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At least 307 records · Page 17

Toroidal-Core Microinductors Biased by Permanent Magnets

The designs of microscopic toroidal-core inductors in integrated circuits of DC-to-DC voltage converters would be modified, according to a proposal, by filling the gaps in the cores with permanent magnets that would apply bias fluxes (see figure). The magnitudes and polarities of the bias fluxes would be tailored to counteract the DC fluxes generated by the DC components of the currents in the inductor windings, such that it would be possible to either reduce the sizes of the cores or increase the AC components of the currents in the cores without incurring adverse effects. Reducing the sizes of the cores could save significant amounts of space on integrated circuits because relative to other integrated-circuit components, microinductors occupy large areas - of the order of a square millimeter each. An important consideration in the design of such an inductor is preventing magnetic saturation of the core at current levels up to the maximum anticipated operating current. The requirement to prevent saturation, as well as other requirements and constraints upon the design of the core are expressed by several equations based on the traditional magnetic-circuit approximation. The equations involve the core and gap dimensions and the magnetic-property parameters of the core and magnet materials. The equations show that, other things remaining equal, as the maximum current is increased, one must increase the size of the core to prevent the flux density from rising to the saturation level. By using a permanent bias flux to oppose the flux generated by the DC component of the current, one would reduce the net DC component of flux in the core, making it possible to reduce the core size needed to prevent the total flux density (sum of DC and AC components) from rising to the saturation level. Alternatively, one could take advantage of the reduction of the net DC component of flux by increasing the allowable AC component of flux and the corresponding AC component of current. In either case, permanent-magnet material and the slant (if any) and thickness of the gap must be chosen according to the equations to obtain the required bias flux. In modifying the design of the inductor, one must ensure that the inductance is not altered. The simplest way to preserve the original value of inductance would be to leave the gap dimensions unchanged and fill the gap with a permanent- magnet material that, fortuitously, would produce just the required bias flux. A more generally applicable alternative would be to partly fill either the original gap or a slightly enlarged gap with a suitable permanent-magnet material (thereby leaving a small residual gap) so that the reluctance of the resulting magnetic circuit would yield the desired inductance.

Lieneweg, Udo↗

Generation and application of multivariate polynomial quadrature rules

The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play a central role in many aspects of scientific computing with complex models. The contribution of this paper is twofold. First, we provide novel mathematical analysis of the polynomial quadrature problem that provides a lower bound for the minimal possible number of nodes in a polynomial rule with specified accuracy. We give concrete but simplistic multivariate examples where a minimal quadrature rule can be designed that achieves this lower bound, along with situations that showcase when it is not possible to achieve this lower bound. Our second contribution is the formulation of an algorithm that is able to efficiently generate multivariate quadrature rules with positive weights on non-tensorial domains. Our tests show success of this procedure in up to 20 dimensions. We test our method on applications to dimension reduction and chemical kinetics problems, including comparisons against popular alternatives such as sparse grids, Monte Carlo and quasi Monte Carlo sequences, and Stroud rules. The quadrature rules computed in this paper outperform these alternatives in almost all scenarios.

97 MATHEMATICS AND COMPUTING↗

Innovative rail transport of a supersized land-based wind turbine blade

Wind turbine blade logistic providers are being challenged with escalating costs and routing complexities as one-piece blade approach lengths of 75 m in various regions of the U.S. land-based market. New lower cost solutions are needed to enable further reductions in the levelized cost of energy (LCOE) and continued market expansion. In this paper, a novel method of using existing U.S. rail infrastructure to deploy 100-m, one-piece blades to U.S. land-based wind sites is numerically investigated. The study removes the constraint that blades must be kept rigid during transport, and it allows bending to keep blades within a clearance profile while navigating horizontal and vertical curvatures. Novel system optimization and blade design processes consider blade structural constraints and rail logistic constraints in parallel to develop a highly flexible, rail-transportable blade. Results indicate maximum deployment potential in the Interior region of the United States and limited deployment potential in other regions. The study concludes that innovative rail transportation solutions combined with advanced rotor technologies can provide a feasible alternative to segmentation and support continued LCOE reductions in the U.S. land-based wind energy market.

