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Nuclear data uncertainty propagation and modeling uncertainty impact evaluation in neutronics core simulation

Uncertainty analysis is a critical requirement in reactor simulation as it is used to quantify the reliability of best-estimate calculation. A comprehensive uncertainty analysis should characterize all sources of uncertainties in a computationally-feasible and scientifically-defendable manner. Here we employ a well-established reduced order modeling (ROM) based uncertainty quantification methodology to propagate uncertainties throughout neutronic calculations. ROM relies on recent advances in randomized data mining techniques applied to large data streams. In our proposed implementation, the nuclear data uncertainties are first propagated from multi-group level through lattice physics calculation to generate few-group parameter uncertainties, described using a vector of mean values and a covariance matrix. Employing an ROM-based compression of the covariance matrix, the few-group uncertainties are then propagated through downstream core simulation in a computationally efficient manner. This straightforward approach, albeit efficient as compared to brute force forward and/or adjoint-based methods, often employs a number of assumptions that have been unquestioned in the literature of neutronic uncertainty analysis. This manuscript argues that these assumptions could introduce another source of uncertainty referred to as modeling uncertainties, whose magnitude needs to be quantified in tandem with nuclear data uncertainties. Thus, our primary goal is to explore the interactions between these two uncertainty sources in order to assess whether modeling uncertainties have an impact on parameter uncertainties. To explore this endeavor, the impact of a number of modeling assumptions on core attributes uncertainties is quantified. The study employs a CANDU reactor model, with Serpent and NEWT as lattice physics solvers and NESTLE-C as core simulator. The modeling assumptions investigated include those related with the uncertainty propagation method employed, e.g., deterministic vs. stochastic, the few-group energy structure employed to represent the cross-sections, the resonance treatment in lattice physics calculation, the reference values for the cross-section, and the number of samples employed to render ROM compression. Results indicate that some of the modeling assumptions could have a non-negligible impact on the core responses propagated uncertainties, highlighting the need for a more comprehensive approach to combine parameter and modeling uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Remote sensing of earth terrain

In remote sensing, the encountered geophysical media such as agricultural canopy, forest, snow, or ice are inhomogeneous and contain scatters in a random manner. Furthermore, weather conditions such as fog, mist, or snow cover can intervene the electromagnetic observation of the remotely sensed media. In the modelling of such media accounting for the weather effects, a multi-layer random medium model has been developed. The scattering effects of the random media are described by three-dimensional correlation functions with variances and correlation lengths corresponding to the fluctuation strengths and the physical geometry of the inhomogeneities, respectively. With proper consideration of the dyadic Green's function and its singularities, the strong fluctuation theory is used to calculate the effective permittivities which account for the modification of the wave speed and attenuation in the presence of the scatters. The distorted Born approximation is then applied to obtain the correlations of the scattered fields. From the correlation of the scattered field, calculated is the complete set of scattering coefficients for polarimetric radar observation or brightness temperature in passive radiometer applications. In the remote sensing of terrestrial ecosystems, the development of microwave remote sensing technology and the potential of SAR to measure vegetation structure and biomass have increased effort to conduct experimental and theoretical researches on the interactions between microwave and vegetation canopies. The overall objective is to develop inversion algorithms to retrieve biophysical parameters from radar data. In this perspective, theoretical models and experimental data are methodically interconnected in the following manner: Due to the complexity of the interactions involved, all theoretical models have limited domains of validity; the proposed solution is to use theoretical models, which is validated by experiments, to establish the region in which the radar response is most sensitive to the parameters of interest; theoretically simulated data will be used to generate simple invertible models over the region. For applications to the remote sensing of sea ice, the developed theoretical models need to be tested with experimental measurements. With measured ground truth such as ice thickness, temperature, salinity, and structure, input parameters to the theoretical models can be obtained to calculate the polarimetric scattering coefficients for radars or brightness temperature for radiometers and then compare theoretical results with experimental data. Validated models will play an important role in the interpretation and classification of ice in monitoring global ice cover from space borne remote sensors in the future. We present an inversion algorithm based on a recently developed inversion method referred to as the Renormalized Source-Type Integral Equation approach. The objective of this method is to overcome some of the limitations and difficulties of the iterative Born technique. It recasts the inversion, which is nonlinear in nature, in terms of the solution of a set of linear equations; however, the final inversion equation is still nonlinear. The derived inversion equation is an exact equation which sums up the iterative Neuman (or Born) series in a closed form and, thus, is a valid representation even in the case when the Born series diverges; hence, the name Renormalized Source-Type Integral Equation Approach.

