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At least 55 records · Page 3

Microscopic signatures of topology in twisted MoTe 2

In moiré materials with flat electronic bands and suitable quantum geometry, strong correlations can give rise to various topological states of matter. The non-trivial band topology of twisted MoTe 2 , which is responsible for its fractional quantum anomalous Hall states, is predicted to arise from a skyrmion lattice texture in the layer pseudospin of the electronic wavefunctions. Tracing the layer polarization of wavefunctions within the moiré unit cell can, thus, offer insights into the band topology. Here we measure the out-of-plane component of the layer-pseudospin skyrmion textures of twisted MoTe 2 using scanning tunnelling microscopy and spectroscopy. We do this by simultaneously visualizing the moiré lattice structure and the spatial localization of its electronic states. We find that the wavefunctions associated with the topological flat bands exhibit a spatially dependent layer polarization within the moiré unit cell, in agreement with our theoretical modelling. Furthermore, our work enables future local probe studies of the intertwined correlated and topological states arising in gate-tunable devices.

Electronic properties and materials↗

Curvature-mediated spin textures in magnetic multi-layered nanotubes

The scientific and technological exploration of artificially designed three-dimensional magnetic nanostructures opens the path to exciting novel physical phenomena, originating from the increased complexity in spin textures, topology, and frustration in three dimensions. Theory predicts that the equilibrium magnetic ground state of two-dimensional systems which reflects the competition between symmetric (Heisenberg) and antisymmetric (Dzyaloshinskii-Moriya interaction (DMI)) exchange interaction is significantly modified on curved surfaces when the radius of local curvature becomes comparable to fundamental magnetic length scales. Here, we present an experimental study of the spin texture in an 8 nm thin magnetic multilayer with growth-induced in-plane anisotropy and DMI deposited onto the curved surface of a 1.8 {\mu}m long non-magnetic carbon nanowire with a 67 nm radius. Using magnetic soft x-ray tomography the three-dimensional spin configuration in this nanotube was retrieved with about 30nm spatial resolution. The transition between two vortex configurations on the two ends of the nanotube with opposite circulation occurs through a domain wall that is aligned at an inclined angle relative to the wire axis. Three-dimensional micromagnetic simulations support the experimental observations and represent a visualization of the curvature-mediated DMI. They also allow a quantitative estimate of the DMI value for the magnetic multilayered nanotube.

Josten, Elisabeth↗

Spin Textures at Conformal Surfaces and Interfaces: CRADA Final Report

The scientific and technological exploration of artificially designed three-dimensional magnetic nanostructures opens the path to exciting novel physical phenomena, originating from the increased complexity in spin textures, topology, and frustration in three dimensions. Theory predicts that the equilibrium magnetic ground state of two-dimensional systems which reflects the competition between symmetric (Heisenberg) and antisymmetric (Dzyaloshinskii-Moriya interaction (DMI)) exchange interaction is significantly modified on curved surfaces when the radius of local curvature becomes comparable to fundamental magnetic length scales. In this CRADA we performed collaboratively an experimental study of the spin texture in an 8 nm thin magnetic multilayer with growth-induced in-plane anisotropy and DMI deposited onto the curved surface of a 1.8µm long non-magnetic carbon nanowire with a 67 nm radius. The sample was fabricated in Juelich and with collaborators at BESSY in Berlin. Using magnetic soft x-ray tomography at the ALBA synchrotron in Spain, the three-dimensional spin configuration in this nanotube was retrieved with about 30nm spatial resolution. The transition between two vortex configurations on the two ends of the nanotube with opposite circulation occurs through a domain wall that is aligned at an inclined angle relative to the wire axis. Three-dimensional micromagnetic simulations support the experimental observations and represent a visualization of the curvature-mediated DMI. They also allow a quantitative estimate of the DMI value for the magnetic multilayered nanotube.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Part-scale microstructure prediction for laser powder bed fusion Ti-6Al-4V using a hybrid mechanistic and machine learning model

