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Modeling and Optimization of a Rotating Packed Bed Contactor with a Tetraamine-Appended Metal−Organic Framework for CO 2 Capture

A potential contactor technology for sorbent-based CO 2 capture is the rotating packed bed that contains separate sections for continuous adsorption and desorption. A heat exchanger can be embedded to remove heat in the adsorption section and add heat in the desorption section. In this work, we develop a two-dimensional (2D) model of a rotating packed bed for use in CO 2 capture applications. Mass and energy balances for the model are developed based on a Ljungström-type air preheater, which accounts for the counter-current axial flow of gas phases in separate sections of the bed and the rotation of a solid sorbent, which cycles between adsorption and desorption sections. The sorbent used for this analysis is the tetraamine-appended metal−organic framework Mg 2 (dobpdc)(3−4− 3), chosen for its stability and affinity for CO 2 at low partial pressures, such as those from a natural gas power plant source. An optimization problem is solved that considers the trade-off between maximizing the productivity of the bed and minimizing energy consumption. Maximum productivity and minimum energy are found to be 8.53 kg/h/m 3 and 3.84 MJ/kg, respectively, when these objectives are optimized independently. It is observed that the flue gas pressure and bed rotational speed are the desired operating variables to vary for model-based design of experiments to reduce uncertainty in parameter estimation, as these two variables yielded the most information content based on the Fisher information matrix.

20 FOSSIL-FUELED POWER PLANTS↗

Project Final Report - Advanced Oxygen Separation from Air Using a Novel Mixed Matrix Membrane

This report describes a summary of the findings of the project. The technical work was divided into three activities: 1) technoeconomic analysis; 2) membrane component development (support layer, selective layer development, and gutter layer formulation); and 3) hollow fiber formation. The technoeconomic analysis includes operating, capital, and materials costs of an oxygen enrichment system with 1-3 stages. The analysis concluded that the desired gas quality (90-95% O2) cannot be reached with a single stage. The triple stage system yielded the best overall product quality at lower membrane performance levels but with the highest cost. For the membrane development activities, functionalized nanodiamonds have been shown to slightly improve membrane formation behaviors and gas permeability performance. For example, support layers based on polysulfone-nanodiamond composites have been formed that increase the material’s O2 permeability by over a factor of 150, however, at the cost of selectivity that suggests a change in transport mechanism. Furthermore, nanodiamonds have been found to improve membrane durability. Improvements in selective and gutter layers also have been accomplished. An additional accomplishment is the demonstration of phase inversion of polysulfone-nanodiamond composites that ensures that hollow fiber formation can be performed. Finally, the interfaces between support, gutter, and selective layers were briefly examined and the resulting membrane material consisting of all three layers gave good performance in an O2 separation from N2. The three-layer prototype membrane gave permeability of 29.2-32.2 Barrers, which equates to permeance of approximately 290-320 GPU, which is lower than the TEA informed goal of 500 GPU. O2/N2 selectivity ranged from 5.2-6.2, which is consistent with the less costly two-stage implementation of the technology. In summary, new materials have been developed for O2 concentration from air and are well-suited to a hollow fiber format.

20 FOSSIL-FUELED POWER PLANTS↗

Quantum reactive scattering calculations for the cold and ultracold Li + LiNa → Li 2 + Na reaction

A first-principles based quantum dynamics study of the Li + LiNa(ν = 0, j = 0) → Li 2 (ν', j') + Na reaction is reported for collision energies spanning the ultracold (1 nK) to cold (1 K) regimes. A full-dimensional ab initio potential energy surface for the ground electronic state of Li 2 Na is utilized that includes an accurate treatment of the long-range interactions. The Li + LiNa reaction is barrierless and exoergic and exhibits a deep attractive potential well that supports complex formation. Thus, significant reactivity occurs even for collision temperatures approaching absolute zero. The reactive scattering calculations are based on a numerically exact time-independent quantum dynamics methodology in hyperspherical coordinates. Total and rotationally resolved rate coefficients are reported at 56 collision energies and include all contributing partial waves. Several shape resonances are observed in many of the rotationally resolved rate coefficients and a small resonance feature is also reported in the total rate coefficient near 50 mK. Furthermore, of particular interest, the angular distributions or differential cross sections are reported as a function of both the collision energy and scattering angle. Unique quantum fingerprints (bumps, channels, and ripples) are observed in the angular distributions for each product rotational state due to quantum interference and shape resonance contributions. The Li + LiNa reaction is under active experimental investigation so that these intriguing features could be verified experimentally when sufficient product state resolution becomes feasible for collision energies below 1 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Operator Relaxation and the Optimal Depth of Classical Shadows

Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli operators via “shallow shadows,” a recently proposed version of classical shadows in which the randomization step is effected by a local unitary circuit of variable depth t. Here we show that the shadow norm (the quantity controlling the sample complexity) is expressed in terms of properties of the Heisenberg time evolution of operators under the randomizing (“twirling”) circuit—namely the evolution of the weight distribution characterizing the number of sites on which an operator acts nontrivially. For spatially contiguous Pauli operators of weight k, this entails a competition between two processes: operator spreading (whereby the support of an operator grows over time, increasing its weight) and operator relaxation (whereby the bulk of the operator develops an equilibrium density of identity operators, decreasing its weight). From this simple picture we derive (i) an upper bound on the shadow norm which, for depth t~log⁡(k), guarantees an exponential gain in sample complexity over the t=0 protocol in any spatial dimension, and (ii) quantitative results in one dimension within a mean-field approximation, including a universal subleading correction to the optimal depth, found to be in excellent agreement with infinite matrix product state numerical simulations. Our Letter connects fundamental ideas in quantum many-body dynamics to applications in quantum information science, and paves the way to highly optimized protocols for learning different properties of quantum states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mechanistic Approach to Analyzing and Improving Unconventional Hydrocarbon Production [Slides]

DOE research is developing the physical basis and tools needed to manage pressure effectively to increase recovery efficiency. By coupling fast, accurate physics with machine learning, DOE is producing science-based platforms any operator can use. DOE’s research portfolio is targeting hydrocarbon transport at multiple scales, with the goal of increasing recovery efficiency. DOE’s research has led to new, fast & accurate platforms for predicting gas production from fractured shales. Using data from the MSEEL-I site to calibrate our physics-based model, we have early results on pressure management. We have shown that both mechanical and chemical processes in the matrix can negatively impact production.

08 HYDROGEN↗

Structure of two-loop SMEFT anomalous dimensions via on-shell methods

We describe on-shell methods for computing one- and two-loop anomalous dimensions in the context of effective field theories containing higher-dimension operators. We also summarize methods for computing one-loop amplitudes, which are used as inputs to the computation of two-loop anomalous dimensions, and we explain how the structure of rational terms and judicious renormalization scheme choices can lead to additional vanishing terms in the anomalous dimension matrix at two loops. We describe the two-loop implications for the Standard Model Effective Field Theory (SMEFT). As a by-product of this analysis we verify a variety of one-loop SMEFT anomalous dimensions computed by Alonso, Jenkins, Manohar and Trott.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

An Evaluation and Qualification of U.S.-Based Research Reactors for Irradiation Capabilities Supporting Advanced Nuclear Systems

Irradiation experiments are a prerequisite for evaluating nuclear reactor system designs, analyzing the performance of these systems, and obtaining licenses. Likewise, irradiation facilities are necessary for producing the radioisotopes used in industrial and medical applications. Recent developments in modeling and simulation capabilities and advancements in computational resources have further enabled the design of irradiation experiments for evaluating radiation-induced phenomena and determining nuclear fuel, material, and system design and safety criteria pertaining to both normal and accident scenarios. These computational tools and models require comprehensive experimental datasets acquired under prototypic radiation conditions—for exploring material and system performance under the uniquely harsh environments found in nuclear reactors—to enable verification and validation for qualification and licensing purposes. However, qualification of irradiation experimental facilities, primarily research and test reactors (RTRs), necessitates that their performance be evaluated based on the irradiation environment (e.g. flux, power, testing capabilities) using an appropriate scoring matrix. Although many university campus RTRs are available for research and development (R&D) activities and initiatives, this study focuses on evaluating and qualifying the irradiation facilities (mostly RTRs) within the United States that are suitable for advanced nuclear fuel, material, and system irradiation experiments aimed at establishing operational-performance limits and informing component and fuel designs so as to improve operational efficiencies and mitigate proliferation vulnerabilities, as well as for radioisotope production aimed at multipurpose applications. As a result, the findings of the present study support the acceleration of nuclear fuel and material qualifications, thus hastening new and advanced nuclear energy system demonstrations and radioisotope production efforts by using extended R&D.