Yueh, Herng-Aung↗

The direct and indirect drivers shaping RNA viral communities in grassland soil

Recent studies have revealed diverse RNA viral communities in soils. Yet, how environmental factors influence soil RNA viruses remains largely unknown. Here, we recovered RNA viral communities from 24 metatranscriptomes sequenced from grassland soils managed under a range of environmental conditions including 1) water content: 100% and 25% water holding capacity, 2) plant presence: planted with tall wheatgrass (Thinopyrum ponticum) and bare soil, 3) cultivar type: Alkar and Jose, and 4) soil depth: 0-5 cm and 15-25 cm. The recovered RNA viral communities were novel with nearly one-third of the RNA viral contigs uniquely detected in the studied grassland. The classified RNA viral contigs are mostly known as eukaryotic RNA viruses (74.7%) belonging to Phyla Duplornaviricota, Kitrinoviricota, Lenarviricota, and Pisuviricota. Eukaryotic RNA viruses of Family Mitoviridae as well as their natural hosts, Fungi, are one of the most dominant taxa. Consistent with the results of nonmetric multidimensional scaling analysis, the four environmental conditions (water content, plant presence, cultivar, and soil depth) significantly influence the assemblages of soil RNA viral communities as suggested by the correlation analysis and the random forest algorithm. The modularity analysis of the factor network and the structural equation modeling further support the hierarchical associations among the four environmental factors and the community factors representing the co-existing eukaryotic, prokaryotic, and RNA viral communities. The soil water content, plant presence, and type of cultivar demonstrate a significant positive impact on eukaryotic RNA viral richness directly as well as indirectly on eukaryotic RNA viral abundance via influencing the co-existing eukaryotic members in this soil. Our data also provide statistical support for the negative influence of soil depth on soil eukaryotic richness and abundances resulting in its indirect impact on soil eukaryotic RNA viral communities. This study provides field-relevant information on how environmental and community factors collectively shape soil RNA communities and contribute to ecological understanding of RNA viral survival under various environmental conditions and virus-host interactions in soil.

Wu, Ruonan↗

One Structure, Two Elements—LuGe 2 Superconductor vs Ordinary Metallic Conductor LuSn 2 . A Case Study on How Site-Selective Germanium for Tin Atom Substitution Leads to Modulating of the Charge Distribution

The substitution of chemically similar elements in a given crystal structure is an effective way to enhance physical properties, but the understanding on such improvements is usually impeded because the substitutions are random, and the roles of the different atoms cannot be distinguished by crystallographic symmetry. Herein, we provide a detailed crystallographic analysis and property measurements for the continuous solid solutions LuGe x Sn 2–x (0 < x < 2). The results show that there is no apparent change of the global symmetry, with the end-members LuGe 2 and LuSn 2 , as well as the intermediate LuGe x Sn 2–x compositions adopting the ZrSi 2 type structure (space group Cmcm, Pearson index oC12). Yet, the refinements of the crystal structures from single-crystal X-ray diffraction data show that Ge–Sn atom substitutions are not random, but occur preferentially at the zig-zag chain. The patterned distribution of two group 14 elements leads to a significant variation in chemical bonding and charge ordering within the other structural fragment, the 2D square nets, thereby resulting in tuned electron transport. The enhancement is greater than the typical Bloch-Gruneisen model, and more akin to the parallel-resistor model. Magnetization measurements on single crystals show bulk superconductivity in all LuGe x Sn 2–x samples with shielding fractions as high as 90%. Specific heat data confirm the effect to originate from residual metallic tin in the material, indicating that Sn atom substitutions in the 2D square nets cause disruptions of the hypervalent bonding and local anisotropy, which ultimately leads to vanishing of the superconducting state in the end-member LuGe 2 . This work sheds light on how the complexity in chemical interactions by two different carbon congeners leads to changes in the physical properties and how they can be correlated with the induced charge distribution. Furthermore, these studies also provide a general approach to modulation of charge density, and thus, of emerging physical properties in other classes of intermetallic systems based on the main-group elements of groups 13 to 15.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Robust wind farm layout optimization