17 WIND ENERGY↗

Quantifying the Impact of Vehicle and Motor Fuel Provisions from the Energy Policy Act on the Sustainability and Resilience of U.S. Cities: Preprint

The Energy Policy Act (EPAct) of 1992, with later amendments, was enacted with the goal of reducing U.S. petroleum consumption by building a core market for alternative fuels and vehicles. The U.S. Department of Energy manages three federal programs related to EPAct; the Sustainable Federal Fleets Program, the State and Alternative Fuel Provider Program, and Clean Cities. Federal agencies and State and Alternative Fuel Provider Fleets are required to submit annual reports that document their compliance with the legislation. Clean Cities is a voluntary program aimed at building partnerships and providing technical expertise to encourage cities to reduce petroleum use in transportation. This study reviews the evolution of these three programs in relation to alternative fuel and vehicle markets and private sector adoption of alternative fueled vehicles to assess the impact of the programs on reduction in petroleum use and greenhouse gas emissions both within the regulated fleets and through development of alternative fuel and vehicle markets. The increased availability of alternative fuels and use of alternative fuels in regulated fleets is expected to improve cities' ability to respond to and quickly recover from both local disasters and short- and long-term regional or national fuel supply interruptions. Our analysis examines the benefits as well as potential drawbacks of alternative fuel use for the resiliency of U.S. cities.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Quantifying the Impact of Vehicle and Motor Fuel Provisions from the Energy Policy Act on the Sustainability and Resilience of U.S. Cities

The Energy Policy Act (EPAct) of 1992, with later amendments, was enacted with the goal of reducing U.S. petroleum consumption by building a core market for alternative fuels and vehicles. The U.S. Department of Energy manages three federal programs related to EPAct; the Sustainable Federal Fleets Program, the State and Alternative Fuel Provider Program, and Clean Cities. Federal agencies and State and Alternative Fuel Provider Fleets are required to submit annual reports that document their compliance with the legislation. Clean Cities is a voluntary program aimed at building partnerships and providing technical expertise to encourage cities to reduce petroleum use in transportation. This study reviews the evolution of these three programs in relation to alternative fuel and vehicle markets and private sector adoption of alternative fueled vehicles to assess the impact of the programs on reduction in petroleum use and greenhouse gas emissions both within the regulated fleets and through development of alternative fuel and vehicle markets. The increased availability of alternative fuels and use of alternative fuels in regulated fleets is expected to improve cities' ability to respond to and quickly recover from both local disasters and short- and long-term regional or national fuel supply interruptions. Our analysis examines the benefits as well as potential drawbacks of alternative fuel use for the resiliency of U.S. cities.

30 DIRECT ENERGY CONVERSION↗

Enhancing Nitrogen Activation in Electrochemical Reduction: The Role of Rare Earth Oxide Surface Configurations

The pursuit of sustainable ammonia synthesis has prompted the exploration of ambient electrochemical nitrogen reduction reaction (e-NRR) as an alternative to the energy-intensive Haber-Bosch process. Here, this study conducted a theoretical investigation into the use of rare earth oxide materials, specifically dysprosium oxide (Dy 2 O 3 ), as potential electrocatalysts for NRR. Utilizing spin-polarized density functional theory calculations, we explored the interaction between Dy 2 O 3 surfaces and nitrogen (N 2 ) molecules, examining the capability of Dy 2 O 3 to adsorb and activate N 2 under ambient conditions. The results indicate that Dy 2 O 3 surfaces exhibit diverse configurations and bonding environments, providing a variety of reactive sites that display different behaviors in N 2 adsorption and activation. The distinctive electronic structure and surface chemistry of a particular Dy 2 O 3 surface configuration were found to significantly enhance the activation of N 2 by promoting charge transfer, which facilitates the NRR process. This research provides deep insights into the mechanistic pathways of N 2 reduction over Dy 2 O 3 , highlighting the surface properties as pivotal in catalysis. These theoretical insights serve as a foundation for the development of novel rare earth-based electrocatalytic materials for efficient ambient e-NRR, potentially transforming ammonia production into a greener and more energy-efficient process.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Updated sustainability status of cadmium telluride thin‐film photovoltaic systems and projections

