Search NASA⌕ Search

SEARCH · Search NASA

Results for “level set methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

SU-E-T-152: Error Sensitivity and Superiority of a Protocol for 3D IMRT Quality Assurance

Purpose: To test if the parameters included in our 3D QA protocol with current tolerance levels are able to detect certain errors and show the superiority of 3D QA method over single ion chamber measurements and 2D gamma test by detecting most of the introduced errors. The 3D QA protocol parameters are: TPS and measured average dose difference, 3D gamma test with 3mmDTA/3% test parameters, and structure volume for which the TPS predicted and measured absolute dose difference is greater than 6%. Methods: Two prostate and two thoracic step-and-shoot IMRT patients were investigated. The following errors were introduced to each original treatment plan: energy switched from 6MV to 10MV, linac jaws retracted to 15cmx15cm, 1,2,3 central MLC leaf pairs retracted behind the jaws, single central MLC leaf put in or out of the treatment field, Monitor Units (MU) increased and decreased by 1 and 3%, collimator off by 5 and 15 degrees, detector shifted by 5mm to the left and right, gantry treatment angle off by 5 and 15 degrees. QA was performed on each plan using single ion chamber, 2D ion chamber array for 2D gamma analysis and using IBA's COMPASS system for 3D QA. Results: Out of the three tested QA methods single ion chamber performs the worst not detecting subtle errors. 3D QA proves to be the superior out of the three methods detecting all of introduced errors, except 10MV and 1% MU change, and MLC rotated (those errors were not detected by any QA methods tested). Conclusion: As the way radiation is delivered evolves, so must the QA. We believe a diverse set of 3D statistical parameters applied both to OAR and target plan structures provides the highest level of QA.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2022

TDCOSMO VIII. A key test of systematics in the hierarchical method of time-delay cosmography

The largest source of systematic errors in the time-delay cosmography method likely arises from the lens model mass distribution, where an inaccurate choice of model could in principle bias the value of $H$ 0 . A Bayesian hierarchical framework has been proposed which combines lens systems with kinematic data, constraining the mass profile shape at a population level. The framework has been previously validated using a small sample of lensing galaxies drawn from hydro-simulations. The goal of this work is to expand the validation to a more general set of lenses consistent with observed systems, as well as confirm the capacity of the method to combine two lens populations: one which has time delay information and one which lacks time delays and has systematically different image radii. For this purpose, we generated samples of analytic lens mass distributions made of baryons+dark matter and fit the subsequent mock images with standard power-law models. Corresponding kinematics data were also emulated. The hierarchical framework applied to an ensemble of time-delay lenses allowed us to correct the $H$ 0 bias associated with model choice to find $H$ 0 within 1.5σ of the fiducial value. We then combined this set with a sample of corresponding lens systems which have no time delays and have a source at lower $z$, resulting in a systematically smaller image radius relative to their effective radius. The hierarchical framework has successfully accounted for this effect, recovering a value of $H$ 0 which is both more precise (σ ~ 2%) and more accurate (0.7% median offset) than the time-delay set alone. This result confirms that non-time-delay lenses can nonetheless contribute valuable constraining power to the determination of $H$ 0 via their kinematic constraints, assuming they come from the same global population as the time-delay set.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Large Deviations for Level Sets of a Branching Brownian Motion and Gaussian Free Fields

We study deviation probabilities for the number of high positioned particles in branching Brownian motion and confirm a conjecture of Derrida and Shi. We also solve the corresponding problem for the two-dimensional discrete Gaussian free field. Our method relies on an elementary inequality for inhomogeneous Galton–Watson processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Performance Results for Sensor Assignment Problem as Solved on a Multi-Node Cluster