Wake interactions in wind farms cause losses in annual energy production (AEP) on the order of 10%. Wind farm designers optimize the layout of the farm to mitigate wake losses, especially in the dominant site-specific wind directions. As wind turbines and wind farms grow in scale, optimization becomes more complex. Offshore wind farms regularly comprise more than 100 wind turbines and are characterized by complex boundaries due to shipping lanes, neighboring wind farms, and other constraints. Layout optimization methods are broadly split between gradient-based and gradient-free approaches. Gradient-based approaches can converge quickly and perform well for smaller, academic problems but are often sensitive to initial conditions and tuning parameters and require expert knowledge to use. On the other hand, gradient-free approaches can be more robust to problem complexities. We present a robust layout optimization approach based on a random search algorithm. The algorithm is intended for those who are not optimization experts and has few tuning parameters that need specification to achieve satisfactory results. Unlike off-the-shelf methods, which use generally available, non-domain-specific optimization routines that accept as inputs an optimization function and constraint definitions, this approach takes advantage of the relative computational costs of the different evaluations by evaluating cheaper computations first (boundary and minimum distance constraints) and running expensive AEP evaluations only if all other checks pass. Moreover, an outer genetic algorithm allows multiple solutions to evolve in parallel, enabling rapid solution development on high-performance computers. We discuss the relative ease of selecting necessary tuning parameters and demonstrate the efficacy of the genetic random search on a complex layout problem consisting of placing 70 turbines in a nonconvex and unconnected boundary region.

17 WIND ENERGY↗

Constitutive Modeling of Nanotube-Reinforced Polymer Composites

In this study, a technique is presented for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Because the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties can no longer be determined through traditional micromechanical approaches that are formulated by using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalent-continuum modeling method. The effective fiber serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube shapes, sizes, concentrations, and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/LaRC-SI (with a PmPV interface) composite systems, one with aligned SWNTs and the other with three-dimensionally randomly oriented SWNTs. The Young's modulus and shear modulus have been calculated for the two systems for various nanotube lengths and volume fractions.

Odegard, G. M.↗

Architectural Dynamics of CaMKII-Actin Networks

Calcium-calmodulin-dependent kinase II (CaMKII) has an important role in dendritic spine remodeling upon synaptic stimulation. Using fluorescence video microscopy and image analysis, we investigated the architectural dynamics of rhodamine-phalloidin stabilized filamentous actin (F-actin) networks cross-linked by CaMKII. We used automated image analysis to identify F-actin bundles and crossover junctions and developed a dimensionless metric to characterize network architecture. Similar networks were formed by three different CaMKII species with a 10-fold length difference in the linker region between the kinase domain and holoenzyme hub, implying linker length is not a primary determinant of F-actin cross-linking. Electron micrographs showed that at physiological molar ratios, single CaMKII holoenzymes cross-linked multiple F-actin filaments at random, whereas at higher CaMKII/F-actin ratios, filaments bundled. Light microscopy established that the random network architecture resisted macromolecular crowding with polyethylene glycol and blocked ATP-powered compaction by myosin-II miniature filaments. Importantly, the networks disassembled after the addition of calcium-calmodulin and were then spaced within 3 min into compacted foci by myosin motors or more slowly (30 min) aggregated by crowding. Single-molecule total internal reflection fluorescence microscopy showed CaMKII dissociation from surface-immobilized globular actin exhibited a monoexponential dwell-time distribution, whereas CaMKII bound to F-actin networks had a long-lived fraction, trapped at crossover junctions. Release of CaMKII from F-actin, triggered by calcium-calmodulin, was too rapid to measure with flowcell exchange (<20 s). The residual bound fraction was reduced substantially upon addition of an N-methyl-D-aspartate receptor peptide analog but not ATP. These results provide mechanistic insights to CaMKII-actin interactions at the collective network and single-molecule level. Our findings argue that CaMKII-actin networks in dendritic spines maintain spine size against physical stress. Upon synaptic stimulation, CaMKII is disengaged by calcium-calmodulin, triggering network disassembly, expansion, and subsequent compaction by myosin motors with kinetics compatible with the times recorded for the poststimulus changes in spine volume.