This paper provides a comprehensive assessment of the up-to-date life-cycle sustainability status of cadmium-telluride based photovoltaic (PV) systems. Current production modules (Series 6 and Series 7) are analyzed in terms of their energy performance and environmental footprint and compared with the older series 4 module production and current single-crystalline Silicon (sc-Si) module production. For fixed-tilt systems with Series 6 modules operating under average US irradiation of 1800 kWh/m 2 /year, the global warming potential (GWP) is reduced from 16 g CO 2eq /kWh in Series 4 systems to 10 CO 2 eq /kWh in Series 6 systems. For operation in US-SW irradiation of 2300 kWh/m 2 /year, the GWP is reduced from 11 to 8 CO 2eq /kWh and for 1-axis tracking systems operating in Phoenix, Arizona, with point-of array irradiation of 3051 kWh/m 2 /year the GWP is reduced to 6.5 CO 2eq /kWh. Similar reductions have happened in all environmental indicators. Energy payback times (EPBT) of currently installed systems range from 0.6 years for fixed–tilt ground–mounted installations at average US irradiation at latitude tilt installations to 0.3 years for one-axis trackers at high US-SW irradiation, considering average fossil-fuel dominated electricity grids with fuel to electricity conversion efficiency of 0.3. The resulting energy return on energy investment (EROI) also depends on the conversion efficiency of the electricity grid and on the operation life expectance. For a 30-year operational life and grid conversion efficiency of 0.3, EROI ranges from 50 (at US average irradiation) to 70 for US-SW irradiation. The EROI declines with increased grid conversion efficiency; for CdTe PV operating in south California with grid conversion efficiency of 49%, the EROI is about 50 and is projected to fall to 30 when the state's 2030 target of 80% renewable energy penetration materializes. Material alternatives that show a potential of further reductions in degradation rates and materials for enhanced encapsulation that would enable longer operation lives have also been investigated. A degradation rate of 0.3%/year, which has been verified by accelerated testing, is assumed in 30-year scenarios; this is projected to be reduced to 0.2%/year in the near-term and potentially to 0.1%/year in the longer term. With such low degradation rates and enhanced edge-sealing, modules can last 40- to 50-years. Consequently, all impact indicators will be proportionally reduced while EROI will increase. This detailed LCA was conducted according to ISO standards and IEA PVPS Task 12 guidelines. Furthermore, the study revealed that the choices of system models, methods and temporal system boundaries can significantly impact the results and points out to the need to include assumptions regarding these choices in the “transparency in reporting” requirements listed in the IEA PVPS Task 12 Guidelines.

14 SOLAR ENERGY↗

Bridging the Gap in Carbon Free Iron Making: How Hydrogen Affects the Reduction of Iron Ore between 900 and 1590 °C

Hydrogen-based reduction of iron ore for iron and steel production has emerged as a promising alternative to coal and natural gas. Unlike other hydrogen-based iron ore reduction studies, this research focuses on a wide temperature range across 900–1590 °C, encompassing reduction in solid, mixed, and liquid (slag) phases. For a 20 min exposure to hydrogen, the reduction degree increased monotonically from ∼35% at 900 °C to >90% at 1550 °C, except between 1100 °C and 1400 °C, where it stagnated ∼60%. This experimental work challenges the widely accepted notion that higher temperatures enhance the reduction process. Instead, it reveals an overlooked kinetic bottleneck, suggesting complex thermodynamic and mass transfer limitations influenced by phase transformations, diffusion barriers, and microstructural changes. Density functional theory-based molecular dynamics simulations indicate that oxygen diffusivity in BCC iron is 3.88 × 10 –5 cm 2 /s which is ∼5–10 times higher than that in FCC iron. This study reports that this stagnant reduction degree in the mixed solid–liquid phase is due to competition of multiple mechanisms, such as surface- and bulk-diffusion, pore collapse mechanisms, and crystallographic transitions.

