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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Real-time scattering in Ising field theory using matrix product states

We study scattering in Ising field theory (IFT) using matrix product states and the time-dependent variational principle. IFT is a one-parameter family of strongly coupled nonintegrable quantum field theories in 1+1 dimensions, interpolating between massive free fermion theory and Zamolodchikov's integrable massive 𝐸 8 theory. Particles in IFT may scatter either elastically or inelastically. In the postcollision wave function, particle tracks from all final-state channels occur in superposition; processes of interest can be isolated by projecting the wave function onto definite particle sectors, or by evaluating energy density correlation functions. Using numerical simulations we determine the time delay of elastic scattering and the probability of inelastic particle production as a function of collision energy. We also study the mass and width of the lightest resonance near the 𝐸 8 point in detail. Close to both the free fermion and 𝐸 8 theories, our results for both elastic and inelastic scattering are in good agreement with expectations from form-factor perturbation theory. Using numerical computations to go beyond the regime accessible by perturbation theory, we find that the high-energy behavior of the two-to-two particle scattering probability in IFT is consistent with a conjecture of Zamolodchikov. Our results demonstrate the efficacy of tensor-network methods for simulating the real-time dynamics of strongly coupled quantum field theories in 1+1 dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

The influence of kinematics of deformation on polycrystalline halite dynamic recrystallization: Full-field simulation of simple shear versus pure shear

Rock salt, composed mainly of halite, flows viscoplastically over a wide range of geological conditions, strongly impacting the dynamic evolution of sedimentary basins and orogens. Understanding how dislocation creep, which involves dislocation glide, intracrystalline recovery and dynamic recrystallization, influences the microstructure and rheology of halite under various deformation kinematics and temperatures is crucial for enhancing knowledge of salt flow dynamics. Here, this study employs a full-field numerical simulation method to compare the viscoplastic deformation of polycrystalline halite under simple shear and pure shear conditions up to a natural strain of ε = 1.5 at temperatures ranging from 100 °C to 300 °C. The results are presented in terms of crystallographic preferred orientation (CPO), grain shape preferred orientation (SPO), subgrain boundary direction, grain size and strain rate distribution. The results indicate that the crystallographic anisotropy of individual halite crystals is transferred to the polycrystalline scale, resulting in strain localization, particularly in simple shear simulations. The kinematics of deformation affect the evolution and distribution of high strain-rate bands, determining the direction of intragranular substructures and the morphology of strain-induced grain boundaries, with minimal impact on grain size. The intensity of grain boundary migration increases with temperature, significantly influencing grain morphology and size, thereby obscuring strain localization, while having little effect on CPOs. At low strain (ε < 1.0), CPOs relative to both the maximum shortening direction and the grain SPO are similar regardless of the deformation kinematics. At high strain (ε > 1.0), simple shear CPOs exhibit three stronger {100} maxima with a monoclinic symmetry relative to the grain SPO compared to the six {100} maxima with an orthotropic symmetry relative to the grain SPO generated under pure shear. Therefore, microstructures and CPOs can serve as indicators of the strain path in polycrystalline halite under various conditions, aiding in determining the shear sense and elucidating the deformation kinematics of salt structures.

58 GEOSCIENCES↗
DOE OSTI2024

Two-dimensional coherent spectrum of high-spin models via a quantum computing approach

