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At least 541 records · Page 30

An improved detailed chemical kinetic model for C3-C4 linear and iso-alcohols and their blends with gasoline at engine-relevant conditions

Propanol and butanol isomers have received significant research attention as promising fuel additives or neat biofuels. Robust chemical kinetic models are needed that can provide accurate and efficient predictions of combustion performance across a wide range of engine relevant conditions. Herein, this study seeks to improve the understanding of ignition and combustion behavior of pure C3-C4 linear and iso-alcohols, and their blends with gasoline at engine-relevant conditions. In this work, a kinetic model with improved thermochemistry and reaction kinetics was developed based on recent theoretical calculations of H-atom abstraction and peroxy radical reaction rates. Kinetic model validations are reported, and the current model reproduces the ignition delay times of the C3 and C4 alcohols well. Variations in reactivity over a wide range of temperatures and other operating conditions are also well predicted by the current model. Recent ignition delay time measurements from a rapid compression machine of neat iso-propanol and iso-butanol [Cheng et al., Proc. Combust Inst. (2020)] and blends with a research grade gasoline [Goldsborough et al., Proc. Combust Inst. (2020)] at elevated pressure (20–40 bar) and intermediate temperatures (780–950 K) were used to demonstrate the accuracy of the current kinetic model at conditions relevant to boosted spark-ignition engines. The effects of alcohol blending with gasoline on the autoignition behavior are discussed. The current model captures the suppression of reactivity in the low-temperature and negative-temperature-coefficient (NTC) region when either isopropanol and isobutanol are added to a research grade gasoline. Sensitivity and reaction flux analysis were performed to provide insights into the relevant fuel chemistry of the C3-C4 alcohols.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Process design for recovering rare-earth elements from mine tailings with low rare-earth concentrations via sequential leaching and solvent extraction

Rare earth elements (REEs) are essential for advanced technologies and yet face significant supply chain risks due to their concentrated global production and limited domestic availability. Addressing this challenge requires efficient processes capable of upgrading low-grade secondary resources such as mine tailings. In this study, we developed a novel separation flowsheet that integrates sequential leaching and 2-stage solvent extraction (SX) processes to recover high-purity heavy REEs (HREEs) and light REEs (LREEs) from a simulated mine-tailing concentrate containing 2.4 wt% total REEs (TREEs; 0.6 wt% LREEs and 1.8 wt% HREEs). Sequential leaching with controlled pH adjustment selectively precipitated REEs while retaining the large amount of impurities in the solution, producing an REE-enriched leachate by following leaching processes with roughly twice the REE concentration and half the impurity concentration compared to that of single-step leaching. The optimized SX flowsheet employed Cyanex 572 to extract HREEs and Fe over LREEs, followed by Fe removal using tributyl phosphate (TBP), while the raffinate stream was processed by SX with di(2-ethylhexyl)phosphoric acid (D2EHPA) to recover LREEs under optimized conditions balancing both extraction efficiency and purity. Although increased extractant availability in the organic phase improved LREE recovery, it also increased co-extraction of Ca, underscoring trade-offs in process optimization. Both HREE- and LREE-rich solutions were subsequently precipitated into solid products via oxalate precipitation, resulting in high-purity REE solids containing ∼92.0 wt% HREEs (∼95.7 wt% TREEs) and ∼92.8 wt% LREEs (∼94.0 wt% TREEs). In conclusion, this proof-of-concept study using simulated mine tailings demonstrates a promising approach for upgrading low-grade REE resources, while highlighting the need for future validation with real materials.

Mine tailings↗

Hybrid electric buses fuel consumption prediction based on real-world driving data

Estimating fuel consumption by hybrid diesel buses is challenging due to its diversified operations and driving cycles. Here, long-term transit bus monitoring data were utilized to empirically compare fuel consumption of diesel and hybrid buses under various driving conditions. Artificial neural network (ANN) based high-fidelity microscopic (1 Hz) and mesoscopic (5–60 min) fuel consumption models were developed for hybrid buses. The microscopic model contained 1 Hz driving, grade, and environment variables. The mesoscopic model aggregated 1 Hz data into 5 to 60-minute traffic pattern factors and predicted average fuel consumption over its duration. The prediction results show mean absolute percentage errors of 1–2% for microscopic models and 5–8% for mesoscopic models. The data were partitioned by different driving speeds, vehicle engine demand, and road grade to investigate their impacts on prediction performance.

