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At least 91 records · Page 5

Mesh generation and energy group condensation studies for the jaguar deterministic transport code

The deterministic transport code Jaguar is introduced, and the modeling process for Jaguar is demonstrated using a two-dimensional assembly model of the Hoogenboom-Martin Performance Benchmark Problem. This single assembly model is being used to test and analyze optimal modeling methodologies and techniques for Jaguar. This paper focuses on spatial mesh generation and energy condensation techniques. In this summary, the models and processes are defined as well as thermal flux solution comparisons with the Monte Carlo code MC21. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Programming Function via Soft Materials (PFvSM) (Final Report)

The PFvSM cluster at the University of Illinois greatly deepened the science of soft materials and expanded the means for embedding within them unprecedented functionalities. We pioneered a mesoscopic approach to materials design that combined leading competencies in fundamental experimental and theoretical soft matter science and fabrication that powerfully establishes equilibrium and nonequilibrium assembly of novel and complex building blocks as a preeminent contributor to progress in materials chemistry. Our cluster’s vision was an integrated program of work centered on soft matter science with the ultimate goal of impacting important energy technologies. As elementary units we employed function-encoded colloids, nanoparticles, large mesh fibrillar gels, deterministically fabricated networks and hybrid objects. These materials were employed as building blocks for diverse model systems that allowed fundamental soft matter principles of wide relevance to be established. Their assembly into materials with useful functional behavior provided new approaches to challenging problems in basic energy science including energy harvesting, transport and storage. To achieve these goals the cluster brought together a team of recognized world-leaders in materials synthesis and processing, in-situ characterization, theory and modeling, and materials design, integration and fabrication

36 MATERIALS SCIENCE↗

Assessing microbial community patterns under incipient soil formation from basalt

Microbial dynamics drive the biotic machinery of early soil evolution. However, integrated knowledge of microbial community establishment, functional associations, and community assembly processes in incipient soil is lacking. This study presents a novel approach of combining microbial phylogenetic profiling, functional predictions, and community assembly processes to analyze drivers of microbial community establishment in an emerging soil system. Rigorous sub-meter sampling of a basalt-soil lysimeter after two years of irrigation revealed the contrasting depth-dependent distribution patterns of soil parameters and community diversity. Phylogenetic analysis of 16S rRNA gene indicated the presence of diverse bacterial and archaeal phyla, with high relative abundance of Actinobacteria on the surface and a consistently high abundance of Proteobacteria at all depths. Predicted functional gene analysis suggested dominant autotrophy signatures, evidence of an incomplete nitrogen cycle, and predicted enzymes of iron (III) to iron (II) conversion followed by intracellular uptake, transport, and regulation. Null modeling revealed microbial community assembly predominantly governed by variable selection. The relative influence of the variable selection decreased with depth, indicating unique and relatively harsh environmental conditions near the surface and more benign conditions with depth. Additionally, high levels of dispersal influenced community composition near the center of the domain, suggesting that spatial processes interact with deterministic selection imposed by the environment. Characterizing the complexity in incipient soils can advance research insights about microbial community diversity and assembly in other incipient systems (e.g., transformation of marginal soils, or soils recovering from disturbances such as fire, erosion, intensive agricultural practices, or contamination).

Sengupta, Aditi↗

Assembly Level Modeling and Transportation Damage Prediction of Used Nuclear Fuel (UNF) Cladding

Under U.S. Nuclear Regulatory Commission (NRC) regulations, UNF must maintain its integrity in such a way that it can withstand the physical forces of handling and transportation associated with restaging the fuel and moving it to a different location such as an interim storage site, a geologic repository, or a treatment/recycling facility. Hence, understanding mechanical performance under cumulative loading stemming from normal conditions of storage (NCS), transfer from storage container to transport container if needed, and normal conditions of transport (NCT) is necessary as it establishes part of the safety basis via maintaining the fuel confining boundary (geometry), maintaining criticality safety, and is one of the critical components to the preservation of retrievability. An initial demonstration of modeling and simulation capabilities was performed as part of a collaborative effort between Pacific Northwest National Laboratory (PNNL), Sandia National Laboratory (SNL), Idaho National Laboratory (INL), Oak Ridge National Laboratory (ORNL), and the Transportation Technology Center Inc. (TTCI). This demonstration completed preliminary deterministic evaluations of moderate-to-high burnup UNF mechanical performance under NCS and NCT conditions. This paper focuses on work performed by PNNL on the assembly level modeling of a UNF assembly and fuel cladding damage predictions under NCT loads. The Finite Element (FE) model created for a 17 x 17 Pressurized Water Reactor (PWR) optimized fuel assembly (OFA) is discussed along with the communications to and from the fuel rod-level and cask-level models. Additionally, the methodology for determining cumulative damage is discussed including the 3000 mile damage prediction from a 10 second simulation. The damage results are shown for five shock and vibration broadened loading histories. It is found that predicted cladding strains were not large enough to cause structural failure, but cyclic strains roughly projected for the entire route were significant in some cases. The total damage from summation of the worst shock and vibration cases evaluated is approximately 18% of the expected fatigue limit. Therefore it is predicted that the fuel rods do not fail during NCT given the assumptions used throughout this initial demonstration.