Laser powder bed fusion (LPBF) Ti-6Al-4V is widely studied for use in structural applications in aerospace and medical industries, but mechanical anisotropy and microstructural inhomogeneity prohibits its wider adoption. Although successful microstructure prediction models have been developed, a remaining challenge is their limited integration across length/time scales and validation by experimental studies. Here, this work proposes a physics-augmented machine learning surrogate model to unite predictions of LPBF temperature, β phase morphology and texture, and α/α’ formation into a single framework that is calibrated and validated with experiments. First, a phase field (PF) model of the martensitic β→α’ transformation is developed and calibrated using data from in-situ synchrotron cyclic heating/cooling studies quantifying the variation of α phase fraction with time. In parallel, an established finite difference-Monte Carlo (FDMC) model predicts the part-scale temperature profile and β grain formation during solidification. A dataset is developed using LPBF cyclic temperature descriptors from the FDMC model as inputs and corresponding α/α’ phase fraction and width from the PF model as outputs. Five machine learning (ML) regression models are tested and optimized, having mean absolute error in testing ≤ 4 %, and the k-nearest neighbors (KNN) model is selected as the best performing. The KNN model is called at the nodal level during post-processing of the FDMC model to replace and downscale the response of the PF model. The combined agility and accuracy of the hybrid FDMC-ML model enables part-scale microstructure predictions that can be further used for property predictions to accelerate AM process optimization.

36 MATERIALS SCIENCE↗

The Illumination of Thunderclouds by Lightning: 3. Retrieving Optical Source Altitude

Abstract Optical space‐based lightning sensors such as the Geostationary Lightning Mapper (GLM) detect and geolocate lightning by recording rapid changes in cloud top illumination. While lightning locations can be determined to within a pixel on the GLM imaging array, these instruments are not individually able to natively report lightning altitude. It has previously been shown that thunderclouds are illuminated differently based on the altitude of the optical source. In this study, we examine how altitude information can be extracted from the spatial distributions of GLM energy recorded from each optical pulse. We match GLM “groups” with Lightning Mapping Array (LMA) source data that accurately report the 3‐D positions of coincident Radio‐Frequency (RF) emitters. We then use machine learning methods to predict the mean LMA source altitudes matched to GLM groups using metrics from the optical data that describe the amplitude, breadth, and texture of the group spatial energy distribution. The resulting model can predict the LMA mean source altitude from GLM group data with a median absolute error of <1.5 km, which is sufficient to determine the location of the charge layer where the optical energy originated. This model is able to capture changes to the source altitude distribution in response to convective processes in the thunderstorm, and the GLM predictions can reveal the vertical structure of individual flashes ‐ enabling 3‐D flash geolocation with GLM for the first time. Future work will account for differences in thunderstorm charge/precipitation structures and viewing angle across the GLM Field of View.

54 ENVIRONMENTAL SCIENCES↗

Dynamical Generation of Higher-Order Spin-Orbit Coupling, Topology, and Persistent Spin Texture in Light-Irradiated Altermagnets

Altermagnets have been identified as the third category of magnetic materials, exhibiting momentum-dependent spin splitting characterized by even powers of momentum. Here, in this Letter, we show that when subjected to elliptically polarized light, these materials serve as an exemplary framework for the dynamic generation of topological bands featuring higher-order spin-orbit coupling (SOC). Notably, while the generated Zeeman field remains invariant to the particular altermagnetic ordering, the induced higher-order SOCs are related to the magnitude and symmetry of the altermagnetic order. Specifically, we show that an altermagnet exhibiting 𝐤 2⁢𝑛 -spin splitting can generate odd-in-𝐤 spin-orbit couplings up to 𝐤 2⁢𝑛−1 . In the limit of circularly polarized light, the only correction is 𝑘 2⁢𝑛−1 , with all lower-order contributions being nullified. Interestingly, light-induced SOCs significantly impact the low-energy band topology, where their Chern numbers change by Δ⁢𝐶 = ±1, 2, 3 for 𝑑, 𝑔, 𝑖-wave altermagnets. Finally, we find a critical field in which a persistent spin texture is realized, a highly desirable state with predicted infinite spin lifetime. Our Letter showcases light as a powerful, controllable tool for engineering complex and exciting phenomena in altermagnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Predicting measures of soil health using the microbiome and supervised machine learning

