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At least 19 records

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps

Lyman continuum observations of solar flares

A study is made of Lyman continuum observations of solar flares, using data obtained by the EUV spectroheliometer on the Apollo Telescope Mount. It is found that there are two main types of flare regions: an overall 'mean' flare coincident with the H-alpha flare region, and transient Lyman continuum kernels which can be identified with the H-alpha and X-ray kernels observed by other authors. It is found that the ground level hydrogen population in flares is closer to LTE than in the quiet sun and active regions, and that the level of Lyman continuum formation is lowered in the atmosphere from a mass column density .000005 g/sq cm in the quiet sun to .0003 g/sq cm in the mean flare, and to .001 g/sq cm in kernels. From these results the amount of chromospheric material 'evaporated' into the high temperature region is derived, which is found to be approximately 10 to the 15th g, in agreement with observations of X-ray emission measures.

Machado, M. E.

On the modes of nanosecond pulsed plasmas for combustion ignition of quiescent CH 4 -air mixtures

The effect of transient plasma modes on ignition kernel development are discussed here for a quiescent CH 4 -air combustion model system. A 10 ns high-voltage pulse was applied to a pin-to-pin electrode in lean fuel-air mixtures at room temperature and atmospheric pressure. High-impedance streamer, transient spark and low-impedance spark discharges were identified based on pulse waveforms of voltage and current. A sustained ignition kernel expansion was observed when the plasma discharge transitioned into a transient spark or spark discharge. The minimum ignition energy was obtained at the transient spark mode, which has less than a third of the energy or Coulomb transfer compared to the low-impedance spark. Employing repetitive 10-pulse sequence at 10 kHz, the lean-fuel limit was extended from an equivalence ratio of 0.6 for the single pulse ignition to 0.5. The use of repetitive pulses also allowed streamer breakdown or spark initiation to occur at a lower voltage.

CH 4

Correlated observations of impulsive UV and hard X-ray bursts in solar flares from the solar maximum mission

An investigation is conducted of the temporal and spatial structures of UV and hard X-ray bursts in a disk and a limb flare observed with instruments on the Solar Maximum Mission satellite. Attention is given to the transient UV brightening before the flare, the impulsive enhancement of UV continuum emission, the relationship between emission source region and particle acceleration region, and large scale excitations. The most active part of the active region appears to be the most flare-productive region. These regions exhibit high UV activities with numerous UV transient bursts occurring in many small kernels.

Cheng, C.-C.

Dynamic evolution of the transition zone plasma in solar flares and active region transients

The dynamic evolution of flares and of transient brightenings in active regions observed during the Solar Maximum Mission (SMM) in the UV lines of Si IV and O IV were studied. Transient brightenings in active regions and in flares occur in small points or kernels, not necessarily the initially bright regions. There is no apparent velocity pattern in which flaring or transient brightenings preferentially occur. At the flaring point, the velocity of the transition zone plasma tends to show larger downflow in the rise phase, and after the peak UV emission the downflow decreases or may even reverse and become upflow. This anticorrelation between velocity and UV intensity holds for some of the transient bright points but is more apparent for the flaring points.

Cheng, Chung-Chieh

Multiphysics Modeling of Microreactors with NEAMS codes, and Validation Based on KRUSTY Reactivity Insertion