used nuclear fuel, UNF, trasportation, damage, fue↗

Adhesion of Self-Complementary, Sinusoidal Surfaces Fabricated Using Two-Photon Polymerization

Microscale, pick-and-place assembly is a non-lithographic assembly method poised to impact diverse fields including flexible electronics, microfluidics and robotics. However, a major technological challenge is the need to deterministically control adhesion between parts. Here, switchable adhesion involving 3D-printed, self-complementary surfaces is demonstrated. Mechanical properties of metasurfaces pressed against flat, rigid substrates are modeled using finite element methods. A series of flat slabs and metastructured slabs with 2D sinusoidal surfaces are printed using two-photon polymerization (2PP) of a shape-memory resin. The surface frequency of featured slabs was varied between $3.\bar3$ mm −1 and $26.\bar6$ mm −1 with similar amplitudes. Adhesion between printed metasurfaces and glass and between printed, self-complementary metasurfaces is studied above and below the cured resin’s glass transition temperature (∼45 °C). Simple heating of adhering surfaces to above 60 °C lowers adhesion, and compression of surfaces while above the glass transition temperature followed by cooling to room temperature elevates adhesion. The nominal adhesive strength between printed, self-complementary surfaces, as determined by the maximum observable pull-off stress, exceeds 3 MPa. Further tailoring complementary surfaces for adhesion control may facilitate microscale disassembly for recovery of components or precious metals.

amorphous materials↗

Testing of ENDF/B-VIII.0 in the GNDS format with LLNL transport codes - 25606

ENDF/B-VIII.0 was released in the Evaluated Nuclear Data Format and the Generalized Nuclear Data Structure format (GNDS), a new international standard for storing nuclear data developed under the auspices of the Nuclear Energy Agency Working Party on Evaluation Cooperation Subgroup 38. GNDS relies on modern coding practices, and offers a structured, flexible and physics-based standard for storing and exchanging nuclear data to address limitations in legacy nuclear data formats such as ENDF-6. GNDS supports the storage of evaluated nuclear data as well as processed data suitable for both deterministic (i.e., multi-group) and Monte Carlo transport codes. Lawrence Livermore National Laboratory has implemented a complete suite of codes to test GNDS data. Simulations for the ENDF/B-VIII.0 cross-section library in GNDS format are presented. Deterministic and Monte Carlo radiation transport simulations with the Ardra and Mercury codes respectively, are validated against reactivities in fast criticality safety benchmark assemblies. Finally, Mercury simulations of {sup 238}U(n,f), {sup 237}Np(n,f) and {sup 239}Pu(n,f) reaction rates in Godiva, Jezebel and Flattop are compared to MCNP results and measured data. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

Prompt Neutron Decay Constants in a Highly Enriched Uranium-Lead Copper Reflected System

Rossi-{alpha} measurements were performed on highly enriched uranium (HEU)-lead copper reflected systems to determine the prompt neutron decay constants. These constants represent an eigenvalue characteristic of these particular critical configurations, which can be experimentally measured by the Rossi-a or pulse neutron source techniques and calculated by a deterministic or Monte Carlo method. In the measurements presented in this summary, highly enriched uranium interleaved with lead plates and reflected with copper were assembled to a high multiplication and the prompt neutron decay constants were determined by the Rossi-{alpha} technique. This research intended to benchmark the lead neutron cross sections; it was a collaboration between the Japanese Atomic Energy Agency (JAEA) Fast Critical Assembly Facility (FCA) in Tokai, Japan and the Los Alamos National Laboratory (LANL) in the U.S. (authors)

