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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.

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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

SURVEY OF COUPLING SCHEMES IN TRADITIONAL COUPLED NEUTRONICS AND THERMAL-HYDRAULICS CODES

The design and the analysis of nuclear power plants (NPPs) require computational codes to predict the behavior of the NPP nuclear components and other systems (i.e., reactor core, primary coolant system, emergency core cooling system, etc.). Coupled calculations are essential to the conduct of deterministic safety assessments. Inasmuch as the physical phenomena that govern the performance of a nuclear reactor are always present simultaneously, ideally computational modeling of a nuclear reactor should include coupled codes that represent all of the active physical phenomena. Such multi-physics codes are under development at several institutions and are expected to become operational in the future. However, in the interim, integrated codes that incorporate modeling capabilities for two to three physical phenomena will remain useful. For example, in the conduct of safety analyses, of paramount importance are codes that couple neutronics and thermal-hydraulics, especially transient codes. Other code systems of importance to safety analyses are those that couple primary system thermal-hydraulics to fission product chemistry, neutronics to fuel performance, containment behavior and structural mechanics to thermal-hydraulics, etc. This paper surveys the methods used traditionally in the coupling of neutronic and thermal-hydraulics codes. The neutron kinetics codes are used for computing the space-time evolution of the neutron flux and, hence, of the power distribution. The thermal-hydraulics codes, which compute mass, momentum and energy transfers, model the coolant flow and the temperature distribution. These codes can be used to compute the neutronic behavior and the thermal-hydraulic states separately. However, the need to account with fidelity for the dynamic feedback between the two sets of properties (via temperature and density effects on the cross section inputs into the neutronics codes) and the requirement to model realistically the transient response of nuclear power plants and to assess the associated emergency systems and procedures imply the necessity of modeling the neutronic and thermal-hydraulics simultaneously within a coupled code system. The focus of this paper is a comparison of the methods by which the coupling between neutron kinetics and thermal-hydraulics treatments has been traditionally achieved in various code systems. As discussed in the last section, the modern approaches to multi-physics code development are beyond the scope of this paper.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Aerodynamic Data Fusion Toward the Digital Twin Paradigm

This paper considers the fusion of two aerodynamic data sets originating from differing types of physical or computer experiments. This paper specifically addresses the fusion of 1) noisy and in-complete fields from wind-tunnel measurements and 2) deterministic but biased fields from numerical simulations. These two data sources are fused in order to estimate the true field that best matches measured quantities that serve as the ground truth. For example, two sources of pressure fields about an aircraft are fused based on measured forces and moments from a wind-tunnel experiment. A fundamental challenge in this problem is that the true field is unknown and cannot be estimated with 100% certainty. A Bayesian framework is employed to infer the true fields conditioned on measured quantities of interest; essentially a statistical correction to the data is performed. The fused data may then be used to construct more accurate surrogate models suitable for early stages of aerospace design. An extension of the proper orthogonal decomposition with constraints is also introduced to solve the same problem. In this work, both methods are demonstrated on fusing the pressure distributions for flow past the RAE2822 airfoil and the Common Research Model wing at transonic conditions. Comparison of both methods reveals that the Bayesian method is more robust when data are scarce and capable of also accounting for uncertainties in the data. Furthermore, given adequate data, the proper-orthogonal-decomposition-based and Bayesian approaches lead to surprisingly similar results.

42 ENGINEERING↗
DOE OSTI2017

SuPer-Homogenization (SPH) Corrected Cross Section Generation for High Temperature Reactor

The deterministic full core simulators require homogenized group constants covering the operating and transient conditions over the entire lifetime. Traditionally, the homogenized group constants are generated using lattice physics code over an assembly or block in the case of prismatic high temperature reactors (HTR). For the case of strong absorbers that causes strong local depressions on the flux profile require special techniques during homogenization over a large volume. Fuel blocks with burnable poisons or control rod blocks are example of such cases. Over past several decades, there have been a tremendous number of studies performed for improving the accuracy of full-core calculations through the homogenization procedure. However, those studies were mostly performed for light water reactor (LWR) analyses, thus, may not be directly applicable to advanced thermal reactors such as HTRs. This report presents the application of SuPer-Homogenization correction method to a hypothetical HTR core.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

Asymptotic diffusion limit of cell temperature discretisation schemes for thermal radiation transport