irradiation experiment↗

Skewness-dependent moments of the pion GPD from nonlocal quark-bilinear correlators

We present lattice QCD calculations of the odd Mellin moments of pion valence-quark generalized parton distribution up to fifth order ⟨𝑥 4 ⟩ and for the skewness range [−0.33, 0] using operator product expansion of bilocal quark-bilinear operators. The calculations are performed on an ensemble with lattice spacing 𝑎 = 0.04 fm and valence pion mass 300 MeV, employing boosted pion states with momenta up to 2.428 GeV and momentum transfers reaching 2.748 GeV 2 . We employ ratio-scheme renormalization and next-to-leading logarithmic resummed perturbative matching. At zero skewness, our results are consistent with previous lattice studies. By combining matrix elements at multiple values of skewness and momentum transfer, skewness-dependent moments are obtained through simultaneous polynomiality-constrained fits.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Expansion of the Direct Feed High-Level Waste Glass Composition in the High Al Range

Baseline glass compositions have been developed and demonstrated for successful immobilization of Hanford high-level waste (HLW) prepared through a pretreatment process. Recent enhanced waste glass formulations have shown promise to increase the waste loading of pretreated sludge compositions from a broader range of HLW feeds. This project proposes to increase the loading of minimally pretreated Hanford HLW in glass by expanding the existing database and glass property-composition models. Estimated direct-feed high level waste (DFHLW) compositions were generated by the Hanford Tank Operations Contractor and used by Pacific Northwest National Laboratory to determine target glass compositions. Gaps in existing data were identified including one high-priority gap in the high Al compositional region. This report summarizes the data collected during the characterization of the DFHLW High Al Glass Matrix. These glasses were intentionally designed with high aluminum concentrations (15 to 30 wt%) and a high likelihood of nepheline formation, which is known to negatively affect glass durability. Some glasses were expected to either fail or approach property constraints to fill data gaps in poorly understood regions of the compositional space due to lack of data. Out of the 50 glasses tested, 14 glasses formed nepheline, while the model predicted nepheline formation in 20 glasses. All quenched glasses met the product consistency test durability constraint; however, 8 glasses failed this constraint after undergoing the canister centerline cooling treatment. Additionally, 17 glasses did not meet the viscosity constraints, 4 failed the EC constraints, and 2 exceeded the allowable T2% for spinel crystal formation. All glasses satisfied the SO 3 solubility limit. The resulting dataset provides valuable information to improve model accuracy and reduce prediction uncertainty. These insights will ultimately support the development of more robust glass formulation strategies, enabling higher waste loadings, reducing operational risks, and expanding the processing envelope.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Sparse matrix‐vector and matrix‐multivector products for the truncated SVD on graphics processors

Summary Many practical algorithms for numerical rank computations implement an iterative procedure that involves repeated multiplications of a vector, or a collection of vectors, with both a sparse matrix and its transpose. Unfortunately, the realization of these sparse products on current high performance libraries often deliver much lower arithmetic throughput when the matrix involved in the product is transposed. In this work, we propose a hybrid sparse matrix layout, named CSRC, that combines the flexibility of some well‐known sparse formats to offer a number of appealing properties: (1) CSRC can be obtained at low cost from the popular CSR (compressed sparse row) format; (2) CSRC has similar storage requirements as CSR; and especially, (3) the implementation of the sparse product kernels delivers high performance for both the direct product and its transposed variant on modern graphics accelerators thanks to a significant reduction of atomic operations compared to a conventional implementation based on CSR. This solution thus renders considerably higher performance when integrated into an iterative algorithm for the truncated singular value decomposition (SVD), such as the randomized SVD or, as demonstrated in the experimental results, the block Golub–Kahan–Lanczos algorithm.