07 ISOTOPE AND RADIATION SOURCES↗

ASME Design Code Rule Changes for Nuclear Graphite

The American Society of Mechanical Engineers Boiler Pressure and Vessel Code (ASME BPVC) Section III, Division 5, Article HHA-3000 outlines graphite core component and graphite core assembly design guidelines. Graphite core components are defined as ?components manufactured from graphite that are installed to form a graphite core assembly within the reactor pressure vessel of a high temperature, graphite moderated fission reactor.? (p. 413) Graphites? inherent defect distributions do not allow for deterministic material reliability. Rather, graphite has variable strength distributions which change by grade. Article HHA-3000 outlines two semi-probabilistic methods, the full and simplified assessments, which set design load limit targets for each of three component structural reliability classes. The Design Task Group was officially recognized as a specialized task group within ASME November of 2023, though we?ve been collaborating since 2022. The purpose of the Design Task Group is to correct, clarify, and make HHA-3000 function as intended. The Design Task Group will sunset once we?ve achieved our objectives. The Design Task Group was specifically told to not write new Code. While there may be more precise and more accurate methods to determine reliability targets, the current methods are conservative, relatively simple to implement, and have thus far been considered satisfactory for setting design reliability targets. Much of the ground-work to write proposal files and background documents for records to make the changes needed to achieve our objective have been completed. The Design Task Group has documented much of their work through papers, presentations, and memorandums. Three memorandums in which INL team members had substantial contributions are found in the Appendices: FEA Modeling for the Baseline Program, Evaluating the Effects on Margin of Updating the Threshold and Shape Parameters in the Full Assessment, and Interpretations of the Full and Simplified Assessments in ASME BPVC. Most of the on-going work to achieve the Design Task Group?s objective will be addressing comments on existing records and moving records through the balloting process. The Design Task Group met bi-weekly mostly through the end of FY2023. Since February 2024, the Design Task Group has mostly been completed with solving and documenting the technical issues associated with the assessments. Unless new tasks are identified, the remaining work of the Design Task Group will be political and editorial.

97 MATHEMATICS AND COMPUTING↗

Design and Analysis of an X-Ray Mirror Assembly Using the Meta-Shell Approach

Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low sensitivity to thermal gradients.

module↗

Meta-shell Approach for Constructing Lightweight and High Resolution X-Ray Optics

Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low thermal distortion. Recent results are discussed including Structural Thermal Optical Performance (STOP) analysis as well as vibration and shock testing of prototype meta-shells.

Lightweight and high resolution optics↗

The FREYA project at VENUS-F - the next step towards MYRRHA

The VENUS-F reactor is a fast, zero-power research reactor. Since 2009 it has used 30% wt. metallic uranium as fuel and solid lead as reflector and coolant simulator. It can also be coupled to a particle accelerator with a neutron producing target and make up a subcritical Accelerator Driven System (ADS). Within the currently ongoing FREYA project, the main tasks being investigated are the validation of online reactivity monitoring of an ADS, the validation of nuclear data and neutronic codes, and the experimental characterization of fast critical and subcritical cores representative for MYRRHA. MYRRHA will be an ADS demonstrator with the option to be operated in critical mode too. So far the only critical core at VENUS-F was assembled using 97 fuel assemblies, each of them consisting of 9 U and 16 Pb rodlets. The core was thoroughly characterized: flux traverses, spectral indices, control rod worth, delayed neutron parameters were measured and compared with Monte Carlo and deterministic calculations. A sensitivity study was also performed focusing on the influence of material impurities, positioning uncertainties, structures and detectors around the core. It was a simple core without any perturbations in the active zone. In the next critical cores that are planned to be investigated in 2015 and 2016, additional elements will be introduced in order to become more representative for MYRRHA. As MYRRHA will use MOX fuel, oxygen will be added into the following core. This will be done by introducing Al{sub 2}O{sub 3} into the fuel assemblies. New fuel assemblies have been already made and are ready to be loaded. Each consists of 13 U, 8 Pb, and 4 Al{sub 2}O{sub 3} rodlets. The new critical core will consist of approximately 40 such fuel assemblies and will be loaded in January 2015. The first results of the characterization measurements will be presented. Additionally, it is planned to investigate coolant void effects. As MYRRHA will be a rather complex system using a number of in-pile sections and heterogeneous elements inside and around the active zone, the next cores will be step by step modified by loading new materials and perturbations with the aim to assemble a MYRRHA mock-up. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

