloy catalysts with insights from configurational space

The high activity and selectivity of Fe-based heterogeneous catalysts toward a variety of reactions that require the breaking of strong bonds are offset in large part by their considerable instability with respect to oxidative deactivation. While it has been shown that the stability of Fe catalysts is considerably enhanced by alloying them with precious metals (even at the single-atom limit), rational design criteria for choosing such secondary metals are still missing. Since oxidative deactivation occurs due to the strong binding of oxygen to Fe and reduction by adsorbed hydrogen mitigates the deactivation, we propose here to use the binding affinity of oxygen and hydrogen adatoms as the basis for rational design. As it would also be beneficial to use cheaper secondary metals, we have scanned over a large subset of 3d–5d mid-to late transition metal single atoms and computationally determined their effect on the oxygen and hydrogen adlayer binding as a function of chemical potential and adsorbate coverage. We further determine the underlying chemical origins that are responsible for these effects and connect them to experimentally tunable quantities. Our results reveal a reliable periodic trend wherein oxygen binding is weakened greatest as one moves right and down the periodic table. Hydrogen binding shows the same trend only at high (but relevant) coverages and otherwise tends to have its binding slightly increased in all systems. Trends with secondary metal coverage are also uncovered and connected to experimentally tunable parameters.

Hensley, Alyssa↗
DOE OSTI2025

D–MOPH–25: diverse MOF–molecule pairs for Henry’s constants prediction

Computational methods like grand-canonical Monte Carlo simulations and machine learning (ML) have accelerated metal–organic frameworks (MOF) exploration but are typically limited to a narrow range of adsorbates due to data availability and force field constraints. In this study, we introduce a dataset of diverse MOF–molecule pairs for Henry’s constant prediction, D–MOPH–25, which systematically explores a diverse chemical space by combining 113 molecular adsorbates with over 5000 MOF structures through an active learning process. D–MOPH–25 constitutes the most diverse adsorbate dataset used in any ML study of molecular adsorption in MOFs to date. Our workflow builds a benchmark for predicting Henry’s constants at 300 K, leveraging conformal prediction for uncertainty quantification. Assessment through Shannon entropy and uniform manifold approximation and projection confirms the comprehensiveness of D–MOPH–25 while highlighting the importance of robust classification to filter out unphysical data points in regression tasks. Although future enhancements in model architecture and sampling criteria could improve predictive performance, our dataset already spans the target space using only 2.31% of total possibilities. This comprehensive dataset facilitates assessment of model generalizability across adsorbate species and can establish a foundation for high-throughput MOF screening and ML-driven separation processes.

active learning↗
DOE OSTI2022

Size-Dependent Nucleation in Crystal Phase Transition from Machine Learning Metadynamics

In this Letter, we present a framework that combines machine learning potential (MLP) and metadynamics to investigate solid-solid phase transition. Here, based on the spectral descriptors and neural networks regression, we develop a scalable MLP model to warrant an accurate interpolation of the energy surface where two phases coexist. Applying it to the simulation of B4–B1 phase transition of GaN under 50 GPa with different model sizes, we observe sequential change of the phase transition mechanism from collective modes to nucleation and growths. When the size is at or below 128 000 atoms, the nucleation and growth appear to follow a preferred direction. At larger sizes, the nuclei occur at multiple sites simultaneously and grow to microstructures by passing the critical size. The observed change of the atomistic mechanism manifests the importance of statistical sampling with large system size in phase transition modeling.

36 MATERIALS SCIENCE↗