33 ADVANCED PROPULSION SYSTEMS↗

Investigation of Off-Stoichiometry in Ternary Nitrides by EDS and HRTEM

We demonstrate an inverted metamorphic multijunction (IMM) photovoltaic cell comprising lattice-mismatched 1.2 eV AlGaInAs and 1.0 eV GaInAs junctions optimized for high-temperature thermophotovoltaic (TPV) applications. This device differs from traditional IMM solar cells because the mismatched junctions are grown at a single lattice constant. This architecture enables removal of the compositionally graded buffer which otherwise filters light from the junctions below and absorbs sub-bandgap light via free-carrier absorption. Sub-bandgap absorption dramatically reduces the efficiency of TPV systems using high reflectivity cells to enable bandedge spectrum filtering. Three components required development to enable this device: 1) a lattice-mismatched 1.2 eV AlGaInAs junction, 2) a metamorphic contact layer grown after the graded buffer, and 3) a transparent tunnel junction that sits in front of the 1.0 eV GaInAs junction. Growth conditions that minimize oxygen defect incorporation maximize AlGaInAs cell quality, enabling a 0.41 V bandgap open circuit voltage offset at 22 mA/cm2 under AM1.5D. A mismatched GaInAs:Se layer is developed as a low resistance contact. Lastly we develop a GaAsSb:C/GaInP:Se tunnel junction suitable for high-power densities with more transparency than the GaAsSb:C/GaInP:Se structure used in past IMM cells. We characterize the tandem device under a high-intensity spectrum that approximates the emission from a 2150 °C blackbody radiator and deduce a projected ideal TPV efficiency of 39.9% at ~30% of the blackbody irradiance, and 36% ideal TPV efficiency under the full 118 W/cm2 irradiance. Improvements to the back-surface reflectivity and series resistance are expected to increase the ideal TPV efficiency well above 40%.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Corrosion of Ferrous Structural Alloys in Biomass Derived Fuels and Organic Acids

This work investigated the corrosivity of biomass-derived liquid fuels and organic acids associated with bio-oils and conducted a corrosion compatibility evaluation of several structural ferrous alloys in the fuels and acids. Here, the acidity parameters and solution conductivity values were higher in raw pyrolysis bio-oils than postprocessed oils with significant corrosion attack for carbon steel and Fe-2.25Cr-1Mo. However, higher-grade stainless steels, ferritic Fe-15Cr (15Cb) and austenitic types 304L and 316L, showed negligible corrosion loss, whereas lower-Cr ferritic grades 409, 410, and 416 were attacked. Metal leaching tests and electrochemical impedance spectroscopy measurements revealed superior corrosion resistance of 316 over 410 stainless steels in solutions of formic and oxalic acids that can be present in bio-oils. The corrosion evaluation methods utilized in this work provide effective screening tools to identify the compatible structural alloys for bio-oils.

09 BIOMASS FUELS↗

Dithionite Inhibits Iron(III) (Hydr)oxide Formation during Olivine Dissolution Advancing Simultaneous CO 2 Mineralization and Nickel Recovery

Increasing CO 2 concentration poses significant global challenges, impacting both environmental and human health. As we strive for a carbon-neutral energy technology transition, the demand for critical elements (e.g., nickel and cobalt) continues to increase, while high-grade ores are depleting. Combining CO 2 mineralization with the recovery of critical elements from low-grade ores offers an innovative solution. Olivine, a magnesium-rich ultramafic with trace amounts of critical elements, is a promising mineral; however, its impurities, such as iron (Fe(III)), hinder the dissolution of Ni and Mg from olivine, reducing its carbonation and critical element recovery. Here, to address this challenge, this study examined Ni dissolution from San Carlos olivine at high temperatures and high CO 2 pressure. We found that iron(III) (hydr)oxide layers impeded olivine dissolution; however, with sodium dithionite (Na 2 S 2 O 4 ), a reducing agent, olivine dissolution is significantly improved by preventing iron(III) (hydr)oxide formation. With Na 2 S 2 O 4 , within 24 h, Mg and Ni dissolution from olivine increased 2.85-fold and 2.66-fold, respectively, compared to samples without Na 2 S 2 O 4 . After seven cycles, with solutions replaced every 24 h, 98.9% of the total Mg and 84.6% of the total Ni were recovered. This approach enhances olivine’s CO 2 mineralization and improves the sustainability of critical element supply.