The NEAMS Multiphysics Applications team continues to assess code usability and functionality for microreactor design and safety analyses, while demonstrating that NEAMS tools capture both steady-state and transient behavior across distinct microreactor concepts. In FY2025, the team advanced full-core, high-fidelity, multiphysics models that solve more complex problems and strengthen verification/validation for several microreactor systems: heat-pipe microreactor (HPMR), gas-cooled microreactor (GCMR), and the KRUSTY experiment. These models employ the MOOSE MultiApp/Transfers architecture with Griffin for neutronics, BISON for heat conduction/thermomechanics, Sockeye for heat pipes, SAM/THM for coolant channels and loops, and SWIFT for hydride behavior, with meshes generated via the MOOSE Reactor Module. The graphite models available in the Grizzly code were also investigated for future analyses. For the HPMR, a Na-HPMR variant was constructed to align with recently validated heat-pipe experiments and Sockeye’s LCVF capability, enabling mechanistic heat-pipe transients and startup modeling. The Na-HPMR will serve as the primary model for HPMR investigations in upcoming tasks. The load-following and single heat-pipe failure scenarios (Griffin/BISON/Sockeye), which were previously modeled for the K-HPMR, were replicated for the Na-HPMR, showing strong negative temperature feedback and highly localized thermal effects, respectively, while the startup case captured vapor-front progression and heat-removal activation. Solid mechanics was added to the previously built K-HPMR full-core model in BISON, showing minimal impact on steady-state reactivity yet enabling stress-field predictions that prepare the path for full-core TRISO performance analyses. For the GCMR, automated steady-state and four transient scenarios were executed using Griffin/BISON/SAM/SWIFT. Results confirm robust inherent safety: power collapses promptly in loss-of-cooling events, the inlet-temperature drop settles to a new equilibrium, and a single-channel blockage yields only a ~30 K local fuel-temperature rise with <0.4% power decrease. SWIFT-predicted hydrogen redistribution affects reactivity during both steady-state and transient conditions, underscoring its importance. A Brayton-cycle balance of plant (BOP) model in SAM/THM demonstrated stable startup behavior, and xenon-driven reactivity during load following was analyzed. To improve TRISO-compact temperature fidelity, a fast multiscale Heat Source Decomposition (HSD) treatment was implemented. Against heterogeneous benchmarks, HSD reduces underprediction of kernel temperatures and lowers predicted peak powers in reactivity-insertion transients compared to previous homogenized models. KRUSTY warm-critical validation progressed from FY2024 baselines: the 15Ȼ insertion shows excellent agreement in peak power (~2% high) and temperature trends, and the 30Ȼ case was automated via a feedback controller that maintained power near 3 kW for ~150 s with close agreement to data. The successful modeling of the warm critical tests has laid a strong foundation for simulating more complex nuclear system tests in the years ahead. Throughout FY2025, developer feedback was provided (e.g., MOOSE batch mesh generation, distributed pre-split meshes, Griffin sweeper on displaced meshes), several new models were contributed to the Virtual Test Bed, and an OECD-NEA WPRS multiphysics benchmark based on the HPMR was initiated to enable broader cross-comparison and best-practice development with the nuclear community at large.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Fine-Grained Application Energy and Power Measurements on the Frontier Exascale System

The increasing complexity and power/energy demands of heterogeneous exascale systems, such as the Frontier supercomputer, present significant challenges for measuring and optimizing power consumption in applications. Current tools either lack the resolution to capture fine-grained power and energy measurements, fail to validate in-band measurements against out-of-band power sensors, or cannot integrate this information with application performance events in a scalable manner. This paper introduces a novel open-source performance toolkit that integrates extended PAPI components with Score-P plugins to enable in-band, fine-grained power and energy measurements, while also supporting validation using power meter measurements for both CPUs and GPUs. One key contribution is the ability to perform millisecond-level power and energy measurements for AMD MI250X GPUs, mapping them to application performance events within a single trace and measurement system that scales. Our toolkit combines coarse-grained measurements from cray_pm counters with high-resolution metrics from rocm_smi and RAPL, converting GPU instantaneous accumulated energy into power to capture both transient and steady-state power behavior, a capability often missed by out-of-band and monitoring tools. By mapping these metrics to specific application regions, developers can identify energy hotspots, address inefficiencies in GPU kernel execution, and validate in-band measurements against external measurements. We demonstrate the effectiveness of this approach through case studies using benchmarks such as GPU rocblas_sgemm, BLIS c_blas_dgemm, and rocHPL, highlighting the variability of the measurements and the impact of transient power spikes on kernel-level efficiency.

