Search for: All records

The vorticity-streamfunction formulation for incompressible inviscid fluids is the basis for many fluid simulation methods in computer graphics, including vortex methods, streamfunction solvers, spectral methods, and Monte Carlo methods. We point out that current setups in the vorticity-streamfunction formulation are insufficient at simulating fluids on general non-simply-connected domains. This issue is critical in practice, as obstacles, periodic boundaries, and nonzero genus can all make the fluid domain multiply connected. These scenarios introduce nontrivial cohomology components to the flow in the form of harmonic fields. The dynamics of these harmonic fields have been previously overlooked. In this paper, we derive the missing equations of motion for the fluid cohomology components. We elucidate the physical laws associated with the new equations, and show their importance in reproducing physically correct behaviors of fluid flows on domains with general topology. 

Alloys of tungsten tetraboride (WB4) with the addition of C and Si were prepared by arc-melting of the constituent elements. The phase purity was established by powder X-ray diffraction (PXRD) and surface morphology by scanning electron microscopy (SEM) analysis. Vickers hardness measurements showed hardness enhancement for alloys with a nominal composition of (W0.98Si0.02):11.6B and (W0.95C0.05):11.6B of 52.2 ± 3.0 and 50.5 ± 2.5 GPa, respectively, compared to 41.2 ± 1.4 GPa for pure WB4. (W0.92Zr0.08):11.6B was determined in previous work to have a hardness of 55.9 ± 2.8 GPa. Bulk moduli were calculated following analysis of high-pressure radial diffraction data and were determined to be 329 ± 4 (K0′ = 2) and 390 ± 9 (K0′ = 0.6) GPa for 8 atom % Zr and 5 atom % C-doping, respectively, compared to 326–339 GPa for pure WB4. Computational analysis was used to determine the dopant positions in the crystal structure, and it was found that Zr primarily substitutes W in the 2c position, Si substitutes for the entire B3 trimers, and C inserts in the Bhex-layer. The hardness enhancement in the case of Zr-doping is attributed primarily to extrinsic hardness effects (nanograin morphology), in the case of C─to intrinsic effects (interlayer bond strengthening), and in the intermediate case of Si─to both intrinsic and extrinsic effects (bond strengthening and fine surface morphology). 

We propose Coadjoint Orbit FLIP (CO-FLIP), a high order accurate, structure preserving fluid simulation method in the hybrid Eulerian-Lagrangian framework. We start with a Hamiltonian formulation of the incompressible Euler Equations, and then, using a local, explicit, and high order divergence free interpolation, construct a modified Hamiltonian system that governs our discrete Euler flow. The resulting discretization, when paired with a geometric time integration scheme, is energy and circulation preserving (formally the flow evolves on a coadjoint orbit) and is similar to the Fluid Implicit Particle (FLIP) method. CO-FLIP enjoys multiple additional properties including that the pressure projection is exact in the weak sense, and the particle-to-grid transfer is an exact inverse of the grid-to-particle interpolation. The method is demonstrated numerically with outstanding stability, energy, and Casimir preservation. We show that the method produces benchmarks and turbulent visual effects even at low grid resolutions. 

Abstract Estuarine total alkalinity (TA), which buffers against acidification, is temporally and spatially variable and regulated by complex, interacting hydrologic and biogeochemical processes. During periods of net evaporation (drought), the Mission-Aransas Estuary (MAE) of the northwestern Gulf of Mexico experienced TA losses beyond what can be attributed to calcification. The contribution of sedimentary oxidation of reduced sulfur to the TA loss was examined in this study. Water column samples were collected from five stations within MAE and analyzed for salinity, TA, and calcium ion concentrations. Sediment samples from four of these monitoring stations and one additional station within MAE were collected and incubated between 2018 and 2021. TA, calcium, magnesium, and sulfate ion concentrations were analyzed for these incubations. Production of sulfate along with TA consumption (or production) beyond what can be attributed to calcification (or carbonate dissolution) was observed. These results suggest that oxidation of reduced sulfur consumed TA in MAE during droughts. We estimate that the upper limit of TA consumption due to reduced sulfur oxidation can be as much as 4.60 × 10⁸ mol day⁻¹in MAE. This biogeochemical TA sink may be present in other similar subtropical, freshwater-starved estuaries around the world. 

We report a low-temperature colloidal synthesis of WSe₂nanocrystals from tungsten hexacarbonyl and diphenyl diselenide in trioctylphosphine oxide (TOPO). We identify TOPO-substituted intermediates, W(CO)₅TOPO andcis-W(CO)₄(TOPO)₂by infrared spectroscopy. To confirm these assignments, we synthesize aryl analogues of phosphine-oxide-substituted intermediates, W(CO)₅TPPO (synthesized previously, TPPO = triphenylphosphine oxide) andcis-W(CO)₄(TPPO)₂andfac-W(CO)₃(TPPO)₃(new structures reported herein). Ligation of the tungsten carbonyl by either the alkyl or aryl phosphine oxides results in facile labilization of the remaining CO, enabling low-temperature decomposition to nucleate WSe₂nanocrystals. The reactivity in phosphine oxides is contrasted with syntheses containing phosphine ligands, where substitution results in decreased CO labilization and higher temperatures are required to induce nanocrystal nucleation. 

Abstract The marine carbonate system is influenced by anthropogenic CO₂uptake, biogeochemical processes, and physical changes that involve freshwater input and removal. Two frequently used parameters to quantify seawater carbonate system are total alkalinity (TA) and total dissolved inorganic carbon (DIC). To account for the physical changes, both TA and DIC are usually normalized to a reference salinity (i.e., nTA and nDIC), and then the relationship between nTA and nDIC is used to identify major biogeochemical processes that regulate the carbonate system, based on process‐specific reaction stoichiometry. However, the theoretical basis of this interpretation has not been holistically examined. In this study, we validated this method under  idealized conditions and discussed the associated assumptions and limitations. Furthermore, we applied this method to interpret field TA and DIC data from a lagoonal estuary in the northwestern Gulf of Mexico. Our results demonstrated that evaluating field data that encompass multiple stations and time periods could be problematic. In addition, various combinations of biogeochemical processes can lead to the same nTA–nDIC relationship, even though the relative importance of each individual process may vary significantly. Therefore, the stoichiometric relationship relying solely on TA and DIC data is not a definitive approach for uncovering dominant biogeochemical processes. Instead, measurements of process‐specific parameters are necessary.