Soil health encompasses a range of biological, chemical, and physical soil properties that sustain the commercial and ecological value of agroecosystems. Monitoring soil health requires a comprehensive set of diagnostics that can be cost-prohibitive for routine analyses. The soil microbiome provides a rich source of information about soil properties, which can be assayed in a high-throughput, cost-effective way. We evaluated the accuracy of random forest (RF) and support vector machine (SVM) regression and classification models in predicting 12 measures of soil health, tillage status, and soil texture from 16S rRNA gene amplicon data with an operationally relevant sample set. We validated the efficacy of the best performing models against independent datasets and also tested best practices for processing microbiome data for use in machine learning. Soil health metrics could be predicted from microbiome data with the best models achieving a Kappa value of ~0.65, for categorical assessments, and a R2 value of ~0.8, for numerical scores. Biological health ratings were better predicted than chemical or physical ratings. Validation with independent datasets revealed that models had general predictive value for soil properties, including yield. The ecological profiles of several taxa important for model accuracy matched the observed relationships with soil health, including Pyrinomonadaceae, Nitrososphaeraceae, and Candidatus Udeaobacter. Models trained at the highest taxonomic resolution proved most accurate, with losses in accuracy resulting from rarefying, sparsity filtering, and aggregating at higher taxonomic ranks. Furthermore, our study provides the groundwork for developing scalable technology to use microbiome-based diagnostics for the assessment of soil health.

16S rRNA gene↗

Androgynous { 10 1 ¯ 2 } twin in zinc

Under ambient conditions, Zn is a hexagonal metal with a large c / a ratio of 1.856. Plastic deformation is predominantly accommodated by basal 〈 a 〉 slip and compression twins on the { 10 1 ¯ 2 } planes. Increasing hydrostatic pressure drastically reduces the c / a ratio of Zn and, when a critical threshold of c / a = 3 at about 10 GPa is crossed, the { 10 1 ¯ 2 } twins are predicted to change from compressive to tensile in nature. What happens at the transition point, when c / a = 3 , remains unknown. Here, we strain-cycle a textured polycrystalline sample of pure Zn at uniform hydrostatic pressures ranging between 2 and 17 GPa, over which the c / a ratio crosses the c / a = 3 compressive-tensile transition for { 10 1 ¯ 2 } twins. During deformation, the state of the sample is monitored through x-ray diffraction to extract texture and internal strain evolution. By comparing the experimental results with the predictions of an elastoviscoplastic polycrystal simulation, we confirm the androgynous nature of { 10 1 ¯ 2 } twin response at low and high pressures. When c / a = 3 , polycrystalline Zn does not display any evidence of twinning and its plastic behavior is controlled by mostly basal and pyramidal 〈 c + a 〉 slip activity, with a very small contribution of prismatic 〈 a 〉 slip. Evidence for the activity of other { 10 1 ¯ n } twinning modes, which have been suggested for Zn under high pressure, are not observed. Published by the American Physical Society 2024

Merkel, Sébastien (ORCID:000000032767581X)↗

Elucidating texture and grain morphology contributions to the micromechanical response of additively manufactured Inconel 625

Microstructural variation of additively manufactured (AM) metal components in comparison to wrought counterparts makes certification for critical applications a challenge. Microscale simulations leveraging modern computational tools may be used to supplement testing of AM microstructures, thus accelerating certification by reducing the number of experiments needed. However, as micromechanical response is closely tied to critical properties like fatigue-life and fracture, utilization of these simulations with macroscale experimental data alone is insufficient. One means to attain microscale experimental data is in situ diffraction data collected from synchrotron X-ray sources. In this work, such data were collected during in situ compression of AM Inconel 625 superalloy. Interpretation of experimental results was assisted by massive (8M element) complementary micromechanical simulations performed on sets of virtual microstructures generated using cellular automata. Together, micromechanical data from diffraction experiments and simulations were used to probe the effects of textured “track” microstructures generated during laser powder bed fusion and directional strength-to-stiffness on micromechanical response. Though fiber-averaged directional strength-to-stiffness ratios were expected to dominate given the high elastic anisotropy of the material, the combination of small variations in texture and specific grain configurations unique to AM microstructures lead to significant variability in micromechanical response after yield. The findings emphasize the importance of high-fidelity microstructural representation that captures key texture components and AM-specific morphology for property prediction of AM metals.

