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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Discrete Data Qualification System and Method Comprising Noise Series Fault Detection

A Sensor Data Qualification (SDQ) function has been developed that allows the onboard flight computers on NASA s launch vehicles to determine the validity of sensor data to ensure that critical safety and operational decisions are not based on faulty sensor data. This SDQ function includes a novel noise series fault detection algorithm for qualification of the output data from LO2 and LH2 low-level liquid sensors. These sensors are positioned in a launch vehicle s propellant tanks in order to detect propellant depletion during a rocket engine s boost operating phase. This detection capability can prevent the catastrophic situation where the engine operates without propellant. The output from each LO2 and LH2 low-level liquid sensor is a discrete valued signal that is expected to be in either of two states, depending on whether the sensor is immersed (wet) or exposed (dry). Conventional methods for sensor data qualification, such as threshold limit checking, are not effective for this type of signal due to its discrete binary-state nature. To address this data qualification challenge, a noise computation and evaluation method, also known as a noise fault detector, was developed to detect unreasonable statistical characteristics in the discrete data stream. The method operates on a time series of discrete data observations over a moving window of data points and performs a continuous examination of the resulting observation stream to identify the presence of anomalous characteristics. If the method determines the existence of anomalous results, the data from the sensor is disqualified for use by other monitoring or control functions.

Fulton, Christopher↗
DOE OSTI2022

Management and Storage of Scientific Data

Scientific discoveries rely heavily on efficient access, search, and management of massive data sets. Data management technologies have, for decades, provided foundational capabilities for scientific computing. Just as storage, input/output (I/O), and data management have been fundamental to simulation-based science for many years, so too are capable data-management technologies key to the success of today’s scientific workflows utilizing data intensive and machine learning (ML) techniques. The Department of Energy, Office of Science, Advanced Scientific Computing Research (ASCR) program has invested broadly in data-management research focused on high-performance computing (HPC) systems, from parallel file systems that store data to application software that makes these systems more productive. Still, advances in technology combined with growing diversity of supported science strongly motivate continued investment in this area. In January 2022, ASCR convened a workshop to identify priority research directions in the area of data management for high-performance and scientific computing. Attendees were challenged to identify promising approaches that would support the breadth of the DOE mission, including the explosion of artificial intelligence (AI) uses and the growing needs of experimental and observational science. Technological and science drivers were identified and considered as they relate to key aspects of data management such as interfaces, architectural design, and FAIR principles (Findable, Accessible, Interoperable, and Reusable). The thoughts of the workshop participants were distilled into a set of four priority research directions with the potential for high impact on DOE science. These research directions are summarized in the following pages.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2012

Predicting the Electronic Properties of 3D, Million-atom Semiconductor nanostructure Architectures

This final report describes the work done by Jack Dongarra (University Distinguished Professor) and Stanimire Tomov (Research Scientist) related to the DOE project entitled Predicting the Electronic Properties of 3D, Million-Atom Semiconductor Nanostructure Architectures. In this project we addressed the mathematical methodology required to calculate the electronic and transport properties of large nanostructures with comparable accuracy and reliability to that of current ab initio methods. This capability is critical for further developing the field, yet it is missing in all the existing computational methods. Additionally, quantitative comparisons with experiments are often needed for a qualitative understanding of the physics, and for guiding the design of new nanostructures. We focused on the mathematical challenges of the project, in particular on solvers and preconditioners for large scale eigenvalue problems that occur in the computation of electronic states of large nanosystems. Usually, the states of interest lie in the interior of the spectrum and their computation poses great difficulties for existing algorithms. The electronic properties of a semiconductor nanostructure architecture can be predicted/determined by computing its band structure. Of particular importance are the 'band edge states' (electronic states near the energy gap) which can be computed from a properly defined interior eigenvalue problem. Our primary mathematics and computational challenge here has been to develop an efficient solution methodology for finding these interior states for very large systems. Our work has produced excellent results in terms of developing both new and extending current state-of-the-art techniques.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Design and evaluation of alphabetic and numeric input methods for virtual reality