Here in this work we present and benchmark a quantum computing approach to calculate the two-dimensional coherent spectrum (2DCS) of high-spin models. Our approach is based on simulating their real-time dynamics in the presence of several magnetic field pulses, which are spaced in time. We utilize the adaptive variational quantum dynamics simulation algorithm for the study due to its compact circuits, which enables simulations over sufficiently long times to achieve the required resolution in frequency space. Specifically, we consider an antiferromagnetic quantum spin model that incorporates Dzyaloshinskii-Moriya interactions and single-ion anisotropy. The obtained 2DCS spectra exhibit distinct peaks at multiples of the magnon frequency, arising from transitions between different eigenstates of the unperturbed Hamiltonian. By comparing the one-dimensional coherent spectrum with 2DCS, we demonstrate that 2DCS provides a higher resolution of the energy spectrum. We further investigate how the quantum resources scale with the magnitude of the spin using two different binary encodings of the high-spin operators: the standard binary encoding and the Gray code. At low magnetic fields both encodings require comparable quantum resources, but at larger field strengths the Gray code is advantageous. Numerical simulations for spin models with increasing number of sites indicate a polynomial system-size scaling for quantum resources. Lastly, we compare the numerical 2DCS with experimental results on a rare-earth orthoferrite system. The observed strength of the magnonic high-harmonic generation signals in the 2DCS of the quantum high-spin model aligns well with the experimental data, showing significant improvement over the corresponding mean-field results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Efficient Simulation of Logical Magic State Preparation Protocols

Developing space- and time-efficient logical magic state preparation (MSP) protocols will likely be an essential step toward building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for simulating logical MSP protocols under the standard circuit-level noise model. When applied to protocols based on code-switching, magic state cultivation, and magic state distillation, our method yields a complexity polynomial in (i) the number of qubits and (ii) the nonstabilizerness, e.g., stabilizer rank or Pauli rank, of the target encoded magic state. The efficiency of our simulation method is rooted in a curious fact: every circuit-level Pauli error in these protocols propagates to a Clifford error at the end. This property is satisfied by a large family of protocols, including those that repeatedly measure a transversal Clifford that squares to a Pauli. We provide a proof-of-principle numerical simulation that prepares a magic state using such logical Clifford measurements. Our work enables practical simulation of logical MSP protocols without resorting to approximations or resource-intensive state-vector simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Hybrid quantum simulations with qubits and qumodes on trapped-ion platforms

We explore the feasibility of gate-based hybrid quantum computing using both discrete (qubit) and continuous (qumode) variables on trapped-ion platforms. Trapped-ion systems have demonstrated record one- and two-qubit gate fidelities and long qubit coherence times, while qumodes, which can be represented by the collective vibrational modes of the ion chain, have remained relatively unex- plored for their use in computing. Using numerical simulations, we show that high-fidelity hybrid gates and measurement operations can be achieved for existing trapped-ion quantum platforms. As an exemplary application, we consider quantum simulations of the Jaynes-Cummings-Hubbard model, which is given by a one-dimensional chain of interacting spin and boson degrees of free- dom. Using classical simulations, we study its real-time evolution and develop a suitable variational quantum algorithm for ground state preparation. Furthermore, our results motivate further studies of hybrid quantum computing in this context, which may lead to direct applications in condensed matter and fundamental particle and nuclear physics.

Lower-dimensional field theories↗
DOE OSTI2026

A robust framework for frictional fault contact in geological formations using a stabilized augmented Lagrangian approach

Numerical simulations are essential to evaluate the performance and safety of engineered subsurface systems such as geological carbon storage sites, enhanced geothermal fields, and oil and gas reservoirs. A key challenge lies in accurately modeling the frictional contact behavior along fault surfaces. This problem involves inequality constraints that arise from the physics of frictional slip, requiring specialized numerical methods to handle the resulting highly nonlinear and path-dependent behavior. Here, in this work, we address this challenge using an Augmented Lagrangian Method (ALM) implemented via the Uzawa algorithm. The formulation employs mixed finite element spaces, combining low-order piecewise linear displacements within the 3D domain cells with piecewise constant tractions defined on the fault surfaces. Furthermore, to ensure stability and satisfy the inf-sup condition, the discrete displacement space is enriched with face bubble functions on both sides of the contact interfaces. This approach offers several advantages over other stabilization techniques that rely on additional terms, and it integrates naturally in the Uzawa framework.