36 MATERIALS SCIENCE↗

Measuring and modeling soil moisture and runoff at solar farms using a disconnected impervious surface approach

Abstract Ground‐mounted photovoltaic sites are often treated as impervious surfaces in stormwater permits. This ignores the pervious soils beneath and between solar arrays and leads to an overestimation of runoff. Our objective was to improve solar farm stormwater hydrology models by explicitly considering the disconnected impervious nature of solar design and site characteristics. Experimental sites established on utility scale solar farms in Colorado, Georgia, Minnesota, New York, and Oregon had perennial vegetative plantings with mean precipitation ranging from 40.6 to 124.5 cm, and soil texture ranging from loamy sand to clay. Soil moisture measurements were collected beneath arrays, under drip edges, and in the vegetated area between arrays at each site. Hydrus‐3D models for soil moisture and stormwater hydrology were developed that accounted for precipitation falling on solar panels, drip edge redistribution of rainfall, infiltration, and runoff in the pervious areas between solar arrays and beneath panels. Drip edge runoff averaged 3‐ to 10‐times incident precipitation at the New York and Minnesota sites, respectively. Root mean square error values between measured sub‐hourly soil moisture and predicted moisture for large measured single storm events averaged 0.029 across all five sites. Predicted runoff depths were strongly affected by precipitation depth, soil texture, soil profile depth, and soil bulk density. Runoff depths across the five experimental sites averaged 13%, 25%, and 45% of the 2‐, 10‐, and 100‐year design storm depths, clearly showing that these solar farms do not behave like impervious surfaces, but rather as disconnected impervious surfaces with substantial infiltration of runoff in the vegetated areas between and beneath solar arrays.

Agriculture↗

Relating flow resistance to equivalent roughness

Describing flow resistance using the physical properties of an underlying surface is a recalcitrant problem in overland flow models. If discharge measurements are available, an equivalent roughness (e.g., Manning’s n) can be calibrated to represent the effects of surface properties within the domain with a single numerical value. Alternatively, the flow resistance can be estimated from discharge and velocity measured at a point, typically a runoff plot outlet. However, such experimental estimates are often inconsistent with the equivalent roughness determined from calibration to discharge, even if both derive from the same dataset. For example, if Manning’s equation is used to parameterize flow resistance, the Manning’s n obtained by calibrating a model to discharge differs from the value of n calculated from measured flow and velocity at the hillslope outlet. Here, this discrepancy is resolved by deriving a correction factor relating experimentally-determined flow resistance to the equivalent roughness. The derived correction factor is tested for four commonly-used resistance formulations using 129 rainfall simulator experiments. The correction factor is necessary to reproduce measured velocities, and yields minor improvements in discharge prediction. Plain Language Summary: Accurate runoff prediction is needed for land and water management in dryland regions, where sporadic and limited rainfall necessitate efficient water use and drought mitigation strategies. The skill of runoff models is known to be hindered by out ability to estimate flow resistance, which is the quantity that describes how energy is lost from flowing water to the underlying surface. Typically, models represent flow resistance with an equivalent roughness, e.g., Manning’s n, that is adjusted until the model can reproduce available discharge observations at watershed scale. However, the flow resistance measured in plot-scale experiments (1–10 m) often exceeds equivalent roughness coefficients by a factor of 10. This means that the direct use of plot-scale experimental data to parameterize runoff models could cause errors in discharge and runoff velocity predictions. Here, we resolve these differences by deriving an analytic correction factor that relates flow resistance to the equivalent roughness required for models to reproduce experimental velocity and discharge data. This correction factor is tested using rainfall simulator data from 129 experiments performed in the US Southwest covering a wide range of precipitation intensities, soil textures and vegetation types. Use of the correction factor substantially improves model prediction of flow velocity, which is needed for reproducing the timing of flood events and the estimation of erosion.