Aliaga, José I.↗

Generalizing mkFit and its Application to HL-LHC

mkFit is an implementation of the Kalman filter-based track reconstruction algorithm that exploits both thread- and data-level parallelism. In the past few years the project transitioned from the R&D phase to deployment in the Run-3 offline workflow of the CMS experiment. The CMS tracking performs a series of iterations, targeting reconstruction of tracks of increasing difficulty after removing hits associated to tracks found in previous iterations. mkFit has been adopted for several of the tracking iterations, which contribute to the majority of reconstructed tracks. When tested in the standard conditions for production jobs, speedups in track pattern recognition are on average of the order of 3.5x for the iterations where it is used (3-7x depending on the iteration). Multiple factors contribute to the observed speedups, including vectorization and a lightweight geometry description, as well as improved memory management and single precision. Efficient vectorization is achieved with both the icc and the gcc (default in CMSSW) compilers and relies on a dedicated library for small matrix operations, Matriplex, which has recently been released in a public repository. While the mkFit geometry description already featured levels of abstraction from the actual Phase-1 CMS tracker, several components of the implementations were still tied to that specific geometry. We have further generalized the geometry description and the configuration of the run-time parameters, in order to enable support for the Phase-2 upgraded tracker geometry for the HL-LHC and potentially other detector configurations. The implementation strategy and high-level code changes required for the HL-LHC geometry are presented. Speedups in track building from mkFit imply that track fitting becomes a comparably time consuming step of the tracking chain.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Investigation of Coincidence Counting for Improving Minimal Detectable Activity of 110m Ag in Single Particle Gamma Analysis

Post-irradiation examination (PIE) of fuel particles from the fourth Advanced Gas Reactor Fuel Development and Qualification (AGR) Program irradiation (AGR-5/6/7) is being performed at Oak Ridge National Laboratory (ORNL). Tristructural isotropic (TRISO)-coated particles and associated compacts for the AGR-5/6/7 experiment fabricated by BWX Technologies Nuclear Operations Group were formed into a graphite matrix compact and irradiated at the Advanced Test Reactor at Idaho National Laboratory. At ORNL, particles are deconsolidated from the graphite matrix compact and individually scanned for emitted gamma rays with the Irradiated Microsphere Gamma Analyzer (IMGA). The IMGA system comprises a single high purity germanium (HPGe) detector, an automated particle handling vacuum system, and an ORTEC DSPEC-50 digital spectrometer for gamma ray analysis. IMGA quantifies gamma ray-emitting fission product inventories of individual TRISO particles, and these inventories can be compared with the measured average inventories per particle and radionuclide inventories predicted by AGR-5/6/7 physics calculations to determine if a particle experienced radionuclide release. Details on IMGA data collection methods can be found in the literature. The TRISO particle’s SiC layer provides structural support, as well as a barrier for fission product release during irradiation or subsequent safety testing. A weakened or compromised SiC layer can be identified by the release of radionuclides, such as 137 Cs, which is detected by IMGA. However, select radionuclides, such as 90 Sr, 110 mAg, and 154 Eu have been shown to migrate through an intact SiC layer. Measurement of the radionuclide 110 mAg is significant as its release has been shown to be particularly sensitive to in-reactor conditions (e.g., temperature) with broad variable particle to-particle release behaviors observed within a single compact. As such, 110 mAg activity is often used for particle selection for comprehensive PIE as bounding 110 mAg retention particles are hypothesized to represent limits in particle behaviors within a compact. As TRISO particle fuel PIE activities continue over time, IMGA measurements of the 110 mAg inventory are eventually hindered because of its relatively short half-life (~250 days). As the fuel ages from its end of irradiation (EOI) date, the measurement uncertainty and minimum detectable activity (MDA) of 110m Ag increase because the detector background continuum begins to dominate. For particles from the second AGR irradiation experiment (AGR-2), the 110m Ag MDA was above 20% of the calculated average particle inventory after approximately five half-lives, and 110m Ag activity was no longer measurable with IMGA after approximately seven half-lives. Therefore, coincidence counting approaches have been explored to determine feasibility of leveraging new approaches to overcome limitations associated with increasing MDA over time.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Thermal Process Technology for Nuclear Applications - 20379

ANSTO's Synroc technology has been developed to provide a safe, secure matrix for the immobilization and final disposal of radioactive waste. Synroc technology will be used to manage radioactive wastes from the production of the radioisotope Molybdenum-99 (Mo-99). This paper shall outline various stages of the process development with specific reference to the thermal treatment technology of calcination. Calcination is a key step in the Synroc process [1-2].The rotary thermal processing system includes: an advanced heating element design for increased robustness and ease of remote operation and maintenance, an enhanced modular design of components for ease of remote maintenance in a hot cell and in compliance with hot cell radioactive environment requirements for safety, reliability and maintainability. In addition to thermal treatment of waste from nuclear medicine production, this technology provides solutions for a variety of nuclear materials processing applications including sintering UO{sub 2} pellets for reactor fuel rods, oxidation of UO{sub 2} pellets, swarf, and powder to U{sub 3}O{sub 8}, de-nitration of Uranyl nitrate and hydrofluorination of UO{sub 2} pellets. The paper will also discuss thermal processing solutions for a range of nuclear applications. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

AGR-5/6/7 Final Release-to-Birth Ratio Data Analysis

AGR-5/6/7 is the last of a series of Advanced Gas Reactor (AGR) experiments conducted in the Advanced Test Reactor (ATR) at Idaho National Laboratory (INL) in support of development and qualification of tristructural isotropic (TRISO) low-enriched fuel for use in the high-temperature gas cooled reactor (HTGR). AGR configuration and irradiation conditions are based on prismatic HTGR technology that is distinguished primarily through the use of helium coolant, a low-power-density ceramic core capable of withstanding very high temperatures, and TRISO-coated particle fuel. The AGR tests provide valuable irradiation-performance data to support fuel process development, qualify fuel for normal operation and accident conditions, and support development and validation of fuel performance and fission-product (FP) transport models and codes. Each AGR test consists of multiple independently controlled and monitored capsules containing fuel compacts placed in a graphite cylinder shrouded by a steel shell. Release-to-birth ratios (R/B) for fission-gas isotopes released from each capsule are calculated from release rates, measured by germanium detectors in the Fission Product Monitoring System (FPMS) installed downstream from each capsule, and birth rates calculated using numerical models of FG generation. The R/Bs are a critical measure of the ability of the fuel kernel, the particle coating layers, and the compact matrix to retain fission-gas atoms, preventing their release into the sweep-gas flow, and the impact of initially defective particles and/or particle-coating failures that occur during irradiation. For fission-gas isotopes, particle failure is defined as failure of all coating layers, allowing gaseous fission atoms to escape from a particle. During the first five cycles (162B ? 165A), R/Bs were stable in the 10-8?10-6 range, and no in-pile particle failures were observed, based on the gross gamma counts. The maximum R/B value of around 2 ? 10-6 for Kr-85m resulted from the presence of as-fabricated exposed kernels (based on the high exposed kernel fraction), the dispersed uranium, and high fuel particle temperatures in Capsule 1. Comparison of capsule-measured R/Bs from these early cycles to predictions using the previously developed AGR R/B model demonstrated FG release from the AGR-5/6/7 TRISO fuel was comparable to that of previous experiments. In addition, the Kr-85m R/B per-exposed-kernel values are comparable to R/B values obtained in AGR-3/4 irradiation experiment and four irradiation experiments performed during 1980s: (1) HRB-17/18, (2) COMEDIE-BD1, (3) HFR B1, and (4) HRB-21. In contrast, all measured R/B values are lower than predictions by the commonly used Richards and German models, which are intentionally conservative. A large number of in-pile particle failures occurred in Capsule 1 by the end of Cycle 166A. During the final four cycles (166A ? 168A), apparent damage to the Capsule 1 gas line appeared to cause FG leakage from that capsule into the other four capsules, resulting in an increase in fission gas (FG) detected in the effluent for all capsules. Isolation of the Capsule 1 gas line during the last three cycles also prevented measurement of its FG release. Thus, R/Bs in all capsules after Cycle 166A are highly uncertain because of undefined amount of leakage from Capsule 1, especially for long-lived isotopes. A few hundred in-pile particle failures were estimated for Capsule 1 before the end of Cycle 166A, but the total number of failures is unknown due to the lack of FG release data in the later cycles. Based primarily on evidence from the gross gamma counts during Cycle 168A, approximately 15 particles failed in Capsule 3 and four particles failed in Capsule 2. In-pile failures in Capsule 3 were anticipated because this capsule was designed to operate beyond the HTGR normal operating temperature range. In contrast, no in-pile failures were identified in the top two capsules (4 and 5) based on the absence of the typical spikes in gross gamma counts and low failure estimates using the AGR model, developed in INL/EXT-14-32970, for R/B of the short-lived isotopes (Kr-89 and Xe-137) with minimal leakage from Capsule 1.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Fermionic mean-field dynamics for spin systems beyond free fermions

We introduce the fermionized time-dependent Hartree–Fock (fTDHF), a real-time quantum dynamics method for spin-1/2 Hamiltonians following their mapping to fermions via the Jordan-Wigner transformation. fTDHF is formally equivalent to exact dynamics in the case of free fermions, and can efficiently handle non-local string operators arising from long-range interactions via transition matrix elements between non-orthogonal Slater determinants. We show that the fTDHF method can be implemented on a classical computer with a cost that scales polynomially with system size, and linearly with the time steps. We benchmark fTDHF against exact dynamics on three separate spin-1/2 models, representing adiabatic preparation of states with long-range correlations, disorder-driven observation of many-body localization, and particle production in the Schwinger model. For each of these systems, fTDHF is shown to reproduce the qualitative dynamics generated by the exact evolutions, while maintaining a simple physical picture due to its mean-field nature.

Dutta, Rishab↗

Effect of oxidative breakers on organic matter degradation, contaminant mobility and critical mineral release during shale-fracturing fluid interactions in the Marcellus Shale

Oil and gas production from organic-rich shale formations has become viable through advancements in multistage hydraulic fracturing. However, fluctuations in oil and gas prices, coupled with the sharp decline in gas production after the initial days of fracturing operations, drive operators to devise strategies for enhancing hydrocarbon production. The use of highly reactive fracturing fluids that include strong oxidizing agents, also known as breakers, can potentially increase well productivity. The oxidative breakers are used to reduce the viscosity of gel-based fluids after the proppant is transported into fracture zones of the target formation. These breakers can also degrade the organic matter, enhancing the release of hydrocarbons. However, chemical byproducts generated by the interaction of oxidative breakers with the shale matrix have not been extensively studied. Here, this study investigated the fluid-rock interactions between Marcellus Shale and synthetic hydraulic fracturing fluid (HFF) solutions comprising three different oxidative breakers, i.e., ammonium persulfate, sodium bromate, and sodium hypochlorite, commonly used in the Appalachian Basin, USA. Our results demonstrate that the type of oxidizing breakers used in the HFF controlled the type and amount of volatile organic compounds (VOCs) and semi-volatile organic compounds (SVOCs) produced. In all HFF reacted effluents, we observed the transformation of VOCs and the presence of organic acids in variable amounts. However, effluents from HFF containing sodium bromate and sodium hypochlorite breakers showed the presence of several halogenated organic compounds. Changes in major ions and mineralogy indicate that carbonate dissolution and barite precipitation were ubiquitous in all shale reacted effluents. Our results also demonstrate that the addition of oxidative breakers increased the concentration of several major and trace elements in the effluents. These elements fall under the critical mineral (CM) or critical element category due to their high demand in emerging technologies and susceptibility to supply chain disruption due to variety of factors. However, before oxidative breakers can be used at a larger field scale to enhance the release and recovery of CM and hydrocarbons, a better understanding is required of the potential environmental impacts associated with the generation and transformation of contaminants during breaker-fluid-rock interaction.

54 ENVIRONMENTAL SCIENCES↗

Dissecting Tensor Cores via Microbenchmarks: Latency, Throughput and Numeric Behaviors

Tensor Cores have been an important unit to accelerate Fused Matrix Multiplication Accumulation (MMA) in all NVIDIA GPUs since Volta Architecture. To program Tensor Cores, users have to use either legacy wmma APIs or current mma APIs. Legacy wmma APIs are more easy-to-use but can only exploit limited features and power of Tensor Cores. Specifically, wmma APIs support fewer operand shapes and can not leverage the new sparse matrix multiplication feature of the newest Ampere Tensor Cores. However, the performance of current programming interface has not been well explored. Furthermore, the computation numeric behaviors of low-precision floating points (TF32, BF16, and FP16) supported by the newest Ampere Tensor Cores are also mysterious. In this paper, we explore the throughput and latency of current programming APIs. Further, we intuitively study the numeric behaviors of Tensor Cores MMA and profile the intermediate operations including multiplication, addition of inner product, and accumulation. All codes used in this work can be found in https://github.com/sunlex0717/DissectingTensorCores.

97 MATHEMATICS AND COMPUTING↗

Classical and quantum computing of shear viscosity for ( 2 + 1 ) D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for ( 2 + 1 )-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density η s is consistent with a well-known holographic result 1 4 π at several temperatures on a 4 × 4 honeycomb lattice with the local electric representation truncated at j max = 1 2 . We also find the ratio of the spectral function and frequency ρ x y ( ω ) ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond j max = 1 2 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including j max truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