Hernandez Mendoza, Oscar [ORNL] (ORCID:00000002538

Linear and nonlinear dynamic analysis by boundary element method

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Ahmad, Shahid

Steady-State and Transient Boundary Element Methods for Coupled Heat Conduction

Boundary element algorithms for the solution of steady-state and transient heat conduction are presented. The algorithms are designed for efficient coupling with computational fluid dynamic discretizations and feature piecewise linear elements with offset nodal points. The steady-state algorithm employs the fundamental solution approach; the integration kernels are computed analytically based on linear shape functions, linear elements, and variably offset nodal points. The analytic expressions for both singular and nonsingular integrands are presented. The transient algorithm employs the transient fundamental solution; the temporal integration is performed analytically and the nonsingular spatial integration is performed numerically using Gaussian quadrature. A series solution to the integration is derived for the instance of a singular integrand. The boundary-only character of the algorithm is maintained by integrating the influence coefficients from initial time. Numerical results are compared to analytical solutions to verify the current boundary element algorithms. The steady-state and transient algorithms are numerically shown to be second-order accurate in space and time, respectively.

Kontinos, Dean A.

HTGR Multiphysics Application Drivers FY26 Updates

This report summarizes FY26 progress under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program's high-temperature gas-cooled reactor (HTGR) application driver work, covering a wide range of activities such as code validation and multi-physics code assessment. 1) A detailed SAM model of the High-Temperature Engineering Test Reactor (HTTR) was developed using a unique-block grouping approach, with an extended parallel thermal network method to capture block-to-block conduction and radiation heat transfer, and applied to steady-state simulations of the HTTR 30~MW and 9~MW cases. 2) In another activity, SAM's newly implemented multi-component gas flow model was validated against the Natural convection Shutdown heat removal Test Facility (NSTF) argon ingress experiment, correctly capturing the density-driven suppression and thermal recovery of natural circulation observed when argon is introduced into the air-cooled Reactor Cavity Cooling System (RCCS) loop. 3) For the OECD/NEA High Temperature Test Facility (HTTF) benchmark, we co-led the international benchmark activities as well as the OECD/NEA final benchmark report to be released at the end of this year. 4) Finally, the coupled Griffin-SAM modeling capability for pebble-bed HTGRs was advanced by verifying the Griffin neutronics solution against Serpent Monte Carlo for a realistic non-uniform temperature distribution, resolving several deficiencies in the SAM-to-Griffin temperature transfer scheme, and enabling distinct fuel kernel, moderator, and coolant temperatures for cross section feedback. These new features were demonstrated in a PBR load-following transient.

Lee, Alvin

Integration of Online Cross-Section Generation Capability with Depletion and Transient Solvers in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE)-based reactor multiphysics analysis application jointly developed by Argonne and Idaho National Laboratories under the DOENE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. In FY25, an online crosssection generation capability based on the Self-Shielding Application Programming Interface (SSAPI) was demonstrated for TRISO-fueled reactor problems under steady-state conditions. This fiscal year, that capability was extended to support depletion and transient multiphysics calculations, enabling high-fidelity analyses that generate self-shielded cross sections on the fly from the actual evolving composition and temperature states rather than from pre-tabulated libraries. For depletion, a two-way coupling was established in which SSAPI computes compact-averaged self-shielded cross sections that the depletion solver then uses to advance the Bateman equations, with the updated compositions returned to SSAPI at each step; the depletion module was refactored to support both library-based and SSAPI-based cross sections, and additional logic was added to track daughter isotopes and to exclude minor isotopes for efficiency. For transient analysis, the SSAPI multigroup library was extended with the kinetics data required for time-dependent calculations, the Improved Quasi-Static (IQS) scheme was coupled with SSAPI, and several supporting capabilities were implemented, including a self-shielding treatment that lets control rods and drums move within a self-shielded model, which had previously been impossible and had ruled out rod- and drum-movement transients with on-the-fly cross sections altogether, a new mixing scheme for delayed-neutron precursor decay constants, a checkpoint-based restart workflow, and performance improvements such as pointwise cross-section interpolation and the bypassing of unnecessary Dancoff factor calculations. The implemented capabilities were verified against Serpent Monte Carlo solutions. For depletion, a prismatic pin-cell problem based on a Next Generation Nuclear Plant (NGNP) Very High Temperature Reactor benchmark showed excellent agreement, with eigenvalue differences within 200 pcm over the entire burnup range (up to 140 MWD/kgU) and fission-product and actinide inventories agreeing to within 0.8% and 2.5%, respectively; a heat-pipe microreactor assembly problem with a much higher fuel loading confirmed the same behavior and quantified the bias introduced when the multigroup equivalence effect is neglected. For transient analysis, a pin-cell problem with a step reactivity insertion and temperature feedback reproduced the analytically expected asymptotic power and showed close agreement between the direct and IQS solutions, and a two-dimensional microreactor core problem with control-drum rotation exercised the new moving-drum self-shielding treatment and demonstrated successful coupling of the online crosssection generation with both the direct and IQS transient methods. The capability was further exercised on a full-core pebble-bed problem, in which Griffin was coupled with the System Analysis Module (SAM) to simulate load-following operation of the gPBR with the Doppler feedback resolved at the TRISO fuel kernel temperature. These developments in Griffin provide a convenient, high-fidelity approach to cross-section generation for advanced thermal reactors with geometrically complex and highly heterogeneous configurations, including TRISO-fueled prismatic and pebble-bed systems, and support steady-state, depletion, and transient multiphysics calculations. They also enable self-shielded cross sections to be evaluated directly at the actual coupled state of the system, thereby establishing a foundation for high-fidelity, fully coupled multiphysics analysis of advanced reactors