58 GEOSCIENCES↗
DOE OSTI2026

U-net architected deep material network training with microstructure local field information

The Deep Material Network (DMN) has recently emerged as a powerful reduced-order modeling framework for simulating the mechanical response of heterogeneous materials such as composites. Unlike most data-driven approaches that directly learn a material’s response under prescribed loading, the DMN acts as a homogenization operator, learning the kinematic constraints and mechanical interactions of the underlying microstructure. However, traditional DMN training relies exclusively on homogenized effective properties derived from Direct Numerical Simulations (DNS), discarding the rich local field data that govern microstructural interactions. In this work, we extend the DMN framework to incorporate such local field information into the offline training process. Utilizing a U-Net architecture, we augment the DMN training objective to include the first and second statistical moments of the local stress fields obtained from linear DNS. This ensures that the learned network topology not only fits the effective stiffness but also accurately reflects the internal local stress and strain partitioning of the microstructure. The results confirm that supervising the localization process during training yields a superior surrogate model, reducing local prediction errors by an order of magnitude and significantly improving generalization to unseen nonlinear constitutive behaviors compared to traditional DMNs.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Theoretical modeling of a bottom-raised oscillating surge wave energy converter structural loadings and power performances

Here, this study presents theoretical formulations to evaluate the fundamental parameters and performance characteristics of a bottom-raised oscillating surge wave energy converter (OSWEC) device. Employing a flat plate assumption and potential flow formulation in elliptical coordinates, closed-form equations for the added mass, radiation damping, and excitation forces/torques in the relevant pitch-pitch and surge-pitch directions of motion are developed and used to calculate the system's response amplitude operator and the forces and moments acting on the foundation. The model is benchmarked against numerical simulations using WAMIT and WEC-Sim, showcasing excellent agreement. The sensitivity of plate thickness on the analytical hydrodynamic solutions is investigated over several thickness-to-width ratios ranging from 1:80 to 1:10. The results show that as the thickness of the benchmark OSWEC increases, the deviation of the analytical hydrodynamic coefficients from the numerical solutions grows from 3% to 25%. Differences in the excitation forces and torques, however, are contained within 12%. While the flat plate assumption is a limitation of the proposed analytical model, the error is within a reasonable margin for use in the design space exploration phase before a higher-fidelity (and thus more computationally expensive) model is employed. A parametric study demonstrates the ability of the analytical model to quickly sweep over a domain of OSWEC dimensions, illustrating the analytical model's utility in the early phases of design.

13 HYDRO ENERGY↗
DOE OSTI2024

Bayesian parameter estimation and evaluation of the K -ω shear stress transport model for plane impinging jets

Numerical simulations with semi-empirical turbulence models are commonly used to model impinging jets, often used for cooling solid surfaces. In this work, the constants in the k-ω shear stress transport model in ANSYS FLUENT are calibrated to experimental velocity and heat transfer data for a plane turbulent impinging air jet to determine if Kennedy-O'Hagan calibration (Kennedy and O'Hagan 2001 J. R. Stat. Soc. B 63 425–64) can improve predictions of near-surface velocities and surface Nusselt numbers for similar flows. Impinging jets have been proposed to cool the target plates of the divertor in future magnetic fusion energy reactors, where simulations are used to estimate divertor performance. The flat-plate divertor (Wang et al 2009 Fusion Sci. Technol .56 1023–7) uses a plane jet of helium issuing from a B = 0.5 mm slot to cool a surface with radius of curvature of 44 B at a distance 4 B from the slot. Predictions from the calibrated numerical model are compared with independent experimental data at different flow conditions, as well as surface temperature data for a flat plate divertor test section. The contribution of this work is evaluation of the accuracy of a calibrated turbulence model for modest extrapolations in flow geometry and flow conditions for a plane impinging jet.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Simulation of Particulate Transport for Delivery of Solid Amendments into the Subsurface: FY24 Status Report