An earlier report described a procedure for optimal sensor set selection and its implementation on a computational cluster. This new and innovative capability was developed to facilitate a reduction in operations staffing levels to improve plant economics. By automating surveillance and maintenance tasks through early detection of degrading sensors and equipment, staff can be more efficiently deployed. The method uses automated reasoning and domain knowledge in the form of the conservation equations to infer from plant measurements the state of equipment health. Inclusion of domain knowledge addresses the problem that exists with pure data-driven methods that there are no rigorous guidelines for determining what constitutes an adequate sensor set. Formalizing the procedure for sensor set selection as we have done results in a more reliable and explainable diagnosis of plant equipment health. Importantly, from the standpoint of the plant owner, personnel are provided with an early and explicit diagnosis of an equipment problem. That in principle automates the process and eliminates having to send personnel into the plant to find the cause as typically occurs when a data-driven method detects an anomaly. In this report we describe first results obtained using a computational cluster to solve the sensor set selection problem as framed above. The case described addresses the problem of equipment health monitoring in the high-pressure (HP) feedwater system of a pressurized light water reactor as seen through the eyes of our collaborating utility partner. Maintenance of this system can amount to millions of dollars per year if equipment health issues go undiagnosed and lead to loss of function. On examining the potential that is inherent in the installed sensor set for diagnosing equipment health degradation, it was found that greater fault resolution capability can be achieved using a sensor set that is 20 percent fewer in number. The take-away is that compared to the installed sensor set there exists a more strategic assignment of sensors that will furnish better health monitoring capability and with fewer sensors. Where the problem defies solution by manual inspection, as is the case here, one can be found by an algorithm. The solution was obtained in four hours using 30 computational cores. The HP feedwater problem as posed above illustrates the added value of approaching the sensor selection problem as one amenable to algorithmic solution. This problem is of interest to advanced reactor designers and to utilities that are setting up remote monitoring and diagnostic centers.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

A projection-free method for representing plane-wave DFT results in an atom-centered basis

Plane wave density functional theory (DFT) is a powerful tool for gaining accurate, atomic level insight into bulk and surface structures. Yet, the delocalized nature of the plane wave basis set hinders the application of many powerful post-computation analysis approaches, many of which rely on localized atom-centered basis sets. Traditionally, this gap has been bridged via projection-based techniques from a plane wave to atom-centered basis. We instead propose an alternative projection-free approach utilizing direct calculation of matrix elements of the converged plane wave DFT Hamiltonian in an atom-centered basis. This projection-free approach yields a number of compelling advantages, including strict orthonormality of the resulting bands without artificial band mixing and access to the Hamiltonian matrix elements, while faithfully preserving the underlying DFT band structure. The resulting atomic orbital representation of the Kohn-Sham wavefunction and Hamiltonian provides a gateway to a wide variety of analysis approaches. We demonstrate the utility of the approach for a diverse set of chemical systems and example analysis approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Comparative Metagenomic Analysis of Soil Microbial Communities across Three Hexachlorocyclohexane Contamination Levels

This paper presents the characterization of the microbial community responsible for the in-situ bioremediation of hexachlorocyclohexane (HCH). Microbial community structure and function was analyzed using 16S rRNA amplicon and shotgun metagenomic sequencing methods for three sets of soil samples. The three samples were collected from a HCHdumpsite (450 mg HCH/g soil) and comprised of a HCH/soil ratio of 0.45, 0.0007, and 0.00003, respectively. Certain bacterial; (Chromohalobacter, Marinimicrobium, Idiomarina, Salinosphaera, Halomonas, Sphingopyxis, Novosphingobium, Sphingomonas and Pseudomonas), archaeal; (Halobacterium, Haloarcula and Halorhabdus) and fungal (Fusarium) genera were found to be more abundant in the soil sample from the HCH-dumpsite. Consistent with the phylogenetic shift, the dumpsite also exhibited a relatively higher abundance of genes coding for chemotaxis/motility, chloroaromatic and HCH degradation (lin genes). Reassembly of a draft pangenome of Chromohalobacter salaxigenes sp. (,8X coverage) and 3 plasmids (pISP3, pISP4 and pLB1; 13X coverage) containing lin genes/clusters also provides an evidence for the horizontal transfer of HCH catabolism genes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

