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At least 703 records · Page 39

Computational and Experimental Investigation of Chiral and Achiral Two‐Dimensional Organic Lead Bromide Perovskites: Octahedral Distortions and Electronic and Optical Properties

A computational investigation is presented, in conjunction with synthesis and experimental characterization, into the structural, electronic, and optical properties of layered two-dimensional organic lead bromide perovskites. Materials based on the chiral (R/S)-4-fluoro-α-methylbenzylammonium (R/S-FMBA), which have been shown to lead to bright room-temperature circularly polarized luminescence, are contrasted with the similar achiral 4-fluorobenzylammonium (FBA). Using density functional theory (DFT) with van der Waals (vdW) corrections, relaxed structures (compared with X-ray diffraction, XRD) and optical absorption spectra (compared with experiments) are studied, as well as band structure and orbital character of transitions. A Python code is developed and provided to calculate octahedral distortions and compare DFT and XRD results, finding that vdW corrections are important for accuracy and that DFT overestimates octahedral tilt angles. (FMBA) 2 PbBr 4 shows among the largest tilt angle differences (often termed Δ β ) reported, 14°–15°, indicating strong inversion symmetry-breaking, which enables its chiral emission. A large resulting Dresselhaus spin-splitting effect is found. The lowest-energy optical transitions involve the perovskite only and are polarized within the layer. This work furthers understanding of structure-property relations with applications to optoelectronics and spintronics.

UV/vis spectroscopy↗

Semiconductor-Based, Solar-Driven Photochemical Cells for Fuel Generation from Carbon Dioxide in Aqueous Solutions

There has been active interest to identify new methods to reduce CO 2 into usable fuel sources. In this work, we demonstrate two types of photo-electrochemical cells (PECs) that photoreduce CO 2 directly to formate in aqueous solutions both in the presence and absence of external bias or additional electron sources. The photocathodes were either a CuFeO 2 /CuO electrode or a bilayer of CdTe on NiO, whereas the photoanode was a bilayer of NiO x on CdS. The PECs were characterized by using both electrochemistry and spectroscopy, and the products formed from CO 2 reduction were characterized and quantified by using 1 H NMR spectroscopy and ESI-MS. In addition, an organohydride catalyst was tested in conjunction with the PECs, which not only showed a significant gain of 85 times in CO 2 reduction (27 μm formate without the catalyst, 2.3 mm formate with it) compared to the NiO/CdTe photocathode system but could also generate methanol under an external bias (10 μm).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electrolyte Engineering Stabilizes Photoanodes Decorated with Molecular Catalysts

Molecular catalysts are promising oxygen evolution promoters in conjunction with photoanodes for solar water splitting. Maintaining the stability of both photoabsorber and cocatalyst is still a prime challenge, with many efforts tackling this issue through sophisticated material designs. Such approaches often mask the importance of the electrode-electrolyte interface and overlook easily tunable system parameters, such as the electrolyte environment, to improve efficiency. We provide a systematic study on the activity-stability relationship of a prominent Fe 2 O 3 photoanode modified with Ir molecular catalysts using in situ mass spectroscopy. After gaining detailed insights into the dissolution behavior of the Ir cocatalyst, a comprehensive pH study is conducted to probe the impact of the electrolyte on the performance. An inverse trend in Fe and Ir stability is found, with the best activity-stability synergy obtained at pH 9.7. The results bring awareness to the overall photostability and electrolyte engineering when advancing catalysts for solar water splitting.

14 SOLAR ENERGY↗

Air‐Stable High‐Voltage Li‐Ion Organic Cathode Enabled by Localized High‐Concentration Electrolyte

While lithium‐ion batteries have revolutionized the field of energy storage, their reliance on critical minerals such as cobalt and nickel raises significant concerns over resource availability and supply chain uncertainty. In this study, we revisit dithiin‐fused dilithium naphthazarin (5,8‐dihydroxy‐1,4‐naphthoquinone) (DNP‐Li) as a high‐voltage Li‐ion organic cathode and evaluate its performance in conjunction with localized high‐concentration electrolyte (LHCE). DNP‐Li exhibits remarkable air and thermal stability, a high operating potential of 3.55 V vs. Li + /Li, and a specific capacity of 232 mAh g −1 , positioning it as one of the most promising candidates among Li‐ion organic cathodes. Furthermore, the electrochemical behavior of DNP‐Li is strongly influenced by the electrolyte composition, giving distinct two‐plateau or four‐plateau voltage profiles accompanied by reversible or irreversible phase transitions in carbonate‐based or LHCE electrolyte formulations, respectively. The reduced solubility of DNP‐Li‐based redox intermediates in LHCE enhances cycling stability, achieving a capacity retention of 85% after 50 cycles at 0.1C and 75% after 160 cycles at 0.5C, demonstrating a significant improvement compared to the carbonate‐based electrolyte. This work highlights the critical role of solute–electrolyte interactions in modulating the electrochemical performance of multielectron small‐molecule organic cathodes, offering new pathways for advancing sustainable and high‐efficiency energy storage technologies.