54 ENVIRONMENTAL SCIENCES↗

Radial Spin Texture of the Weyl Fermions in Chiral Tellurium

Trigonal tellurium, a small-gap semiconductor with pronounced magneto-electric and magneto-optical responses, is among the simplest realizations of a chiral crystal. We have studied by spin- and angle-resolved photoelectron spectroscopy its unconventional electronic structure and unique spin texture. We identify Kramers-Weyl, composite, and accordionlike Weyl fermions, so far only predicted by theory, and show that the spin polarization is parallel to the wave vector along the lines in k space connecting high-symmetry points. Our results clarify the symmetries that enforce such spin texture in a chiral crystal, thus bringing new insight in the formation of a spin vectorial field more complex than the previously proposed hedgehog configuration. Our findings thus pave the way to a classification scheme for these exotic spin textures and their search in chiral crystals.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Thermodynamics of Liquid Immiscibility in Iron-Silicate Melt Systems: A Study of Nuclear Fallout Glass

In a ground-interacting nuclear explosion, elements derived from environmental and anthropogenic material, such as iron, silicon, and aluminum, can be incorporated into the fireball. When significant amounts of metals are entrained, the resulting melt may display immiscible textures. The composition of these textures is a record of the temperature of formation and cooling rates (or thermodynamic stability) of the melts and can provide unique constraints on the early cooling conditions of these events. Here, a thermodynamic approach using calculated phase diagrams, the CALPHAD method, is used to predict temperature and composition ranges where stable liquid immiscibility might result in the textures observed in nuclear fallout glass. Sensitivity of the immiscibility to the presence of relative Al, Ca, and Mg content is also explored and compared to fallout samples, and partition coefficients are introduced to understand the preferred distribution of components into each liquid phase.

36 MATERIALS SCIENCE↗

Virtual texture analysis to understand microstructure effects on deformation twinning and detwinning behavior in BCC metals

Understanding and predicting deformation twinning contributions to plastic deformation in BCC metals has been a long-standing challenge due to the interplay with dislocation slip and non-Schmid effects that render an asymmetry under tension and compression. This paper uses molecular dynamics simulations to understand the effect of unloading and grain orientation on deformation twinning in a nanocrystalline Fe (nc-Fe) system as a model BCC metal. The nc-Fe system is loaded under uniaxial stress tension and compression to understand the effect of grain orientation (Schmid effects) on deformation twinning behavior and the tension/compression asymmetry (non-Schmid effects). A new virtual texture analysis “VirTex” tool is used to understand the role of grain orientation on the nucleation of twins and their contributions to the observed stress–strain response. For certain grain orientations, the twinnability is observed to be different in tension and compression. In addition, the flow stress accommodation from twins in certain grains is observed to be different in tension and compression and different from that for the grains. Subsequent unloading leads to detwinning in the deformed microstructures, where the extent of detwinning depends on the strain from which the system is unloaded and on the morphology of the twin. Lastly, the simulations are carried out to analyze the role of the Schmid factor on the twinnability and asymmetry in tension and compression.

Kannan, Aadhithyan [University of Connecticut, Sto↗

Spin dynamics of the centrosymmetric skyrmion material GdRu 2 Si 2

Magnetic skyrmion crystals are traditionally associated with non-centrosymmetric crystal structures; however, it has been demonstrated that skyrmion crystals can be stabilized by competing interactions in centrosymmetric crystals. To understand and optimize the physical responses associated with topologically nontrivial skyrmion textures, it is important to quantify their magnetic interactions by comparing theoretical predictions with spectroscopy data. Here, we present neutron diffraction and spectroscopy data on the centrosymmetric skyrmion material GdRu 2 Si 2 and show that the key spectroscopic features can be explained by magnetic interactions calculated using density functional theory. We further show that the recently proposed 2-q “topological spin stripe” structure yields better agreement with our data than a 1-q helical structure and identify how the magnetic structure evolves with temperature.

36 MATERIALS SCIENCE↗

The impact of anisotropic thermal expansion on the isothermal annealing of polycrystalline α -uranium