Park, H.

Maize Rough Endosperm6 (rgh6) Encodes A Predicted Dead-Box RNA Helicase and Affects Mirna Processing in Endosperm Development

Maize rough endosperm (rgh) mutants have defective kernels with a rough, etched, or pitted endosperm surface. Molecular genetic analysis of this mutant class has identified multiple RNA processing proteins critical to endosperm development. Here, we report on the developmental and molecular function of the rgh6 locus. The rgh6 mutant was isolated from the UniformMu transposon tagging population. Mutant kernels have reduced endosperm size and defective embryos that develop in a more apical position than typical for defective embryos. TB translocation crosses revealed that rgh6 mutant endosperm inhibits normal embryo development. Positional cloning of the rgh6 locus found that it encodes a predicted DEAD-box RNA helicase. Consistent with a predicted function for RNA processing, transient expression of a RGH6-GFP fusion protein is localized to nucleolus and nuclear speckles in Nicotiana benthamiana leaves. Rgh6 transcripts are highly expressed in endosperm epidermal cell types such as the aleurone, basal endosperm cell layer, embryo surrounding region, and endosperm adjacent to scutellum. Markers of these cell types show increased levels in rgh6 mutant kernels. Mutant endosperm tissues have increased precursor microRNA (pre-miRNA) and decreased mature miRNA relative to normal sibling endosperm, indicating that rgh6 is required for miRNA processing. The transcript levels for most miRNA target genes accumulate to a higher level in rgh6 mutant tissue. These results suggest that miRNA processing and regulation of miRNA target genes are required for normal endosperm development.

Plant Sciences

Meteorological drivers of the low-cloud radiative feedback pattern effect and its uncertainty

The radiative feedback pattern effect remains a large source of uncertainty for both projections of future trends and interpretations of past trends in global temperature. The pattern effect is defined as the difference in feedbacks between transient and long-term simulations, and past work shows that is primarily attributed to changes in the marine low-cloud radiative feedback. Here we use low cloud meteorological kernels to map out both the primary cloud controlling factors through which changing surface temperature patterns drive changes in low-cloud feedback, as well as the sources of model spread. We find that the pattern effect is almost entirely driven by changes in estimated inversion strength (EIS) in the Southern Hemisphere, particularly in the South East Pacific and Southern Ocean. In both past and future simulations, inter-model spread is primarily caused by model differences in the sensitivity of low clouds to the environmental conditions, rather than differences in the simulated evolution of environmental conditions.

