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DOE OSTI2025

Electrical Validation Testing for ORPC MHK Generator, Modification 6: ORPC SBV for MHK Generator System (CRADA Final Report)

For the U.S. Department of Energy’s (DOE) 2016 Small Business Voucher for Marine and Hydrokinetic (MHK) System, Second Round 2016, ORPC intends to work with the National Renewable Energy Laboratory (NREL) to perform dynamometer testing of the MHK generator systems and its associated controls and inverters. ORPC will provide the generator, variable frequency drives (VFD), controls, and inverter for this testing. NREL will utilize the NREL Energy Systems Integration Facility (ESIF) and dynamometer facilities at the National Wind Technology Center (NWTC) for this work. Modification 6: Additionally, NREL will conduct a feasibility study for implementing passive DC rectification at the turbine.

17 WIND ENERGY↗

DOE OSTI2021

Accomplishments and Year-End Performance Report; Wind Energy Program: Fiscal Year 2021

The National Wind Technology Center (NWTC), located at the U.S. Department of Energy's (DOE's) National Renewable Energy Laboratory (NREL) Flatirons Campus, has been a driving force in advancing wind energy technology research worldwide since its designation as a DOE national research center in 1992. Enabled by the Flatirons Campus's world-class facilities, scientists, engineers, analysts, and researchers are pushing the frontiers of science to pursue wind energy innovation. In Fiscal Year (FY) 2021, NREL continued to provide the technical expertise, research capabilities, and industry understanding to support DOE's ambitious climate action and research goals by advancing technology, addressing market and deployment barriers, and driving down costs with more efficient, reliable, and predictable wind energy systems. One of several highlights, NREL received an R&D 100 Special Recognition Award for its Thermoplastic Resin System for Wind Turbine Blades. This breakthrough in the wind turbine manufacturing process will enable the production of recyclable blades that are stronger, longer, and less expensive, while increasing energy capture, decreasing energy and transportation costs, and increasing blade reliability. In a year when the entire U.S. economy struggled to address workforce gaps, an NREL study compared wind industry needs, training programs, and hiring practices with perspectives from students and recent college graduates. Researchers hope that, by pinpointing areas of disconnect, the expectations of employers who have difficulty filling entry-level jobs can better align with the preparation of the potential applicants who find it hard to break into the field. The lab also made numerous new data and modeling resources available in FY 2021. Recent NREL releases include a modeling tool for predicting the power performance and structural loads of wind turbines within a wind farm (FAST.Farm), a computational framework for modeling golden eagle behavior near wind farms, and 20 years of offshore wind data. Updates were also made to the widely used Wind Plant Integrated Systems Design and Engineering Model (WISDEM), which couples engineering and cost models to examine system-level trade-offs. Now, bolstered by a renewed national commitment to tackle climate change and revitalize the U.S. economy through increased investment in clean energy - particularly in offshore wind energy - NREL stands poised to lead the way to a sustainable future that powers the United States with significant levels of reliable, low-cost, accessible wind energy. This report provides an overview of the achievements NREL made on behalf of DOE's Wind Energy Technologies Office (WETO) and other partners during FY 2021 (between Oct. 1, 2020, and Sept. 30, 2021).

Flatirons Campus↗

DOE OSTI2026

Urea-to-Ammonia Conversion at Proteus mirabilis Modified Pt–Ni/BDD Electrodes

Efficient wastewater recycling technologies are essential for long-duration space missions and sustainable water management on Earth. Here, a bioelectrochemical system integrating Proteus mirabilis with a platinum–nickel-modified boron-doped diamond electrode (Pt–Ni/BDDE) for urea-to-ammonia conversion in synthetic urine is presented. Immobilized P. mirabilis catalyzes enzymatic ureolysis, converting urea into ammonia, which is subsequently oxidized electrochemically, and no direct electrochemical urea oxidation is observed. Cyclic voltammetry (CV) of P. mirabilis on Pt–Ni/BDDE in 0.1 M urea and synthetic urine revealed a broad anodic oxidation peak at approximately 0.55–0.75 V vs Ag/AgCl (sat. KCl), corresponding to ammonia oxidation. Control experiments using bare BDDE and Pt–Ni/BDDE in synthetic urine showed no oxidation peak, establishing that the bioelectrocatalytic response originates exclusively from the bioelectrode interface. Chronoamperometry studies revealed that immobilization potential and time critically influenced bacterial adhesion and electrochemical response, with optimal conditions yielding a maximum current density of 0.0055 mA·cm –2 . These quantitative results establish that microbial ureolysis can be efficiently coupled with advanced electrode materials for urea-to-ammonia conversion, offering a promising self-sustaining strategy for urine processing and water recovery in closed-loop life support systems.