This paper attempts to unify the asymptotic diffusion limit analysis of thermal radiation transport schemes, for a linear-discontinuous representation of the material temperature reconstructed from cell centred temperature unknowns, in a process known as ‘source tilting’. The asymptotic limits of both Monte Carlo (continuous in space) and deterministic approaches (based on linear-discontinuous finite elements) for solving the transport equation are investigated in slab geometry. The resulting discrete diffusion equations are found to have nonphysical terms that are proportional to any cell-edge discontinuity in the temperature representation. Based on this analysis it is possible to design accurate schemes for representing the material temperature, for coupling thermal radiation transport codes to a cell centred representation of internal energy favoured by ALE (arbitrary Lagrange–Eulerian) hydrodynamics schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference↗
DOE OSTI2019

Chance Constraints for Improving the Security of AC Optimal Power Flow

This paper introduces a scalable method for improving the solutions of ac optimal power flow (AC OPF) with respect to deviations in predicted power injections from wind and other uncertain generation resources. The aim of this paper is on providing solutions that are more robust to short-term deviations, and that optimize both the initial operating point and a parametrized response policy for control during fluctuations. We formulate this as a chance-constrained optimization problem. To obtain a tractable representation of the chance constraints, we introduce a number of modeling assumptions and leverage recent theoretical results to reformulate the problem as a convex, second-order cone program, which is efficiently solvable even for large instances. Our experiments demonstrate that the proposed procedure improves the feasibility and cost performance of the OPF solution, while the additional computation time is on the same magnitude as a single deterministic AC OPF calculation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

First-of-a-Kind Risk-Informed Digital Twin for Operational Decision Making

A digital twin (DT) is a digital model or a collection of models of a physical entity. DTs in the nuclear arena can be used from plant design through decommissioning. Decisions are typically a priori or made offline. Risk-informed decision making is identifying what can go wrong, its frequency, and the consequences of its failure. Ideally risk-informed decision making reflects the current state of the plant and provides a decision in real time. Traditionally, probabilistic risk assessments (PRAs) evaluate the failures of safety systems, the risk of core damage, and the offsite dose as the consequence. However, this DT evaluates the decisions on the control side rather than the protection side. It uses the same risk methods to probabilistically inform the decision-making process but in a different way. Rather than evaluating the risk of core damage, this DT evaluates the likelihood of avoiding a trip set point while maintaining plant safety. Performance-based assessments are identified via its probabilistic evaluation of operational alternatives based on system status. Because the purpose of the control system is to maintain system variables within prescribed operating ranges, upsets or challenges that can exceed a trip set point resulting in a plant transient and a challenge to plant mitigating systems based on actual plant conditions, are evaluated to safely maintain the plant within the operating ranges. The probabilistic portion of the model is autonomously and automatically adjusted, and the metric of interest (i.e. likelihood of avoiding a trip set point) is recalculated. The digital representation of the physical system (i.e. the DT) performs a deterministic performance–based assessment of the probabilistically identified alternatives identified to validate the probabilistic assessment. A decision-making algorithm selects the appropriate option based on the probabilistic and deterministic assessments and transmits a control signal to a component(s) to initiate a corrective action or informs an operator of its decision.

digital twin↗
DOE OSTI2025

Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, which are evaluated via kernel density estimation of the associated conditional cumulative distributions. Furthermore, we extend the construction to random field data via the Karhunen–Loève expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model and a synthetic example controlled by a parameter that enables a switch from unimodal to bimodal response distributions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Coupling the System Analysis Module with SAS4A/SASSYS-1

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

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2015

Constant-complexity stochastic simulation algorithm with optimal binning

At the molecular level, biochemical processes are governed by random interactions between reactant molecules, and the dynamics of such systems are inherently stochastic. When the copy numbers of reactants are large, a deterministic description is adequate, but when they are small, such systems are often modeled as continuous-time Markov jump processes that can be described by the chemical master equation. Gillespie’s Stochastic Simulation Algorithm (SSA) generates exact trajectories of these systems, but the amount of computational work required for each step of the original SSA is proportional to the number of reaction channels, leading to computational complexity that scales linearly with the problem size. The original SSA is therefore inefficient for large problems, which has prompted the development of several alternative formulations with improved scaling properties. We describe an exact SSA that uses a table data structure with event time binning to achieve constant computational complexity with respect to the number of reaction channels for weakly coupled reaction networks. We present a novel adaptive binning strategy and discuss optimal algorithm parameters. We compare the computational efficiency of the algorithm to existing methods and demonstrate excellent scaling for large problems. This method is well suited for generating exact trajectories of large weakly coupled models, including those that can be described by the reaction-diffusion master equation that arises from spatially discretized reaction-diffusion processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem

A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a general solution to the measurement problem, inasmuch it allows to derive the Born rule as an average over hidden-variables, describing not the state of the quantum entity, but its interaction with the measuring system. According to this modelization, a quantum measurement is to be understood, in general, as a tripartite process, formed by an initial deterministic decoherence-like process, a subsequent indeterministic collapse-like process, and a final deterministic purification-like process. We also show that quantum probabilities can be generally interpreted as the probabilities of a first-order non-classical theory, describing situations of maximal lack of knowledge regarding the process of actualization of potential interactions, during a measurement. - Highlights: • An extended Bloch representation of quantum measurements is given. • Quantum measurements are explained in terms of hidden-measurement interactions. • Quantum measurements are explained as tripartite processes. • The Born rule results from a universal average, over all possible measurement processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Thermal Neutron Scattering Law (TNSL) Implementation and Testing in FUDGE

Thermal neutron scattering law processing capabilities have been recently implemented in the LLNL code FUDGE (For Updating Data and Generating Evaluations). FUDGE is now capable of producing processed TNSL data for use in Monte Carlo or deterministic transport. To test this new capability, LLNL scientists performed an extensive intercomparison between the Mercury, Ardra, COG and MCNP transport codes. This intercomparison helped probe differences between how TNSL data are handled by the transport codes and by two different processing codes (LLNL’s FUDGE and LANL’s NJOY). This report summarizes recent improvements in FUDGE TNSL capabilities as well as results from the code intercomparison.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

A stochastic flow-capturing model to optimize the location of fast-charging stations with uncertain electric vehicle flows

Here, we develop a model to optimize the location of public fast charging stations for electric vehicles (EVs). A difficulty in planning the placement of charging stations is uncertainty in where EV charging demands appear. For this reason, we use a stochastic flow-capturing location model (SFCLM). A sample-average approximation method and an averaged two-replication procedure are used to solve the problem and estimate the solution quality. We demonstrate the use of the SFCLM using a Central-Ohio based case study. We find that most of the stations built are concentrated around the urban core of the region. As the number of stations built increases, some appear on the outskirts of the region to provide an extended charging network. We find that the sets of optimal charging station locations as a function of the number of stations built are approximately nested. We demonstrate the benefits of the charging-station network in terms of how many EVs are able to complete their daily trips by charging midday—six public charging stations allow at least 60% of EVs that would otherwise not be able to complete their daily tours without the stations to do so. We finally compare the SFCLM to a deterministic model, in which EV flows are set equal to their expected values. We show that if a limited number of charging stations are to be built, the SFCLM outperforms the deterministic model. As the number of stations to be built increases, the SFCLM and deterministic model select very similar station locations.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2018

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

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

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

The packing problem of uncertain multicasts

Summary Multicast performs better than unicast in delivering the same content from a fixed single source to a set of destinations. Many efforts have been made to optimize such kind of deterministic multicast, such as minimizing the transmission cost of each multicast session. In practice, it is not necessary that the source of each multicast session has to be in a specific location, as long as certain constraints are satisfied. Accordingly, applications usually meet a novel multicast with uncertain sources, ie, uncertain multicast. That is, multiple nodes have the responsibility to act as the root node of a multicast session. Prior proposals have addressed an uncertain multicast by constructing the minimum cost forest. However, it is still unknown how to efficiently share the network resources, when a set of uncertain multicast occupies the network simultaneously. To tackle such a challenging issue, we present the packing problem of uncertain multicasts (MPU) to minimize the total transmission cost, under the constraint of link capacity. We prove that the MPU problem is NP‐hard. An intrinsic solution is constructing the minimum cost forest for each uncertain multicast individually. This method, however, is inefficient and may be infeasible because of the constraint of link capacity. Thus, we design 2 dedicated greedy methods, named priority‐based and adjusting congested link, to approximate the optimal solution. The comprehensive results indicate that both of our 2 methods can find a feasible solution for the MPU problem. Moreover, given a set of uncertain multicasts, the adjusting congested link method can generate a desired transmission structure for each uncertain multicast and achieve the least total cost when packing them.