In today’s virtual reality (VR), users have various ways to influence their VR experience, including alphanumeric input. While typing characters and numbers is straightforward on desktop computers, it presents challenges and opportunities in head-mounted display VR due to specific interaction methods and a lack of real-world visual stimuli. Addressing these open questions, our work implements and evaluates ten approaches to alphabetic and numeric inputs in VR. Here, we describe the design motivation behind these input methods and evaluate them in a user study with 40 participants divided into groups for alphabetic and numeric keyboards. This comparison investigates each method’s performance and user interactions. Our findings suggest that different input methods significantly impact words per minute and error rates, and that certain keyboard designs may receive better subjective evaluations despite poorer objective performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Multiscale Reduced Order Modeling and Parameter Estimation for Climate Sciences

Several problems in earth system modeling are dependent on highly multiscale phenomena, such as turbulence, where computational modeling is challenging and expensive. This issue is exacerbated in atmospheric and oceanic domains, due to inherent high-dimensionality of the problem. One approach to this problem has been reduced order modeling (ROM); which aims to represent the key physics of the phenomena as a low-dimensional system. AI methods have huge potential in building accurate, stable ROMs and parameter estimation for these ROMs, as it requires extracting nonlinearities and patterns from simulation and/or observational data. Developing physics-based AI approaches specialized for the complexities of multiscale data, along with strategies to account for uncertainties, will revolutionize rapid modeling, analysis and decision making for earth system problems of practical interest.

58 GEOSCIENCES↗
DOE OSTI2024

A Contextually-Aware Sensitivity Analysis to Guide the Design of Randomized Least Squares Solvers in Applications

Our work on the DOE-sponsored project “A Contextually-Aware Sensitivity Analysis to Guide the Design of Randomized Least Squares Solvers in Applications,” was an effort to address critical challenges in nu merical computing and its applications to optimization. The increasing demand for robust and scalable solutions to large-scale linear algebra problems has highlighted the limitations of traditional approaches, particularly in heterogeneous and extreme-scale computing environments. Randomized Numerical Linear Algebra (RandNLA) offers a promising framework to address these challenges, and this proposal builds on this foundation by introducing innovations in sensitivity analysis and computational adaptability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Probing Oxidation-Driven Amorphized Surfaces in a Ta(110) Film for Superconducting Qubit

Recent advances in superconducting qubit technology have led to significant progress in quantum computing, but the challenge of achieving a long coherence time remains. Despite the excellent lifetime performance that tantalum (Ta) based qubits have demonstrated to date, the majority of superconducting qubit systems, including Ta-based qubits, are generally believed to have uncontrolled surface oxidation as the primary source of the two-level system loss in two-dimensional transmon qubits. Therefore, atomic-scale insight into the surface oxidation process is needed to make progress toward a practical quantum processor. Here, in this study, the surface oxidation mechanism of native Ta films and its potential impact on the lifetime of superconducting qubits were investigated using advanced scanning transmission electron microscopy (STEM) techniques combined with density functional theory calculations. The results suggest an atomistic model of the oxidized Ta(110) surface, showing that oxygen atoms tend to penetrate the Ta surface and accumulate between the two outermost Ta atomic planes; oxygen accumulation at the level exceeding a 1:1 O/Ta ratio drives disordering and, eventually, the formation of an amorphous Ta 2 O 5 phase. In addition, we discuss how the formation of a noninsulating ordered TaO 1–δ (δ < 0.1) suboxide layer could further contribute to the losses of superconducting qubits. Subsurface oxidation leads to charge redistribution and electric polarization, potentially causing quasiparticle loss and decreased current-carrying capacity, thus affecting superconducting qubit coherence. The findings enhance the comprehension of the realistic factors that might influence the performance of superconducting qubits, thus providing valuable guidance for the development of future quantum computing hardware.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Model Parameter Development for Complex Materials: Species-Specific Diffusion Barriers in 316 Stainless Steel from Systematic DFT Calculations