54 ENVIRONMENTAL SCIENCES↗

Preparation and Characterization of Various Kraft Lignins and Impact on Their Pyrolysis Behaviors

Lignin-derived chemicals and fuel products have received much attention in the context of bio-refinery. In this study we prepared and characterized various lignin samples from black liquor (BL), a major byproduct from the pulp and paper manufacturing processes, and studied the pyrolysis behaviors of these isolated lignin samples at 600 °C under a N2 atmosphere. Three lignin samples were isolated from the Kraft pulping BL of Loblolly pine linerboard grade process (KL, obtained by direct evaporation; L10, obtained by precipitation at pH 10; L3, obtained by precipitation at pH 3), while another three were from the Kraft pulping BL of Loblolly pine bleach grade process (KB, B10, B3). The inorganic elements present in lignin samples were analyzed using an inductively coupled plasma (ICP) analyzer. The KL and KB samples contained a larger amount of inorganic elements, especially Na and S, than did the other lignin samples. Owing to large quantities of inorganic elements, the ash contents in KL and KB were higher than in the precipitated lignin samples (L10, B10, L3, and B3). These inorganic elements have a significant effect on the subsequent pyrolysis process, as a result, more extensive depolymerization of lignin occurred in KL and KB samples, leading to the formation of fewer pyrolysis oils, with lower molecular weights. NMR analyses of pyrolysis oils show that more methoxyl groups and ether bonds were cleaved, resulting in fewer methoxyl groups and aromatic C–O bonds for the KL and KB heavy oil than for the precipitated lignin heavy oil.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Toward a Diverse Next-Generation Energy Workforce: Teaching Artificial Photosynthesis and Electrochemistry in Elementary Schools through Active Learning

Artificial photosynthesis is a promising approach to generate commodity chemicals using abundant chemical feedstocks and renewable energy sources. Despite its importance, affordable and effective hands-on classroom activities that demonstrate artificial photosynthesis and teach key concepts, especially for primary school students, are lacking. Educating young students on this topic is a critical step in the development of the next-generation energy workforce, especially one that is diverse in race and gender. Here, we hypothesize that an effective approach to educate a broad range of young students on the topic of artificial photosynthesis is through the use of an active learning-based lesson plan that employs cheap and accessible materials. This hypothesis is confirmed by evaluating the understanding of fifth grade students with a survey before and after a lesson plan on artificial photosynthesis that uses active-learning techniques and uses safe and highly accessible materials (baking soda, tap water, plastic jars, Ni coil, alligator clips, and a solar cell) to perform solar-powered water splitting. The lesson plan and survey questions are designed to align with the educational outcomes for fifth grade classrooms in California and to address four general learning objectives: (1) Motivations of Artificial Photosynthesis, (2) Applications of Artificial Photosynthesis, (3) Inputs and Outputs of Artificial Photosynthesis, and (4) Engineering Design for Artificial Photosynthesis. The survey data demonstrate a statistically significant improvement in overall student understanding from the lesson plan. Importantly, the data show that the lesson plan presented here is effective at narrowing the performance gap between minority students and overly represented groups.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Polymer, Additives, and Processing Effects on N95 Filter Performance

The current severe acute respiratory syndrome coronavirus 2 (SARS-COV-2) pandemic has highlighted the need for personal protective equipment, specifically filtering facepiece respirators like N95 masks. While it is common knowledge that polypropylene (PP) is the industry standard material for filtration media, trial and error is often required to identify suitable commercial precursors for filtration media production. This work aims to identify differences between several commercial grades of PP and demonstrate the development of N95 filtration media with the intent that the industry partners can pivot and help address N95 shortages. Three commercial grades of high melt flow index PP were melt blown at Oak Ridge National Laboratory and broadly characterized by several methods including differential scanning calorimetry (DSC), X-ray diffraction (XRD), and neutron scattering. Despite the apparent similarities (high melt flow and isotacticity) between PP feedstocks, the application of corona charging and charge enhancing additives improve each material to widely varying degrees. From the analysis performed here, the most differentiating factor appears to be related to crystallization of the polymer and the resulting electret formation. Materials with higher crystallization onset temperatures, slower crystallization rates, and larger number of crystallites form a stronger electret and are more effective at filtration.

36 MATERIALS SCIENCE↗

Decontamination of SARS-CoV-2 and Other RNA Viruses from N95 Level Meltblown Polypropylene Fabric Using Heat under Different Humidities

In March of 2020, the World Health Organization declared a pandemic of coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The pandemic led to a shortage of N95-grade filtering facepiece respirators (FFRs), especially surgical-grade N95 FFRs for protection of healthcare professionals against airborne transmission of SARS-CoV-2. We and others have previously reported promising decontamination methods that may be applied to the recycling and reuse of FFRs. In this study we tested disinfection of three viruses, including SARS-CoV-2, dried on a piece of meltblown fabric, the principal component responsible for filtering of fine particles in N95-level FFRs, under a range of temperatures (60–95 °C) at ambient or 100% relative humidity (RH) in conjunction with filtration efficiency testing. We found that heat treatments of 75 °C for 30 min or 85 °C for 20 min at 100% RH resulted in efficient decontamination from the fabric of SARS-CoV-2, human coronavirus NL63 (HCoV-NL63), and another enveloped RNA virus, chikungunya virus vaccine strain 181/25 (CHIKV-181/25), without lowering the meltblown fabric’s filtration efficiency.

60 APPLIED LIFE SCIENCES↗

Porous but Mechanically Robust All-Inorganic Antireflective Coatings Synthesized using Polymers of Intrinsic Microporosity

Herein, we introduce polymer of intrinsic microporosity 1 (PIM-1) to design single-layer and multilayered all-inorganic antireflective coatings (ARCs) with excellent mechanical properties. Using PIM-1 as a template in sequential infiltration synthesis (SIS), we can fabricate highly uniform, mechanically stable conformal coatings of AlO x with porosities of ~50% and a refractive index of 1.41 compared to 1.76 for nonporous AlO x that is perfectly suited for substrates commonly used in high-end optical systems or touch screens (e.g., sapphire, conductive glass, bendable glass, etc.). We show that such films can be used as a single-layer ARC capable of reduction of the Fresnel reflections of sapphire to as low as 0.1% at 500 nm being deposited only on one side of the substrate. We also demonstrate that deposition of the second layer with higher porosity using block copolymers enables the design of graded-index double-layered coatings. AlO x structures with just two layers and a total thickness of less than 200 nm are capable of reduction of Fresnel reflections under normal illumination to below 0.5% in a broad spectral range with 0.1% reflection at 700 nm. Additionally, and most importantly, we show that highly porous single-layer and graded-index double-layered ARCs are characterized by high hardness and scratch resistivity. The hardness and the maximum reached load were 7.5 GPa and 13 mN with a scratch depth of about 130 nm, respectively, that is very promising for the structures consisting of two porous AlO x layers with 50% and 85% porosities, correspondingly. Such mechanical properties of coatings can also allow their application as protective layers for other optical coatings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Linear complexions enable unprecedented ductility retention in neutron irradiated ferritic steel

Herein, the operando formation of Si-enriched linear complexions during neutron irradiation enables Grade 91 ferritic steel to overcome the strength–ductility tradeoff, one of the most critical life-limiting challenges facing nuclear structural alloys. Linear complexions are a distinct yet confined chemical and structural state at a dislocation, which are rarely reported in engineering alloys. Ferritic steels are amongst the most ubiquitous engineering alloys for current and future nuclear components, but they are susceptible to irradiation hardening and embrittlement. Here, exceptional ductility retention exceeding 90% of pre-irradiation levels is obtained in Grade 91 synthesized using powder metallurgy with hot isostatic pressing (PM-HIP). Powder processing artifacts promote a high density of screw dislocation arrays, on which β-FeSi 2 linear complexions form due to Si segregation during irradiation. Screw dislocation dipoles undergo pinning and unpinning on linear complexions, resulting in extended yielding and significant ductility retention post-irradiation. These findings represent a significant advancement toward design of alloys and manufacturing processes that can autonomously self-regulate their microstructural resilience in-operando during irradiation, enabling exceptional ductility rather than embrittlement.

Chatterjee, Arya [University of Illinois, Urbana, ↗

High-throughput printing of combinatorial materials from aerosols

The development of new materials and their compositional and microstructural optimization are essential in regard to next-generation technologies such as clean energy and environmental sustainability. However, materials discovery and optimization have been a frustratingly slow process. The Edisonian trial-and-error process is time consuming and resource inefficient, particularly when contrasted with vast materials design spaces 1 . Whereas traditional combinatorial deposition methods can generate material libraries 2,3 , these suffer from limited material options and inability to leverage major breakthroughs in nanomaterial synthesis. Here we report a high-throughput combinatorial printing method capable of fabricating materials with compositional gradients at microscale spatial resolution. In situ mixing and printing in the aerosol phase allows instantaneous tuning of the mixing ratio of a broad range of materials on the fly, which is an important feature unobtainable in conventional multimaterials printing using feedstocks in liquid–liquid or solid–solid phases 4–6 . We demonstrate a variety of high-throughput printing strategies and applications in combinatorial doping, functional grading and chemical reaction, enabling materials exploration of doped chalcogenides and compositionally graded materials with gradient properties. The ability to combine the top-down design freedom of additive manufacturing with bottom-up control over local material compositions promises the development of compositionally complex materials inaccessible via conventional manufacturing approaches.

36 MATERIALS SCIENCE↗

Opportunities and challenges for the expansion of LFP battery supply chains

Global markets for energy storage are growing rapidly, with some applications transitioning from traditional LiNi x Mn y Co 1−x−y O 2 (NMC) toward LiFePO 4 (LFP) due to cost, safety, and performance advantages. Battery growth has seeded interest in critical material supplies such as high-purity lithium precursors. In contrast, challenges in securing high-purity iron and phosphorus, historically not considered critical materials, are often overlooked. Precursors must remain inexpensive to maintain LFP's current cost advantage, which leverages the low-cost (∼$\$100$ per t) FeSO 4 byproduct from titanium dioxide manufacturing and will not be available as LFP manufacturing expands. As an alternative, iron is mined primarily for steel manufacturing, for which the existing supply chain and beneficiation process is optimized. LFP batteries require small iron volumes compared to steel (0.11%), but profit margins associated with existing low-cost iron ores and high costs (∼$27 000 per t) associated with low volume high-purity iron oxides may limit interest in manufacturing small volumes of high-purity, specialized iron battery precursors. The complementary LFP precursor, phosphoric acid (H 3 PO 4 ), is primarily utilized in fertilizers. Of the current phosphate ore demand for fertilizers, 4–22.8% would be required to meet projected 2045 LFP H 3 PO 4 demand, suggesting significant supply chain planning is needed to achieve projected demand. If only higher-grade material is considered, demand jumps to 15–77% of current world production. While lithium precursor purity requirements have been evaluated (Li 2 CO 3 is commonly defined as ≥99.5%), “battery grade” iron and phosphorus precursors remain poorly defined, with no internationally accessible and widely adopted standard, further challenging expanding industry by creating manufacturing uncertainty and increasing potential costs.

25 ENERGY STORAGE↗

PRIME: a real-time cyber-physical systems testbed: from wide-area monitoring, protection, and control prototyping to operator training and beyond

As the power grid continues to evolve with advanced wide-area monitoring, protection, and control (WAMPAC) algorithms, there is an increasing need for realistic testbed environments with industry-grade software and hardware-in-the-loop (HIL) to perform verification and validation studies. Such testbed environments serve as ideal platforms to perform WAMPAC prototyping, operator training, and also to study the impacts of different types of cyberattack scenarios on the operation of the grid. In this paper, we introduce PRIME (PNNL cybeR physIcal systeMs tEstbed): the testbed that integrates real-time transmission system simulator with commercial industry grade energy management system (EMS) software and remote hardware-in-the-loop (RHIL). PRIME is an end-to-end, modular testbed that allows high-fidelity RHIL experimentation of a power system. We present two detailed case studies (fault location and clearing in transmission system, and operator training) to showcase the capabilities of our PRIME testbed. Finally, we briefly discuss some of the potential limitations of our testbed in terms of scalability and flexibility to setup larger test systems and identify directions for future work to address those limitations.

42 ENGINEERING↗

TDCOSMO. X. Automated modeling of nine strongly lensed quasars and comparison between lens-modeling software

When strong gravitational lenses are to be used as an astrophysical or cosmological probe, models of their mass distributions are often needed. We present a new, time-efficient automation code for the uniform modeling of strongly lensed quasars with GLEE, a lens-modeling software for multiband data. By using the observed positions of the lensed quasars and the spatially extended surface brightness distribution of the host galaxy of the lensed quasar, we obtain a model of the mass distribution of the lens galaxy. We applied this uniform modeling pipeline to a sample of nine strongly lensed quasars for which images were obtained with the Wide Field Camera 3 of the Hubble Space Telescope. The models show well-reconstructed light components and a good alignment between mass and light centroids in most cases. We find that the automated modeling code significantly reduces the input time during the modeling process for the user. The time for preparing the required input files is reduced by a factor of 3 from ~3 h to about one hour. The active input time during the modeling process for the user is reduced by a factor of 10 from ~ 10 h to about one hour per lens system. This automated uniform modeling pipeline can efficiently produce uniform models of extensive lens-system samples that can be used for further cosmological analysis. A blind test that compared our results with those of an independent automated modeling pipeline based on the modeling software Lenstronomy revealed important lessons. Quantities such as Einstein radius, astrometry, mass flattening, and position angle are generally robustly determined. Other quantities, such as the radial slope of the mass density profile and predicted time delays, depend crucially on the quality of the data and on the accuracy with which the point spread function is reconstructed. Better data and/or a more detailed analysis are necessary to elevate our automated models to cosmography grade. Nevertheless, our pipeline enables the quick selection of lenses for follow-up and further modeling, which significantly speeds up the construction of cosmography-grade models. This important step forward will help us to take advantage of the increase in the number of lenses that is expected in the coming decade, which is an increase of several orders of magnitude.

79 ASTRONOMY AND ASTROPHYSICS↗

Shock response of cobalt-based cemented tungsten carbides at pressures up to 100 GPa

In the present study, shock wave experiments are conducted on General Carbide cemented tungsten carbides with 3.7 wt.% and 6.0 wt.% cobalt binder to determine their shock compression response up to 100 GPa. A three-stage particle velocity profile is observed in the experiments -- an initial elastic-rise to the Hugoniot elastic limit (HEL), an elastic-plastic ramp indicating post-yield hardening, and finally a rise to the peak shocked Hugoniot state. The results of the experiments are used to determine the HEL, shock velocity (U s ) vs. particle velocity (u p ) Hugoniot relationship, and the longitudinal stress vs. specific volume Hugoniot relationship for the two samples. Here, the HEL for the WC 3.7wt% Co and WC 6.0wt% Co samples was determined to be ~4.45 GPa and 3.72 GPa, respectively. The U s – u p relation was determined to be U s = 4.97(0.006)+1. 446 (0.018) u p for WC 3.7 wt.% Co and U s = 4.93(0.006)+1. 454(0.017)u p for the WC 6.0 wt.% Co sample at peak particle velocities>0.75 km/s. For both WC grades, in the particle velocity regime less than ~0.75 km/s, the measured shock wave velocities were found to be larger than those predicted by the linear U s –u p Hugoniot relationship, indicating the two WC samples to preserve substantial strength in the post-yield deformation regime. Both WC grades show a catastrophic drop in shear stress carrying capacity when shocked to longitudinal stresses greater than ~70 GPa.

36 MATERIALS SCIENCE↗

Chiral algebra, localization, modularity, surface defects, and all that

We study the 2D vertex operator algebra (VOA) construction in 4D N = 2 superconformal field theories on S 3 × S 1 , focusing on both old puzzles and new observations. The VOA lives on a two-torus T 2 ⊂ S 3 × S 1 , it is 1 2 Z -graded, and this torus is equipped with the natural choice of spin structure (1,0) for the Z + 1 2 -graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserves the VOA, we find that it admits discrete deformations, which allows access to the remaining spin structures (1,1), (0,1), and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle and the two-point functions and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the T-transformation acts on our four partition functions and lifts to a large diffeomorphism on S 3 × S 1 . More interestingly, we generalize the four partition functions on the torus to an infinite family labeled by both the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the S-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the Ω-background.

97 MATHEMATICS AND COMPUTING↗