Long-term changes in the seasonality of Baltic sea level

The seasonal cycle accounts for about 40% of the total sea level variability in the Baltic Sea. In a climate change context, changes are expected to occur, not only in mean levels but also in the seasonal characteristics of sea level. The present study addresses the quantification of changes in the seasonal cycle of sea level from a set of century-long tide gauge records in the Baltic Sea. In order to obtain robust estimates of the changes in amplitude and phase of the seasonal cycle, we apply different methods, including continuous wavelet filtering, multi-resolution decomposition based on the maximal overlap discrete wavelet transform, auto-regressive-based decomposition, singular spectrum analysis and empirical mode decomposition. The results show that all methods generally trace a similar long-term variability of the annual cycle amplitudes, and we focus on discrete wavelet analysis as the natural counterpart of classical moving Fourier analysis. In contrast to previous studies suggesting the existence of long-term changes in the seasonal cycle, in particular an increase of the annual amplitude, we find alternating periods of high and low amplitudes without any clear indication of systematic long-term trends. The derived seasonal patterns are spatially coherent, discriminating the stations in the Baltic entrance from the remaining stations in the Baltic basin, for which zonal wind accounts for typically more than 40% of the variations in amplitude.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Multi-fidelity learning for interatomic potentials: low-level forces and high-level energies are all you need

The promise of machine learning interatomic potentials (MLIPs) has led to an abundance of public quantum mechanical (QM) training datasets. The quality of an MLIP is directly limited by the accuracy of the energies and atomic forces in the training dataset. Unfortunately, most of these datasets are computed with relatively low-accuracy QM methods, e.g. density functional theory with a moderate basis set. Due to the increased computational cost of more accurate QM methods, e.g. coupled-cluster theory with a complete basis set (CBS) extrapolation, most high-accuracy datasets are much smaller and often do not contain atomic forces. The lack of high-accuracy atomic forces is quite troubling, as training with force data greatly improves the stability and quality of the MLIP compared to training to energy alone. Because most datasets are computed with a unique level of theory, traditional single-fidelity (SF) learning is not capable of leveraging the vast amounts of published QM data. In this study, we apply multi-fidelity learning (MFL) to train an MLIP to multiple QM datasets of different levels of accuracy, i.e. levels of fidelity. Specifically, we perform three test cases to demonstrate that MFL with both low-level forces and high-level energies yields an extremely accurate MLIP—far more accurate than a SF MLIP trained solely to high-level energies and almost as accurate as a SF MLIP trained directly to high-level energies and forces. Therefore, MFL greatly alleviates the need for generating large and expensive datasets containing high-accuracy atomic forces and allows for more effective training to existing high-accuracy energy-only datasets. Indeed, low-accuracy atomic forces and high-accuracy energies are all that are needed to achieve a high-accuracy MLIP with MFL.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Bond Dissociation Energies of the Actinide Halides AnX, An = Ac–Lr and X = F–I, Utilizing Relativistic Composite Coupled Cluster Approaches

Bond dissociation energies (BDEs) have been calculated for the set of actinide halides AnX with An=Ac, Pa, and Np-Lr and X=F-I. Two composite thermochemistry methods based on the Feller-Peterson-Dixon (FPD) approach have been utilized, one involving spinor-based relativistic CCSD(T) calculations where spin-orbit (SO) was included at the orbital level and another using scalar relativistic CCSD(T) with a posteriori SO contributions based on 2-component multireference configuration interaction calculations. The method that was chosen for a given actinide halide was based on which representation yielded the best single determinant reference determinant for the coupled cluster calculation. The spinor-based method was chosen for all cases except for AmX, CmX, and BkX. Both composite approaches included contributions accounting for basis set truncation, outer-core correlation, the Gaunt interaction, and QED. The scalar FPD results, as well as the spinor-based calculations for AcF, also included higher order electron correlation up through CCSDT(Q). In addition to BDEs, CCSD(T) equilibrium bond lengths, harmonic frequencies, and vibrational anharmonicity constants are reported for all species. Last, the FPD BDEs for the fluorides were used to confirm the trend across the actinide series previously predicted by Gibson using bonding models based atomic promotion energies that provide a single 6d electron for bonding. In particular the local minimum in the BDEs at AmF is confirmed in the present calculations. Furthermore, the BDEs for LrX are predicted to be slightly larger than those of AcX, making them the largest in the actinide halide series.

