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DOE OSTI2022

GenMod: A generative modeling approach for spectral representation of PDEs with random inputs

Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation

The combination of neural networks and quantum Monte Carlo methods has arisen as a promising path forward for highly accurate electronic structure calculations. Previous proposals have combined equivariant neural network layers with a final antisymmetric layer in order to satisfy the antisymmetry requirements of the electronic wavefunction. However, to date it is unclear if one can represent antisymmetric functions of physical interest, and it is difficult to precisely measure the expressiveness of the antisymmetric layer. Here, this work attempts to address this problem by introducing explicitly antisymmetrized universal neural network layers. This approach has a computational cost which increases factorially with respect to the system size, but we are nonetheless able to apply it to small systems to better understand how the structure of the antisymmetric layer affects its performance. We first introduce a generic antisymmetric (GA) neural network layer, which we use to replace the entire antisymmetric layer of the highly accurate ansatz known as the FermiNet. We demonstrate that the resulting FermiNet-GA architecture can yield effectively the exact ground state energy for small atoms and molecules. We then consider a factorized antisymmetric (FA) layer which more directly generalizes the FermiNet by replacing the products of determinants with products of antisymmetrized neural networks. We find, interestingly, that the resulting FermiNet-FA architecture does not significantly outperform the FermiNet. This strongly suggests that the sum of products of antisymmetries is a key limiting aspect of the FermiNet architecture. To explore this further, we investigate a slight modification of the FermiNet, called the full determinant mode, which replaces each product of determinants with a single combined determinant. We find that the full single-determinant FermiNet closes a large part of the gap between the standard single-determinant FermiNet and FermiNet-GA on small atomic and molecular problems. Surprisingly, on the nitrogen molecule at a dissociating bond length of 4.0 Bohr, the full single-determinant FermiNet can outperform the largest standard FermiNet calculation with 64 determinants.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Data driven investigation to understand the influence of total solids on biological biogas upgrading

In situ biogas upgrading achieves CO 2 conversion to CH 4 via hydrogenotrophic methanogenesis; however, gas-liquid mass transfer constraints limit the upgrading performance. Recognizing that optimization studies often underrepresent the effects of total solids (TS) and organic loading rate (OLR), this study undertook a holistic, statistics driven assessment of operating conditions for in situ H 2 assisted biogas upgrading, centering the analysis on TS and OLR. A dataset of 31 studies was compiled and comprised 99 observations. A rigorous analytical framework was employed, combining data standardization, fixed- and random-effects (REML) weighted regressions with cluster-robust errors, stratified analyses, and machine learning. Mixed-effects meta regression indicated that TS was the main factor explaining differences of methane fraction (CH 4 %) when considering the between studies heterogeneity. Focusing on a near-stoichiometric subset (H 2 /CO 2 ≈ 4:1), TS remained significant. Stratified results showed a stronger negative relationship between TS and CH 4 % in UASB reactors than in CSTRs, with a negative effect under mesophilic conditions and no significant effect under thermophilic conditions. A Random Forest model corroborated the statistical findings, consistently ranking H 2 /CO 2 ratio, OLR, TS, and hydrogen injection rate (HIR) as the most influential predictors. These findings delineate trends across increasing TS levels, particularly between 1% and 10%, and provide preliminary insights for TS above 15% in in situ biogas upgrading. They further provide insights for the influence of TS by reactor type and temperature, thereby advancing the evidence base for implementing biological CO 2 conversion to CH 4 in practice.

In situ biogas upgrading↗

DOE OSTI2020

Historic and modern approaches for discovery of abandoned wells for methane emissions mitigation in Oil Creek State Park, Pennsylvania