On-the-fly response function generation method for composite coarse mesh

The hybrid stochastic deterministic transport code COMET, based on the incident response expansion theory, is used to model reactor cores with high fidelity and formidable computational speed. COMET models a reactor core using a library of incident flux response expansion coefficients that are pre computed for all the unique lattice cells (e.g., fuel assemblies, reflector blocks, etc.) in the core. In order to further improve its computational efficiency in pre-calculating the response library a new response function generation method is developed to compute the response functions for the composite coarse meshes made of a smaller set of unique lattices on the fly within the COMET's deterministic transport core sweep. The efficiency is achieved by eliminating a number of unique lattices that can be made up from the reduced set of unique meshes on the fly. The numerical process consists of the following steps. First, the boundary condition on composite coarse mesh boundaries is projected onto the expansion basis to compute the incident flux moments on external surfaces of all the basic (reduced set of unique) coarse meshes. Secondly, the deterministic sweeping solver in COMET is used to converge on the outgoing/incoming flux expansion moments crossing interfaces between the basic coarse meshes. Thirdly, the response functions for the composite coarse meshes are constructed as a superposition on the fly. The new response function generation method was tested on 88 composite coarse meshes consisting of CANDU fuel bundles and moderator blocks. It was found that response functions generated by the new method agree very well with those generated by direct Monte Carlo calculations. The average and maximum relative differences in the surface-to-surface response coefficients computed by the two methods are 0.10% and 0.20%, respectively. Similarly, the average and maximum relative differences in the response fission densities are 0.13% and 0.43%, respectively. These discrepancies are within one standard deviation of the stochastic uncertainties. The new method is five times faster than the original direct Monte Carlo method. The size of the response function library for the new method is five times smaller than that for the original method, leading to significantly less requirement for the computer hard drive space and memory. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Verification & Validation of High-Order Short-Characteristics-Based Deterministic Transport Methodology on Unstructured Grids

The research team has developed a practical, high-order, discrete-ordinates, short characteristics neutron transport code for three-dimensional configurations represented on unstructured tetrahedral grids that can be used for realistic reactor physics applications at both the assembly and core levels. This project will perform a comprehensive verification and validation of this new computational tool against both a continuous-energy Monte Carlo simulation (e.g. MCNP) and experimentally measured data, an essential prerequisite for its deployment in reactor core modeling. Verification is divided into three phases. The team will first conduct spatial mesh and expansion order refinement studies to monitor convergence of the numerical solution to reference solutions. This is quantified by convergence rates that are based on integral error norms computed from the cell-by-cell difference between the code’s numerical solution and its reference counterpart. The latter is either analytic or very fine- mesh numerical solutions from independent computational tools. For the second phase, the team will create a suite of code-independent benchmark configurations to enable testing the theoretical order of accuracy of any particular discretization of the discrete ordinates approximation of the transport equation. For each tested case (i.e. mesh and spatial approximation order), researchers will execute the code and compare the resulting numerical solution to the exact solution on a per cell basis to determine the distribution of the numerical error. The final activity comprises a comparison to continuous-energy Monte Carlo solutions for zero-power critical configuration measurements at Idaho National Laboratory’s Advanced Test Reactor (ATR). Results of this comparison will allow the investigators to distinguish between modeling errors and the above-listed discretization errors introduced by the deterministic method, and to separate the sources of uncertainty.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Optical induction scheme for assembling nondiffracting aperiodic Vogel spirals

We introduce an experimental approach to realize aperiodic photonic lattices based on multiplexing of nondiffracting Bessel beams. This holographic optical induction scheme takes advantage of the well localized Bessel beam as a basis to assemble two-dimensional photonic lattices. We present the realization of an optically induced two-dimensional golden-angle Vogel spiral lattice, which belongs to the family of deterministic aperiodic structures. With our technique, a very broad class of photonic refractive index landscapes now becomes accessible to optical induction, which could not be realized with established distributed holographic techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Improved Neutronics Treatment of Burnable Poisons for the Prismatic HTR