Vacancy-mediated diffusion barriers in 316 stainless steel have been systematically calculated using density functional theory to provide essential parameters for mesoscale microstructure evolution models. A statistical sampling approach employing 210 nudged elastic band calculations across multiple special quasi-random structures captures the effects of local chemical environments in this concentrated alloy. The computational methodology addresses challenges specific to chemically disordered systems, including proper magnetic treatment throughout multi-step calculations and validation against experimental structural properties. The calculated activation barriers reveal clear species-dependent diffusion behavior with the hierarchy Ni >> Fe ˜ Cr >> Mo. Nickel exhibits the highest barriers (0.74–1.31 eV, mean 1.045 eV), confirming its role as the slowest-diffusing major component. Iron and chromium show similar moderate barriers averaging 0.587 eV and 0.522 eV, respectively. Remarkably, molybdenum demonstrates exceptionally low barriers (0.12–0.28 eV, mean 0.194 eV), suggesting much higher mobility than previously recognized and potentially significant implications for precipitation kinetics and microstructure evolution. The barrier ranges remain consistent across different 316 SS compositions, supporting parameter transferability for modeling applications. The overall mean barrier of 0.64 eV provides a practical approximation for phase field simulations, while species-specific values enable detailed treatments of diffusion-controlled processes. This systematic approach establishes a validated framework for generating diffusion parameters in other concentrated alloys where experimental data are limited, while providing the first systematic set of species-specific barriers for predictive modeling of 316 stainless steel microstructure evolution.

36 MATERIALS SCIENCE↗
DOE OSTI2012

Neutron and X-ray Detectors

The Basic Energy Sciences (BES) X-ray and neutron user facilities attract more than 12,000 researchers each year to perform cutting-edge science at these state-of-the-art sources. While impressive breakthroughs in X-ray and neutron sources give us the powerful illumination needed to peer into the nano- to mesoscale world, a stumbling block continues to be the distinct lag in detector development, which is slowing progress toward data collection and analysis. Urgently needed detector improvements would reveal chemical composition and bonding in 3-D and in real time, allow researchers to watch “movies” of essential life processes as they happen, and make much more efficient use of every X-ray and neutron produced by the source The immense scientific potential that will come from better detectors has triggered worldwide activity in this area. Europe in particular has made impressive strides, outpacing the United States on several fronts. Maintaining a vital U.S. leadership in this key research endeavor will require targeted investments in detector R&D and infrastructure. To clarify the gap between detector development and source advances, and to identify opportunities to maximize the scientific impact of BES user facilities, a workshop on Neutron and X-ray Detectors was held August 1-3, 2012, in Gaithersburg, Maryland. Participants from universities, national laboratories, and commercial organizations from the United States and around the globe participated in plenary sessions, breakout groups, and joint open-discussion summary sessions. Sources have become immensely more powerful and are now brighter (more particles focused onto the sample per second) and more precise (higher spatial, spectral, and temporal resolution). To fully utilize these source advances, detectors must become faster, more efficient, and more discriminating. In supporting the mission of today’s cutting-edge neutron and X-ray sources, the workshop identified six detector research challenges (and two computing hurdles that result from the corresponding increase in data volume) for the detector community to overcome in order to realize the full potential of BES neutron and X-ray facilities. Resolving these detector impediments will improve scientific productivity both by enabling new types of experiments, which will expand the scientific breadth at the X-ray and neutron facilities, and by potentially reducing the beam time required for a given experiment. These research priorities are summarized in the table below. Note that multiple, simultaneous detector improvements are often required to take full advantage of brighter sources. High-efficiency hard X-ray sensors: The fraction of incident particles that are actually detected defines detector efficiency. Silicon, the most common direct-detection X-ray sensor material, is (for typical sensor thicknesses) 100% efficient at 8 keV, 25%efficient at 20 keV, and only 3% efficient at 50 keV. Other materials are needed for hard X-rays. Replacement for 3He for neutron detectors: 3He has long been the neutron detection medium of choice because of its high cross section over a wide neutron energy range for the reaction 3He + n —> 3H + 1H + 0.764 MeV. 3He stockpiles are rapidly dwindling, and what is available can be had only at prohibitively high prices. Doped scintillators hold promise as ways to capture neutrons and convert them into light, although work is needed on brighter, more efficient scintillator solutions. Neutron detectors also require advances in speed and resolution. Fast-framing X-ray detectors: Today’s brighter X-ray sources make time-resolved studies possible. For example, hybrid X-ray pixel detectors, initially developed for particle physics, are becoming fairly mature X-ray detectors, with considerable development in Europe. To truly enable time-resolved studies, higher frame rates and dynamic range are required, and smaller pixel sizes are desirable. High-speed spectroscopic X-ray detectors: Improvements in the readout speed and energy resolution of X-ray detectors are essential to enable chemically sensitive microscopies. Advances would make it possible to take images with simultaneous spatial and chemical information. Very high-energy-resolution X-ray detectors: The energy resolution of semiconductor detectors, while suitable for a wide range of applications, is far less than what can be achieved with X-ray optics. A direct detector that could rival the energy resolution of optics could dramatically improve the efficiency of a multitude of experiments, as experiments are often repeated at a number of different energies. Very high-energy-resolution detectors could make these experiments parallel, rather than serial. Low-background, high-spatial-resolution neutron detectors: Low-background detectors would significantly improve experiments that probe excitations (phonons, spin excitations, rotation, and diffusion in polymers and molecular substances, etc.) in condensed matter. Improved spatial resolution would greatly benefit radiography, tomography, phase-contrast imaging, and holography. Improved acquisition and visualization tools: In the past, with the limited variety of slow detectors, it was straightforward to visualize data as it was being acquired (and adjust experimental conditions accordingly) to create a compact data set that the user could easily transport. As detector complexity and data rates explode, this becomes much more challenging. Three goals were identified as important for coping with the growing data volume from high-speed detectors: Facilitate better algorithm development. In particular, algorithms that can minimize the quantity of data stored. Improve community-driven mechanisms to reduce data protocols and enhance quantitative, interactive visualization tools. Develop and distribute community-developed, detector-specific simulation tools. Aim for parallelization to take advantage of high-performance analysis platforms. Improved analysis work flows: Standardize the format of metadata that accompanies detector data and describes the experimental setup and conditions. Develop a standardized user interface and software framework for analysis and data management. The diversity of detector improvements required is necessarily as broad as the range of scientific experimentation at BES facilities. This workshop identified a variety of avenues by which detector R&D can enable enhanced science at BES facilities. The Research Directions listed above will be addressed by focused R&D and detector engineering, both of which require specialized infrastructure and skills. While U.S. leadership in neutron and X-ray detectors lags behind other countries in several areas, significant talent exists across the complex. A forum of technical experts, facilities management, and BES could be a venue to provide further definition.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Ising Processing Units: Potential and Challenges for Discrete Optimization