59 BASIC BIOLOGICAL SCIENCES↗

Estimating soybean yields from high-temporal-resolution multi-source data using deep learning

Accurate and timely crop yield prediction is crucial for ensuring food security and maintaining stable agricultural markets. In recent years, there has been a surge in interest in leveraging high-temporal-resolution, multi-source data for effective crop growth monitoring and yield estimation. A notable challenge arises from the difficulty in capturing the intricate interactions between variables across different time steps within these high-temporal-resolution time series datasets. This complexity hinders the reliable extraction of yield information from voluminous and often noisy datasets, especially during periods of extreme weather events. Here, in this study, we propose an Attention and Graph Isomorphism Network-enhanced Bi-directional Long Short-Term Memory network (AGB-LSTM) for estimating county-level soybean yield in the United States. This model integrates a diverse set of remote sensing data, including Near-Infrared Reflectance of Vegetation (NIRv), Sun-Induced chlorophyll Fluorescence (SIF), and Gross Primary Productivity (GPP), along with environmental covariates. The AGB-LSTM effectively leverages information related to crop yield from high-temporal-resolution time series data (5-days), achieving an accuracy of R²= 0.67 and rRMSE = 14.46%. This approach significantly outperforms traditional machine learning methods such as Random Forest (RF) (R²= 0.52, rRMSE = 17.36%) and Bi-LSTM (R²= 0.58, rRMSE = 16.17%). Sensitivity experiments with different time steps and ranges demonstrated that our model could accurately and stably predict yields 1 to 2 months before harvest. Moreover, data with a finer temporal resolution consistently improved prediction performance, resulting in an approximately 20% increase in and an approximately 20% decrease in rRMSE compared to using monthly composites. We also evaluated the robustness of the model under extreme climate events and observed strong performance (R²= 0.50, rRMSE = 21.32%). Finally, yield mapping for major soybean-producing regions in North America in 2023 revealed spatial patterns that closely matched USDA yield reports. Our findings suggest that the AGB-LSTM model is a promising and effective method for estimating yield and has notable potential for global crop yield forecasting.

Deep learning↗

Thermodynamics of order and randomness in dopant distributions inferred from atomically resolved imaging

Abstract Exploration of structure-property relationships as a function of dopant concentration is commonly based on mean field theories for solid solutions. However, such theories that work well for semiconductors tend to fail in materials with strong correlations, either in electronic behavior or chemical segregation. In these cases, the details of atomic arrangements are generally not explored and analyzed. The knowledge of the generative physics and chemistry of the material can obviate this problem, since defect configuration libraries as stochastic representation of atomic level structures can be generated, or parameters of mesoscopic thermodynamic models can be derived. To obtain such information for improved predictions, we use data from atomically resolved microscopic images that visualize complex structural correlations within the system and translate them into statistical mechanical models of structure formation. Given the significant uncertainties about the microscopic aspects of the material’s processing history along with the limited number of available images, we combine model optimization techniques with the principles of statistical hypothesis testing. We demonstrate the approach on data from a series of atomically-resolved scanning transmission electron microscopy images of Mo x Re 1- x S 2 at varying ratios of Mo/Re stoichiometries, for which we propose an effective interaction model that is then used to generate atomic configurations and make testable predictions at a range of concentrations and formation temperatures.

25 ENERGY STORAGE↗

Quantum fragmentation in the extended quantum breakdown model

We introduce a one-dimensional (1D) extended quantum breakdown model comprising a fermionic and a spin degree of freedom per site, and featuring a spatially asymmetric breakdown-type interaction between the fermions and spins. Furthermore, our model resembles the breakdown process of particles incident into a cloud chamber with nonzero quantum amplitudes of both exciting and not exciting the local vapor atoms. We analytically show that, in the absence of any magnetic field for the spins, the model exhibits Hilbert space fragmentation within each symmetry sector into exponentially many Krylov subspaces and hence displays nonthermal dynamics. Here, we demonstrate that the fragmentation naturally occurs in an entangled basis and thus provides an example of “quantum fragmentation.” Besides establishing the nature of fragmentation analytically, we also study the long-time behavior of the entanglement entropy and its deviation from the expected Page value as a probe of ergodicity in the system. Upon introducing a magnetic field for the spins, most of the Krylov subspaces merge and the model becomes chaotic. Finally, we study the effects of strong randomness on the system and observe behavior similar to that of many-body localized systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Unraveling the implications of finite specimen size on the interpretation of dynamic experiments for polycrystalline aluminum through direct numerical simulations