Ren, Bangbang↗
DOE OSTI2019

A comprehensive modeling procedure for estimating statistical properties of forced ignition

In this work, a comprehensive modeling procedure for estimating the probability of ignition with application to high altitude relights of aircraft combustors is developed. In these configurations, an ignitor is used to introduce high-enthalpy discharge into a fuel-laden but stratified flow. Because of the inherent variabilities inflow conditions, kernel discharge process, and the chaotic turbulent flow, ignition cannot be described deterministically, but only as a probabilistic measure. The proposed modeling framework consists of three components. The turbulent flow is represented using the large eddy simulation (LES) framework. The ignition process is modeled using a manifold approach, where the initial kernel evolution is represented using a homogeneous reactor while the latter part of the evolution is represented as a competition between diffusion and chemical reactions using a flamelet-type mapping. A combined lookup table that can track the evolution of the kernel through these two distinct reaction stages is developed. The table lookup variables are solved within the LES framework. The resulting simulation tool is then embedded within an uncertainty quantification approach, where variations in the turbulent flow, as well as operating and kernel properties, are simulated using a Monte-Carlo-based sampling approach. Techniques to reduce computational cost are used to obtain a robust, numerically accurate, and physically representative model for engine relight. The method is validated using experimental data for ignition of methane/air mixtures. Due to the comprehensive nature of the modeling procedure, it is found that the simulation tool reproduces experimentally observed ignition probabilities over a wide range of operating conditions.

42 ENGINEERING↗
DOE OSTI2026

Quantum Time-Space Tradeoffs for Matrix Problems

We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra problems—including matrix-vector product, matrix inversion, matrix multiplication and powering—existing classical time-space tradeoffs, several of which are tight for every space bound, also apply to quantum algorithms with at most a constant factor loss. For example, for almost all fixed matrices 𝐴, including the discrete Fourier transform matrix, we prove that quantum circuits with at most 𝑇 input queries and 𝑆 qubits of memory require 𝑇 = Ω⁢(𝑛 2 /𝑆) to compute matrix-vector product 𝐴⁢𝑥 for 𝑥 ∈{0,1 𝑛 . We similarly prove that matrix multiplication for 𝑛 ×𝑛 binary matrices requires 𝑇 = Ω⁢(𝑛 3 /$\sqrt{𝑆}$). Because many of our lower bounds are matched by deterministic algorithms with the same time and space complexity, our results show that quantum computers cannot provide any asymptotic advantage for these problems with any space bound. We obtain matching lower bounds for the stronger notion of quantum cumulative memory complexity—the sum of the space per layer of a circuit. We also consider Boolean (i.e., AND-OR) matrix multiplication and matrix-vector products, improving the previous quantum time-space tradeoff lower bounds for 𝑛 × 𝑛 Boolean matrix multiplication to 𝑇 = Ω⁢(𝑛 2.5 /𝑆 1/4 ) from 𝑇 = Ω⁢(𝑛 2.5 /𝑆 1/2 ). Our improved lower bound for Boolean matrix multiplication is based on a new coloring argument that extracts more from the strong direct product theorem that was the basis for prior work. To obtain our tight lower bounds for linear algebra problems, we require much stronger bounds than strong direct product theorems. We obtain these bounds by adding a new bucketing method to the quantum recording-query technique of Zhandry that lets us apply classical arguments to upper bound the success probability of quantum circuits.

lower bounds↗
DOE OSTI2015

MT71x: Multi-Temperature Library Based on ENDF/B-VII.1

The Nuclear Data Team has released a multitemperature transport library, MT71x, based upon ENDF/B-VII.1 with a few modifications as well as additional evaluations for a total of 427 isotope tables. The library was processed using NJOY2012.39 into 23 temperatures. MT71x consists of two sub-libraries; MT71xMG for multigroup energy representation data and MT71xCE for continuous energy representation data. These sub-libraries are suitable for deterministic transport and Monte Carlo transport applications, respectively. The SZAs used are the same for the two sub-libraries; that is, the same SZA can be used for both libraries. This makes comparisons between the two libraries and between deterministic and Monte Carlo codes straightforward. Both the multigroup energy and continuous energy libraries were verified and validated with our checking codes checkmg and checkace (multigroup and continuous energy, respectively) Then an expanded suite of tests was used for additional verification and, finally, verified using an extensive suite of critical benchmark models. We feel that this library is suitable for all calculations and is particularly useful for calculations sensitive to temperature effects.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