Lakraychi, Alae Eddine [Department of Electrical a↗

A Dendrite-Resistant Sodium/Porous-Carbon Anode for Solid-State Batteries – Strategies and Challenges for Low-Pressure Operation

Sodium solid-state batteries (Na-SSB) have gained interest recently due to the abundance of Na over Li, but they still tend to fail due to dendrites under practical current densities and cycling capacities. To overcome this, Na-SSBs are frequently tested with impractically high applied pressure. In this work, a porous carbon interfacial layer is utilized in conjunction with Na-ß”-Al2O3 solid electrolytes to enable Na-cycling at milder cell pressures. This sodium/porous carbon layer enables improved solid-state Na cycling in symmetric cells, up to a current density of 10 mA cm-2 at 25 °C. Cycling up to 1 mAh cm-2 is challenging with low pressure, but 1 mAh cm-2 capacity can be reliably cycled at 1 mA cm-2 at an elevated temperature of 60 °C in symmetric cells. Finally, the evolution of the interface and sodium/carbon anode is evaluated with cryogenic ion-milling and cross-sectional imaging revealing that, depending on testing temperature, pressure, current density, and capacity, void formation, Na-extraction from porous carbon, delamination of the porous carbon matrix, or a combination of these occurs at the interface between Na-metal and BASE. Despite this, excellent dendrite resistance is achieved, and a full-cell design utilizing a Na-transition metal oxide cathode is still able to achieve an areal capacity of ~ 2.7 mAh cm-2 at 0.125 mA cm-2. This work demonstrates an alternative pathway toward a Na-metal anode for Na-SSBs without the requirement of excessive stack pressure.

low-cost↗

In situ monitoring of H and O stable isotopes in soil water reveals ecohydrologic dynamics in managed soil systems [Urban ecohydrologic dynamics revealed by in situ monitoring of H and O stable isotopes in soil water]

The water cycle in urban and hydrologically managed settings is subject to perturbations that are dynamic on small spatial and temporal scales; the effects of which may be especially profound in soils. We deploy a membrane inlet-based laser spectroscopy system in conjunction with soil moisture and temperature sensors to monitor soil water dynamics and H and O stable isotope ratios (δ 2 H and δ 18 O values) in a seasonally irrigated urban-landscaped garden soil over the course of 9 months between the cessation of irrigation in the autumn and the onset of irrigation through the summer. Here, we find that soil water δ 2 H and δ 18 O values predominately reflect seasonal precipitation and irrigation inputs. A comparison of total soil water by cryogenic extraction and mobile soil water measured by in situ water vapor probes reveals that initial infiltration events after long periods of soil drying (the autumn season in this case) emplace water into the soil matrix that is not easily replaced by, or mixed with, successive pulses of infiltrating soil water. Tree stem xylem water H and O stable isotope composition did not match that of available water sources. Our findings suggest that partitioning of soil water into mobile and immobile “pools” and resulting ecohydrologic separation may occur in engineered and hydrologically managed soils and not be limited to natural settings. Furthermore, the laser spectroscopy method detailed here has potential to yield insights in a variety of critical zone and vadose zone studies, potential that is heightened by the simplicity and portability of the system.