Normal and Pressure-shear plate impact (NPI and PSPI) experiments are popular experimental techniques for studying the mean-field macroscopic behavior of polycrystalline metals under high-rate dynamic loading. However, since both configurations rely upon geometry for subjecting the specimen to high strain rates, these experiments often involve a limited specimen size. Moreover, because of the inherent heterogeneities present within polycrystalline metals, it is difficult to ascertain if the size of the specimen and/or regions where measurements are made are sufficiently large for making representative inferences about the mean-field macroscopic properties from single-point velocity measurements. In the present study, we quantify the expected measurement variability on observable point measurements in NPI and PSPI experiments by carrying out direct numerical simulations (DNS) of statistically representative polycrystalline microstructures subjected to dynamic compression and compression-shear loading. In particular, we consider the role of specific material heterogeneities (e.g. the grain-to-grain difference in size, crystallographic orientation) on dispersion in the normal and transverse particle velocity records and on local fluctuations in key state variables (e.g. velocity, accumulated plastic strain) by incorporating these effects directly into a representative synthetic microstructure geometry and crystalline description of pure polycrystalline aluminum. The form of the present study is a large parametric investigation, consisting of ten ensembles of one hundred simulations. Each of the thousand simulations reflects a randomly realized synthetic microstructure in one of five cases of decreasing average grain size for the two loading configurations. Our analysis of the DNS results demonstrates that for both of these experimental configurations, the grain size directly correlates with the coefficient of variation (CV) in simulated point measurements, showing a convergent decrease in CV to zero (i.e. particle velocity record approaches the mean-field value) with decreasing grain size. Remarkably, the magnitude of variations in the particle velocity record is shown to be largest where the deviatoric stresses are most significant. In the case of NPI, this occurs at the elastic and plastic wavefront, whereas, in the case of PSPI, the magnitude of fluctuations are approximately constant throughout the experimental window time. The reasoning for the scatter in particle velocity due to the heterogeneous microstructure is demonstrated to be dependent on the mechanisms for accommodating deformation and on the interaction of reflection waves generated at sites of heterogeneities occurring at the scale of grains. Lastly, we develop a power-law description for the magnitude of scattering versus characteristic length, which provides a statistical framework for assessing the required number of grains per characteristic specimen dimension for minimizing scatter within these two experimental configurations (NPI, PSPI).

36 MATERIALS SCIENCE↗

Molecular Modes Elucidate the Nuclear Magnetic Resonance Relaxation of Viscous Fluids

The Bloembergen, Purcell, and Pound (BPP) theory of nuclear magnetic resonance (NMR) relaxation in fluids dating back to 1948 continues to be the linchpin in interpreting NMR relaxation data in applications ranging from characterizing fluids in porous media to medical imaging (MRI). The BPP theory is founded on assuming molecules are hard spheres with 1 H– 1 H dipole pairs reorienting randomly; assumptions that are severe in light of modern understanding of liquids. Nevertheless, it is intriguing to this day that the BPP theory was consistent with the original experimental data for glycerol, a hydrogen-bonding molecular fluid for which the hard-sphere-rigid-dipole assumption is inapplicable. To better understand this incongruity, atomistic molecular simulations are used to compute 1 H NMR T 1 relaxation dispersion (i.e., frequency dependence) in two contrasting cases: glycerol, and a (non hydrogen-bonding) viscosity standard. At high viscosities, simulations predict distinct functional forms of T 1 for glycerol compared to the viscosity standard, in agreement with modern measurements, yet both in contrast to BPP theory. The cause of these departures from BPP theory is elucidated, without assuming any relaxation models and without any free parameters, by decomposing the simulated T 1 response into dynamic molecular modes for both intramolecular and intermolecular interactions. The decomposition into dynamic molecular modes provides an alternative framework to understand the physics of NMR relaxation for viscous fluids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interphase Chromosome Conformation and Chromatin-Chromatin Interactions in Human Epithelial Cells Cultured Under Different Gravity Conditions