The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, presents new opportunities for hybrid-optimization algorithms that leverage these kinds of specialized hardware. In this work, we propose the idea of an Ising processing unit as a computational abstraction for these emerging tools. Challenges involved in using and bench- marking these devices are presented, and open-source software tools are proposed to address some of these challenges. The proposed benchmarking tools and methodology are demonstrated by conducting a baseline study of established solution methods to a D-Wave 2X adiabatic quantum computer, one example of a commercially available Ising processing unit.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Accelerating DCA++ (Dynamical Cluster Approximation) Scientific Application on the Summit supercomputer

Optimizing scientific applications on today’s accelerator-based high performance computing systems can be challenging, especially when multiple GPUs and CPUs with heterogeneous memories and persistent non-volatile memories are present. An example is Summit, an accelerator-based system at the Oak Ridge Leadership Computing Facility (OLCF) that is rated as the world’s fastest supercomputer to-date. New strategies are thus needed to expose the parallelism in legacy applications, while being amenable to efficient mapping to the underlying architecture.In this paper we discuss our experiences and strategies to port a scientific application, DCA++, to Summit. DCA++ is a highperformance research application that solves quantum manybody problems with a cutting edge quantum cluster algorithm, the dynamical cluster approximation.Our strategies aim to synergize the strengths of the different programming models in the code. These include: (a) streamlining the interactions between the CPU threads and the GPUs, (b) implementing computing kernels on the GPUs and decreasing CPU-GPU memory transfers, (c) allowing asynchronous GPU communications, and (d) increasing compute intensity by combining linear algebraic operations.Full-scale production runs using all 4600 Summit nodes attained a peak performance of 73.5 PFLOPS with a mixed precision implementation.We observed a perfect strong and weak scaling for the quantum Monte Carlo solver in DCA++, while encountering about 2× input/output (I/O) and MPI communication overhead on the time-to-solution for the full machine run. Our hardware agnostic optimizations are designed to alleviate the communication and I/O challenges observed, while improving the compute intensity and obtaining optimal performance on a complex, hybrid architecture like Summit.