Ammonia↗

DOE OSTI2021

Science Breakthroughs 2030. Final report

Agriculture is a fundamental societal activity, characterized by many different landscapes, crops, markets, and participants. Food, agricultural, and biofuels products are central to the daily life of all citizens, though most do not recognize the fragility of the environment that brings forth this abundance. As is noted in the 2012 report from the President's Council of Advisors on Science and Technology, Agricultural Preparedness and the United States Agricultural Research Enterprise (PCAST, 2012) the food and agricultural system faces constant challenges in: Managing new pests, pathogens, and invasive plants. Increasing the efficiency of water use. Growing food in a changing climate. Reducing the environmental footprint of agriculture. Managing the production of bioenergy. Producing safe and nutritious food. Assisting with global food security and maintaining abundant yields. Science Breakthroughs 2030 was organized to identify the most compelling research directions in food and agriculture, in particular those empowered by the application of insights and tools from disciplines of science and engineering not typically associated with food and agricultural research. A committee appointed by the Chairman of the National Research Council explored ideas for research directions with input from the scientific community, with the objective of producing a report describing ambitious and achievable scientific pathways to address major problems and create new opportunities in food and agriculture. Following numerous meetings, a jamboree, and town hall, the appointed committee prepared a report that has subsequently become a reference for federal agencies supporting research in the food and agricultural space. It highlights five key areas for research investment with broad application across food and agriculture: integrated systems research; sensor development; data mining and information sciences, genomics; and the microbiome.

09 BIOMASS FUELS↗

DOE OSTI2020

Herbaceous Feedstock 2020 (State of Technology Report)

The Energy Independence and Security Act (EISA) of 2007 required a minimum supply of 36 million gallons of renewable fuels per year by 2022. In order to achieve these goals, the Bioenergy Technologies Office (BETO) has set cost and technology targets for producing advanced and cellulosic biofuels. One of the targets is to validate feedstock supply infrastructures and systems with 90% overall operating effectiveness and field-to-reactor throat delivered cost less than $85.51/dry ton (2016). As stated by the 2017 Multi-Year Program Plan (DOE 2017), the research and development focus of the Feedstock Technologies (FT) platform is reducing the cost, improving the supply chain logistic efficiency, improving biomass quality, and increasing the supply volume. In addition, BETO oversees annual State of Technology (SOT) report that assesses current technologies that are relevant to BETO’s targets based on actual data and experimental results. Feedstocks are essential to achieving BETO goals because the cost, quality, and quantity of feedstock available and accessible at any given time limit the maximum volume of biofuels that can be produced. In accordance with the 2016 Multi-Year Program Plan (DOE 2016a), FT focuses on (1) reducing the delivered cost of sustainably produced biomass, (2) preserving and improving the physical and chemical quality parameters of harvested biomass to meet the individual needs of biorefineries and other biomass users, and (3) expanding the quantity of feedstock materials accessible to the bioenergy industry. This is done by identifying, developing, demonstrating, and validating efficient and economical integrated systems for harvest and collection, storage, handling, transport, and preprocessing raw biomass from a variety of crops to reliably deliver the required supplies of high-quality, affordable feedstocks to biorefineries as the industry expands. The elements of cost, quality, and quantity are key considerations when developing advanced feedstock supply concepts and systems (DOE 2016a).

09 BIOMASS FUELS↗

DOE OSTI2021

Monitoring agroecosystem productivity and phenology at a national scale: A metric assessment framework

Effective measurement of seasonal variations in the timing and amount of production is critical to managing spatially heterogeneous agroecosystems in a changing climate. Although numerous technologies for such measurements are available, their relationships to one another at a continental extent are unknown. Using data collected from across the Long-Term Agroecosystem Research (LTAR) network and other networks, we investigated correlations among key metrics representing primary production, phenology, and carbon fluxes in croplands, grazing lands, and crop-grazing integrated systems across the continental U.S. Metrics we examined included gross primary productivity (GPP) estimated from eddy covariance (EC) towers and modelled from the Landsat satellite, Landsat NDVI, and vegetation greenness (Green Chromatic Coordinate, GCC) from tower-mounted PhenoCams for 2017 and 2018. Overall, our analysis compared production dynamics estimated from three independent ground and remote platforms using data for 34 agricultural sites constituting 51 site-years of co-located time series. Pairwise sensor comparisons across all four metrics revealed stronger correlation and lower root mean square error (RMSE) between end of season (EOS) dates (Pearson R ranged from 0.6 to 0.7 and RMSE from 32.5 to 67.8) than start of season (SOS) dates (0.46 to 0.69 and 40.4 to 66.2). Overall, moderate to high correlations between SOS and EOS metrics complemented one another except at some lower productivity grazing land sites where estimating SOS can be challenging. Growing season length estimates derived from 16-day satellite GPP (179.1 days) were significantly longer than those from PhenoCam G CC (70.4 days, p adj < 0.0001) and EC GPP (79.6 days, p adj < 0.0001). Landscape heterogeneity did not explain differences in SOS and EOS estimates. Annual integrated estimates of productivity from EC GPP and PhenoCam G CC diverged from those estimated by Landsat GPP and NDVI at sites where annual production exceeds 1000 gC/m –2 yr –1 . Based on our results, we developed a “metric assessment framework” that articulates where and how metrics from satellite, eddy covariance and PhenoCams complement, diverge from, or are redundant with one another. The framework was designed to optimize instrumentation selection for monitoring, modeling, and forecasting ecosystem functioning with the ultimate goal of informing decision-making by land managers, policy-makers, and industry leaders working at multiple scales.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Integrated Safety Management System Description

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOE OSTI2025

NLR HPC Facility Power Usage Effectiveness (PUE) Data

Timeseries of Energy Systems Integration Facility (ESIF) Data Center Power Usage Effectiveness (PUE) Data provided in Parquet and compressed CSV formats Power Metrics Timeseries Fields: ts: Timestamp cooling_kw: Cooling (kilowatts) - Captures the power used by fans and pipe trace heaters associated with outdoor cooling equipment. The dedicated tower filter pump power is also captured as cooling load. energy_reuse: Energy Reuse Effectiveness hvac_kw: Heating, ventilation, and air conditioning (kilowatts) - Captures fan walls, fan coils that support the data center electrical rooms, and the make-up air unit. it_power_kw: IT equipment (kilowatts) - Captures power used by the IT equipment on the data center floor. plug_and_light_kw: Lights and utility plugs (kilowatts) - Captures power associated with the data center and dedicated mechanical room. The crank-case heater for the emergency standby generator is also captured as light and plug load. pue: Power Usage Effectiveness pump_kw: Pumps (kilowatts) - Captures power from pumps that move water in the data center Energy Recover Water loop and the Tower Water loops, and also captures power used by the boost pumps that circulate water through the fan walls. Note: The tower filter pump runs constantly to filter water from the data center cooling tower system, so 2.67 kilowatts are attributed to this pump and that is not reflected in this data field. day: Day of month Outside Weather Station Timeseries Fields: ts: Timestamp outside_air_humidity: Outside air humidity - Relative humidity percent outside_air_temp: Outside air temperature - Degrees Fahrenheit day: Day of month More detail: High-Performance Computing Data Center Power Usage Effectiveness

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Integrated Safety Management System Description (PG470252) (V.10)

Personnel at Sandia National Laboratories (hereinafter referred to as Sandia) comply with United States Department of Energy (DOE) Policy 450.4A, Chg 1, Integrated Safety Management Policy, and implement an Integrated Safety Management System (ISMS) to ensure safe operations. Sandia personnel integrate safety into management and work practices at all levels so missions are accomplished while protecting Members of the Workforce, the public, and the environment. As a result, safety is effectively integrated into all facets of work planning and execution. Thus the management of safety functions becomes an integral part of mission accomplishment and meets the requirements outlined in the DOE Acquisition Regulation (DEAR) 970.5223-1, Integration of Environment, Safety, and Health into Work Planning and Execution, clause incorporated by reference into the Prime Contract. The DEAR 970.5223-1, Integration of Environment, Safety, and Health into Work Planning and Execution, clause requires DOE contractors to manage and perform work in accordance with a documented Safety Management System that fulfills conditions of the DEAR clause at a minimum. For purposes of this clause, safety encompasses environment, safety, and health (ES&H), including pollution prevention and waste minimization.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2024

Physical Properties of Moist, Fermented Corn Grain after Processing by Grinding or Milling

A novel biomass production system, integrating the co-harvesting and co-storage of moist corn grain and stover, promises a reduction in delivered feedstock costs. In this innovative method, the dry grain traditionally utilized for feed or biofuel production will now be processed at a considerably greater moisture content. The adoption of this approach may necessitate a substantial redesign of existing material handling infrastructure to effectively accommodate the handling and storage of moist grain after processing by milling or grinding. A comprehensive study was conducted to quantify the physical properties of this grain after processing with a knife processor or a hammermill. The geometric mean particle size, bulk and tapped density, sliding angle, material coefficient of friction, and discharged angle of repose were quantified. Five grain treatments, either fermented or unfermented, and having different moisture contents, were used. After processing, the moist, fermented ground grain exhibited a significantly smaller particle size compared to the dry grain. Additionally, both moist processed grains resulted in a decreased bulk density and increased material sliding angle, friction coefficient, and angle of repose. The examined metrics collectively suggest that handling, mixing, and storing moist ground grain will pose significant challenges compared to conventional dry ground grain. This increased difficulty may lead to substantially higher costs, a crucial factor that must be carefully considered when evaluating the overall economics of implementing this new biomass production system using combined harvesting and storage of corn grain and stover.

Blazer, Keagan J.↗

DOE OSTI2019

SANS coupled with fluid invasion approaches for characterization of overall nanopore structure and mesopore connectivity of organic-rich marine shales in China

The pore structure of shales, including pore morphology, connectivity, pore volume, specific surface area (SSA), and pore size distribution (PSD), is a significant factor in controlling gas storage and transport and the migration mechanisms of hydrocarbons. However, the lack of comprehensive characterization for both accessible and inaccessible pore structure increases the difficulty of gas-in-place estimation and gas exploration. In order to investigate the nanoscale pore system, integration of high-pressure mercury intrusion porosimetry (MIP), low-pressure N 2 /CO 2 adsorption (LNA/LCA), and small-angle neutron scattering (SANS) were employed to obtain a multi-scale quantitative characterization of the nanopore structure of organic-rich marine shale samples from the Longmaxi and Niutitang Formations in China. In this work, PSDs obtained from the combined techniques appropriately cover an overall nanopore size range of shale (0.35–15,000 nm) and overcome the limits of the individual method. Uni-, bi, and multi-modal PSDs were observed, but the sizes of a significant portion of the nanopores observed in these shales range from 0.35 to 100 nm. Pore volumes and surface areas of micropores (<2 nm), mesopores (2–50 nm), and macropores (>50 nm) were characterized based on the best performance window of each technique: LCA for micropores; LNA and SANS for mesopores; and MIP for macropores. It was found that micropores are the major contributor to the total SSA for both the Longmaxi and Niutitang shales. With respect to pore volume, however, the contribution to the total pore volume has a trend of micropore < mesopore < macropore for the Longmaxi shale samples, but micro-/mesopore volumes are greater than macropore volumes for samples of the Niutitang shale. Strong correlations were also observed between total organic carbon (TOC) content and micropore volume and surface area, which implies that organic matter is a controlling factor in the micropore system of organic-rich shales. In addition, strong correlations between methane adsorption capacity and both micro-/mesopore volumes and SSAs indicate that micro-/mesopores are governing factors for methane storage. Furthermore, the fractions of accessible mesopore volume and surface area were quantitatively estimated by SANS and LNA. Correlation analyses suggest that the accessibility of the mesopore surface area could be an indicator for gas transport and storage in mesopores in organic matter. Thus, a shale with higher connectivity could have higher gas diffusion capability but lower gas adsorption capacity, and vice versa.

