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At least 721 records · Page 40

ECAR-7300 Rev 1 Verification and Validation of MCNP6.2 for MARVEL Neutronic Analysis

This report documents the verification and validation (V&V) efforts of the Monte Carlo N-Particle transport code (MCNP) version 6.2 on the Sawtooth supercomputer for the Microreactor Applications Research Validation and Evaluation (MARVEL) microreactor required for the preliminary documented safety analysis. This document records V&V for a safety, hazards, analysis, and design software used for design and analysis of safety class structures, system and components (SSC)s.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

Electrification of Pakistan's Transport System: Modeling Electric Vehicle Penetration and Energy Supply Chain Impacts

Initial analysis of the National Electric Vehicle Policy (NEVP) of Pakistan was undertaken by an integrated energy planning team from November 2019 through August 2020. This technical reference document seeks to present the background, inputs and assumptions, methodology, and results of the policy analysis in detail. The intended audience is the technical modeler, analyst, or reviewer who seeks to understand specifically the modeling effort within this initial analytical phase, with the end-goal of interpreting, re-producing, or modifying the simulations or extending the models to conduct follow-on studies subsequently. These studies may examine in greater detail the energy sector, impacts to emissions, charging station infrastructure needs, and overall benefits-cost trade of the policy, among other areas of interest.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Harnessing stratospheric diffusion barriers for enhanced climate geoengineering

Stratospheric sulfate aerosol geoengineering is a proposed method to temporarily intervene in the climate system to increase the reflectance of shortwave radiation and reduce mean global temperature. In previous climate modeling studies, choosing injection locations for geoengineering aerosols has, thus far, only utilized the average dynamics of stratospheric wind fields instead of accounting for the essential role of time-varying material transport barriers in turbulent atmospheric flows. Here we conduct the first analysis of sulfate aerosol dispersion in the stratosphere, comparing what is now a standard fixed-injection scheme with time-varying injection locations that harness short-term stratospheric diffusion barriers. We show how diffusive transport barriers can quickly be identified, and we provide an automated injection location selection algorithm using short forecast and reanalysis data. Within the first 7 d days of transport, the dynamics-based approach is able to produce particle distributions with greater global coverage than fixed-site methods with fewer injections. Additionally, this enhanced dispersion slows aerosol microphysical growth and can reduce the effective radii of aerosols up to 200–300 d after injection. While the long-term dynamics of aerosol dispersion are accurately predicted with transport barriers calculated from short forecasts, the long-term influence on radiative forcing is more difficult to predict and warrants deeper investigation. Statistically significant changes in radiative forcing at timescales beyond the forecasting window showed mixed results, potentially increasing or decreasing forcing after 1 year when compared to fixed injections. We conclude that future feasibility studies of geoengineering should consider the cooling benefits possible by strategically injecting sulfate aerosols at optimized time-varying locations. Our method of utilizing time-varying attracting and repelling structures shows great promise for identifying optimal dispersion locations, and radiative forcing impacts can be improved by considering additional meteorological variables.

54 ENVIRONMENTAL SCIENCES↗

Quantifying the Impact of Transportation on Climate - Energy Analytics Dashboard: Preprint

The investment decisions within the nation's transportation sector have traditionally been prioritized and measured against safety and travel efficiency goals. Increasingly, federal, state, and local policies are requiring consideration of energy use and emissions in the design of our transportation infrastructure. Yet the processes, analytics, and knowledge to include these new metrics into transportation decisions are lacking. Although targeted studies and before and after analysis are performed from time to time, no comprehensive real-time monitoring systems provide energy and emissions to the same level as congestion and safety. To address this gap, this paper developed and demonstrated the Transportation Energy Analytics Dashboard, or TEAD, to raise awareness of the energy and emission impacts to the same level of observability as that of safety and mobility concerns.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗

Evaluation of Hydrogen Gas Generation and Permeation in the 9979 Type AF Shipping Package

The 9979 Type AF Shipping Packaging is a cost-effective radioactive material package designed by Savannah River National Laboratory (SRNL) that consists of two primary components: a foamed outer drum for structural protection and an inner containment drum. The packaging was designed to transport Highly Enriched Uranium (HEU), Low Enriched Uranium (LEU), and other isotopes not exceeding a Type A quantity. These contents have the potential to generate flammable hydrogen gas during transport due to the degradation of hydrogenous materials (e.g. water vapor, plastics, etc) by high-energy alpha radiation. Since 10 CFR 71.43(h) prohibits the incorporation of packaging features explicitly designed for continuous venting, alternative justification was required to demonstrate that the requirements of 10 CFR 71.43(d) for negligible reactions between packaging components and contents were satisfied. An analysis was performed to demonstrate that the potential for hydrogen gas generation over a one-year period was limited by the effects of permeation through the packaging materials. The rate of hydrogen collection was evaluated for both the inner containment drum and the outer structural drum under 10 CFR 71.71 Normal Conditions of Transport (NCT). The analysis concludes that the Lower Flammability Limit (LFL) for hydrogen gas will not be reached in a one-year shipping period assuming a minimum void volume is maintained within the drum.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Mining Nontraditional Water Sources for a Distributed Hydrogen Economy

Securing decarbonized economies for energy and commodities will require abundant and widely available green H 2 . Ubiquitous wastewaters and nontraditional water sources could potentially feed water electrolyzers to produce this green hydrogen without competing with drinking water sources. Herein, we show that the energy and costs of treating nontraditional water sources such as municipal wastewater, industrial and resource extraction wastewater, and seawater are negligible with respect to those for water electrolysis. We also illustrate that the potential hydrogen energy that could be mined from these sources is vast. Based on these findings, we evaluate the implications of small-scale, distributed water electrolysis using disperse nontraditional water sources. Techno-economic analysis and life cycle analysis reveal that the significant contribution of H 2 transportation to costs and CO 2 emissions results in an optimal levelized cost of hydrogen at small- to moderate-scale water electrolyzer size. The implications of utilizing nontraditional water sources and decentralized or stranded renewable energy for distributed water electrolysis are highlighted for several hydrogen energy storage and chemical feedstock applications. Finally, we discuss challenges and opportunities for mining H 2 from nontraditional water sources to achieve resilient and sustainable economies for water and energy.

54 ENVIRONMENTAL SCIENCES↗

Microstructural impacts on ionic conductivity of oxide solid electrolytes from a combined atomistic-mesoscale approach

Abstract Although multiple oxide-based solid electrolyte materials with intrinsically high ionic conductivities have emerged, practical processing and synthesis routes introduce grain boundaries and other interfaces that can perturb primary conduction channels. To directly probe these effects, we demonstrate an efficient and general mesoscopic computational method capable of predicting effective ionic conductivity through a complex polycrystalline oxide-based solid electrolyte microstructure without relying on simplified equivalent circuit description. We parameterize the framework for Li 7- x La 3 Zr 2 O 12 (LLZO) garnet solid electrolyte by combining synthetic microstructures from phase-field simulations with diffusivities from molecular dynamics simulations of ordered and disordered systems. Systematically designed simulations reveal an interdependence between atomistic and mesoscopic microstructural impacts on the effective ionic conductivity of polycrystalline LLZO, quantified by newly defined metrics that characterize the complex ionic transport mechanism. Our results provide fundamental understanding of the physical origins of the reported variability in ionic conductivities based on an extensive analysis of literature data, while simultaneously outlining practical design guidance for achieving desired ionic transport properties based on conditions for which sensitivity to microstructural features is highest. Additional implications of our results are discussed, including a possible connection between ion conduction behavior and dendrite formation.

25 ENERGY STORAGE↗

Insights into pathological mechanisms and interventions revealed by analyzing a mathematical model for cone metabolism

This work analyzes a mathematical model for the metabolic dynamics of a cone photoreceptor, which is the first model to account for energy generation from fatty acids oxidation of shed photoreceptor outer segments (POS). Multiple parameter bifurcation analysis shows that joint variations in external glucose, the efficiency of glucose transporter 1 (GLUT1), lipid utilization for POS renewal, and oxidation of fatty acids affect the cone’s metabolic vitality and its capability to adapt under glucose-deficient conditions. The analysis further reveals that when glucose is scarce, cone viability cannot be sustained by only fueling energy production in the mitochondria, but it also requires supporting anabolic processes to create lipids necessary for cell maintenance and repair. In silico experiments are used to investigate how the duration of glucose deprivation impacts the cell without and with a potential GLUT1 or oxidation of fatty acids intervention as well as a dual intervention. The results show that for prolonged duration of glucose deprivation, the cone metabolic system does not recover with higher oxidation of fatty acids and requires greater effectiveness of GLUT1 to recover. Finally, time-varying global sensitivity analysis (GSA) is applied to assess the sensitivity of the model outputs of interest to changes and uncertainty in the parameters at specific times. The results reveal a critical temporal window where there would be more flexibility for interventions to rescue a cone cell from the detrimental consequences of glucose shortage.

59 BASIC BIOLOGICAL SCIENCES↗

Multimodal CO2 Transportation Cost Model

This model provides a cost estimate for transporting CO2 via truck or rail in the United States using commercially available equipment and technologies. The model includes an analysis of direct and indirect CO2 emissions to determine costs per net tonne of CO2 transported. Publicly available data and methods published in the peer-reviewed literature are used to the extent possible; references are available at the bottom of the "Calculations" sheet. Upstream (i.e., liquefaction, buffer storage) and downstream (i.e., buffer storage, reconditioning) activities are included in the model of emissions and costs. All capital and operating expenditures are estimated in the "Calculations" sheet. The cost of financing the project is determined in the "FINEX" sheet. All user inputs are done via drop down menus in on the "User Interface" sheet. Summary results are also provided on the "User Interface" sheet.

Myers, CoreyA↗

System Studies for Global Nuclear Assurance and Security (GNAS): 3S Risk Analysis for Portable Nuclear Reactors (Volume II) -- Conclusions and Implications

Growing interest in compact, easily transportable sources of baseload electricity has manifested in the proposal and early deployment of portable nuclear reactors (PNRs). PNRs are sought because they are scalable, efficient, and cost-effective for meeting energy demands in unique, remote, or contested areas. For example, Russia's KLT-40S Akademik Lomonosov is a floating nuclear power plant (FNPP) that successfully reached the Arctic coastal city of Pevek. It began providing power to the local grid in December 2019. While providing such key advantages as having a highly flexible power generation mechanism, FNPPs appear to directly challenge international norms and conventions for nuclear safety, safeguards, and security. FNPPs are neither a purely fixed nuclear fuel cycle activity nor a purely transportation-based nuclear fuel cycle activity. In response, Sandia's Mitigating International Nuclear Enogy Risks (MINER) research perspective frames this discussion in terms of risk complexity and the interdependencies between safety, safeguards, and security in FNPPs, and PNRs more generally. This systems study is a technically rigorous analysis of the safety, safeguards, and security risks of FNPP technologies. This research's aims are three-fold. The first aim is to provide analytical evidence to support safety, safeguards, and security claims related to PNRs and FNPPs (Study Report Volume I). Second, this study aims to introduce a systems- theoretic approach for exploring interdependencies between the technical evaluations (Study Report Volume II). The third aim is to show Sandia's ability for prompt, rigorous, and technical analysis to support emerging complex MINER mission objectives.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Bridge Seismic Screening Tool (BSST), Version 2.0

The Regional Resiliency Assessment Program (RRAP) is a cooperative assessment of specific critical infrastructure within a designated geographic area and a regional analysis of the surrounding infrastructure that addresses a range of infrastructure resilience issues that could have regionally and nationally significant consequences. In 2018, DHS’s Cybersecurity and Infrastructure Security Agency (CISA) sponsored the Oregon Transportation Systems RRAP project in coordination with the Office of the Governor (under the oversight of the state resilience officer), the Oregon Office of Emergency Management (OEM), the Oregon Department of Transportation (ODOT), and other regional stakeholders (CISA 2021). This project focuses on assessing the impacts of a Cascadia Subduction Zone (CSZ) earthquake on state transportation systems and, in particular, how those impacts may affect the ability of emergency response efforts to move supplies into the region. The intended outcome of this analysis is the prioritization of transportation routes and modes for additional planning, investment, hardening, or other activities to enhance their resilience—and therefore, to enhance their ability to support response and recovery efforts following a CSZ earthquake. An important part of this transportation system-level assessment has been to assess the seismic vulnerability of the state highway system. In doing so, the RRAP project team used the Bridge Seismic Screening Tool (BSST) to assess, at a system-level, the potential impacts that a CSZ earthquake could have on state highway bridges (Bergerson et al. 2019).1 Argonne National Laboratory (Argonne), in collaboration with the Washington State Department of Transportation (WSDOT), originally developed the BSST as part of the 2017 Washington State Transportation Systems RRAP project, a sister project to the 2018 Oregon Transportation Systems RRAP project. Argonne updated the BSST during this more recent project in Oregon based on feedback from stakeholders and subject matter experts (SMEs) on the original version of the tool. The first step in the BSST is to assess the seismic vulnerability of roadway bridges following a CSZ earthquake to determine a projected or potential damage state. Damage states then help determine approximate reopening times for bridge crossings.2 This document provides details on the BSST methodology, the implementation of that tool to analyze the projected damage incurred in a CSZ earthquake scenario, and the determination of corresponding reopening times of interstate, state highway, and local bridges following such an event.

58 GEOSCIENCES↗

Outgassing of implanted He via short circuit transport along phase and grain boundaries in vapor co-deposited Cu-W nanocomposites

We investigate the response of physical vapor co-deposited copper (Cu)-tungsten (W) nanocomposites to helium (He) implantation. Nuclear reaction analysis (NRA) reveals that a substantial fraction of He implanted into these materials escapes during implantation. Analysis of nanocomposite microstructure shows that the He loss is likely due to its transport out of the material by diffusion along phase and grain boundaries. Lastly, our findings suggest that solid-state interfaces such as phase and grain boundaries are short circuit diffusion pathways for transport of He.

36 MATERIALS SCIENCE↗

Transforming Energy Through Sustainable Mobility: Expanding Low-Carbon Transportation R&D Solutions

As the nation's premier laboratory for cutting-edge transportation decarbonization research and development solutions, the National Renewable Energy Laboratory (NREL) pioneers the creation and deployment of sustainable mobility technologies and strategies, with a focus on slashing transportation sector greenhouse gas emissions and combatting climate change. Trucks, planes, cargo ships, and other difficult-to-decarbonize vehicles are part of this essential transition for the transportation sector, which is currently the nation's largest source of the greenhouse gas emissions. NREL provides the scientific building blocks needed to spur innovation through multifaceted analysis, research, and engineering. This work acts as a catalyst to help industry bring affordable, high-performance, energy-efficient, and low-emission modes of transport and related infrastructure to market sooner. Our researchers collaborate closely with academic, government, and industry partners to design better batteries, drivetrains, and engines. They develop technologies for high-power charging, thermal management, energy storage, and power electronics. They are also reimagining fuels and combustion while creating sustainable lightweight materials. Unbiased expert guidance - backed by credible data and analysis, tools, and scientific rigor - empowers partners to make informed decisions about sustainable transportation. NREL recognizes that communities with limited mobility options face reduced access to employment opportunities, health care, and education, lowering overall quality of life. Alongside partners, NREL experts are creating transportation solutions that meet community-identified needs and increase mobility equity in historically underserved and overburdened communities. Rather than providing a one-size-fits-all solution, we take an interdisciplinary approach to mobility equity that considers the needs and challenges of diverse groups, maximizing benefits at the individual, community, and societal levels.

ADVANCED PROPULSION SYSTEMS↗

Distribution of Infiltration in the 216-U-10 and 216-B-3 Pond Systems 1944-1997

A modeling system to simulate fate and transport of contaminant plumes in groundwater beneath the Central Plateau to support the Cumulative Impact Evaluation (CIE) and Composite Analysis (CA) is being developed. The CIE will evaluate the cumulative effect of multiple Central Plateau radiological and chemical sources on groundwater quality (DOE/RL-2018-69, Cumulative Impact Evaluation Technical Approach Document ). This will enable cleanup decisions to be evaluated in the context of all Central Plateau waste sites and existing groundwater conditions. The CA evaluates the cumulative effect of all sources of radioactive materials on radiological dose to future members of the public (DOE/RL-2018-60, Annual Status Report (FY 2018): Composite Analysis of Low Level Waste Disposal in the Central Plateau of the Hanford Site ). Fate and transport modeling will be used to forecast future groundwater concentrations for both the CIE and CA. The CIE/CA subsurface modeling system is divided into source (inventory), vadose zone, and saturated zone facets. Source inventory is a necessary input to the vadose zone facet, and releases from the vadose zone to groundwater are inputs to the saturated zone facet. The vadose zone facet simulates historical and future releases from the vadose zone to groundwater for both liquid waste and solid waste disposal sites. Effluent release volumes and radionuclide inventory estimates for liquid waste sites are contained in ECFHANFORD- 17-0079, Hanford Soil Inventory Model (SIM-v2) Calculated Radionuclide Inventory of Direct Liquid Discharges to Soil in the Hanford Site’s 200 Areas , herein referred to as SIM-v2. The liquid waste sites in SIM-v2 include the 216-B-3 Pond near 200 East Area and the 216-U-10 Pond in 200 West Area. The 216-B-3 Pond system consisted of a main pond and 3 expansion lobes that were operational during overlapping time periods. It also included influent ditches, but these are not listed as liquid waste sources in SIM-v2 and are not included in the CIE/CA modeling. The total effluent volume released to the pond system was measured, but the partitioning of this volume to the various expansion lobes was not determined and is not accounted for in SIM-v2. Regarding the 216-U-10 Pond, it received water from several influent ditches. The pond and the influent ditches are listed as liquid waste sites in SIM-v2 and are included as sources in the CIE/CA modeling. Because water in the ditches flowed into the pond, only a portion of the effluent volumes and contaminant inventories assigned to the ditches in SIM-v2 infiltrated from the ditches. Thus, partitioning of infiltration and contaminant inventories between the ditches and the pond is not fully accounted for in SIM-v2. Further, some of the water in the 216-U-10 Pond entered overflow ditches and the amount of this overflow was not recorded and is not accounted for in SIM-v2. Thus, the purpose of this Environmental Calculation File (ECF) is to partition the infiltration of wastewater and contaminant inventory between the main pond and each expansion lobe of the 216-B-3 Pond system, and to partition the infiltration of wastewater and contaminant inventory between the ditches and pond of the 216-U-10 Pond system.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Integrated Molten Salt Reactor Modeling Capabilities in NEAMS Thermal Hydraulics Tools

The DOE neams program supports a full range of computational thermal fluids analysis capabilities and code developments for a broad range of advanced reactor concepts. The research and development approach under the thermal fluids technical area synergistically combines three length and time scales in a hierarchical multi-scale approach. To enable multi-scale thermal fluids capability using these codes, a key joint effort has been underway to develop an integrated system- and engineering-scale thermal fluids analysis capability, through integration of SAM and Pronghorn codes, both based on the MOOSE framework. This report summarizes recent advances in developing an integrated system- and engineering-scale modeling capability for the msr concept, which has gained significant interest in recent years. A consistent framework was established by coupling Pronghorn and SAM through the Saline interface, with thermophysical properties provided by the Molten Salt Thermal Property Database (MSTDB-TP). Further improvements were made to the coupling schemes and domain-overlapping strategies, enhancing the stability and robustness of multi-code simulations. Verification and validation efforts demonstrate the accuracy of this integration across a range of benchmark problems, including one-dimensional heated pipe flows, three-dimensional natural convection loops with evolving isotopic compositions, and \gls{msre} demonstration cases. Within Pronghorn, new capabilities were introduced to model corrosion and noble-metal plating phenomena, supported by an extended thermal-hydraulics framework and refined turbulence treatments. To capture two-phase flow behavior, a multiphase Euler–Euler model was implemented in Pronghorn, including advanced closure relations, high-resolution advection techniques, and capillary force reconstruction. Preliminary verification cases confirm the fidelity of the approach, while planned validation efforts target canonical multiphase benchmarks and application to msr components such as the msre pump bowl. Finally, updates to SAM’s msr mass transfer modeling were extended to consider noble gas migration into porous structures like graphite. The point kinetics model was updated to include reactivity feedback contributions from any defined species, such as xenon. The gas transport model was expanded for applicability to gas mixtures, bubble efflux phenomena, and species transport between liquid and gas phases. A selection of multi-scale Sherwood number correlations from MOSCATO/NekRS and multi-phase correlations from literature have been added for improved accuracy in calculating mass transfer coefficients. A companion effort on developing system-level redox corrosion has also been incorporated into SAM. Collectively, these enhancements strengthen the predictive capability of SAM and Pronghorn for simulating MSR thermal-hydraulics, corrosion, multiphase behavior, and fission-product transport, providing a more complete toolset for design, safety analysis, and licensing support of next-generation \gls{msr}s.

42 - ENGINEERING↗

Investigation of core transport changes in DIII-D discharges with off-axis T e profile peaks

Abstract DIII-D discharges that transition to H-mode solely with off-axis electron cyclotron heating (ECH) often exhibit strong off-axis peaking of electron temperature profiles at the heating location. Electron heat transport properties near these off-axis temperature peaks have been studied using modulated ECH. The Fourier analyzed electron temperature data have been used to infer electron thermal diffusivity. Comparisons with numerical solutions of the time-dependent electron thermal equation find that the data are consistent with a narrow region with electron diffusivity χ e an order of magnitude lower than the average value across the plasma, suggesting an electron internal transport barrier (ITB) near the ECH heating location. Detailed profile analysis and equilibrium reconstructions suggest that the formation of these ITBs are correlated with off-axis values of the safety factor q being near 1. Furthermore, the ECH driven H-mode discharges demonstrate more rapid electron heating rate near the ECH deposition location than L-mode discharges with higher auxiliary ECH heating power. Additional modeling attributes this difference to the modification of electron heat transport in the core at the L-H transition, which also sustains the off-axis electron temperature peaks.

Physics↗

Comprehensive new insights on the potential use of SiC as plasma-facing materials in future fusion reactors

Abstract The performance of silicon carbide as an alternative plasma facing material (PFM) was studied at various irradiation conditions relevant to ion energies and fluxes of a fusion reactor. This analysis involves detailed modeling of subsurface plasma/material interactions, sputtered particle transport above the surface and redeposition, and related changes in material composition and microstructure induced by steady-state and Edge Localized Mode ion fluxes. Transition of a crystalline SiC surface to semi-crystalline and amorphous phases was analyzed based on advanced modeling of DIII-D tokamak experiments where SiC was irradiated in single- and multiple- L-mode and H-mode discharges. This analysis shows that displacement damage, particle deposition/redeposition, and D accumulation on the SiC divertor surface can lead to significant microstructural changes that result in enhanced sputtering erosion in comparison with the original crystalline material. However, the resulting total net erosion rate for a full-coverage, advanced tokamak, SiC coated divertor may well be acceptably low. Moreover, the C sputtering yield from the evolved SiC surface can be seven times lower than from a pure graphite surface; this would imply significantly reduced tritium co-deposition rates in a D-T tokamak reactor, compared with a pure carbon surface. It was also determined that chemical sputtering of both C and Si should not result in any noticeable effect on the net erosion, for attached plasma regimes. Our results thus show encouraging results overall for use of SiC as a PFM in tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Structural Aspects of Neutron Survival Probabilities

The neutron survival probability (and related quantities including probabilities of extinction and initiation) is a central element of the broader stochastic theory of neutron populations and finds application in fields including reactor start-up, analysis of reactor power bursts and criticality accidents, and safeguards. In a full neutron transport formulation, the equation governing the single-neutron survival probability is a backward or adjoint-like integro-partial differential equation with the added complexity of being highly nonlinear. Analogous formulations of this equation exist in the context of many approximate theories of neutron transport, with the point kinetics formulation having received significant theoretical attention since the 1940s. This work continues this tradition by providing a novel analysis of the single-neutron survival probability equation using the tools of boundary layer theory. The analysis reveals that the “fully dynamic” solution of the single-neutron survival probability equation—and some key probability distributions derived from it—may be cast as a singular perturbation around the underlying quasi-static single-neutron probability of initiation. In this perturbation solution, the expansion parameter is the ratio of the neutron generation time to a macroscopic time scale characterizing the overall system evolution; this interpretation illuminates some of the fundamental structural aspects of neutron survival phenomena.

97 MATHEMATICS AND COMPUTING↗