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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 1,135 records · Page 63

Robust decentralized frequency control: A leaky integrator approach

We investigate the robustness of the so-called leaky integral frequency controller for the power network. In particular, using a strict Lyapunov function, we show the closed-loop system is robust in the input-to-state stability sense to measurement noise in the controller. Moreover, an interesting and explicit trade-off between controller performance and robustness is discussed and illustrated using a benchmark study of the 39-bus New England reference network.

Weitenberg, Erik↗

A Multi-Mission Space Avionics Architecture

As the budget for the space industry is dwindling, a reusable avionics architecture applicable across multiple missions is urgently needed to reduce the development and production costs of flight projects. This paper presents a multi-mission avionics architecture which employs interface standards extensively, sot hat avionics systems can be built rapidly by assembling subsystems and instruments in a plug-and-play manner. The key feature of this architecture is a "backbone" standard parallel bus which can accommodate various standard interfaces through a repertoire of I/O modules. Hence, specific ;mission requirements can be met by selecting and integrating the appropriate subsystems and instruments into the system. This architecture can also adopt different "backbone" buses, implement redundant processors, and support distributed processing. An example of the architecture using the MOPS6000 from the Southwest Research Institute is also described. Experiments will be done in the Flight System Testbed (FST) of the Jet Propulsion Laboratory to benchmark the MOPS6000 and to demonstrate its multi-mission capability.

Avionics↗

A Performance Analysis on Soil Dielectric Models Over Organic Soils in Alaska for Passive Microwave Remote Sensing of Soil Moisture

Passive microwave remote sensing of soil moisture (SM) requires a physically based dielectric model that quantitatively converts the volumetric SM into the soil bulk dielectric constant. Mironov 2009 is the dielectric model used in the operational SM retrieval algorithms of the NASA Soil Moisture Active Passive (SMAP) and the ESA Soil Moisture and Ocean Salinity (SMOS) missions. However, Mironov 2009 suffers a challenge in deriving SM over organic soils, as it does not account for the impact of soil organic matter (SOM) on the soil bulk dielectric constant. To this end, we presented a comparative performance analysis of nine advanced soil dielectric models over organic soil in Alaska, four of which incorporate SOM. In the framework of the SMAP single-channel algorithm at vertical polarization (SCA-V), SM retrievals from different dielectric models were derived using an iterative optimization scheme. The skills of the different dielectric models over organic soils were reflected by the performance of their respective SM retrievals, which was measured by four conventional statistical metrics, calculated by comparing satellite-based SM time series with in-situ benchmarks. Overall, SM retrievals of organic-soil-based dielectric models tended to overestimate, while those from mineral-soil-based models displayed dry biases. All the models showed comparable values of unbiased root-mean-square error (ubRMSE) and Pearson Correlation (R), but Mironov 2019 exhibited a slight but consistent edge over the others. An integrated consideration of the model inputs, the physical basis, and the validated accuracy indicated that the separate use of Mironov 2009 and Mironov 2019 in the SMAP SCA-V for mineral soils (SOM < 15%) and organic soils (SOM ≥ 15%) would be the preferred option.

Soil Moisture↗

Chlorine Validation through Critical Integral Experiments

An increased interest in the validation of chlorine nuclear data, specifically 35Cl, in recent years has led to the prioritization of conducting chlorine critical experiments for nuclear data validation and criticality safety evaluations. A previous experiment was conducted with PVC and CPVC (chlorinated polyvinyl chloride) to reduce the margin of subcriticality for PF-4 operations with aqueous plutonium chloride solutions. Challenges in determining the composition of specific polymers, namely the CPVC, made it difficult to characterize, and therefore benchmark. Additional materials that were utilizable for chlorine validation were not immediately clear, as form, strength, purity, and composition are all important. A series of possible absorber materials were identified and studied, but ultimately granular sodium chloride was chosen. In addition to the needs of LANL’s PF-4 other industry collaborators have brought attention to the need for chlorine validation. Specifically, the need for HEU electrorefining with LiCl salts at Y-12 was taken into consideration for this experiment, with the experimental configurations being finely tuned to best meet their needs. Needs for validation were also presented by Idaho National Lab (INL) and TerraPower for validation of their Molten Chloride Reactor Experiment (MCRE) and Molten Chloride Fast Reactor (MCFR) and have also been considered.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Acoustic Emission Methods for the Health Evaluation of Integrated Pressure Components

At the request of the Pressure Systems Senior Discipline Expert, to overcome the access and detectable flaw size limitations of other nondestructive evaluation (NDE) methods for integrated components, a technique akin to seismology was advanced to perceive the earliest signs of cracking in titanium components before they escalate into serious issues. In this project we achieved a landmark in Acoustic Emission (AE) testing with the first NASA Probability of Detection (POD) study. This is an important first step to the certification of the AE method for flight components and was based on the testing of notched panels. By working closely with industry allies and employing approved methods from the boiler and pressure vessel sector, we not only met but surpassed all POD benchmarks with our test and acceptance criteria. In experiments involving solution heat-treated and aged 6Al-4V-Ti alloy tested with broadband sensors, we recorded a 96% success rate, with zero false positives reported. Our research shows that in some cases, AE testing can locate smaller cracks than other NDE methods. An industry tool for scaling results to full pressure vessels is highlighted. However, before applying our findings to NASA components, tests to validate the transfer functions are advised.

acoustic↗

Oxygen Evolution Reaction in Alkaline Environment: Material Challenges and Solutions

Abstract The oxygen evolution reaction (OER) generally exists in electrochemistry‐enabled applications that are coupled with cathodic reactions like hydrogen evolution, carbon dioxide reduction, ammonia synthesis, and electrocatalytic hydrogenation. The OER heavily impacts the overall energy efficiency of these devices because the sluggish OER kinetics result in a huge overpotential, thus, a large amount of efficient catalysts are needed. The benchmark iridium and ruthenium (Ir/Ru)‐based materials (mostly used in acid media) are, however, significantly limited by their scarcity. Non‐precious metal‐based catalysts (NPMCs) have emerged as the most promising alternatives; however, they tend to degrade quickly under the harsh operating conditions of typical OER devices. Another challenge is the unsatisfying performance of OER catalysts when integrated in real‐world devices. Herein, the OER active sites for three mainstream types of NPMCs including non‐precious transition metal oxides/(oxy)hydroxides, metal‐free carbon materials, and hybrid non‐precious metal and carbon composites are reviewed. In addition, possible degradation mechanisms for active sites and mitigation strategies are discussed in detail. This review also provides insights into the gaps between R&D of NPMCs for the OER and their applications in practical devices.

Xie, Xiaohong↗

Decomposing causality into its synergistic, unique, and redundant components

Causality lies at the heart of scientific inquiry, serving as the fundamental basis for understanding interactions among variables in physical systems. Despite its central role, current methods for causal inference face significant challenges due to nonlinear dependencies, stochastic interactions, self-causation, collider effects, and influences from exogenous factors, among others. While existing methods can effectively address some of these challenges, no single approach has successfully integrated all these aspects. Here, we address these challenges with SURD: Synergistic-Unique-Redundant Decomposition of causality. SURD quantifies causality as the increments of redundant, unique, and synergistic information gained about future events from past observations. The formulation is non-intrusive and applicable to both computational and experimental investigations, even when samples are scarce. We benchmark SURD in scenarios that pose significant challenges for causal inference and demonstrate that it offers a more reliable quantification of causality compared to previous methods.

applied mathematics↗

Characterizing the multisectoral impacts of future global hydrologic variability

There is significant uncertainty in how global water supply will evolve in the future, due to uncertain climate, socioeconomic, and land use change drivers and variability of hydrologic processes. It is critical to characterize the potential impacts of uncertainty in future water supply given its importance for food and energy production. In this work, we introduce a framework that integrates stochastic hydrology and human-environmental systems to characterize uncertainty in future water supply and its multisector impacts. We develop a global stochastic watershed model and demonstrate that this model can generate a large ensemble of realizations of basin-scale runoff with global coverage that preserves the mean, variance, and spatial correlation of a historical benchmark. We couple this model with a well-known human-environmental systems model to explore the impacts of runoff variability on the water and agricultural sectors across spatial scales. We find that the impacts of future hydrologic variability vary across sectors and regions. Impacts are felt most strongly in the water and agricultural sectors for basins that are expected to have unsustainable water use in the future, such as the Indus River basin. For this basin, we find that the variability in future irrigation water withdrawals and irrigated cropland increase over time due to uncertainty in renewable water supply. We also use the Indus basin to show how our stochastic ensemble can be leveraged to explore the global multisector consequences of local extreme runoff conditions. This work introduces a novel technique to explore the propagation of future hydrologic variability across human and natural systems and spatial scales.

54 ENVIRONMENTAL SCIENCES↗

PRIME: An evaluation framework for protein representation inference and generalization in viral mutation space

Background Protein language models (PLMs) have revolutionized protein fitness prediction, yet their application to rapidly evolving viral pathogens is often confounded by extreme sequence homology. This homology leads to “data leakage” in standard random validation splits, yielding inflated performance metrics that fail to translate into real-world biosurveillance utility. Results We present Protein Representation Inference for Mutation Evaluation (PRIME), a framework that integrates domain-specific fine-tuning with a rigorous position-stratified validation protocol to evaluate viral threats. Using a dataset of 347,432 SARS-CoV-2 receptor binding domain (RBD) sequences, we demonstrate that while random training data split yields deceptive R 2 values (> 0.90), they fail to generalize to novel mutational sites. By benchmarking models up to 650 M parameters, we show that domain-specific fine-tuning of the ESM-C 600 M model with correctly stratified data provides an initial demonstration of predictive signal for binding affinity and expression at unseen mutational sites of binding affinity and expression on unseen sites (R 2 ~0.23), a significant advancement over base foundation models which exhibit no predictive power (R 2 <0). PRIME’s embedding-based clustering identified 3.03% of bat coronavirus sequences as candidates for further experimental prioritization based on their functional similarity to human-infective strains in embedding space, offering a perspective complementary to traditional phylogenetic methods. Conclusion PRIME establishes a new benchmark for the application of PLMs in pathogen surveillance. Our findings demonstrate that state-of-the-art models and fine-tuning, when paired with stratified validation, provide biologically meaningful insights into pathogen evolution and zoonotic risk.

59 BASIC BIOLOGICAL SCIENCES↗

Validation of MCNP6.1 for Criticality Safety of Pu-Metal, -Solution, and -Oxide Systems

Guidance is offered to the Los Alamos National Laboratory Nuclear Criticality Safety division towards developing an Upper Subcritical Limit (USL) for MCNP6.1 calculations with ENDF/B-VII.1 nuclear data for three classes of problems: Pu-metal, -solution, and -oxide systems. A benchmark suite containing 1,086 benchmarks is prepared, and a sensitivity/uncertainty (S/U) method with a generalized linear least squares (GLLS) data adjustment is used to reject outliers, bringing the total to 959 usable benchmarks. For each class of problem, S/U methods are used to select relevant experimental benchmarks, and the calculational margin is computed using extreme value theory. A portion of the margin of sub criticality is defined considering both a detection limit for errors in codes and data and uncertainty/variability in the nuclear data library. The latter employs S/U methods with a GLLS data adjustment to find representative nuclear data covariances constrained by integral experiments, which are then used to compute uncertainties in k eff from nuclear data. The USLs for the classes of problems are as follows: Pu metal, 0.980; Pu solutions, 0.973; dry Pu oxides, 0.978; dilute Pu oxide-water mixes, 0.970; and intermediate-spectrum Pu oxide-water mixes, 0.953.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Compare predictions of transient fission gas release by empirical and mechanistic models to experiments in high burnup UO 2 fuel

Understanding and predicting fuel performance at high burnup require improving our understanding of transient fission gas release. High-burnup operations enable new mechanisms of fission gas release, which affect fuel performance. The Nuclear Regulatory Commission has recently published its interpretation of existing fuel fragmentation, relocation, and dispersal data in a research information letter. There, transient fission gas release was identified as one of the main factors that contributes to fuel fragmentation, relocation, and dispersal, and therefore limits fuel extension to high burnup. However, transient fission gas release is a complex phenomenon that cannot be fully described by simple empirical descriptions. This report summarizes the development of a mechanistic model for high-burnup transient fission gas release in the fuel performance code BISON. This research was supported by the Nuclear Energy Advanced Modeling and Simulation program during fiscal year 2023 to improve our understanding of high-burnup transient fission gas release and ability to predict it as a function of operation history. To support the development of a mechanistic transient fission gas release model, the existing Simple Integrated Fission Gas Release and Swelling (Sifgrs) model in BISON has been completely refactored to make it more modular and extensible. This effort supports the model's application to high-burnup conditions, its extension to other fuel forms, and the continuous improvement of its current features. Once refactoring was completed, models for high-burnup structure formation, fission gas transfer from non-restructured fuel to high-burnup structure, high-burnup structure intragranular and intergranular fission gas behavior, high-burnup structure bubble evolution, fuel pulverization, and the resulting transient fission gas release were tested and implemented in the Simple Integrated Fission Gas Release and Swelling (Sifgrs) model or tightly coupled to it. The new mechanistic model was then compared to an empirical model developed in parallel by a Nuclear Energy University Program project using a Studsvik high-burnup loss-of-coolant-accident assessment case. Finally, the report details the preliminary BISON results for a benchmark activity organized by the Nuclear Energy Agency to evaluate fuel performance codes' predictive capabilities for burst fission gas release. This work represents an important step toward a mechanistic understanding of fission gas release in high-burnup conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Airfoil Computational Fluid Dynamics - 2k shapes, 25 AoA's, 3 Re numbers

This dataset contains aerodynamic quantities - including flow field values (momentum, energy, and vorticity) and summary values (coefficients of lift, drag, and momentum) - for 1,830 airfoil shapes computed using the HAM2D CFD (computational fluid dynamics) model. The airfoil shapes were designed using the separable shape tensor parameterization that encodes two-dimensional shapes as elements of the Grassmann manifold. This data-driven approach learns two independent spaces of parameter from a collection of sample airfoils. The first captures large-scale, linear perturbations, and the second defines small-scale, higher-order perturbations. For this dataset, we used the G2Aero database of over 19,000 airfoil shapes to learn a parameter space that captured a wide array of shape characteristics. We sampled airfoil designs over both parameter spaces to explore the full range of possible shape variations. The aerodynamic quantities for the generated airfoil were obtained using the HAM2D code, which is a finite-volume Reynolds-averaged Navier-Stokes (RANS) flow solver. We employ a fifth-order WENO scheme for spatial reconstruction with Roe's flux difference scheme for inviscid flux and second-order central differencing for viscous flux. A preconditioned GMRES method is applied for implicit integration. The Spalart-Allmaras 1-eq turbulence model is used for the turbulence closure, and the Medida-Baeder 2-eq transition model is applied to account for the effects of laminar turbulent transition. The airfoil grid is generated with a total of 400 points on the airfoil surface, the initial wall-normal spacing of y+ = 1, and an outer boundary located at 300 chord lengths away from the wall. The CFD simulations are performed at a freestream Mach number of 0.1, for or three different Reynolds' numbers (3M, 6M, and 9M), and for 25 angles of attack from -4 deg. to 20 deg. with 1 degree increments. Across all these various parameters, this dataset includes the results from over 250,000 CFD simulations. The simulations were performed using the Bridges-2 system at the Pittsburgh Supercomputing Center in February 2023 as part of the INTEGRATE project funded by the Advanced Research Projects Agency - Energy, in the U.S. Department of Energy. The data was collected, reformatted, and preprocessed for this OEDI submission in July 2023 under the Foundational AI for Wind Energy project funded by the U.S. Department of Energy Wind Energy Technologies Office. This dataset is intended to serve as a benchmark against which new artificial intelligence (AI) or machine learning (ML) tools may be tested. Baseline AI/ML methods for analyzing this dataset have been implemented, and a link to their repository containing those models has been provided. The .h5 data file structure can be found in the GitHub Repository resource under explore_airfoil_2k_data.ipynb.

2k↗

Airfoil Computational Fluid Dynamics - 9k shapes, 2 AoA's

This dataset contains aerodynamic quantities - including flow field values (momentum, energy, and vorticity) and summary values (coefficients of lift, drag, and momentum) - for 8,996 airfoil shapes, computed using the HAM2D CFD (computational fluid dynamics) model. The airfoil shapes were designed using the separable shape tensor parameterization that encodes two-dimensional shapes as elements of the Grassmann manifold. This data-driven approach learns two independent spaces of parameter from a collection of sample airfoils. The first captures large-scale, linear perturbations, and the second defines small-scale, higher-order perturbations. For this data, we used the G2Aero database of over 19,000 airfoil shapes to learn a parameter space that captured a wide array of shape characteristics. We fixed the linear deformations to be the mean over the database and sampled new shapes over a four-dimensional parameter space of higher-order perturbation. This sampling approaches allows for isolated analysis of non-linear airfoil shape deformations while holding other aspects (e.g., airfoil thickness) approximately constant. The aerodynamic quantities for the generated airfoil were obtained using the HAM2D code, which is a finite-volume Reynolds-averaged Navier-Stokes (RANS) flow solver. We employ a fifth-order WENO scheme for spatial reconstruction with Roe's flux difference scheme for inviscid flux and second-order central differencing for viscous flux. A preconditioned GMRES method is applied for implicit integration. The Spalart-Allmaras 1-eq turbulence model is used for the turbulence closure, and the Medida-Baeder 2-eq transition model is applied to account for the effects of laminar turbulent transition. The airfoil grid is generated with a total of 400 points on the airfoil surface, the initial wall-normal spacing of y+ = 1, and an outer boundary located at 300 chord lengths away from the wall. The CFD simulations are performed at a freestream Mach number of 0.1, Reynolds number of 9M, and at two angles of attack, 4 deg. and 12 deg. The simulations were performed using the Bridges-2 system at the Pittsburgh Supercomputing Center in February 2023 as part of the INTEGRATE project funded by the Advanced Research Projects Agency - Energy in the U.S. Department of Energy. The data was collected, reformatted, and preprocessed for this OEDI submission in July 2023 under the Foundational AI for Wind Energy project funded by the U.S. Department of Energy Wind Energy Technologies Office. This dataset is intended to serve as a benchmark against which new artificial intelligence (AI) or machine learning (ML) tools may be tested. Baseline AI/ML methods for analyzing this dataset have been implemented, and a link to their repository containing those models has been provided. The .h5 data file structure can be found in the GitHub Repository resource under explore_airfoil_9k_data.ipynb.

9k↗

Resolving ECRH deposition broadening due to edge turbulence in DIII-D

Microwave heat pulse propagation experiments have demonstrated a correlation between millimeter-scale turbulence and deposition profile broadening of electron cyclotron (EC) waves on the DIII-D tokamak. In a set of discharges in DIII-D, a variation in edge density fluctuations on the mm-scale is associated with 40%–150% broader deposition profiles, expressed in terms of normalized minor radius, as compared with equilibrium ray tracing. The 1D power profile is determined from transport analysis of the electron temperature response to EC power modulation using perturbative analysis with a square wave power modulation at 20–70 Hz, producing a series of Fourier harmonics that are fit collectively to resolve transport. Fitting an integrated heat flux expressed in the Fourier basis of the modulation to diffusive, convective, and coupled transport terms in a linear model can resolve the broadened EC deposition width from the power perturbation to resolve a broadening in each case. The best fit degree of beam broadening observed scales approximately linearly with the Doppler backscattering measured fluctuation level in the steep gradient region. Quantifying the effect of edge fluctuation broadening on EC current drive power needs of future devices will require 3D full-wave codes that can be validated on the current generation of machines. These DIII-D experiments provide a quantitative measure of fluctuation effects and a dataset to benchmark full-wave simulations that can model and eventually predict nonlinear effects neglected by 1D equilibrium beam and ray tracing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Search for Higgs boson decays to beyond-the-Standard-Model light bosons in four-lepton events with the ATLAS detector at $ \sqrt{s}=13 $ TeV

A search is conducted for a beyond-the-Standard-Model boson using events where a Higgs boson with mass 125 GeV decays to four leptons (ℓ = e or μ). This decay is presumed to occur via an intermediate state which contains one or two on-shell, promptly decaying bosons: H → ZX/XX → 4ℓ, where X is a new vector boson Z d or pseudoscalar a with mass between 1 and 60 GeV. The search uses pp collision data collected with the ATLAS detector at the LHC with an integrated luminosity of 36.1 fb -1 at a centre-of-mass energy s√=13 TeV. No significant excess of events above Standard Model background predictions is observed; therefore, upper limits at 95% confidence level are set on modelindependent fiducial cross-sections, and on the Higgs boson decay branching ratios to vector and pseudoscalar bosons in two benchmark models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Short-term electricity load forecasting: Application-driven evaluation of machine learning models across spatial and temporal scales

As we transition towards a decarbonized economy, the integration of variable renewable energy resources and new demands (e.g., electric vehicles, heat pumps) into the electricity grid places unprecedented pressure on grid operators to effectively anticipate and manage peak load. In this context, machine learning algorithms are proving to be indispensable for accurate short-term load forecasting, a crucial task to address these challenges. This study benchmarks 6 machine learning algorithms, including three neural networks and three tree-based algorithms, across various levels of spatial aggregation and time horizons (1, 4, 8, 24, and 48 h). The central contribution of this work is the comparison and analysis of load forecasting models not only based on statistical metrics, but also based on a novel error metric, which evaluates the cost implications of forecast errors for power system stakeholders. Results show that tree-based models outperform neural networks, based on statistical metrics, and yield less skewed error distributions for most spatial scales. However, through the lens of the novel error metric, neural networks are the more competitive choice, especially for forecast horizons that exceed 8 h. The study concludes with actionable recommendations to grid operators and highlights the need for the development of error metrics that link forecasting accuracy to operational costs. To promote transparency and open science, the datasets and Python code are open-sourced via a supplementary repository.

Houben, Nikolaus↗

The Random Ray Method for neutral particle transport

A new approach to solving partial differential equations (PDEs) based on the method of characteristics (MOC) is presented. The Random Ray Method (TRRM) uses a stochastic rather than deterministic discretization of characteristic tracks to integrate the phase space of a problem. TRRM is potentially applicable in a number of transport simulation fields where long characteristic methods are used, such as neutron transport and gamma ray transport in reactor physics as well as radiative transfer in astrophysics. In this study, TRRM is developed and then tested on a series of exemplar reactor physics benchmark problems. The results show extreme improvements in memory efficiency compared to deterministic MOC methods, while also reducing algorithmic complexity, allowing for a sparser computational grid to be used while maintaining accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