Actinides↗
DOE OSTI2016

Development of a Low-Level Ar-37 Calibration Standard

Argon-37 is an important environmental signature of an underground nuclear explosion. Producing and quantifying low-level 37Ar standards is an important step in the development of sensitive field measurement instruments for use during an On-Site Inspection, a key provision of the Comprehensive Nuclear-Test-Ban Treaty. This paper describes progress at Pacific Northwest National Laboratory (PNNL) in the development of a process to generate and quantify low-level 37Ar standard material, which can then be used to calibrate sensitive field systems at activities consistent with soil background levels. The 37Ar used for our work was generated using a laboratory-scale, high-energy neutron source to irradiate powdered samples of calcium carbonate. Small aliquots of 37Ar were then extracted from the head space of the irradiated samples. The specific activity of the head space samples, mixed with P10 (90% stable argon:10% methane by mole fraction) count gas, is then derived using the accepted Length-Compensated Internal-Source Proportional Counting method. Due to the low activity of the samples, a set of three Ultra-Low Background Proportional-Counters designed and fabricated at PNNL from radio-pure electroformed copper was used to make the measurements in PNNL’s shallow underground counting laboratory. Very low background levels (<10 counts/day) have been observed in the spectral region near the 37Ar emission feature at 2.8 keV. Two separate samples from the same irradiation were measured. The first sample was counted for 12 days beginning 28 days after irradiation, the second sample was counted for 24 days beginning 70 days after irradiation (the half-life of 37Ar is 35.0 days). Both sets of measurements were analyzed and yielded very similar results for the starting activity (~0.1 Bq) and activity concentration (0.15 mBq/ccSTP argon) after P10 count gas was added. A detailed uncertainty model was developed based on the ISO Guide to the Expression of Uncertainty in Measurement. This paper presents a discussion of the measurement analysis, along with assumptions and uncertainty estimates.

Absolute radiation measurement↗
DOE OSTI2015

Stochastic Richardson Extrapolation Based Numerical Error Estimation for Kinetic Plasma Simulations

We present a numerical error estimation technique specifically formulated to deal with stochastic code output with multiple discretization parameters. This method is based on multiple fits to an error model with arbitrary convergence rates and cross-coupling terms, performed using nonlinear optimization. The fitting approach varies by the type of residual norm which influences the importance of outliers, and weights which influences the relative importance of data points in the coarse and refined regions of discretization parameter space. To account for the influence of stochastic noise, these fits are performed on multiple bootstrap values based on the underlying response data set. Using an automated discretization domain selection scheme, the fits are performed on a series of reduced sets of discretization levels in order to find an optimal fully-converged result estimate in the minimum variance sense; this automated approach enables straightforward analysis of multiple quantities of interest and/or time and spatially-dependent response data. The overall numerical error analysis method is useful for verification and validation problems for stochastic simulation methods and forms a key component in the overall uncertainty quantification process. The method was demonstrated for steady and unsteady electron diode problems simulated using a particle-in-cell kinetic plasma code, demonstrating excellent results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Local existence of N=1 supersymmetric gauge theory in four Dimensions

In this paper, we shall prove the local existence of N=1 supersymmetry gauge theory in 4 dimension. We start from the Lagrangian for coupling chiral and vector multiplets with constant gauge kinetic function and only considering a bosonic part by setting all fermionic field to be zero at level equation of motion. We consider a U(n) model as isometry for scalar field internal geometry. And we use a nonlinear semigroup method to prove the local existence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Random coordinate descent: A simple alternative for optimizing parameterized quantum circuits

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the collapse of quantum states after measurements. Thus, gradient estimations constitute a significant overhead in a gradient-based optimization of such quantum circuits. This paper introduces a random coordinate descent algorithm as a practical and easy-to-implement alternative to the full gradient descent algorithm. This algorithm only requires one partial derivative at each iteration. Motivated by the behavior of measurement noise in the practical optimization of parameterized quantum circuits, this paper presents an optimization problem setting that is amenable to analysis. Under this setting, the random coordinate descent algorithm exhibits the same level of stochastic stability as the full gradient approach, making it as resilient to noise. The complexity of the random coordinate descent method is generally no worse than that of the gradient descent and can be much better for various quantum optimization problems with anisotropic Lipschitz constants. Theoretical analysis and extensive numerical experiments validate our findings. Published by the American Physical Society 2024