Hundreds of oil wells were drilled along Oil Creek in Pennsylvania in the mid-16 1800s, birthing the modern oil industry. No longer in operation, many wells are now classified as abandoned, and, due to their age, their locations are either unknown or inaccurately recorded. These historic well sites present environmental, safety, and economic concerns in the form of possible methane leaks and physical hazards. Airborne magnetic and LiDAR surveys were conducted in the Pioneer Run watershed in Oil Creek State Park to find abandoned wells in a historically significant but physically challenging location. Wells were drilled in this area prior to modern geolocation and legal documentation. Although a large number of old wells were abandoned summarily without remediation of the site, much of the land area within Oil Creek State Park is now covered in trees and dense underbrush, which can obscure wellheads. The thick vegetation and steep terrain limited the possibility of ground-based surveys to easily find well sites for methane emissions studies. The data from remote sensing surveys were used to corroborate potential well locations from historic maps and photographs. Potential well sites were verified in a ground-based field survey and monitored for methane emissions. Two historic photographs documenting oil activity in the late 1800s were georeferenced using a combination of magnetic and LiDAR data. LiDAR data, which were more useful in georeferencing and in field verification, identified 290 field locations in the Pioneer Run watershed, 86% of which were possible well sites. Sixty-two percent of the ground-verified wells remained unplugged and comprised the majority of leaking wells. The mean methane emissions factor for unplugged wells was 0.027 ± 0.099 kg/day, lower than other Appalachian Basin methane emissions estimates. LiDAR was used for the first time, in combination with an airborne magnetic survey, to reveal underground oil industry features and inform well identification and remediation efforts in difficult-to-navigate regions. In the oldest oil fields, where well casing has been removed or wood conductor casing was installed, historic photographs provide additional lines of evidence for oil wells where ground disturbances have concealed surface features. Identification of well sites is necessary for mitigation efforts, as unplugged wells emit methane, a potent greenhouse gas.

02 PETROLEUM↗

DOE OSTI2022

The lay of the land: What we know about non-operating agricultural and absentee forest landowners in the U.S. and Europe

While non-operating agricultural and absentee forest landowners across the U.S. and Europe are an important group of landowners, our understanding of them remains relatively limited. In this paper, we conduct a systematic literature review on these landowners to encapsulate a current lay of the land in terms of what we know about these landowners and move the dialogue on this topic forward. Eighty-one articles are identified in our search of empirical literature. For each of the landowner types, we discuss their demographics and the three primary themes that emerged related to land management: participation in land management decisions, attitudes regarding land use and ownership, and resource needs in working with these landowners. For agricultural non-operating landowners, we find limited participation in land management decisions, particularly among women, a variety of individual and social factors play a role in involvement, and while they have pro-conservation attitudes, implementation of conservation practices is more limited. Absentee forest landowners we find are more willing to use management plans, yet less willing to engage in active management and risk reduction. These landowners have a range of attitudes regarding land use, with studies highlighting recreation, conservation, and profit motivations. In conclusion, our review concludes with identifying specific needs for more research and outreach on these landowners.

absentee↗

DOE OSTI2025

Upcycling of post-consumer mixed polyolefin feedstock: An economic and technical evaluation

Here, this study reports techno-economic and life cycle analyses to evaluate the economic and environmental impacts of mechanically recycled PE/PP blends in the presence of rheology modifiers. Additionally, fiber-reinforced composites derived from the compatibilized blends were prepared and evaluated for their performance compared with virgin plastics. Results suggest that compatibilized PE/PP blends exhibit a 70% lower selling price compared to virgin PE. Furthermore, these blends achieved a 74% reduction in greenhouse gas emissions or climate change impact compared to the virgin counterpart. Fiber-reinforced composites from compatibilized PE/PP blends demonstrated improved or comparable mechanical properties relative to composites made from virgin PE/PP blends. Based on their favorable cost and environmental impact, along with performance comparable to virgin composites, compatibilized PP/PE composites made from post-consumer plastics can find applications in large-scale composite manufacturing.

Fiber reinforced plastics (FRP)↗

DOE OSTI2025

Climate-extreme modeling framework for sustainable flood management in the Arabian Peninsula

Evaluating extreme precipitation events (EPEs) is essential for building climate-resilient water management strategies, but it remains a major challenge in ungauged basins. Using the 26,070 km 2 Wadi al-Rummah basin in central Saudi Arabia as a case study, we developed an alternative, reliable, cost-effective satellite-based framework that combines empirically derived EPE thresholds, imagery-calibrated 2D hydrodynamic modeling, GRACE water-storage diagnostics, and bias-corrected CMIP6 projections to assess flood hazards and recharge potential under current and future climate scenarios in ungauged basins. The integrated approach and the resulting findings followed four key steps: (1) Identified a 22.5 mm EPE threshold, the 80th percentile of 3-day GPM/IMERG rainfall (2000–2024), aligned with flood-triggering events (Nov 2018: 23–28 mm; Apr, 2023: 42 mm); (2) Developed and calibrated a RiverFlow2D model using Sentinel-2 and PlanetScope imagery for the November 2018 flood, accurately reproducing flood depth and extent (RMSE ≤0.31 m; fuzzy-Dice ≥0.91), and estimating runoff (41 %), infiltration (25 %), and evaporation (34 %); (3) Independently validated the model with the April 2023 event (RMSE ≤0.35 m; fuzzy-Dice ≥0.86); (4) Conducted climate projections (2025–2100) from five bias-corrected NEX-GDDP CMIP6 models that revealed a 34 % increase in EPE intensity under SSP2-4.5 and 48 % under SSP5-8.5 scenarios, relative to 20th-century baselines. Our findings indicate that while intensifying extremes in the 21st century increase flood risk, the results highlight the potential for episodic recharge if effective retention strategies are employed, and offer a transferable model for climate-informed planning in data-scarce arid regions.

CMIP6↗

DOE OSTI2022

Gas diffusion through variably-water-saturated zeolitic tuff: Implications for transport following a subsurface nuclear event

Noble gas transport through geologic media has important applications in the characterization of underground nuclear explosions (UNEs). Without accurate transport models, it is nearly impossible to distinguish between xenon signatures originating from civilian nuclear facilities and UNEs. Understanding xenon transport time through the earth is a key parameter for interpreting measured xenon isotopic ratios. One of the most challenging aspects of modeling gas transport time is accounting for the effect of variable water saturation of geological media. In this study, we utilize bench-scale laboratory experiments to characterize the diffusion of krypton, xenon, and sulfur hexafluoride (SF6) through intact zeolitic tuff under different saturations. Here, we demonstrate that the water in rock cores with low partial saturation dramatically affects xenon transport time compared to that of krypton and SF6 by blocking sites in zeolitic tuff that preferentially adsorb xenon. This leads to breakthrough trends that are strongly influenced by the degree of the rock saturation. Xenon is especially susceptible to this phenomenon, a finding that is crucial to incorporate in subsurface gas transport models used for nuclear event identification. We also find that the breakthrough of SF6 diverges significantly from that of noble gases within our system. When developing field scale models, it is important to understand how the behavior of xenon deviates from chemical tracers used in the field, such as SF6 (Carrigan et al., 1996). These new insights demonstrate the critical need to consider the interplay between rock saturation and fission product sorption during transport modeling, and the importance of evaluating specific interactions between geomedia and gases of interest, which may differ from geomedia interactions with chemical tracers.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2022

Updated neutrino mass constraints from galaxy clustering and CMB lensing-galaxy cross-correlation measurements

In this work, we revisit cosmological constraints on the sum of the neutrino masses Σm v from a combination of full-shape BOSS galaxy clustering [P(k)] data and measurements of the cross-correlation between Planck Cosmic Microwave Background (CMB) lensing convergence and BOSS galaxy overdensity maps [$C_{l}^{kg}$], using a simple but theoretically motivated model for the scale-dependent galaxy bias in auto- and cross-correlation measurements. We improve upon earlier related work in several respects, particularly through a more accurate treatment of the correlation and covariance between P(k) and $C_{l}^{kg}$ measurements. When combining these measurements with Planck CMB data, we find a 95% confidence level upper limit of Σm v sum of neutrino masses < 0.14 eV, while slightly weaker limits are obtained when including small-scale ACTPol CMB data, in agreement with our expectations. We confirm earlier findings that (once combined with CMB data) the full-shape information content is comparable to the geometrical information content in the reconstructed BAO peaks given the precision of current galaxy clustering data, discuss the physical significance of our inferred bias and shot noise parameters, and perform a number of robustness tests on our underlying model. While the inclusion of $C_{l}^{kg}$ measurements does not currently appear to lead to substantial improvements in the resulting Σm v of neutrino mass constraints, we expect the converse to be true for near-future galaxy clustering measurements, whose shape information content will eventually supersede the geometrical one.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Dynamic coevolution of baseflow and multiscale groundwater flow system during prolonged droughts

Field and numerical studies suggest that baseflow is composed of waters from a spectrum of groundwater flow paths termed the Groundwater Flow System (GWFS) – from shallow hillslope contributions to watershed-scale deep circulation originating in headwaters and discharging into lowland rivers. Here, we explore the evolution of the GWFS under prolonged droughts to understand its dynamics and multiscale nature, and to elucidate its role in baseflow generation and recession at the watershed scale. In this work, we consider three drought scenarios of varying severity and simulate groundwater flow in a 2-D cross-section of an idealized watershed with deep permeable bedrock, tracking the evolution of flow paths, baseflow, and residence times during the recession process. We find that baseflow generation at different drainage stages, and within different subwatersheds, is influenced distinctly by flow paths of different scales, depending on the relative strength of the flow paths and the position of the subwatersheds relative to the recharge/discharge zones of the deeper watershed-scale groundwater circulation. Despite having the same local relief, geology, and climate, baseflow from each subwatershed has a distinct recession behavior and time-dependent residence time distribution. Also, the hydraulic and transport characteristics of baseflow generation co-evolve and are strongly affected by the connection state of the water table to subwatersheds. These findings suggest that asynchrony and dissimilarity of baseflow generation from hillslopes under the impact of the watershed-scale groundwater flow, and interactions with local-scale and intermediate-scale groundwater flow, must be taken into account when interpreting baseflow recession data and building conceptual baseflow models at the watershed scale.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Trends and meteorological drivers of extreme daily reservoir evaporation events in the western United States

Extreme daily evaporation from reservoir surfaces can lead to significant short-term water losses, affecting water quality, water supply, and reservoir operation strategies. Historical trends in daily reservoir evaporation events have eluded the scientific and operational communities, largely due to a lack of long-term, consistent data record. This study quantifies trends in extreme daily reservoir evaporation events at 165 major reservoirs located in the western U.S. Here, we use the place-based energy balance and aerodynamic Daily Lake Evaporation Model (DLEM) driven by multiple meteorological data products (RTMA, gridMET, Daymet) to estimate daily evaporation rates at these reservoirs from 1981 to 2022. The results—while are based on different meteorological forcing datasets—consistently indicate that the California, Lower Colorado, and Rio Grande hydrologic regions are more prone to higher daily evaporation extremes. Compared to the rest of western U.S, these three regions also experience a more pronounced increasing trend in the annual maximum daily evaporation rate, at about 0.3 mm day -1 decade -1 during 1981-2022. The results show that heat and dryness are the main drivers to the increasing trend of extreme evaporation, while extreme wind speed is the primary contributor to exceptionally high daily evaporation events across all regions. This phenomenon is particularly prominent in the arid Lower Colorado region, but less significant in the cold and humid Pacific Northwest region. We also find that the correlation between extreme wind speed and extreme evaporation degrades as the time scale increases from daily, to monthly and seasonal. Our findings have strong implications for the pattern and distribution of extreme evaporation events at the western U.S. reservoirs, and illustrate how various drivers influence extreme evaporation across different time scales.

13 HYDRO ENERGY↗

DOE OSTI2026

Urban wash-off of tire wear particles

Tire wear particles (TWPs) are an important class of microplastics due to their toxicity and abundance. Because most TWPs are generated on impervious road surfaces, urban wash-off is the critical first phase of waterborne transport from their zone of production to stormwater drainage. However, little is known about the driving factors behind their mobilization. In this study, we use a rainfall simulator to investigate how surface roughness, rainfall intensity, and surface slope affect wash-off behaviors of TWPs. We also analyze how the size and shape of mobilized TWPs change over the course of simulated storm events. We found that low surface roughness, high rainfall intensity (most significant factor), and low slope result in the most rapid conveyance of TWP load. On average, large particles (>1000 µm) travelled faster than small particles (<125 µm). Particle shape explained a very small amount of variance in TWP wash-off velocity but was found to be more important under higher surface roughness conditions. In addition to wash-off velocity, we found similar conditions controlled the percent mobilization of TWPs. Low surface roughness and high rainfall intensity resulting in higher TWP wash-off rates is consistent with mineral sediment wash-off behavior. Conversely, low surface slope and large particle size leading to faster conveyance is directly opposed to mineral sediment wash-off. Our findings suggest drag-dominated flow and that sufficient runoff depth is the most important parameter governing TWP wash-off. These findings are important first steps to understanding wash-off behaviors of TWPs and informing future modeling efforts and mitigation strategies.

13 HYDRO ENERGY↗

DOE OSTI2024

APOA2 increases cholesterol efflux capacity to plasma HDL by displacing the C-terminus of resident APOA1

The ability of high-density lipoprotein (HDL) to promote cellular cholesterol efflux is a more robust predictor of cardiovascular disease protection than HDL-cholesterol levels in plasma. Previously, we found that lipidated HDL containing both apolipoprotein A-I (APOA1) and A-II (APOA2) promotes cholesterol efflux via the ATP-binding cassette transporter (ABCA1). In the current study, we directly added purified, lipid-free APOA2 to human plasma and found a dose-dependent increase in whole plasma cholesterol efflux capacity. APOA2 likewise increased the cholesterol efflux capacity of isolated HDL with the maximum effect occurring when equal masses of APOA1 and APOA2 coexisted on the particles. Follow-up experiments with reconstituted HDL corroborated that the presence of both APOA1 and APOA2 were necessary for the increased efflux. Using limited proteolysis and chemical cross-linking mass spectrometry, we found that APOA2 induced a conformational change in the N- and C-terminal helices of APOA1. Using reconstituted HDL with APOA1 deletion mutants, we further showed that APOA2 lost its ability to stimulate ABCA1 efflux to HDL if the C-terminal domain of APOA1 was absent, but retained this ability when the N-terminal domain was absent. Based on these findings, we propose a model in which APOA2 displaces the C-terminal helix of APOA1 from the HDL surface which can then interact with ABCA1—much like it does in lipid-poor APOA1. These findings suggest APOA2 may be a novel therapeutic target given this ability to open a large, high-capacity pool of HDL particles to enhance ABCA1-mediated cholesterol efflux.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

Surface magnetic anisotropy-mediated spin Hall magnetoresistance and spin Seebeck effects in a YIG/Pt heterostructure

The role of magnon-phonon coupling in the low-temperature behavior of the spin Seebeck effect (SSE) in YIG/Pt has been puzzling for more than a decade. Here, to elucidate the origin of the anomalous peak around 80 K, we investigate the temperature evolution of SSE, spin Hall magnetoresistance (SMR), and magnetic anisotropy in the same YIG/Pt heterostructure. We find that these effects, along with magnetic damping, show the peaks at the same temperature (~80 K). This simultaneous occurrence, where no heat is applied in the case of SMR, rules out the phonon-magnon drag related origin of SSE in the YIG/Pt system. We further show that the intrinsic surface anisotropy behavior in YIG is responsible for controlling the SSE, SMR, and magnetic damping in the YIG/Pt structure. Our findings not only help to understand these effects fundamentally but also provide an effective way for improving them by manipulating the surface magnetic anisotropy for spin caloritronic applications.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Laser-induced forces on atoms during ultrafast demagnetization

Laser-induced femtosecond demagnetization has attracted a broad attention as a possible candidate for information storage technology. However, whether or not lattice vibration directly participates in demagnetization has been highly controversial over a decade. A recent electron diffraction experiment attributed the demagnetization to the polarized phonon effect, but a similar x-ray diffraction experiment attributed it to the Einstein–de Haas effect. Common to both experiments is that neither the angular momentum of the lattice nor the rotation of the sample was directly probed. Here, we report our first first-principles calculation of forces on atoms induced by an ultrafast laser during ultrafast demagnetization. We employ two complementary methods: (i) the frozen lattice with electronic excitation and (ii) frozen excitation but moving the lattice. We find that the forces on atoms start at –50 fs and peak around 30 fs. The magnitude of the force is far smaller than the empirical estimates. Within the limit of our theory, our results suggest that the polarized phonon effect and the Einstein–de Haas effect are unlikely to be the main course of demagnetization. As a result, we expect that our finding has a profound impact on the future direction of laser-induced dynamics in magnetic and quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Soliton motion induced along ferromagnetic skyrmion chains in chiral thin nanotracks

Using atomistic magnetic simulations we investigate the soliton motion along a pinned skyrmion chain containing an interstitial skyrmion. We find that the soliton can exhibit stable motion along the chain without a skyrmion Hall effect for an extended range of drives. Under a constant drive the solitons have a constant velocity. We also measure the skyrmion velocity–current curves and identify the signatures of different phases including a pinned phase, stable soliton motion, and quasi-free motion at higher drives where all of the skyrmions depin from the pinning centers and move along the rigid wall. In the quasi-free motion regime, the velocity is oscillatory due to the motion of the skyrmions over the pinning sites. For increasing pinning strength, the onset of soliton motion shifts to higher values of current density. We also find that for stronger pinning, the characteristic velocity–current shape is affected by the annihilation of single or multiple skyrmions in the drive interval over which the soliton motion occurs. Our results indicate that stable skyrmion soliton motion is possible and that the solitons could be used as information carriers instead of the skyrmions themselves for technological applications.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Crystal plasticity including a phase-field deformation twinning model for the high-rate deformation of cyclotetramethylene tetranitramine

A new finite strain thermomechanical model for the high-rate deformation of the β-polymorph of cyclotetramethylene tetranitramine (β-HMX) has been developed and applied to simulations of plate impact experiments. The crystal plasticity model is based on a model developed previously for RDX (Luscher et al. 2017), which is extended to incorporate deformation twinning. Twinning during normal plate impacts is simulated with a phase-field twin model. First, material parameters governing the kinetics of dislocation slip are calibrated on the subset of simulations which had negative Schmid factors for the twin system. Second, a parametric study of the twin material parameters was performed to find suitable values. Overall, the results of the simulations with the phase-field twinning model are reported for impacts on several crystal orientations. We find that the twin growth decreases with increasing distance from the impact surface because of dissipation of the shock front via dislocation-mediated plasticity, and that the simulated interface velocity with and without phase-field twinning do not show appreciable differences. These modeling results suggest that the significance of twinning in β-HMX cannot be determined with traditional loading configurations and diagnostics.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Coupled cluster and dislocation dynamics modeling of microstructure evolution in irradiated materials

We develop here a coupled cluster and dislocation dynamics framework to study the microstructure evolution of irradiated materials. The framework not only accounts for the three dimensional diffusion of radiation-generated clusters, but also their interaction with dislocation networks and the resultant climb motion of discrete dislocations within finite crystals. The framework is solved with a superposition solution scheme, and is applied to investigate the evolution of the irradiation-induced dislocation loops in zirconium (Zr), considering the effects of various bias factors including the diffusion anisotropy difference (DAD) of interstitials and interstitial clusters, the dislocation bias of defects to discrete dislocation segments, and the production bias of defects from the radiation cascade. We find that the DAD is the most critical factor influencing the kinetics of the loop evolution in Zr, while the recombination/interaction of mobile defects can induce a strong spatial dependence of the loop evolution together with the DAD. Here, the method is also adopted to study the evolution of interstitial $\langle$a$\rangle$ and vacancy $\langle$c$\rangle$ dislocation loop ensembles consistent with the microstructure observed during irradiation-induced growth of Zr. Our findings not only reveal the spatial dependence of the size and ellipticity of the dislocation loops, but also suggest a limit on the anisotropy factor of interstitials to reproduce the co-growth of $\langle$a$\rangle$ and $\langle$c$\rangle$ loops in zirconium, in good agreement with experimental observations and other simulation results.

Bias factors↗