Although grain growth impacts microstructural evolution in a wide variety of materials systems, the effect of anisotropic thermal expansion on grain boundary mobility and texture evolution has not been widely studied. Anisotropic thermal expansion occurs in multiple non-cubic metals, and the thermomechanical processing behavior of these materials can be better understood with further study into the impact of thermal expansion on grain boundary mobility and texture evolution. In this work, we develop a mesoscale phase field model of grain growth that includes the effect of anisotropic thermal expansion, which is applied to study polycrystalline α-uranium, a highly anisotropic metal. Three-dimensional simulations on polycrystalline a-uranium with and without thermal expansion eigenstrains are performed to study the grain boundary mobility and texture evolution as a function of temperature. A strain-free temperature of 933 K is selected, and the system is studied at within the range of 873 – 933 K at intervals of ten degrees, resulting in increasing thermal eigenstrain with decreasing temperature. We also estimate a grain boundary mobility prefactor and activation energy based on existing experimental data of isothermal annealing of α-uranium. The grain boundary mobility is found to display significant deviation from Arrhenius behavior with the inclusion of thermal expansion eigenstrain as the amount of thermal eigenstrain (and thus elastic strain energy within the system) increases. This result explains an experimentally observed grain boundary mobility deviation from Arrhenius behavior. Furthermore, the texture evolution is affected, such that the grain orientations become less random with increasing thermal eigenstrain, which could explain experimentally observed texture behavior. These results indicate that the effect of thermal expansion should be considered when predicting the thermomechanical processing behavior of α-uranium and other materials with anisotropic thermal expansion.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Resilience in soil bacterial communities of the boreal forest from one to five years after wildfire across a severity gradient

Wildfires can represent a major disturbance to ecosystems, including soil microbial communities belowground. Furthermore, fire regimes are changing in many parts of the world, altering and often increasing fire severity, frequency, and size. The boreal forest and taiga plains ecoregions of northern Canada are characterized by naturally-occurring stand-replacing wildfires on a 40–350 year basis. We previously studied the effects of wildfire on soil microbial communities one year post-fire across 40 sites, spanning a range of burn severity. Here, we return to the same sites five years post-fire to test a series of hypotheses about the effects of fire on bacterial community composition. We ask questions on two themes: which factors control bacterial community composition during post-fire recovery, and how does the importance of different fire-responsive traits change during post-fire recovery? We find the following: Five years post-fire, vegetation community, moisture regime, pH, total carbon, texture, and burned/unburned all remained significant predictors of bacterial community composition with similar predictive value (R 2 ). Bacterial communities became more similar to unburned sites five years post-fire, across the range of severity, suggesting resilience, while general structure of co-occurrence networks remained similar one and five years post-fire. Fast growth potential, as estimated using predicted 16S rRNA copy numbers, was no longer significantly correlated with burn severity five years post-fire, indicating the importance of this trait for structuring bacterial community composition may be limited to relatively short timescales. Many taxa that were enriched in burned sites one year post-fire remained enriched five years post-fire, although the degree to which they were enriched generally decreased. Specific taxa of interest from the genera Massilia, Blastococcus, and Arthrobacter all remained significantly enriched, suggesting that they may have traits that allow them to continue to flourish in the post-fire environment, such as tolerance to increased pH or ability to degrade pyrogenic organic matter. This hypothesis-based work expands our understanding of the post-fire recovery of soil bacterial communities and raises new hypotheses to test in future studies.

59 BASIC BIOLOGICAL SCIENCES↗

Control of Cement Timing, Mineralogy, and Texture on Hydro-chemo-mechanical Coupling from CO2 Injection into Sandstone: A Synthesis

Carbon capture, utilization, and storage (CCUS) has been widely applied to enhance oil recovery (CO2-EOR). A thorough investigation of the impact of injecting CO2 into a heterogeneous reservoir is critical to understanding the overall reservoir robustness and storage performance. We conducted fifteen flow-through tests on Morrow B sandstone that allowed for chemical reactions between a CO2-rich brackish solution and the sandstones, and four creep/flow-through tests that simultaneously allowed for chemical reactions and stress monitoring. From fluid chemistry and X-ray computed tomography, we found that the dissolution of disseminated cements and the precipitation of iron-rich clays did not significantly affect the permeability and geomechanical properties. Minor changes in mechanical properties from Brazilian and creep tests indicated that the matrix structure was well-supported by early diagenetic quartz overgrowth cement and the reservoir’s compaction history at deep burial depths. However, one sample experienced a dissolution of poikilotopic calcite, leading to a permeability increase and significant tensile strength degradation due to pore opening, which overcame the effect of the early diagenetic cements. We concluded that the Morrow B sandstone reservoir is robust for CO2 injection. Most importantly, cement timing, the abundance and texture of reactive minerals, and the reservoir’s burial history are critical in predicting reservoir robustness and storage capacity for CO2 injection.

Wu, Zhidi (ORCID:0000000338869492)↗