Ding, Zhiyan (ORCID:000000018863403X)↗
DOE OSTI2022

An Assessment of Hydropower Potential at National Conduits

In support of the mission of the US Department of Energy Water Power Technologies Office to promote domestic next-generation hydropower growth, this study provides a first-of-its-kind assessment of the hydropower development potential on existing water conduits nationwide. This study evaluates the potential for conduit hydropower development in the municipal, agricultural, and industrial sectors across the United States. The research team developed systematic methods to evaluate conduit hydropower capacity potential (MW) and energy generation potential (GWh/year) at four categories of conduits across the United States. They include the following: (1) Water supply pipelines for municipal and industrial uses, (2) Wastewater discharge conduits from municipal and industrial systems, (3) Agricultural water conduits including irrigation canals and ditches in the 17 western states that rely heavily on irrigation, and (4) Thermoelectric power plant cooling water discharge conduits. For each type of conduit, the team developed and implemented a method to estimate hydraulic head and annual water flows—and the hydropower potential—based on analyses of satellite imagery, topography, and existing data sets on water systems and power plants. These methods support a consistent, replicable estimate of conduit hydropower potential across 3 sectors and all 50 states, aggregated at the county and state levels. The assessment was conducted at the reconnaissance level, considering resources that could be available for development at the state and national levels using present-day assumptions about conduit hydropower technology.

13 HYDRO ENERGY↗
DOE OSTI2020

Assessing United States County-Level Exposure for Research on Tropical Cyclones and Human Health

Tropical cyclone epidemiology can be advanced through exposure assessment methods that are comprehensive and consistent across space and time, as these facilitate multiyear, multistorm studies. Further, an understanding of patterns in and between exposure metrics that are based on specific hazards of the storm can help in designing tropical cyclone epidemiological research. a) Provide an open-source data set for tropical cyclone exposure assessment for epidemiological research; and b) investigate patterns and agreement between county-level assessments of tropical cyclone exposure based on different storm hazards. We created an open-source data set with data at the county level on exposure to four tropical cyclone hazards: peak sustained wind, rainfall, flooding, and tornadoes. The data cover all eastern U.S. counties for all land-falling or near-land Atlantic basin storms, covering 1996–2011 for all metrics and up to 1988–2018 for specific metrics. We validated measurements against other data sources and investigated patterns and agreement among binary exposure classifications based on these metrics, as well as compared them to use of distance from the storm’s track, which has been used as a proxy for exposure in some epidemiological studies. Our open-source data set was typically consistent with data from other sources, and we present and discuss areas of disagreement and other caveats. Over the study period and area, tropical cyclones typically brought different hazards to different counties. Therefore, when comparing exposure assessment between different hazard-specific metrics, agreement was usually low, as it also was when comparing exposure assessment based on a distance-based proxy measurement and any of the hazard-specific metrics. Our results provide a multihazard data set that can be leveraged for epidemiological research on tropical cyclones, as well as insights that can inform the design and analysis for tropical cyclone epidemiological research.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

First-principles investigation on Rydberg and resonance excitations: A case study of the firefly luciferin anion

The optical properties of an isolated firefly luciferin anion are investigated by using first-principles calculations, employing the many-body perturbation theory to take into account the excitonic effect. The calculated photoabsorption spectra are compared with the results obtained using the time-dependent density functional theory (TDDFT) employing the localized atomic orbital (AO) basis sets and a recent experiment in vacuum. The present method well reproduces the line shape at the photon energy corresponding to the Rydberg and resonance excitations but overestimates the peak positions by about 0.5 eV. However, the TDDFT-calculated positions of some peaks are closer to those of the experiment. We also investigate the basis set dependency in describing the free electron states above vacuum level and the excitons involving the transitions to the free electron states and conclude that AO-only basis sets are inaccurate for free electron states and the use of a plane wave basis set is required.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARiational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporate the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory that are relevant to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation theory problems and sensitivity problems and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport based sensitivity capability as evident from the thousands of percent errors observed in the 21 group hexagonal fast reactor problem (covered in Section 7).

Smith, M. A.↗
DOE OSTI2025

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