For particulate-based amendments to be viable for field-scale remediation at the Hanford Site (e.g., 200 DV-1 Operable Unit), particles need to be delivered a sufficient radial distance from an injection well and retained at concentrations high enough for effective treatment. An accurate description of the particle radius of influence (ROI) is critical for developing an overall remediation strategy. However, field-scale particle simulations are currently limited due to insufficient simulation capabilities and a lack of experimental data to validate and parameterize particle transport models. To help build toward field-scale deployment, this fiscal year (FY) we have (1) developed a pre screening tool to estimate particle transport, (2) implemented particle transport models within PFLOTRAN, and (3) conducted preliminary estimations of particle ROI. While field-scale numerical simulations will ultimately be necessary before remedy design and field implementation, we have developed a pre-screening tool that offers valuable estimations of expected particle injectability and ROI in a 1-D system. The advantage of the tool is that it does not require extensive laboratory experiments and instead makes predictions based solely on routine laboratory measurements. This tool can assist in down-selection and decision-making by identifying which particle amendment systems are worth pursuing in future laboratory experiments, such as 1-D column tests and beyond. With any system, scaling up from the lab to the field presents challenges. Currently, there is no field data available for model calibration or validation. However, the theoretical particle models being developed herein are the best tools available to guide progress toward field deployment. To help bridge this gap and verify model predictions, larger-scale lab experiments are being proposed. To advance simulation capabilities, six particle transport models are being integrated into the reactive transport simulator PFLOTRAN. These include colloid filtration theory (CFT) and five additional particle transport models (M1-M5). Each model, from M1 to M5, progressively incorporates additional particle transport and retention processes. Ultimately, the simplest model capable of accurately describing 1-D column data will be selected and parameterized. During FY24, the CFT and M1 model have been fully implemented within PFLOTRAN. Using an existing 1 D column experiment, the two currently implemented particle transport models (CFT and M1), and associated parameters, were fit to this experiment. While simpler model formulations are helpful for estimations, these formulations could not fully describe particle transport and retention behavior in the previous 1-D column experiment. Thus, additional complexities will need to be considered, which will be accounted for in the M2-M5 model formulations. Additionally, because a viscous, shear thinning fluid was required to keep particles in suspension, considerations for flow will also need to also be accounted for. Therefore, a new immiscible two-phase flow mode is currently being implemented in PFLOTRAN. With some modifications, this new flow module could also support simulation of non-Newtonian liquid amendments, foams, and emulsions. We also estimated the expected ROI of solid amendments using 1-D simulations. The average predicted ROI was approximately 15 ft for micron-sized zero valent iron (mZVI) suspended in xanthan gum (XG). Using the pre screening tool and ROI estimates, additional amendment-delivery laboratory characterization and experiments are proposed. The results from additional experiments can be used to validate and parametrize particulate transport model formulations, which will ultimately provide predictive capabilities for field amendment-delivery systems.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Ponderomotive electron physics captured in a single-fluid extended magnetohydrodynamics model

The ponderomotive force, arising from the interaction between electromagnetic waves and plasma, plays a critical role in laser fusion, astrophysical plasmas, and laser diagnostics. Traditionally, modeling this force requires multi-fluid or particle-in-cell simulations due to its strong coupling to electron-scale dynamics. In this work, we demonstrate that a one-fluid, two-temperature extended magnetohydrodynamics (XMHD) model—augmented with a generalized Ohm's law (GOL) including electron inertia—can accurately reproduce key ponderomotive effects. We derive the ponderomotive force within this framework using a phasor-based approach and then validate its nonlinear manifestations through direct numerical simulations in the PERSEUS code, where steepening and density modulation phenomena typically associated with kinetic-scale models are reproduced. These results and prior work establish XMHD as a robust and efficient alternative for modeling nonlinear laser–plasma dynamics, bridging the gap between ideal MHD and fully kinetic approaches.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Emergence of Diverse Failure Patterns in Weathering‐Induced Landslides: Insights From Particle Finite Element Simulations