07 ISOTOPE AND RADIATION SOURCES↗

Simple measurements in a complex system: soil community responses to nitrogen amendment in a Pinus taeda forest

Abstract Microorganisms regulate the decomposition of soil organic matter and the flow of plant‐available nutrients. In a temperate pine forest in North Carolina, USA , where nitrogen (N) had been experimentally added for eight years, we combined DNA ‐based measures of fungal and bacterial biomass and composition with measures of seven extracellular enzymes (ecoenzymes). These measures were then correlated with soil chemistry. Our goals were to evaluate the relative sensitivity and repeatability of multiple structural and functional measures of community organization to long‐term N deposition. Measurements were conducted at three litter/soil depths, corresponding to the litter, Oa, and mineral A horizons (max depth 10 cm) with ten spatial replicates per experimental plot. Soil chemistry differed significantly with soil depth and N amendment. Total biomass (soil DNA ), as well as fungal and bacterial biomass (measured by qPCR ), was greatest in the litter horizon and declined significantly with depth. Ecoenzyme activity patterns also changed with soil depth, transitioning from high levels of C, N, and P metabolizing activities in the litter horizon to increased oxidative activities at the lower depth. Under N amendment, soil pH decreased and nitrate concentrations increased in all three soil horizons. Correspondingly, the estimated microbial C use efficiency decreased in N‐amended soils at all depths, despite differences in microbial biomass, community composition, and soil chemistry. Overall, bacterial composition was most responsive to nitrogen amendment, but the taxonomic context of the response varied with soil horizons in conjunction with shifts in soil chemistry and enzyme activities. While a single measure that would incorporate all of the C, N, and P metabolizing activities did not emerge, many measures correlated with each other, and/or with depth and/or N amendment.

54 ENVIRONMENTAL SCIENCES↗

Regional patterns of postwildfire streamflow response in the Western United States: The importance of scale‐specific connectivity

Abstract Wildfires can impact streamflow by modifying net precipitation, infiltration, evapotranspiration, snowmelt, and hillslope run‐off pathways. Regional differences in fire trends and postwildfire streamflow responses across the conterminous United States have spurred concerns about the impact on streamflow in forests that serve as water resource areas. This is notably the case for the Western United States, where fire activity and burn severity have increased in conjunction with climate change and increased forest density due to human fire suppression. In this review, we discuss the effects of wildfire on hydrological processes with a special focus on regional differences in postwildfire streamflow responses in forests. Postwildfire peak flows and annual water yields are generally higher in regions with a Mediterranean or semi‐arid climate (Southern California and the Southwest) compared to the highlands (Rocky Mountains and the Pacific Northwest), where fire‐induced changes in hydraulic connectivity along the hillslope results in the delivery of more water, more rapidly to streams. No clear streamflow response patterns have been identified in the humid subtropical Southeastern United States, where most fires are prescribed fires with a low burn severity, and more research is needed in that region. Improved assessment of postwildfire streamflow relies on quantitative spatial knowledge of landscape variables such as prestorm soil moisture, burn severity and correlations with soil surface sealing, water repellency, and ash deposition. The latest studies furthermore emphasize that understanding the effects of hydrological processes on postwildfire dynamic hydraulic connectivity, notably at the hillslope and watershed scales, and the relationship between overlapping disturbances including those other than wildfire is necessary for the development of risk assessment tools.

Hallema, Dennis W.↗

Exploring young adult texts within the Historically Responsive Literacy Framework with preservice teachers

Abstract While culturally responsive texts have become more common in teacher education, too often, preservice teachers (PTs) are not asked to examine how to use these books pedagogically. To address this issue, in a young adult (YA) literature course, the Framework for Culturally and Historically Responsive Literacy (HRL) (Muhammad, 2000) Cultivating genius: An equity framework for culturally and historically responsive literac y, 2020; Scholastic) was used in conjunction with representative and inclusive YA trade books. Data analysis was conducted on PT's course work, including HRL unit plans, to determine whether PTs were able to implement Muhammad's (2020) framework using YA texts. The findings of this study show that PTs' understanding of the HRL tenets was at varying levels. While there were unit plans with learning goals that matched Muhammad's purpose and definition for each tenet and YA connections for every tenet, PTs showed a better understanding of the tenets of identity and intellect than skills and Criticality. Implications of these findings including exposing PTs to learning frameworks “written by people of color and designed for children of color” (Muhammad, 2020, p. 11) to create instruction that meets their future students' needs and does not just skim the surface of culturally responsive pedagogies.

Pule, Heather↗

Expression of a Degradation-Resistant β-Catenin Mutant in Osteocytes Protects the Skeleton From Mechanodeprivation-Induced Bone Wasting

ABSTRACT Mechanical stimulation is a key regulator of bone mass, maintenance, and turnover. Wnt signaling is a key regulator of mechanotransduction in bone, but the role of β-catenin—an intracellular signaling node in the canonical Wnt pathway—in disuse mechanotransduction is not defined. Using the β-catenin exon 3 flox (constitutively active [CA]) mouse model, in conjunction with a tamoxifen-inducible, osteocyte-selective Cre driver, we evaluated the effects of degradation-resistant β-catenin on bone properties during disuse. We hypothesized that if β-catenin plays an important role in Wnt-mediated osteoprotection, then artificial stabilization of β-catenin in osteocytes would protect the limbs from disuse-induced bone wasting. Two disuse models were tested: tail suspension, which models fluid shift, and botulinum-toxin (botox)-induced muscle paralysis, which models loss of muscle force. Tail suspension was associated with a significant loss of tibial bone mass and density, reduced architectural properties, and decreased bone formation indices in uninduced (control) mice, as assessed by dual-energy X-ray absorptiometry (DXA), micro-computed tomography (µCT), and histomorphometry. Activation of the βcatCA allele in tail-suspended mice resulted in little to no change in those properties; ie, these mice were protected from bone loss. Similar protective effects were observed among botox-treated mice when the βcatCA was activated. RNAseq analysis of altered gene regulation in tail-suspended mice yielded 35 genes, including Wnt11, Gli1, Nell1, Gdf5, and Pgf, which were significantly differentially regulated between tail-suspended β-catenin stabilized mice and tail-suspended nonstabilized mice. Our findings indicate that selectively targeting/blocking of β-catenin degradation in bone cells could have therapeutic implications in mechanically induced bone disease. © 2019 American Society for Bone and Mineral Research.

59 BASIC BIOLOGICAL SCIENCES↗

Shift of daily rainfall peaks over the Beijing–Tianjin–Hebei region: An indication of pollutant effects?

Aerosol impacts on diurnal variations of rainfall over the Beijing–Tianjin–Hebei region are investigated by comparing the observations between polluted and clean days in early summer (June 1 to July 20) before the rainy season begins. The 2002–2012 hourly rainfall measurements in conjunction with environmental data reveal that during high‐pollution days the peak of heavy rainfall shifted ~4 hr earlier while the peak of light rainfall delayed by 2–3 hr. Detailed analyses of meteorological conditions associated with the shifts suggest that the former is mainly caused by enhanced lower‐level aerosol heating during the daytime which increases the lower‐troposphere instability and facilitates the convective rainfall occurrence, and the latter is related to decreases of conversion of cloud droplets into raindrops associated with aerosol increases. Nevertheless, conducting model sensitivity simulations to better understand aerosol–cloud microphysics–precipitation interactions is warranted.

Zhou, Siyuan↗

In-situ Synthesis of PuCl 3 and Corresponding Raman and Density Functional Theory Vibrational Modes

The experimental and calculated Raman spectrum of PuCl 3 has been reported for the first time. PuCl 3 is a primary species found in plutonium metal refinement, specifically in pyrochemical salt processes including multicycle direct oxide reduction, metal chlorination, and electrorefining. As such, Raman signatures of PuCl 3 could serve as potential forensic indicators of material process history. A novel technique for synthesizing PuCl 3 from the in situ chlorination of plutonium metal with HCl was developed to establish these signatures. Cerium metal surrogates were utilized to ensure optimization of the plutonium experiments and to minimize personnel exposure, and all experiments were carried out in a Raman reaction chamber designed for air-tight, high vacuum environments. In situ Raman spectroscopy was employed in conjunction with density functional theory (DFT) to investigate the vibrational modes of PuCl 3 . Associated mixed oxy and hydroxyl phases are also reported. The combined Raman and DFT results have eliminated inconsistencies in Raman mode assignments for the MX 3 family of metal chlorides having P6 3 /m symmetry, and IR modes derived from the DFT calculations are additionally presented. The data observed in this study are of potential interest to nuclear forensic analyses, nuclear sample aging, nuclear energy, plutonium processing, and stockpile stewardship.

36 MATERIALS SCIENCE↗

Assessment of task‐based performance from five clinical DBT systems using an anthropomorphic breast phantom

Purpose Digital breast tomosynthesis (DBT) is a limited‐angle tomographic breast imaging modality that can be used for breast cancer screening in conjunction with full‐field digital mammography (FFDM) or synthetic mammography (SM). Currently, there are five commercial DBT systems that have been approved by the U.S. FDA for breast cancer screening, all varying greatly in design and imaging protocol. Because the systems are different in technical specifications, there is a need for a quantitative approach for assessing them. In this study, the DBT systems are assessed using a novel methodology with an inkjet‐printed anthropomorphic phantom and four alternative forced choice (4AFC) study scheme. Method A breast phantom was fabricated using inkjet printing and parchment paper. The phantom contained 5‐mm spiculated masses fabricated with potassium iodide (KI)‐doped ink and microcalcifications (MCs) made with calcium hydroxyapatite. Images of the phantom were acquired on all five systems with DBT, FFDM, and SM modalities where available using beam settings under automatic exposure control. A 4AFC study was conducted to assess reader performance with each signal under each modality. Statistical analysis was performed on the data to determine proportion correct (PC), standard deviations, and levels of significance. Results For masses, overall detection was highest with DBT. The difference in PC was statistically significant between DBT and SM for most systems. A relationship was observed between increasing PC and greater gantry span. For MCs, performance was highest with DBT and FFDM compared to SM. The difference between PC of DBT and PC of SM was statistically significant for all manufacturers. Conclusions This methodology represents a novel approach for evaluating systems. This study is the first of its kind to use an inkjet‐printed anthropomorphic phantom with realistic signals to assess performance of clinical DBT imaging systems.

Ikejimba, Lynda C.↗

Size Selectivity of Sampling Gears Used to Sample Kokanee

Abstract Kokanee Oncorhynchus nerka provide valued recreational fisheries and also serve as a prey resource for economically, socially, and ecologically important fishes. As such, management of kokanee is a major focus of natural resource agencies. Kokanee are typically monitored using midwater trawls, but the interpretation of data collected using midwater trawls is difficult due to the unknown size selectivity of the gear. We sought to assess the length selectivity of midwater trawls by comparing estimates obtained from midwater trawls with estimates obtained from gill nets adjusted for size selectivity. Experimental curtain gill nets and midwater trawls were used in conjunction to sample kokanee in seven lentic systems in Idaho. The size selectivity of gill nets was estimated by accounting for the probability of encounter and the probability of retention. Estimates of size selectivity were then used to adjust the length distribution of fish sampled in gill nets. The adjusted length distribution of fish sampled in gill nets was compared with estimates obtained from midwater trawls to identify potential size selectivity of midwater trawls. A pattern of size selectivity was apparent for both sampling techniques. The average length of kokanee sampled with midwater trawls was 111 mm; whereas, kokanee sampled with gill nets had a mean length of 235 mm. Our results suggest experimental gill nets are useful for common sampling of kokanee (e.g., trend monitoring) because the gear is less size selective than midwater trawls and is adjustable for size selectivity. However, midwater trawls are likely the best gear for addressing questions associated with early life history. Overall, our results provide a better understanding of gill-net and midwater trawl selectivity and ultimately improve the ability to sample and manage the species.

Klein, Zachary B.↗

Spatial and temporal overlap between hatchery- and natural-origin steelhead and Chinook Salmon during spawning in the Klickitat River, Washington, USA

Abstract Objective A goal of many segregated salmonid hatchery programs is to minimize potential interbreeding between hatchery- and natural-origin fish. Our objective was to assess this on the Klickitat River, Washington, USA. Methods We used radiotelemetry to evaluate spatiotemporal spawning overlap between hatchery- and natural-origin steelhead Oncorhynchus mykiss and spring Chinook Salmon O. tshawytscha. We estimated percentages of tagged fish that spawned naturally in the Klickitat River subbasin, emigrated from the Klickitat River, or died before spawning. A kernel density analysis was used to estimate probability of spatiotemporal overlap between hatchery- and natural-origin spawners. Result For steelhead, 12% of hatchery-origin and 50% of natural-origin fish spawned naturally. For spring Chinook Salmon, 18% of hatchery-origin and 44% of natural-origin fish spawned naturally. Tag loss may result in underestimates in these percentages. Most hatchery-origin steelhead (90%) spawned downstream of river kilometer (rkm) 32, and 75% spawned from November to mid-March. The majority of natural-origin steelhead (64%) spawned upstream of rkm 32, and 75% spawned from mid-March to late May. Spawn timing of hatchery-origin Chinook Salmon (early August to mid-September) overlapped with that of natural-origin Chinook Salmon (late July to late September), and fish of both origins spawned in the same 30-km reach of the river. We estimated the percentage of hatchery-origin spawners (pHOS) on the natural spawning grounds to be 12% for steelhead and 40% for spring Chinook Salmon across all study years. For steelhead, we estimated the overlap probability to be 25% (95% CI = 22.5–28%). For spring Chinook Salmon, tight spatial clustering of hatchery-origin fish resulted in a lower overlap estimate of 21% (13–31%). Conclusion We suggest adjusting pHOS estimates using these overlap estimates or similar spatiotemporal data on actual spawner proximity and possible interactions, and that these types of analyses be used in conjunction with gene flow analysis to accurately evaluate effects of individual hatchery programs.