In prismatic block High Temperature Reactors (HTR), highly absorbing material such a burnable poison (BP) cause local flux depressions and large gradients in the flux across the blocks which can be a challenge to capture accurately with traditional homogenization methods. The purpose of this paper is to quantify the error associated with spatial homogenization, spectral condensation and discretization and to highlight what is needed for improved neutronics treatments of burnable poisons for the prismatic HTR. A new triangular based mesh is designed to separate the BP regions from the fuel assembly. A set of packages including Serpent (Monte Carlo), Xuthos (1storder Sn), Pronghorn (diffusion), INSTANT (Pn) and RattleSnake (2ndorder Sn) is used for this study. The results from the deterministic calculations show that the cross sections generated directly in Serpent are not sufficient to accurately reproduce the reference Monte Carlo solution in all cases. The BP treatment produces good results, but this is mainly due to error cancellation. However, the Super Cell (SC) approach yields cross sections that are consistent with cross sections prepared on an “exact” full core calculation. In addition, very good agreement exists between the various deterministic transport and diffusion codes in both eigenvalue and power distributions. Future research will focus on improving the cross sections and quantifying the error cancellation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Reasons for 2011 Release of the Evaluated Nuclear Data Library (ENDL2011.0)

LLNL's Computational Nuclear Physics Group and Nuclear Theory and Modeling Group have collaborated to create the 2011 release of the Evaluated Nuclear Data Library (ENDL2011). ENDL2011 is designed to sup- port LLNL's current and future nuclear data needs. This database is currently the most complete nuclear database for Monte Carlo and deterministic transport of neutrons and charged particles, surpassing ENDL2009.0 [1]. The ENDL2011 release [2] contains 918 transport-ready eval- uations in the neutron sub-library alone. ENDL2011 was assembled with strong support from the ASC program, leveraged with support from NNSA science campaigns and the DOE/Offce of Science US Nuclear Data Pro- gram.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

SU-G-TeP1-15: Toward a Novel GPU Accelerated Deterministic Solution to the Linear Boltzmann Transport Equation

Purpose: To develop a Graphic Processor Unit (GPU) accelerated deterministic solution to the Linear Boltzmann Transport Equation (LBTE) for accurate dose calculations in radiotherapy (RT). A deterministic solution yields the potential for major speed improvements due to the sparse matrix-vector and vector-vector multiplications and would thus be of benefit to RT. Methods: In order to leverage the massively parallel architecture of GPUs, the first order LBTE was reformulated as a second order self-adjoint equation using the Least Squares Finite Element Method (LSFEM). This produces a symmetric positive-definite matrix which is efficiently solved using a parallelized conjugate gradient (CG) solver. The LSFEM formalism is applied in space, discrete ordinates is applied in angle, and the Multigroup method is applied in energy. The final linear system of equations produced is tightly coupled in space and angle. Our code written in CUDA-C was benchmarked on an Nvidia GeForce TITAN-X GPU against an Intel i7-6700K CPU. A spatial mesh of 30,950 tetrahedral elements was used with an S4 angular approximation. Results: To avoid repeating a full computationally intensive finite element matrix assembly at each Multigroup energy, a novel mapping algorithm was developed which minimized the operations required at each energy. Additionally, a parallelized memory mapping for the kronecker product between the sparse spatial and angular matrices, including Dirichlet boundary conditions, was created. Atomicity is preserved by graph-coloring overlapping nodes into separate kernel launches. The one-time mapping calculations for matrix assembly, kronecker product, and boundary condition application took 452±1ms on GPU. Matrix assembly for 16 energy groups took 556±3s on CPU, and 358±2ms on GPU using the mappings developed. The CG solver took 93±1s on CPU, and 468±2ms on GPU. Conclusion: Three computationally intensive subroutines in deterministically solving the LBTE have been formulated on GPU, resulting in two orders of magnitude speedup. Funding support from Natural Sciences and Engineering Research Council and Alberta Innovates Health Solutions. Dr. Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).

60 APPLIED LIFE SCIENCES↗

A nodal transport method for coupled fast-thermal reactor analysis

We report that for efficient core analyses of coupled fast-thermal reactors, a new deterministic method has been developed based on the variational nodal transport method of VARIANT. A new multigroup cross section generation procedure was devised by combining Monte Carlo lattice calculations for thermal assemblies and the two-step procedure of the MC 2 -3 code for fast assemblies. To reduce assembly homogenization errors in nodal transport calculations, a new nodal equivalence method was developed based on the partial current discontinuity factor (PCDF) and incorporated in VARIANT. A practical procedure to calculate PCDFs with fixed source supercell calculations was also devised. The performance of the proposed method was investigated using a test problem derived from the versatile coupled test reactor (VCTR) design. The new procedure produced multigroup cross sections accurately for all assemblies. VARIANT transport calculations with PCDFs produced accurate multiplication factor and power distribution compared to reference Serpent-2 Monte Carlo solutions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