Balduzzi, Giovanni↗
DOE OSTI2023

Engineering Functionalized 2D Metal-Organic Frameworks Nanosheets with Fast Li + Conduction for Advanced Solid Li Batteries

Solid-state batteries can ensure high energy density and safety in lithium metal batteries, while polymer electrolytes are plagued by slow ion kinetics and low selective transport of Li + . Metal-organic frameworks (MOFs) are proposed as emerging fillers for solid-state poly(ethylene oxide)(PEO) electrolytes, however, developing functionalized MOFs and understanding their roles on ion transfer has proven challenging. Herein, combining computational and experimental results, the functional group regulation in MOFs can effectively change surficial charge distribution and limit anion movement is revealed, providing a potential solution to these issues. Specifically, functionalized 2D MOF sheets are designed through molecular engineering to construct high-performance composite electrolytes, where the electron-donating effect of substituents in 2D-MOFs effectively limits the movement of ClO 4 - and promotes mechanical properties and ion migration numbers (0.36 up to 0.64) of PEO. As a result, Li/Li cells with composite electrolyte exhibit superior cyclability for 1000 h at a current density of 0.2 mA cm -2 . Meanwhile, the solid LiFePO 4 /Li battery delivers highly reversible capacities of 148.8 mAh g -1 after 200 cycles. In conclusion, these findings highlight a new approach for anion confinement through the use of functional group electronic effects, leading to enhanced ionic conductivity, and a feasible direction for high-performance solid-state batteries.

25 ENERGY STORAGE↗
DOE OSTI2025

Atomistic Mechanisms of the Crystallographic Orientation‐Dependent Cu 1.8 S Conductive Channel Formation in Cu 2 S‐Based Memristors

Achieving multiple types of resistive switching in a single material with controlled ionic motion is a key challenge in neuromorphic computing, traditionally addressed by combining materials with distinct switching behaviors. Here, Cu 2-x S is identified as a promising candidate to overcome this limitation due to its hierarchical phase transitions. Using in situ biasing experiments, reversible and non-reversible phase transitions (and resistive switching) are demonstrated in γ-Cu 2 S by controlling the compliance current. The formation of parallel high-digenite Cu 1.8 S channels, orientated along the γ-Cu 2 S [201] crystallographic direction, drives the nonvolatile resistive switching. These channels emerge via an intermediate δ-Cu 2 S phase and are stabilized at room temperature by residual strains, alongside β-Cu 2 S phase. In conclusion, the work clarifies the complex, electrically triggered phase transformations in γ-Cu 2 S, and highlights the potential of Cu 2-x S as a versatile material for neuromorphic computing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

MgSiP 2 : An Infrared Nonlinear Optical Crystal with a Large Non‐Resonant Phase‐Matchable Second Harmonic Coefficient and High Laser Damage Threshold

Superior infrared nonlinear optical (NLO) crystals are in urgent demand in the development of lasers and optical technologies for communications and computing. The critical challenge is to find a crystal with large non‐resonant phase‐matchable NLO coefficients and high laser damage threshold (LDTs) simultaneously, which however scale inversely. This work reports such a material, MgSiP 2, that exhibits a large second harmonic generation (SHG) coefficient of d 14 ≈ d 36 = 89 ± 5 pm V −1 at 1550 nm fundamental wavelength, surpassing the commercial NLO crystals AgGaS 2 , AgGaSe 2 , and ZnGeP 2 . First principles theory reveals the polarizability and geometric arrangement of the [SiP 4 ] tetrahedral units as the origin of this large nonlinear response. Remarkably, it also exhibits a high LDT value of 684 GW cm −2 , which is six times larger than ZnGeP 2 and three times larger than CdSiP 2 . It has a wide transparency window of 0.53–10.35 µm, allowing broadband tunability. Further, it is Type I and Type II phase‐matchable with large effective SHG coefficients of d eff,I ≈80.2 pm V −1 and d eff,II ≈73.4 pm V −1 . The outstanding properties of MgSiP 2 make it a highly attractive candidate for optical frequency conversion in the infrared.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Ligand enhanced activity of in situ formed nanoparticles for photocatalytic hydrogen evolution

