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In this review, we survey the latest approaches and techniques developed to overcome the spectral bias towards low frequency of deep neural network learning methods in learning multiple frequency solutions of partial differential equations. Open problems and future research directions are also discussed. 

Large volumes of fluid flow through aged oceanic crust. Given the scale of this water flux, the exchange of organic and inorganic carbon that it mediates between the crust and deep ocean can be significant. However, off-axis carbon fluxes in older oceanic crust are still poorly constrained because access to low-temperature fluids from this environment is limited. At North Pond, a sedimented depression located on 8-million-year-old crust on the flank of the Mid-Atlantic Ridge, circulating crustal fluids are accessible through drilled borehole observatories. Here, fluids are cool (≤ 20°C), oxygenated and bear strong geochemical similarities to bottom seawater. In this study, we report concentrations and isotopic composition of dissolved organic and inorganic carbon from crustal fluids that were sampled six years after the installation of borehole observatories, which better represent the fluid geochemistry prior to drilling and perturbation. Radiocarbon-based signatures within carbon reservoirs support divergent shallow and deep fluid pathways within the crust. We also report a net loss of both dissolved inorganic carbon (DIC) and dissolved organic carbon (DOC) from the fluid during isolation in the crust. The removal of DOC is isotopically selective and consistent with microbe-mediated DOC oxidation. The loss of DIC is consistent with carbonate precipitation, although geochemical signatures of DIC addition to the fluids from DOC oxidation and basalt weathering are also evident. Extrapolated to global fluxes, systems like North Pond could be responsible for a net loss of ~10^11 mol C/yr of DIC and ~10^11 mol C/yr of DOC during the circulation of fluids through oceanic crust at low temperatures. 

The ocean has absorbed anthropogenic carbon dioxide (C_anthro) from the atmosphere and played an important role in mitigating global warming. However, how much C_anthrois accumulated in coastal oceans and where it comes from have rarely been addressed with observational data. Here, we use a high-quality carbonate dataset (1996–2018) in the U.S. East Coast to address these questions. Our work shows that the offshore slope waters have the highest C_anthroaccumulation changes (ΔC_anthro) consistent with water mass age and properties. From offshore to nearshore, ΔC_anthrodecreases with salinity to near zero in the subsurface, indicating no net increase in the export of C_anthrofrom estuaries and wetlands. Excesses over the conservative mixing baseline also reveal an uptake of C_anthrofrom the atmosphere within the shelf. Our analysis suggests that the continental shelf exports most of its absorbed C_anthrofrom the atmosphere to the open ocean and acts as an essential pathway for global ocean C_anthrostorage and acidification. 

Abstract Dissolved inorganic carbon (DIC) and its stable carbon isotope (δ¹³C‐DIC) are valuable parameters for studying the aquatic carbon cycle and quantifying ocean anthropogenic carbon accumulation rates. However, the potential of this coupled pair is underexploited as only 15% or less of cruise samples have been analyzed forδ¹³C‐DIC because the traditional isotope analysis is labor‐intensive and restricted to onshore laboratories. Here, we improved the analytical precision and reported the protocol of an automated, efficient, and high‐precision method for ship‐based DIC andδ¹³C‐DIC analysis based on cavity ring‐down spectroscopy (CRDS). We also introduced a set of stable in‐house standards to ensure accurate and consistent DIC andδ¹³C‐DIC measurements, especially on prolonged cruises. With this method, we analyzed over 1600 discrete seawater samples over a 40‐d cruise along the North American eastern ocean margin in summer 2022, representing the first effort to collect a large dataset ofδ¹³C‐DIC onboard of any oceanographic expedition. We evaluated the method's uncertainty, which was 1.2 μmol kg⁻¹for the DIC concentration and 0.03‰ for theδ¹³C‐DIC value (1σ). An interlaboratory comparison of onboard DIC concentration analysis revealed an average offset of 2.0 ± 3.8 μmol kg⁻¹between CRDS and the coulometry‐based results. The cross‐validation ofδ¹³C‐DIC in the deep‐ocean data exhibited a mean difference of only −0.03‰ ± 0.07‰, emphasizing the consistency with historical data. Potential applications in aquatic biogeochemistry are discussed. 

The yield surface of a material is a criterion at which macroscopic plastic deformation begins. For crystalline solids, plastic deformation occurs through the motion of dislocations, which can be captured by discrete dislocation dynamics (DDD) simulations. In this paper, we predict the yield surfaces and strain-hardening behaviors using DDD simulations and a geometric manifold learning approach. The yield surfaces in the three-dimensional space of plane stress are constructed for single-crystal copper subjected to uniaxial loading along the [100] and [110] directions, respectively. With increasing plastic deformation under loading, the yield surface expands nearly uniformly in all directions, corresponding to isotropic hardening. In contrast, under [110] loading, latent hardening is observed, where the yield surface remains nearly unchanged in the orientations in the vicinity of the loading direction itself but expands in other directions, resulting in an asymmetric shape. This difference in hardening behaviors is attributed to the different dislocation multiplication behaviors on various slip systems under the two loading conditions. 

The increasing oceanic absorption of atmospheric CO₂decreases the ocean's carbonate and pH levels, harming marine life. This review covers carbonate electrochemical sensors based on ionophores for the advancement of ocean acidification research. 

Abstract The stable isotope ratio of dissolved inorganic carbon (δ¹³C‐DIC) is a valuable tracer for investigating carbon cycling in aquatic environments. However, its potential remains underutilized due to limited data availability. Fewer than 15% of cruise samples are analyzed forδ¹³C‐DIC, as isotope analysis using isotope ratio mass spectrometry is labor‐intensive and restricted to onshore laboratories. We present over 3500δ¹³C‐DIC measurements from the 2023 Global Ocean Ship‐based Hydrographic Investigations Program A16N cruise in the North Atlantic. Notably, three‐quarters of these measurements were conducted onboard using a CO₂extraction device coupled with cavity ring‐down spectroscopy, a more efficient and cost‐effective method. This extensive dataset providesδ¹³C‐DIC values with spatial resolution comparable to other ocean carbonate chemistry and biogeochemical parameters. This dataset supports improved quantification of anthropogenic CO₂uptake and storage, and may facilitate the development of algorithms to estimateδ¹³C‐DIC in under sampled regions.