08 HYDROGEN↗

HERMeS Thruster Magnetic Field Topology Optimization Study: Performance, Stability, and Wear Results

NASA's Hall Effect Rocket with Magnetic Shielding (HERMeS) 12.5kW Technology Demonstration Unit-1 (TDU-1) has been the subject of extensive technology maturation in preparation for flight system development. The TDU-1 thruster implements a magnetically shielded field topology and has demonstrated the elimination of the discharge channel erosion as a life limiting mechanism. Extensive wear testing the TDU Hall thrusters has identified the thruster front pole covers as the next life limiting component. This effort aims to explore and investigate alternate magnetic field topologies to assess whether reductions in the front pole cover erosion can be attained while still maintaining very low erosion rates on the discharge channel walls. Four candidate magnetic field topologies that reduce the effectiveness of the shielding along the discharge channel walls with the intent to also reduce the erosion rates along the front pole covers were designed. Three of the four candidate magnetic field topologies (B1, B2, and B4) have been manufactured and were subjected to an extensive test campaign that includes laser induced fluorescence (LIF), performance, stability, wear, plume, and thermal characterization. In Phase I, LIF measurements along the discharge chamber centerline found that upstream retraction of the thruster's peak magnetic field does result in an upstream shift of the acceleration zone but the magnitude of the shift does not correspond one-to-one to the shift in the location of the peak radial magnetic field magnitude. Phase II test segment results found at a normalized thruster magnetic field setting of 1, the thruster performance was very similar for all configurations. Discharge current waveforms ripple data indicated that configurations Bo, B1, and B2 has similar oscillatory profiles with the B2 configuration transitioning to higher oscillatory mode at 400V instead of the 450V observed for configurations B0 and B1. Configuration B4 ripple data indicates that the thruster was operating in a very oscillatory mode above 350V. Inner front pole cover erosion rates for configuration B1 were approximately 65% relative to B0 and the erosion rates for configuration B2 were 40% relative to B0. Analysis of the performance, stability, and wear test results of configurations B0, B1, B2, and B4 indicates that configuration B2 may present an alternative option for B0 because it mostly maintained the same performance and stability as configuration B0 but with 40% of the inner front pole cover erosion rate.

Kamhawi, Hani↗

Evaluating the Thermodynamics of Electrocatalytic N 2 Reduction in Acetonitrile

The synthesis of ammonia by proton-coupled electroreduction of dinitrogen (N2) represents a sustainable alternative to currently practiced hydrogenation methods. Developments in this area require knowledge of the standard reduction potentials that describe the thermodynamics of N2 reduction. The first collection of N2 reduction standard potentials in organic solvent are reported here. The potentials for reduction of N2 to ammonia (NH3), hydrazine (N2H4), and diazene (N2H2) in acetonitrile (MeCN) solution are derived using thermochemical cycles. Ammonia is the thermodynamically favored product, with a 0.43 V difference between NH3 and N2H4 and a 1.26 V difference between NH3 and N2H2. The thermodynamics for reduction of N2 to the protonated products ammonium (NH4+) and hydrazinium (N2H5+) under strongly acidic conditions are also presented. Comparison with previously determined values for the H+/H2 potential in MeCN reveals a 63 mV thermodynamic preference for N2 reduction to NH3 over H2 production. Combined with knowledge of the kinetics of electrode-catalyzed H2 evolution, a wide working region is identified to guide future electrocatalytic studies.

Lindley, Brian M.↗

Co-occurring genomic capacity for anaerobic methane and dissimilatory sulfur metabolisms discovered in the Korarchaeota

Phylogenetic and geological evidence supports the hypothesis that life on Earth originated in thermal environments and conserved energy through methanogenesis or sulfur reduction. Here we describe two populations of the deeply rooted archaeal phylum Korarchaeota, which were retrieved from the metagenome of a circumneutral, suboxic hot spring that contains high levels of sulfate, sulfide, methane, hydrogen and carbon dioxide. One population is closely related to ‘Candidatus Korarchaeum cryptofilum OPF8’, while the more abundant korarchaeote, ‘Candidatus Methanodesulfokores washburnensis’, contains genes that are necessary for anaerobic methane and dissimilatory sulfur metabolisms. Phylogenetic and ancestral reconstruction analyses suggest that methane metabolism originated in the Korarchaeota, whereas genes for dissimilatory sulfite reduction were horizontally transferred to the Korarchaeota from the Firmicutes. Interactions among enzymes involved in both metabolisms could facilitate exergonic, sulfite-dependent, anaerobic oxidation of methane to methanol; alternatively, ‘Ca. M. washburnensis’ could conduct methanogenesis and sulfur reduction independently. Metabolic reconstruction suggests that ‘Ca. M. washburnensis’ is a mixotroph, capable of amino acid uptake, assimilation of methane-derived carbon and/or CO 2 fixation by archaeal type III-b RuBisCO for scavenging ribose carbon. Our findings link anaerobic methane metabolism and dissimilatory sulfur reduction within a single deeply rooted archaeal population and have implications for the evolution of these traits throughout the Archaea.