One consistent challenge of both computational and empirical catalyst screening is ensuring that the variables chosen for the screen are driving the performance analyzed. Furthermore, we compare photocatalytic hydrogen evolution from in situ formed Au and Au/Cu nanoparticles to nanoparticles of the same composition synthesized prior to being used as catalysts, as well as compare them to in situ formed Au and Au/Cu nanoparticles in the presence of exogeneous ligand. For all experiments, we observed that ligand-terminated nanoparticles performed better than un-stabilized in situ formed nanoparticles. We tested the generality of this result by studying Co, Ni, and Pd in the same system and also observed that the introduction of nanoparticle ligand leads to enhanced catalytic activity. Taken together, these results suggest 1) nanoparticle ligands can be beneficial, and even necessary, to produce catalysts with sustained activity 2) For computational prediction of these catalysts, factors relating to particle formation and stability need to be considered when both generating predictions as well as interpreting experimental results based on those predictions

08 HYDROGEN↗
DOE OSTI2016

Charge distribution and hydrogen bonding of a collagen α 2 ‐chain in vacuum, hydrated, neutral, and charged structural models

A challenging task in computational biophysics is to ascertain the solvent effect on the electronic structure and interatomic bonding at the atomistic level. Simulations must be carried out on reasonably large biomolecules for accurate calculations to yield valid results. We report the results of a calculation on collagen model in the form of a peptide under three different environments: vacuum, solvated and with neutral and charged sites. Quantitative results and analysis of the partial charge (PC) distribution on each amino acid are discussed. A significant charge transfer of more than 1 electron from protein to water molecules is found with similar results when the model contains charged sites. The main contributions to the interatomic bonding are from hydrogen bonds (HBs) between water‐water and water‐protein pairs. A connection between PC and HBs can be established since the nonpolar amino acids form no HBs and have the smallest PC and vice versa. The ab initio PC obtained are used in the NAMD simulation showing significant improvement over the default values as reflected in the root mean square deviation of atomic positions in the MD steps and the total free energy in energy minimization. These results could facilitate the interpretation of data on interaction of various ligands in charged proteins in relation to isoelectric points. © 2016 Wiley Periodicals, Inc.

Eifler, Jay↗
DOE OSTI2024

Rethinking Programming Paradigms in the QC-HPC Context

Programming for today’s quantum computers is making significant strides toward modern workflows compatible with high performance computing (HPC), but fundamental challenges still remain in the integration of these vastly different technologies. Quantum computing (QC) programming languages share some common ground, as well as their emerging runtimes and algorithmic modalities. In this short paper, we explore avenues of refinement for the quantum processing unit (QPU) in the context of many-tasks management, asynchronous or otherwise, in order to understand the value it can play in linking QC with HPC. Through examples, we illustrate how its potential for scientific discovery might be realized.

Wong, Elaine↗
DOE OSTI2022

Approximate symmetries in d = 4 CFTs with an Einstein gravity dual

By applying the stress-tensor-scalar operator product expansion (OPE) twice, we search for algebraic structures in d = 4 conformal field theories (CFTs) with a pure Einstein gravity dual. We find that a rescaled mode operator defined by an integral of the stress tensor T ++ on a d = 2 plane satisfies a Virasoro-like algebra when the dimension of the scalar is large. The structure is enhanced to include a Kac-Moody-type algebra if we incorporate the T -- component. In our scheme, the central terms are finite. It remains challenging to directly compute the stress-tensor sector of d = 4 scalar four-point functions at large central charge, which, based on holography and bootstrap methods, were recently shown to have a Virasoro/ $\mathcal{W}$-algebra vacuum block-like structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