Weathering is a fundamental driver of landslide evolution over geological timescales. Despite its ubiquity and importance, quantifying how weathering drives the progressive destabilization of rock slopes remains challenging. In this work, we develop a unified computational framework based on the particle finite element method to investigate the evolution of weathering‐induced landslides, from long‐term weathering to short‐term slope failure and runout dynamics. The framework integrates key processes, including weathering front propagation, time‐dependent strength degradation, rupture surface development, and post‐failure runout dynamics. Through numerical simulation experiments, we elucidate how interactions among weathering characteristics (type, intensity, and rate law), bedrock strength, fracture distribution, and slope geometry govern the failure modes and kinematics of weathering‐induced landslides. Simulations show that matrix‐dominated weathering leads to shallow translational failures, whereas fracture‐dominated weathering produces deep‐seated rotational and compound landslides. Pre‐existing fractures and slope morphology also strongly influence the movement of destabilized landmasses, affecting the failure pattern (e.g., kinematic mode and rupture surface geometry) and post‐failure behavior (e.g., runout velocity). We further demonstrate that the failure time and volume of weathered slopes are governed by the competition between gravitational driving forces and cohesive resisting forces during progressive destabilization. These findings provide new insights into the fundamental mechanisms that drive the emergence of diverse failure patterns of weathering‐induced landslides with important implications for landslide hazard assessment.

Wang, Liang [Eidgenoessische Technische Hochschule↗
DOE OSTI2024

Modeling and simulations of hydrodynamic shocks in a plasma flowing across randomized ICF scale laser beams

High-energy laser beams interacting with flowing plasmas can produce a plasma response that leads to deflection of the beam, beam bending. Such beams have usually a speckle structure generated by optical smoothing techniques that reduce the spatial and temporal coherence in the laser field pattern. The cumulative plasma response from laser speckles slows down the velocity of the incoming flow by momentum conservation. For slightly super-sonic flow the cumulative plasma response to the ponderomotive force exerted by the beam speckle ensemble is the strongest, such that slowing down the flow to subsonic velocities leads eventually to the generation of a shock around the cross section of the beam. This scenario has been predicted theoretically and is confirmed here by our hydrodynamic simulations in two dimensions with speckled beams and in one dimension with a reduced model. The conditions of shock generation are given in terms of the ponderomotive pressure, speckle size and the flow velocity. The nonlinear properties of the shocks are analyzed using Rankine–Hugoniot relations. According to linear theory, temporally smoothed laser beams exhibit a higher threshold for shock generation. Numerical simulations with beams that are smoothed by spectral dispersion compare well with the linear theory results, diverging from those produced by beams with only a random phase plates in the nonlinear regime. The conditions necessary for shock generation and their effects on the laser plasma coupling in inertial confinement fusion (ICF) experiments are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Heterogeneous energetic material damage simulator (HEDS): A deep learning approach to simulate damage–sensitivity linkages

Damage in the microstructures of energetic materials (EMs), such as propellants and plastic bonded explosives (PBXs), can significantly alter their response to external loads. Both sensitization and desensitization can occur, causing concerns with safety and performance in the field; predictive models that connect damage and the sensitivity of EMs can enable design and provide confidence in their robustness and reliability. However, modeling of damage evolution is challenging for real microstructures of EMs; samples of damaged EMs are difficult to obtain, thereby hindering experiments and direct numerical simulations to determine the sensitivity of EMs at various stages of damage. Here, we develop an approach to generate synthetic, i.e., in silico produced, damaged microstructures for use in simulations to connect damage levels to sensitivity. The development of the present workflow to generate and impose varying levels of damage in microstructures, known as HEDS (Heterogeneous Energetic Material Damage Simulator), begins with a small set of images of damaged PBXs and combines a collection of deep neural network techniques to generate microstructures with varying levels of damage. By making the synthetic microstructures conform closely to those observed in available real, imaged microstructures, we develop an ensemble of damaged microstructures that can be used for in silico shock experiments. HEDS develops these microstructure ensembles as level set fields, which are directly employed in a sharp interface Eulerian hydrocode where shock simulations are performed to quantify the energy release rate from hotspot fields generated in the microstructure. These capabilities can be useful for the analysis and assessment of changes in the sensitivity of EMs and to design formulations that are less susceptible to damage-induced changes in sensitivity and performance.