59 BASIC BIOLOGICAL SCIENCES↗

Photocatalytic reduction of CO2 using CdS nanorods on porous anodic alumina support

Highlights: • Commercial grade quality of aluminum foil was used to fabricate uniformly ordered PAA. • A more compassionate method of SILAR was adopted for synthesis on CdS on PAA. • Photocatalytic reduction of CO{sub 2} was carried on flat sheet reactor with mirror reflectors, which proves to be a potential candidate for large scale application. • Enhanced photocatalytic reduction of CO{sub 2} was obtained, when CdS was retained along the pore wall of the support. - Abstract: Solar reduction of CO{sub 2} to valuable chemicals has captured attention of several researchers due to its cumulative effect on reduction of global warming and also as an alternative to fossil fuels. Hexagonally ordered porous anodic alumina (PAA), prepared from commercial aluminium foil, was used as a support for CdS photocatalyst due to its unique honeycomb structure. The CdS nanorods were vertically grown on the PAA template by successive ion layer adsorption reaction (SILAR) method. The photocatalytic reduction of CO{sub 2} by CdS to CH{sub 3}OH was investigated using a flat sheet reactor under 10 W LED lamp. A peak CH{sub 3}OH formation at 144.5 μmol/g/h with 45.4% of photocatalytic efficiency and 1.97% of CO{sub 2} conversion efficiency in a single pass were obtained.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

NASA Alternate Fecal Canister On-orbit Performance and Applicability to Exploration Missions

NASA developed a collapsible canister for the collection and containment of fecal deposits on long range exploration missions as well as on space stations where mass and volume are of great impact on spacecraft and propulsion designs. Developed as an alternative to the exploration toilet hard-sided canister, the container is a smaller volume for stowage in the unfilled state which allows better use of constrained volume on smaller vehicles for longer missions while still providing the important features of odor and solid/liquid contents containment when in the filled state. A reduction in mass was also achieved for the alternate fecal canister itself, although weight of the lid and contents are common to both the hard-side canister, and the alternate fecal canister. Details of the design, flight build and certification, and technology demonstration on ISS will be discussed. The discussion will include interface requirements and design solutions for use with the Universal Waste Management System (UWMS) as well as future extensibility for other toilet systems.

toilet↗

NASA Glenn Research Center Experience Using DOE Midwest Region Super ESPC

The energy crisis of 1973 prompted the Federal Government and private industry to look into alternative methods to save energy. At the same time the constant reduction of operations and maintenance funds during the last 5 years forced Glenn Research Center (GRC) to look for alternative funding sources to meet the mandate to reduce energy consumption. The Super Energy Savings Performance Contract (ESPC) was chosen as a viable source of facility improvement funding that can create larger project scope and help replace aging, inefficient equipment. This paper describes Glenn's participation in the Department of Energy (DOE) Super ESPC program. This program provided Glenn cost savings in the performance of energy audits, preparation of documents, evaluation of proposals, and selection of energy service company (ESCO).

Zala, Laszlo F.↗

Pendent Relay Enhances H 2 O 2 Selectivity during Dioxygen Reduction Mediated by Bipyridine-Based Co–N 2 O 2 Complexes