Microgravity has been shown to alter global gene expression patterns and protein levels both in cultured cells and animal models. It has been suggested that the packaging of chromatin fibers in the interphase nucleus is closely related to genome function, and the changes in transcriptional activity are tightly correlated with changes in chromatin folding. This study explores the changes of chromatin conformation and chromatin-chromatin interactions in the simulated microgravity environment, and investigates their correlation to the expression of genes located at different regions of the chromosome. To investigate the folding of chromatin in interphase under various culture conditions, human epithelial cells, fibroblasts, and lymphocytes were fixed in the G1 phase. Interphase chromosomes were hybridized with a multicolor banding in situ hybridization (mBAND) probe for chromosome 3 which distinguishes six regions of the chromosome as separate colors. After images were captured with a laser scanning confocal microscope, the 3-dimensional structure of interphase chromosome 3 was reconstructed at multi-mega base pair scale. In order to determine the effects of microgravity on chromosome conformation and orientation, measures such as distance between homologous pairs, relative orientation of chromosome arms about a shared midpoint, and orientation of arms within individual chromosomes were all considered as potentially impacted by simulated microgravity conditions. The studies revealed non-random folding of chromatin in interphase, and suggested an association of interphase chromatin folding with radiation-induced chromosome aberration hotspots. Interestingly, the distributions of genes with expression changes over chromosome 3 in cells cultured under microgravity environment are apparently clustered on specific loci and chromosomes. This data provides important insights into how mammalian cells respond to microgravity at molecular level.

International Space Station↗

Distinguishing one from many using super-resolution compressive sensing

We present that distinguishing whether a signal corresponds to a single source or a limited number of highly overlapping point spread functions (PSFs) is a ubiquitous problem across all imaging scales, whether detecting receptor-ligand interactions in cells or detecting binary stars. Super-resolution imaging based upon compressed sensing exploits the relative sparseness of the point sources to successfully resolve sources which may be separated by much less than the Rayleigh criterion. However, as a solution to an underdetermined system of linear equations, compressive sensing requires the imposition of constraints which may not always be valid. One typical constraint is that the PSF is known. However, the PSF of the actual optical system may reflect aberrations not present in the theoretical ideal optical system. Even when the optics are well characterized, the actual PSF may reflect factors such as non-uniform emission of the point source (e.g. fluorophore dipole emission). As such, the actual PSF may differ from the PSF used as a constraint. Similarly, multiple different regularization constraints have been suggested including the l 1 -norm, l 0 -norm, and generalized Gaussian Markov random fields (GGMRFs), each of which imposes a different constraint. Other important factors include the signal-to-noise ratio of the point sources and whether the point sources vary in intensity. In this work, we explore how these factors influence super-resolution image recovery robustness, determining the sensitivity and specificity. In conclusion, we determine an approach that is more robust to the types of PSF errors present in actual optical systems.

42 ENGINEERING↗

Adjusted Graphite Thermal Scattering Data Applied to Fluoride-Salt-Cooled Reactors