Fang, Irene (ORCID:0009000844557122)↗
DOE OSTI2025

Turbulence-Resolving Simulations of Hurricane Laura (2020): Insights Into Extreme Winds and Eyewall Turbulence

Extreme weather events pose significant risks to coastal and offshore energy infrastructure. In this work, we investigate the structure of mean winds and turbulence near the surface ( z < 300 m) that occurred during Hurricane Laura in 2020 on the US Gulf Coast. To this end, we perform turbulence-resolving simulations (..delta..x = 33.33 m) that encompass the entire eyewall of Hurricane Laura by introducing a novel method that we will refer to as Moving-Mesoscale to Static-LES Integrated Coupling (MOSAIC). The simulation results are validated against surface, boundary-layer, and mid-tropospheric observations. Our analysis of the extreme wind conditions near the surface indicates that the mean wind and turbulence profiles vary greatly at and near the eyewall, resulting in extreme values of mean wind speed (U > 50 m * s-1) and turbulence kinetic energy (k ~ 50 m2 * s-2) at altitudes above 50 m . To investigate in detail the nature of turbulence within the eyewall of the storm, we conduct higher-resolution simulations (..delta..x = 11.11 m) of a portion of the hurricane. We provide a comprehensive statistical description of turbulence in the eyewall region, highlighting the need to employ ..delta..x ~ 10 m grid spacing to capture the integral length-scales near the surface, second- and higher-order central moments (i.e., skewness and kurtosis), and spectral coherence in the flow accurately. These numerical simulations provide the most detailed description of mean winds and turbulent conditions within the eyewall of a historical tropical cyclone to date, illustrating how high-resolution simulations can enhance limited turbulence measurements in hurricanes and giving insight into the extreme conditions threatening offshore and coastal infrastructure.

17 WIND ENERGY↗
DOE OSTI2025

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

Here, this work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Dynamical ejecta from binary neutron star mergers: Impact of a small residual eccentricity and of the equation of state implementation

Predicting the properties of the matter ejected during and after a neutron star merger is crucial to our ability to use electromagnetic observations of these mergers to constrain the masses of the neutron stars, the equation of state of dense matter, and the role of neutron star mergers in the enrichment of the Universe in heavy elements. Furthermore, our ability to reliably provide such predictions is however limited by a broad range of factors, including the finite resolution of numerical simulations, their treatment of magnetic fields, neutrinos, and neutrino-matter interactions, and the approximate modeling of the equation of state of dense matter. In this manuscript, we study specifically the role that a small residual eccentricity and different implementations of the same equation of state have on the matter ejected during the merger of a 1.3M ⊙ –1.4M ⊙ binary neutron star system. We find that a residual eccentricity e ~ 0.01, as measured ~ 4–6 orbits before merger, causes O(25%–30%) changes in the amount of ejected mass, mainly due to changes in the amount of matter ejected as a result of core bounces during merger. We note that O(1%) residual eccentricities have regularly been used in binary neutron star merger simulations as proxy for circular binaries, potentially creating an additional source of error in predictions for the mass of the dynamical ejecta.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Efficient truncations of SU( N c ) lattice gauge theory for quantum simulation

Quantum simulations of lattice gauge theories offer the potential to directly study the nonperturbative dynamics of quantum chromodynamics, but naive analyses suggest that they require large computational resources. Large 𝑁 𝑐 expansions are performed to order 1/𝑁 𝑐 to simplify the Hamiltonian of pure SU⁡(𝑁𝑐) lattice gauge theories. A reformulation of the electric basis is introduced with a truncation strategy based on the construction of local Krylov subspaces with plaquette operators. Numerical simulations show that these truncated Hamiltonians are consistent with traditional lattice calculations at relatively small couplings. It is shown that the computational resources required for quantum simulation of time evolution generated by these Hamiltonians is 17–19 orders of magnitude smaller than previous approaches, provided that the truncations in this work can reach lattice spacings in three-dimensional simulations comparable to the two-dimensional simulations performed.

Lattice QCD↗