58 GEOSCIENCES↗

DOE OSTI2019

Future integrated mobility-energy systems: A modeling perspective

After over a century of petroleum dominance, the transportation sector is on the verge of radical transformations driven by rapid technology advancement of alternative fuels, automation, information technologies that create new mobility options and business models, and policies at all levels of government. While the technologies and fuels that will move people and goods in the future remain uncertain, the future transportation system will be more integrated with smart buildings, the electric grid, renewables, and information ecosystems, allowing for great opportunities to exploit these interconnections. Modeling tools for analyzing integrated mobility-energy systems require a deep understanding of these interconnections, of the infrastructure required to support alternative fuel vehicles, and a more nuanced understanding of transportation energy needs across multiple segments and spatiotemporal scales. In this paper, we assess the landscape of existing tools used to represent and model future mobility systems and their interactions with other energy systems. Here, we conclude that (a) out-of-sample extrapolation of emerging trends and future anticipated developments is more important than ever due to the plethora of factors driving disruptive change in mobility systems; (b) understanding adoption opportunities for alternative fuel light-duty vehicles requires modeling intra-household decisions affecting travel demand and mode choice; (c) mobility and energy systems need to be modeled as an integrated continuum, breaking the traditional approach in which dynamic energy supply models use relatively simple transportation demand and vice-versa; and (d) increased spatiotemporal fidelity and scalability are required to dynamically couple transportation/mobility and energy supply models and capitalize on these unprecedented interconnection opportunities.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

Performance analysis of novel thermal storage integrated heat pump system in a residential building at the hot climate for demand flexibility

A novel thermal energy storage integrated heat pump system was proposed to reshape the electricity load profile of residential buildings while maintaining thermal comfort. High-fidelity computer simulations are needed for evaluating the feasibility of the proposed system. This study investigates the annual performance of the proposed system through Modelica-based system simulations. A rule-based control strategy was developed to shift the electric demand of a typical single-family house in Atlanta, GA from peak to off-peak hours to utilize the Time-of-Use electricity rate to lower the energy costs for conditioning the building. For comparison, a conventional air-source heat pump system serving the same building was also developed. Simulation results indicate that the proposed system is capable of shifting around 90% of the building's electricity consumption for meeting the thermal demand from peak to off-peak hours on a daily basis. In addition, the annual power consumption and operating cost for running the HVAC system can be reduced by 6% and 34%, respectively, compared with the conventional air-source heat pump.

Shi, Liang↗

DOE OSTI2024

Oxidation‐Driven Enhancement of Intrinsic Properties in MXene Electrodes for High‐Performance Flexible Energy Storage

Abstract MXenes, a novel class of 2D materials, exhibit great potential for energy storage due to their unique layered structure and excellent electrical conductivity. However, improving the intrinsic electrochemical storage capacity of MXenes remains a significant challenge, often requiring the incorporation of other Faradaic materials. Oxidation, in particular, poses a key issue that impacts the capacity of MXene devices. In this study, controlled oxidation is employed to create nanoscale holes within MXene, transforming them into holey MXene (H‐MXene) nanosheets. These porous structures shorten ion transport distances and increase ion transport pathways, thereby significantly enhancing the electrochemical storage capacity of MXenes. The resulting H‐MXene micro‐supercapacitors (MSCs) demonstrate exceptional performance, achieving an aerial capacitance 2.5 times that of unmodified MXene electrodes, along with excellent cycling stability, retaining 91.7% of their capacitance after 10 000 cycles. Additionally, a flexible integrated system combining energy storage and sensing functionalities is developed, showcasing its scalability in self‐powered sensing applications. The incorporation of self‐healing polyurethane (PU) enables the device to retain 90% of its storage capacity after undergoing self‐healing. This study presents a novel approach for developing high‐performance MXene‐based energy storage devices and provides valuable insights into efficient ion transport and storage in 2D materials.