Generally, cobalt–N 2 O 2 complexes show selectivity for hydrogen peroxide during electrochemical dioxygen (O 2 ) reduction. We recently reported a Co(III)–N 2 O 2 complex with a 2,2'-bipyridine-based ligand backbone which showed alternative selectivity: H 2 O was observed as the primary reduction product from O 2 (71 ± 5%) with decamethylferrocene as a chemical reductant and acetic acid as a proton donor in methanol solution. We hypothesized that the key selectivity difference in this case arises in part from increased favorability of protonation at the distal O position of the key intermediate Co(III)–hydroperoxide species. To interrogate this hypothesis, in this study we have prepared a new Co(III) compound that contains pendent –OMe groups poised to direct protonation toward the proximal O atom of this hydroperoxo intermediate. Mechanistic studies in acetonitrile (MeCN) solution reveal two regimes are possible in the catalytic response, dependent on added acid strength and the presence of the pendent proton donor relay. In the presence of stronger acids, the activity of the complex containing pendent relays becomes O 2 dependent, implying a shift to Co(III)–superoxide protonation as the rate-determining step. Interestingly, the inclusion of the relay results in primarily H 2 O 2 production in MeCN, despite minimal difference between the standard reduction potentials of the three complexes tested. EPR spectroscopic studies indicate the formation of Co(III)–superoxide species in the presence of exogenous base, with greater O 2 reactivity observed in the presence of the pendent –OMe groups.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hydrogen Peroxide‐Induced Overoxidation of Fe−N−C Catalysts: Implications for ORR Activity

Fe−N−C (iron-nitrogen-carbon) electrocatalysts have emerged as promising alternatives to precious metals for the oxygen reduction reaction (ORR), but they remain insufficiently stable for widespread adoption in fuel cell technologies. One plausible mechanism to explain this lack of stability, and the associated catalyst degradation, is oxidative attack on the catalyst surface by hydrogen peroxide, a non-selective byproduct of the ORR. In this work, we perform a detailed analysis of this degradation mechanism, using a combination of periodic Density Functional Theory (DFT) calculations and ab-initio molecular dynamics (AIMD) simulations to probe the thermodynamics and kinetics of hydrogen peroxide activation on a series of candidate active sites for the Fe−N−C catalyst. The results demonstrate that carbon atoms neighbouring FeN 4 active sites can be strongly over-oxidized via formation of hydroxyl or epoxy groups when hydrogen peroxide is present in the electrolyte. In most cases, the interaction between the over-oxidizing groups and the ORR reaction intermediates reduces the ORR activity, and we further propose that the over-oxidized sites are likely precursors to irreversible carbon corrosion and further catalyst deactivation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Iridium Complexes with Proton-Responsive Azole-Type Ligands as Effective Catalysts for CO 2 Hydrogenation

Pentamethylcyclopentadienyl iridium (Cp*Ir) complexes with bidentate ligands consisting of a pyridine ring and an electron-rich diazole ring were prepared. Their catalytic activity towards CO 2 hydrogenation in 2.0 M KHCO 3 aqueous solutions (pH 8.5) at 50 °C, under 1.0 MPa CO 2 /H 2 (1:1) have been reported as an alternative to photo- and electrochemical CO 2 reduction. Bidentate ligands incorporating an electron-rich diazole ring improved the catalytic performance of the Ir complexes compared to the bipyridine ligand. Complexes 2, 4 and 6, possessing both a hydroxy group and an uncoordinated NH group, which are proton-responsive and capable of generating pendent-bases in basic media, recorded high initial TOF values of 1300 h -1 , 1550 h -1 and 2000 h -1 , respectively. Here, spectroscopic and computational investigations revealed that the reversible deprotonation changes the electronic properties of the complexes and causes interactions between pendent base and substrate and/or solvent water molecules, resulting in the high catalytic performance in basic media.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The topologically twisted index of $ \mathcal{N} $ = 4 super-Yang-Mills on T 2 × S 2 and the elliptic genus

We examine the topologically twisted index of $ \mathcal{N} $ = 4 super-Yang-Mills with gauge group SU(N ) on T 2 × S 2 , and demonstrate that it receives contributions from multiple sectors corresponding to the freely acting orbifolds T 2 /$ \mathbb{Z} $m × $ \mathbb{Z} $n where N = mn . After summing over these sectors, the index can be expressed as the elliptic genus of a twodimensional $ \mathcal{N} $ = (0, 2) theory resulting from Kaluza-Klein reduction on S 2 . This provides an alternate path to the ‘high-temperature’ limit of the index, and confirms the connection to the right-moving central charge of the $ \mathcal{N} $ = (0, 2) theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