58 GEOSCIENCES

SlimIO: Lightweight I/O Path Design for Write Isolation in FDP-backed In-Memory Databases

In-Memory Databases (IMDBs) are widely used with HPC applications to manage transient data, often using snapshot-based persistence for backups. Redis, a representative IMDB, employs both snapshot and Write-Ahead Log (WAL) mechanisms, storing data on persistent devices via the traditional kernel I/O path. This method incurs syscall overhead, I/O contention between processes, and SSD garbage collection (GC) delays. To address these issues, we propose SlimIO, which adopts I/O passthru to minimize syscall overhead and inter-process I/O interference. Additionally, it leverages Flexible Data Placement (FDP) SSDs as backup storage to avoid performance degradation from SSD GC. Experimental results show that SlimIO reduces snapshot time by up to 25%, increases query throughput by up to 30% during non-snapshot periods, and lowers 99.9%-ile latency by up to 50%. Furthermore, it achieves a write amplification factor (WAF) of 1.00, indicating no redundant internal writes, thus extending SSD lifespan.

Lee, Sangyun [Sogang University]

Modeling stochastic fluctuations in relativistic kinetic theory

Using the information current, we develop a Lorentz-covariant framework for modeling equilibrium fluctuations in relativistic kinetic theory in the grand-canonical ensemble. The resulting stochastic theory is proven to be causal and covariantly stable, and its predictions do not depend on the choice of spacetime foliation used to define the grand-canonical probabilities. As expected, in a box containing N > 5 particles, Boltzmann’s molecular chaos postulate is broken with (almost exact) probability N -1/2 , leading to a breakdown of the Boltzmann equation in small systems. Here, we also verify that, in ultrarelativistic gases, transient hydrodynamics already accounts for at least 80% of the equilibrium fluctuations of the stress-energy tensor at a given time. Finally, we compute the correlators at nonequal times for two selected collision kernels: that of a chemically active diluted solution, and that of ultrarelativistic scalar particles self-interacting via a quartic potential. For the former, we compute the density-density correlators analytically in real space, and dehydrodynamization of the stochastic theory is proven to occur whenever the mean free path diverges at high energy.

Astronomy & Astrophysics

A hereditary integral, transient network approach to modeling permanent set and viscoelastic response in polymers

An efficient numerical framework is presented for modeling viscoelasticity and permanent set of polymers. It is based on the hereditary integral form of transient network theory, in which polymer chains belong to distinct networks each with different natural equilibrium states. Chains continually detach from previously formed networks and reattach to new networks in a state of zero stress. The free energy of these networks is given in terms of the deformation gradient relative to the configuration at which the network was born . A decomposition of the kernel for various free energies allows for a recurrence relationship to be established, bypassing the need to integrate over all time history. The technique is established for both highly compressible and nearly incompressible materials through the use of neo-Hookean, Blatz–Ko, Yeoh, and Ogden-Hill material models. Multiple examples are presented showing the ability to handle rate-dependent response and residual strains under complex loading histories.

Finite element method

End-To-End Decentralized Transmission Line Protection in IBR-Dominated Weak Grids Using Interpretable Data-Driven Methods

Traditional transmission line protection relies on predictable synchronous-based fault signatures, which frequently fail under the non-standard, current-limited fault characteristics of Inverter-Based Resources (IBRs). This study investigates how to achieve secure, communication-free fault isolation in IBR-dominated weak grids without relying on opaque, computationally heavy "black-box" machine learning algorithms. To address this, we propose a novel, standalone, and inherently interpretable data-driven protection framework. Unlike centralized methods requiring multi-terminal communication, this decentralized approach relies solely on local measurements using a hierarchical linear-kernel Support Vector Machine (SVM). The methodology decomposes the protection task into four sequential stages that mimic traditional protection elements: fault detection and fault direction identification, fault type classification, zone classification, and location estimation. This multi-stage architecture allows for specialized feature engineering at each stage, combining high computational efficiency with logic traceability. The framework's end-to-end performance was validated via C-code and PSCAD/EMTDC co-simulation, utilizing a real-world utility network and an OEM black-box IBR model. The proposed relay achieves 97.2% overall accuracy and provides a reliable trip decision within a 2.5-cycle window. The results confirm 100% accuracy in fundamental fault detection, reliable zone selectivity across low to moderate fault resistances, and robust security against non-fault transients, proving its immediate viability for integration into commercial numerical relays.

24 POWER TRANSMISSION AND DISTRIBUTION

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS