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At least 397 records · Page 22

Implementation of the Windowed Multipole Method in Shift

The windowed multipole (WMP) method has been implemented in the Shift Monte Carlo (MC) radiation transport code with support for both CPU and GPU execution. With this method, small WMP data libraries (~100 MB) can be used to accurately Doppler broaden cross sections to arbitrary temperatures “on the fly” during an MC simulation. This approach yields significant memory savings relative to traditional methods, making it ideal for high-fidelity analysis such as coupled multiphysics simulations. This document provides the exact forms of the WMP equations used by Shift, as well as a detailed description of the structure of WMP HDF5 data files provided by the Massachusetts Institute of Technology (MIT). The Shift implementation has been validated against the OpenMC radiation transport code, with excellent agreement demonstrated for 70 nuclides across an operative range of temperatures. CPU and GPU performance testing using a small module reactor (SMR) problem demonstrated that this method decreases the neutron tracking rate by a factor of ~2 on the Summitdev machine. A new set of WMP data being developed in-house will employ novel methods to improve tracking rates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

ICME and In-Situ Process Monitoring for Rapid Qualification of Components Made by Laser-based Powder Bed Additive Manufacturing Processes for Nuclear Structural Applications

Additive manufacturing (AM) through selective powder bed melting of successive layers is being considered as disruptive technology for rapid production of low-cost nuclear reactor internal components with complex geometries. However, there is a potential for non-uniform distribution of physical features, such as porosity or microstructural differences, due to variations of temperature across a component build. These heterogeneities make the deployment of traditional material qualification and non-destructive evaluation of AM components difficult. This research project explored the feasibility of using in-situ process monitoring methods and integrated computational materials engineering (ICME) principles as an alternate qualification methodology and approach. This project included six individual tasks: (i) design of artifacts relevant to the nuclear power industry, (ii) evaluation of laser processing and in-situ measurements, (iii) computational modeling, (iv) ex-situ microstructural characterization, (v) evaluation of scaling the methodology for large-scale structures, and (vi) development of a data package to codes and standards organizations. As a part of this research, laser powder bed fusion of metals (316L, Alloy 718, and Ti6Al4V) was explored. This document provides an overview of the research performed over three years and serves as the final U.S. Department of Energy report for this project. In the third year, the project focused on the following activities: (a) in-situ infrared and optical imaging of each layer during processing of representative stainless steel geometries; (b) development of methodologies to analyze the data; and (c) application of ICME methodologies and other experiments to estimate the relevance of defects and microstructure to tensile properties.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

ICME and In-Situ Process Monitoring for Rapid Qualification of Components Made by Laser-based Powder Bed Additive Manufacturing Processes for Nuclear Structural Applications

Additive manufacturing (AM) through selective powder bed melting of successive layers is being considered as disruptive technology for rapid production of low-cost nuclear reactor internal components with complex geometries. However, there is a potential for non-uniform distribution of physical features, such as porosity or microstructural differences, due to variations of temperature across a component build. These heterogeneities make the deployment of traditional material qualification and non-destructive evaluation of AM components difficult. This research project explored the feasibility of using in-situ process monitoring methods and integrated computational materials engineering (ICME) principles as an alternate qualification methodology and approach. This project included six individual tasks: (i) design of artifacts relevant to the nuclear power industry, (ii) evaluation of laser processing and in-situ measurements, (iii) computational modeling, (iv) ex-situ microstructural characterization, (v) evaluation of scaling the methodology for large-scale structures, and (vi) development of a data package to codes and standards organizations. As a part of this research, laser powder bed fusion of metals (316L, Alloy 718, and Ti6Al4V) was explored. This document provides an overview of the research performed over three years and serves as the final U.S. Department of Energy report for this project. In the third year, the project focused on the following activities: (a) in-situ infrared and optical imaging of each layer during processing of representative stainless steel geometries; (b) development of methodologies to analyze the data; and (c) application of ICME methodologies and other experiments to estimate the relevance of defects and microstructure to tensile properties.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

ICME and In-Situ Process Monitoring for Rapid Qualification of Components Made by Laser-based Powder Bed Additive Manufacturing Processes for Nuclear Structural Applications

Additive manufacturing (AM) through selective powder bed melting of successive layers is being considered as disruptive technology for rapid production of low-cost nuclear reactor internal components with complex geometries. However, there is a potential for non-uniform distribution of physical features, such as porosity or microstructural differences, due to variations of temperature across a component build. These heterogeneities make the deployment of traditional material qualification and non-destructive evaluation of AM components difficult. This research project explored the feasibility of using in-situ process monitoring methods and integrated computational materials engineering (ICME) principles as an alternate qualification methodology and approach. This project included six individual tasks: (i) design of artifacts relevant to the nuclear power industry, (ii) evaluation of laser processing and in-situ measurements, (iii) computational modeling, (iv) ex-situ microstructural characterization, (v) evaluation of scaling the methodology for large-scale structures, and (vi) development of a data package to codes and standards organizations. As a part of this research, laser powder bed fusion of metals (316L, Alloy 718, and Ti6Al4V) was explored. This document provides an overview of the research performed over three years and serves as the final U.S. Department of Energy report for this project. In the third year, the project focused on the following activities: (a) in-situ infrared and optical imaging of each layer during processing of representative stainless steel geometries; (b) development of methodologies to analyze the data; and (c) application of ICME methodologies and other experiments to estimate the relevance of defects and microstructure to tensile properties.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

ICME and In-Situ Process Monitoring for Rapid Qualification of Components Made by Laser-based Powder Bed Additive Manufacturing Processes for Nuclear Structural Applications

Additive manufacturing (AM) through selective powder bed melting of successive layers is being considered as disruptive technology for rapid production of low-cost nuclear reactor internal components with complex geometries. However, there is a potential for non-uniform distribution of physical features, such as porosity or microstructural differences, due to variations of temperature across a component build. These heterogenities make the deployment of traditional material qualification and non-destructive evaluation of AM components difficult. This research project explored the feasibility of using in-situ process monitoring methods and integrated computational materials engineering (ICME) principles as an alternate qualification methodology and approach. This project included six individual tasks: (i) design of artifacts relevant to the nuclear power industry, (ii) evaluation of laser processing and in-situ measurements, (iii) computational modeling, (iv) ex-situ microstructural characterization, (v) evaluation of scaling the methodology for large-scale structures, and (vi) development of a data package to codes and standards organizations. As a part of this research, laser powder bed fusion of metals (316L, Alloy 718, and Ti6Al4V) was explored. This document provides an overview of the research performed over three years and serves as the final U.S. Department of Energy report for this project. In the third year, the project focused on the following activities: (a) in-situ infrared and optical imaging of each layer during processing of representative stainless steel geometries; (b) development of methodologies to analyze the data; and (c) application of ICME methodologies and other experiments to estimate the relevance of defects and microstructure to tensile properties.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Massively Parallel Bayesian Model Calibration and Uncertainty Quantification with Applications to Nuclear Fuels and Materials

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. Fuel behavior in a nuclear reactor is governed by a complex network of mechanisms interacting with various other physics aspects in the reactor system. Any model developed to represent the fuel behavior will likely be idealized resulting in uncertainties in their predictions compared to the observed data. As such, this report was motivated by the need to identify the sources of uncertainties and quantify and propagate them through the fuel model outputs. Such quantification of uncertainties will establish a level of model trustworthiness, identify approaches to improve the model trustworthiness, and even guide optimal experiment design for maximal information gain. To accomplish the uncertainty quantification for computational models, this report has relied on the Bayesian framework which provides probabilistic treatment of models their inputs and outputs. The current state-of-the-art on performing Bayesian Uncertainty Quantification (UQ) for nuclear engineering models using High Performance Computing (HPC) resources have been reviewed. Implementation of capabilities for massively parallel Bayesian UQ in Multiphysics Object-Oriented Simulation Environment (MOOSE) is discussed. Several verification cases are discussed to verify the accuracy of the quantified uncertainties using the developed computational capabilities in MOOSE. Then, the problem of quantifying the uncertainties in TRI-Structural isOtropic (TRISO) fuel silver release is addressed. For the first time, the uncertainties arising from the TRISO Fission Gas Release (FGR) model due to model inadequacy and experimental noise are quantified. Also, the Bayesian capabilities are applied to the calibration of the MATPRO creep model, a widely used model in several fuel assessment cases. The impact of the prediction uncertainties in the MATPRO model on the fuel cladding behavior as part of the TRIBULATION assessment case (which is an integral effects case) is investigated. This report concludes with a discussion on the future work for the UQ for computational models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Coupling Finite Element and Finite Volume Simulation Within MOOSE

This work focuses on adding capability to couple finite element (FE) variables into finite volume (FV) physics within INL’s Multiphysics Object-Oriented Simulation Environment (MOOSE). This coupling can allow for improvement of multiphysics simulations where one set of physics is best suited for an FE discretization, while another set is best suited for an FV discretization. Electrohydrodynamics, which govern liquid metal reactor concepts and plasma dynamics, is a fitting example where the electromagnetic field equations are solved with FE and the fluid flow is solved with FV. The new FE to FV coupling method can be summarized as taking the element or face average of the FE variable value or gradient and applying that quantity directly in the FV equation objects.

97 MATHEMATICS AND COMPUTING↗

ICME and In-Situ Process Monitoring for Rapid Qualification of Components Made by Laser-based Powder Bed Additive Manufacturing Processes for Nuclear Structural Applications

Additive manufacturing (AM) through selective powder bed melting of successive layers is being considered as disruptive technology for rapid production of low-cost nuclear reactor internal components with complex geometries. However, there is a potential for non-uniform distribution of physical features, such as porosity or microstructural differences, due to variations of temperature across a component build. These heterogenities make the deployment of traditional material qualification and non-destructive evaluation of AM components difficult. This research project explored the feasibility of using in-situ process monitoring methods and integrated computational materials engineering (ICME) principles as an alternate qualification methodology and approach. This project included six individual tasks: (i) design of artifacts relevant to the nuclear power industry, (ii) evaluation of laser processing and in-situ measurements, (iii) computational modeling, (iv) ex-situ microstructural characterization, (v) evaluation of scaling the methodology for large-scale structures, and (vi) development of a data package to codes and standards organizations. As a part of this research, laser powder bed fusion of metals (316L, Alloy 718, and Ti6Al4V) was explored. This document provides an overview of the research performed over three years and serves as the final U.S. Department of Energy report for this project. In the third year, the project focused on the following activities: (a) in-situ infrared and optical imaging of each layer during processing of representative stainless steel geometries; (b) development of methodologies to analyze the data; and (c) application of ICME methodologies and other experiments to estimate the relevance of defects and microstructure to tensile properties.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Coupling the System Analysis Module with SAS4A/SASSYS-1

SAS4A/SASSYS-1 is a simulation tool used to perform deterministic analysis of anticipated events as well as design basis and beyond design basis accidents for advanced reactors, with an emphasis on sodium fast reactors. SAS4A/SASSYS-1 has been under development and in active use for nearly forty-five years, and is currently maintained by the U.S. Department of Energy under the Office of Advanced Reactor Technology. Although SAS4A/SASSYS-1 contains a very capable primary and intermediate system modeling component, PRIMAR-4, it also has some shortcomings: outdated data management and code structure makes extension of the PRIMAR-4 module somewhat difficult. The user input format for PRIMAR-4 also limits the number of volumes and segments that can be used to describe a given system. The System Analysis Module (SAM) is a fairly new code development effort being carried out under the U.S. DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SAM is being developed with advanced physical models, numerical methods, and software engineering practices; however, it is currently somewhat limited in the system components and phenomena that can be represented. For example, component models for electromagnetic pumps and multi-layer stratified volumes have not yet been developed. Nor is there support for a balance of plant model. Similarly, system-level phenomena such as control-rod driveline expansion and vessel elongation are not represented. This report documents fiscal year 2016 work that was carried out to couple the transient safety analysis capabilities of SAS4A/SASSYS-1 with the system modeling capabilities of SAM under the joint support of the ART and NEAMS programs. The coupling effort was successful and is demonstrated by evaluating an unprotected loss of flow transient for the Advanced Burner Test Reactor (ABTR) design. There are differences between the stand-alone SAS4A/SASSYS-1 simulations and the coupled SAS/SAM simulations, but these are mainly attributed to the limited maturity of the SAM development effort. The severe accident modeling capabilities in SAS4A/SASSYS-1 (sodium boiling, fuel melting and relocation) will continue to play a vital role for a long time. Therefore, the SAS4A/SASSYS-1 modernization effort should remain a high priority task under the ART program to ensure continued participation in domestic and international SFR safety collaborations and design optimizations. On the other hand, SAM provides an advanced system analysis tool, with improved numerical solution schemes, data management, code flexibility, and accuracy. SAM is still in early stages of development and will require continued support from NEAMS to fulfill its potential and to mature into a production tool for advanced reactor safety analysis. The effort to couple SAS4A/SASSYS-1 and SAM is the first step on the integration of these modeling capabilities.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Development and verification of the pyIsoDep depletion package for nuclear thermal propulsion reactors

Nuclear thermal propulsion technology is currently being developed by the National Air and Space Administration for future manned Mars missions. There are multiple on-going activities to develop and enhance computational capabilities, single- and multi-physics, to advance the readiness level of this technology. The prediction of short-lived fission products is crucial to understand the reactivity penalty and the decay heat production during the different burnout stages of the vehicle. Generally, the solution entails coupled neutronic-depletion analysis. However, such simulations are somewhat expensive, especially if the duration of each engine burn is to be optimized. Therefore, there is a need to complement such high-fidelity techniques with time-efficient alternatives that do not require the sequential neutronic and depletion analysis. This paper details the methods and capabilities of pyIsoDep, an open-source code used for depletion analysis of nuclear thermal propulsion reactors. The package is general, in principle, and thus can be applied to any fission system, and can potentially be extended for fusion systems. The package was developed to provide a flexible and efficient alternative to pre-existing higher order depletion codes that could integrate well into mission and transient analysis of nuclear thermal propulsion reactors. Finally, this paper presents a validation and verification of pyIsoDep against analytical and Serpent-generated solutions. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Resonance treatment using pin-based pointwise energy slowing-down method

A new resonance self-shielding method using a pointwise energy solution has been developed to overcome the drawbacks of the equivalence theory. The equivalence theory uses a crude resonance scattering source approximation, and assumes a spatially constant scattering source distribution inside a fuel pellet. These two assumptions cause a significant error, in that they overestimate the multi-group effective cross sections, especially for {sup 238}U. The new resonance self-shielding method solves pointwise energy slowing-down equations with a sub-divided fuel rod. The method adopts a shadowing effect correction factor and fictitious moderator material to model a realistic pointwise energy solution. The slowing-down solution is used to generate the multi-group cross section. With various light water reactor problems, it was demonstrated that the new resonance self-shielding method significantly improved accuracy in the reactor parameter calculation with no compromise in computation time, compared to the equivalence theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

IAEA Coordinated Research Project on HTGR Physics, Thermal-Hydraulics, and Depletion Uncertainty Analysis Prismatic HTGR Benchmark Specification: Phase II

In February 2009, the Technical Working Group on Gas Cooled Reactors of the International Atomic Energy Agency (IAEA) recommended that the proposed Coordinated Research Project (CRP) on the High-Temperature Gas Cooled Reactor (HTGR) Uncertainty Analysis in Modeling (UAM) be implemented. This CRP is a continuation of the previous IAEA and Organisation for Economic Cooperation and Development (OECD)/Nuclear Energy Agency (NEA) international activities on verification and validation of available analytical capabilities for HTGR simulation for design and safety evaluations. Within the framework of these activities different numerical and experimental benchmark problems were performed, and insight was gained about specific physics phenomena and the adequacy of analysis methods. Because the prismatic design specification included in this report is based directly on the OECD/NEA Modular HTGR (MHTGR) 350 MW benchmark, participants in both activities can leverage their core models developed for the OECD/NEA benchmark for this CRP benchmark with only minor changes. The CRP on the HTGR UAM Phase II specifications is also directly linked to the Phase I specification document, since the core models required for Phase II exercises are constructed using the lattice models and cross-section libraries developed for Phase 1. It was decided at the Third Research Coordination Meeting (RCM) in May 2017 that the initial scope of CRP activities will be reduced to match the formally approved remaining contract period (June 2019), as well as limited funding and resource availability. A summary of the revised Phases I–IV exercise definitions is provided here.

42 ENGINEERING↗

MC 2 -3: Multigroup Cross Section Generation Code for Fast Reactor Analysis

This paper presents the methods and performance of the MC2 -3 code, which is a multigroup cross-section generation code for fast reactor analysis, developed to improve the resonance self-shielding and spectrum calculation methods of MC2 -2 and to simplify the current multistep schemes generating region-dependent broad-group cross sections. Using the basic neutron data from ENDF/B data files, MC2 -3 solves the consistent P1 multigroup transport equation to determine the fundamental mode spectra for use in generating multigroup neutron cross sections. A homogeneous medium or a heterogeneous slab or cylindrical unit cell problem is solved in ultrafine (2082) or hyperfine (~400 000) group levels. In the resolved resonance range, pointwise cross sections are reconstructed with Doppler broadening at specified temperatures. The pointwise cross sections are directly used in the hyperfine group calculation, whereas for the ultrafine group calculation, self-shielded cross sections are prepared by numerical integration of the pointwise cross sections based upon the narrow resonance approximation. For both the hyperfine and ultrafine group calculations, unresolved resonances are self-shielded using the analytic resonance integral method. The ultrafine group calculation can also be performed for a two-dimensional whole-core problem to generate region-dependent broad-group cross sections. Verification tests have been performed using the benchmark problems for various fast critical experiments including Los Alamos National Laboratory critical assemblies; Zero-Power Reactor, Zero-Power Physics Reactor, and Bundesamt für Strahlenschutz experiments; Monju start-up core; and Advanced Burner Test Reactor. Verification and validation results with ENDF/B-VII.0 data indicated that eigenvalues from MC2 -3/DIF3D agreed well with Monte Carlo N-Particle5 MCNP5 or VIM Monte Carlo solutions within 200 pcm and regionwise one-group fluxes were in good agreement with Monte Carlo solutions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

MPACT 4.4 Theory Manual

MPACT is a three-dimensional (3D) full-core neutron transport code capable of calculating subpin power distributions. Calculations are based on the Boltzmann transport equation for neutron fluxes for problems in which the detailed geometrical configuration of fuel components such as the pellet and cladding are explicitly retained. The cross-section data needed for the neutron transport calculation are obtained directly from a multigroup cross section library, which has traditionally been used by lattice physics codes to generate few-group homogenized cross sections for nodal core simulators. Hence, MPACT assumes neither a priori homogenization nor group condensation for the full core spatial solution. The 3D MPACT transport solution can be obtained using the method of characteristics (MOC), which employs discrete ray tracing within each fuel pin. However, for practical reactor applications, the direct application of MOC to 3D core configurations requires an excessive amount of memory and computing time due to the very large number of rays. For practical 3D full-core calculations, MPACT commonly uses an approximate “2D/1D” method that treats the radial (x and y) variables differently from the axial (z) variable. In particular, the radial dependence of the solution is calculated using transport theory, and the axial dependence is calculated using diffusion or P 3 theory. The 2D/1D method requires the core to be divided into a vertical stack of axial slices with a thickness of Δ z ≈ 5–10 cm. Each axial slice is divided radially into coarse spatial cells with boundaries that usually constitute the pin cell boundaries, for which Δ x = Δ y ≈ 1.5 cm. Then, each coarse radial cell (pin cell) is divided into 50–100 fine radial cells, which resolve the angular flux in the fuel, cladding, and moderator regions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Characterizing Reactor Operations from Realistic Simulated Environmental Samples: Combining High-Performance Computing and Data Analytics

Environmental sampling is a common technique employed by inspectors and facility operators in nuclear safeguards, proliferation detection, and process monitoring contexts. Interpreting measurements performed on samples or collections of samples and ensuring the information extracted is accurate and precise is difficult. To date, these analyses have relied on simulated data to enable systematic studies; however, these models are inherently limited by the fidelity of the models and the implicit spatial averaging of isotopic composition or other signatures of interest. To advance this capability, we have refined the spatial discretization and expanded the range of physics in the simulation codes we use to perform reactor simulations and depletion calculations. This allows us to generate data that are more representative of real environmental samples, especially for the length scale of the isotopic composition and associated variation. Accordingly, these new data allow a more realistic assessment of traditional and new data analytic analysis methods. Here we present motivation for developing reactor simulations using high-performance computing methods and resources, impacts of these new simulations on our assessment of data analysis and interpretation methods, and initial results of developing and systematically testing data analytic methods designed to overcome the challenges expected of real-world samples. We also quantify the performance of these analyses using defensible statistical methods.

Dayman, Ken J.↗

Supporting Risk-informed Decision-making During Reactor Accidents

Uncertainty in severe accident evolution and outcome is driven by event bifurcations that represent distinctive challenges to defensive layers and tend to promote the emergence of discrete classes of core damage and accident risk. This discrete set of "attractor" states arise from the complex networks of competing physical phenomena and conditional event cascades occurring as the overall system degrades – a process that yields increasing degrees of freedom and accident progression pathways. Characterization of these event spaces has proven elusive to more traditional data interrogation methods, but proves tractable by application of more advanced data collection and machine learning approaches. Through application of these approaches we demonstrate a conceptual framework that enables real-time/robust, risk-informed decision-making support to improve accident mitigation and encourage “graceful exits” during low probability, extreme events limiting accident consequences. In this analysis, we simulated over 8,000 short-term station blackout (STSBO) accidents with the state-of-the-art integral severe accident code, MELCOR, and demonstrate the potential for ML approaches to predict simulation outcomes. We chose to pair ML tools with interpretable and mechanistic event trees for the considered STSBO accident space to predict the likelihood of future event paths along the tree. In addition to the current state of the system, we use information from recent trajectories of temperature, pressure, and other physical features, combining both the current state and past trajectories to forecast future event paths. Finally, we simulate the random injection of variable amounts of water to quantify the efficacy of available actions at reducing risks along the many branches in the event tree. We identify scenarios and windows of opportunity to mitigate risk as well as scenarios in which such actions are unlikely to alter the accident end-state.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Reactor antineutrino flux and anomaly

Reactor antineutrinos have played a significant role in establishing the standard model of particle physics and the theory of neutrino oscillations. In this article, we review the reactor antineutrino flux and in particular the reactor antineutrino anomaly (RAA) coined over a decade ago. RAA refers to a deficit of the measured antineutrino inverse beta decay rates at very short-baseline reactor experiments compared to the theoretically improved predictions (i.e. the Huber–Mueller model). Since the resolution of several previous experimental anomalies have led to the discovery of non-zero neutrino mass and mixing, many efforts have been invested to study the origin of RAA both experimentally and theoretically. The progress includes the observation of discrepancies in antineutrino energy spectrum between data and the Huber–Mueller model, the re-evaluation of the Huber–Mueller model uncertainties, the potential isotope-dependent rate deficits, and the better agreement between data and new model predictions using the improved summation method. Importantly, these developments disfavor the hypothesis of a light sterile neutrino as the explanation of RAA and supports the deficiencies of Huber–Mueller model as the origin. Looking forward, more effort from both the theoretical and experimental sides is needed to fully understand the root of RAA and to make accurate predictions of reactor antineutrino flux and energy spectrum for future discoveries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