Thermal scattering data is a key component of fission reactor simulation. While most materials can be reasonably modeled with a free gas approximation, the moderators in thermal systems require a more rigorous treatment to sufficiently capture their specific neutron interaction physics. Graphite does not typically feature as a principle moderator in power reactors in service today, but remains an attractive prospect for a number of new reactor concepts currently in development. In comparison to light water, a material nearly ubiquitous in thermal reactors, graphite offers a better neutron economy by way of a small absorption cross section, high thermodynamic stability and can be incorporated into the structure of the core itself. Graphite in its purest form is a crystalline material composed of stacked layers of graphene, a hexagonal planar lattice of carbon atoms. In-plane, each carbon atom is covalently bonded to 3 neighbouring carbon atoms, creating a strong bond, while between planes only a weak van der Waals force exists. Pure graphite has a density of 2.26 g/cm{sup 3}. However, reactor-grade contains a significant amount of carbon binder, leading to a porous bulk medium with randomly oriented micro crystals. Densities of 1.5 - 1.9 g/cm{sup 3} are typical for reactor-grade graphite, corresponding to porosities on the order of 10-30%. This deviation from pure crystalline graphite should be accounted for in the thermal scattering data. When an incident neutron is in or near the thermal region, its de Broglie wavelength is the same order as the molecular bond lengths, leading to elastic scattering. At similar energies, the dynamics of the moderator lattice (in the case of solid moderators) can cause inelastic scattering. For these moderators, special cross sections should be calculated and used in reactor simulations. To generate this thermal scattering data, parameters pertaining to the properties and structure of the material in question are fed into a nuclear data processing code, such as NJOY. Within NJOY is a module called LEAPR which is used to generate the thermal scattering law S(α,β), which is in turn is fed into another module THERMR which is used to generate thermal cross sections that factor in the molecular-scale scattering phenomena. The core of the thermal scattering law is the phonon spectrum ρ(β) which describes the modes of excitation of the material lattice. An investigation into the phonon frequency spectrum was conducted at North Carolina State University (NCSU) for reactor-grade graphite which accounts for porosity. This phonon spectrum was calculated using the ab initio density functional theory (DFT) code VASP. The inelastic cross section calculated using this spectrum was found to have good agreement with relevant experimental data. The resulting spectra differed from the benchmark spectrum produced by Young and Koppel, the same data used in current nuclear data evaluations. The latter uses the lattice dynamics of perfect crystalline graphite with four force constants fitted to the model from thermodynamics data from reactor-grade (porous) graphite, which yields a reasonable approximation to the phonon spectrum of reactor-grade graphite.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

An Algorithm for the Transport of Anisotropic Neutrons

One major obstacle to human space exploration is the possible limitations imposed by the adverse effect of long-term exposure to the space environment. Even before human spaceflight began, the potentially brief exposure of astronauts to the very intense random solar particle events (SPE) were of great concern. A new challenge appears in deep space exploration from exposure to the low-intensity heavy-ion flux of the galactic cosmic rays (GCR) since the missions are of long duration and the accumulated GCR exposures can be high. Because cancer induction rates increase behind low to rather large thicknesses of aluminum shielding, according to available biological data on mammalian exposures to GCR like ions, the shield requirements for a Mars mission are prohibitively expensive in terms of mission launch costs. Therefore, a critical issue in the Human Exploration and Development of Space enterprise is cost effective mitigation of risk associated with ionizing radiation exposure. In order to estimate astronaut risk to GCR exposure and associated cancer risks and health hazards, it is necessary to do shield material studies. To determine an optimum radiation shield material it is necessary to understand nuclear interaction processes such as fragmentation and secondary particle production which is a function of energy dependent cross sections. This requires knowledge of material transmission characteristics either through laboratory testing or improved theoretical modeling. Here ion beam transport theory is of importance in that testing of materials in the laboratory environment generated by particle accelerators is a necessary step in materials development and evaluation for space use. The approximations used in solving the Boltzmann transport equation for the space setting are often not sufficient for laboratory work and those issues are a major emphasis of the present work.

Tweed, J.↗

Constitutive Modeling of Nanotube-Reinforced Polymer Composite Systems

In this study, a technique has been proposed for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Since the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties of the SWNT/polymer composites can no longer be determined through traditional micromechanical approaches that are formulated using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalent-continuum modeling method. The effective fiber retains the local molecular structure and bonding information and serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube sizes and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/polyethylene composite systems, one with continuous and aligned SWNT and the other with discontinuous and randomly aligned nanotubes.

Odegard, Gregory M.↗

Constitutive Modeling of Nanotube-Reinforced Polymer Composite Systems

In this study, a technique has been proposed for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Since the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties of the SWNT/polymer composites can no longer be determined through traditional micromechanical approaches that are formulated using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalent-continuum modeling method. The effective fiber retains the local molecular structure and bonding information and serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube sizes and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/polyethylene composite systems, one with continuous and aligned SWNT and the other with discontinuous and randomly aligned nanotubes.

Odegard, Gregory M.↗