Zendt, Joseph S.↗

Optimal Polynomial Smoothers and One‐Sided V‐Cycles for Poisson Problems

The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier‐Stokes equations needs robust preconditioning strategies. One such strategy is multigrid. To realize the potential of multigrid methods, effective smoothing strategies are needed. Chebyshev polynomial smoothers, in conjunction with pointwise Jacobi or additive Schwarz methods (ASMs), prove to be an effective smoother. Other polynomial smoothers, however, may provide superior convergence to the multigrid preconditioner. The authors compare the standard Chebyshev polynomial smoothers to both the novel fourth‐kind Chebyshev polynomial smoothers proposed by Lottes as well as smoothers based on the polynomial of best uniform approximation to as proposed by Kraus, Vassilevski, and Zikatanov. At the cost of symmetry, further improvements may be made. For example, a order polynomial smoother on both sides of the V‐cycle may be substituted with an order polynomial smoother on one side at no additional cost. The choice of omitting the postsmoother in favor of higher‐order polynomial presmoothing is advantageous in cases where the multigrid approximation property constant is large. The authors consider a 2D model problem based on finite differences to motivate the choice of polynomial smoother, order, and whether to apply postsmoothing for the target application of high‐order ‐geometric multigrid methods for GPU architectures. Results from both domains demonstrate the substantial improvement of these approaches over the standard Chebyshev polynomial smoother with a symmetric V‐cycle.

97 MATHEMATICS AND COMPUTING↗

Error modeling for surrogates of dynamical systems using machine learning: Machine-learning-based error model for surrogates of dynamical systems

A machine learning–based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (eg, random forests, and LASSO) to map a large set of inexpensively computed “error indicators” (ie, features) produced by the surrogate model at a given time instance to a prediction of the surrogate-model error in a quantity of interest (QoI). This eliminates the need for the user to hand-select a small number of informative features. The methodology requires a training set of parameter instances at which the time-dependent surrogate-model error is computed by simulating both the high-fidelity and surrogate models. Using these training data, the method first determines regression-model locality (via classification or clustering) and subsequently constructs a “local” regression model to predict the time-instantaneous error within each identified region of feature space. We consider 2 uses for the resulting error model: (1) as a correction to the surrogate-model QoI prediction at each time instance and (2) as a way to statistically model arbitrary functions of the time-dependent surrogate-model error (eg, time-integrated errors). We then apply the proposed framework to model errors in reduced-order models of nonlinear oil-water subsurface flow simulations, with time-varying well-control (bottom-hole pressure) parameters. The reduced-order models used in this work entail application of trajectory piecewise linearization in conjunction with proper orthogonal decomposition. Moreover, when the first use of the method is considered, numerical experiments demonstrate consistent improvement in accuracy in the time-instantaneous QoI prediction relative to the original surrogate model, across a large number of test cases. When the second use is considered, results show that the proposed method provides accurate statistical predictions of the time- and well-averaged errors.

97 MATHEMATICS AND COMPUTING↗

Modeling curved interfaces without element‐partitioning in the extended finite element method

Summary In this paper, we model holes and material interfaces (weak discontinuities) in two‐dimensional linear elastic continua using the extended finite element method on higher‐order (spectral) finite element meshes. Arbitrary parametric curves such as rational Bézier curves and cubic Hermite curves are adopted in conjunction with the level set method to represent curved interfaces. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes' theorem to reduce integration to the boundary of the domain. Numerical integration on cut elements requires the evaluation of a one‐dimensional integral over a parametric curve, and hence, the need to partition curved elements is eliminated. To improve stiffness matrix conditioning, ghost penalty stabilization and the Jacobi preconditioner are used. For material interface problems, we develop an enrichment function that captures weak discontinuities on spectral meshes. Taken together, we show through numerical experiments that these advances deliver optimal algebraic rates of convergence with h ‐refinement ( p =1,2,…,5) and exponential rates of convergence with p ‐refinement ( p =1,2,…,7) for elastostatic problems with holes and material inclusions on Cartesian p th‐order spectral finite element meshes.

Chin, Eric B.↗