Cheng, Yongfa [Department of Materials Science and↗

DOE OSTI2023

A GPT‐4 Reticular Chemist for Guiding MOF Discovery**

Abstract We present a new framework integrating the AI model GPT‐4 into the iterative process of reticular chemistry experimentation, leveraging a cooperative workflow of interaction between AI and a human researcher. This GPT‐4 Reticular Chemist is an integrated system composed of three phases. Each of these utilizes GPT‐4 in various capacities, wherein GPT‐4 provides detailed instructions for chemical experimentation and the human provides feedback on the experimental outcomes, including both success and failures, for the in‐context learning of AI in the next iteration. This iterative human‐AI interaction enabled GPT‐4 to learn from the outcomes, much like an experienced chemist, by a prompt‐learning strategy. Importantly, the system is based on natural language for both development and operation, eliminating the need for coding skills, and thus, make it accessible to all chemists. Our collaboration with GPT‐4 Reticular Chemist guided the discovery of an isoreticular series of MOFs, with each synthesis fine‐tuned through iterative feedback and expert suggestions. This workflow presents a potential for broader applications in scientific research by harnessing the capability of large language models like GPT‐4 to enhance the feasibility and efficiency of research activities.

Chemistry↗

DOE OSTI2023

Coherent Combining for High‐Power Kerr Combs

Abstract Kerr frequency combs enable the miniaturization of comb sources for applications such as data communications and spectroscopy. However, due to the high field confinement and effective nonlinearity, Kerr combs typically operate with low output comb powers. While nonsolitonic Kerr combs operating in the normal group velocity dispersion (GVD) regime can access high pump‐to‐comb conversion efficiencies and relatively flat spectral profiles, many frequency comb applications require even higher comb‐line powers that are otherwise fundamentally unattainable without the use of optical amplifiers. A high efficient coherent beam combining of Kerr combs is demonstrated via on‐chip synchronization to greatly enhanced comb‐line powers. Two normal GVD Kerr combs are coherently combined for a 2.9 dB increase in comb power compared to a single comb while maintaining a high total pump‐to‐comb conversion efficiency of 26%. Lastly, it is shown that via spectral engineering of two normal GVD combs, it should be possible to significantly increase the spectral flatness of a combined comb. This platform enables fully integrated systems with powers that can readily exceed that of an individual comb system by more than an order of magnitude.

Kim, Bok Young↗

DOE OSTI2025

Dilute Regeneration-Driven Membrane Capacitive Deionization of Synthetic Seawater Using Nanopatterned Membranes and Prussian Blue Analog Electrodes

Membrane capacitive deionization (MCDI) offers energy-efficient seawater desalination but is limited at high salinity by membrane resistance and incomplete electrode regeneration. Nanopatterned ion-exchange membranes, dilute regeneration protocols, and Prussian blue analog (PBA)-functionalized electrodes are combined in a flow-by-MCDI cell. Nanopatterned ion-exchange membranes (hexagonal, octagonal, double-ring, rectangular) enhance interfacial ion transport, with hexagonal geometry delivering ≈12.5% greater surface area and the best performance. PBA-functionalized electrodes increase salt adsorption and charge-transfer kinetic rates. The integrated system lowers the area-specific resistance by 45 Ω cm2, resulting in a 500 mV reduction in the cell voltage for a current density of 2 mA cm−2 for a 35 000 ppm NaCl feed. This improves the energy-normalized salt adsorption six fold (64–382 mmol J−1). Low salinity (2000 ppm) and mixed-salt regeneration sustains a ≈39% water recovery and stable performance for at least seven cycles. Overall, combining nanopatterned membranes, which promote confinement-enhanced ion mobility, and PBA electrodes, which enhance salt adsorption, improved the energy efficiency of MCDI.

Hasan, Mahmudul↗

DOE OSTI2021

Revisiting the multi-monopole point of SU( N ) $\mathcal{N}$ = 2 gauge theory in four dimensions

Motivated by applications to soft supersymmetry breaking, we revisit the expansion of the Seiberg-Witten solution around the multi-monopole point on the Coulomb branch of pure SU(N) $\mathcal{N}$ = 2 gauge theory in four dimensions. At this point N - 1 mutually local magnetic monopoles become massless simultaneously, and in a suitable duality frame the gauge couplings logarithmically run to zero. We explicitly calculate the leading threshold corrections to this logarithmic running from the Seiberg-Witten solution by adapting a method previously introduced by D’Hoker and Phong. We compare our computation to existing results in the literature; this includes results specific to SU(2) and SU(3) gauge theories, the large-N results of Douglas and Shenker, as well as results obtained by appealing to integrable systems or topological strings. We find broad agreement, while also clarifying some lingering inconsistencies. Finally, we explicitly extend the results of Douglas and Shenker to finite N, finding exact agreement with our first calculation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