Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Critical Benchmarks”

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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Effect of Nuclear Data Covariances on Integral Experiment Design with Sensitivity and Uncertainty Analysis

Washington River Protection Solutions (WRPS) uses MCNP6.2 and the Whisper code for criticality safety analyses of the Hanford Tank Farm. Together the codes derive baseline upper subcritical limits (USLs) for the waste models using experimental benchmarks. Whisper returns higher USLs, i.e. , has less of a conservative penalty, when the neutronic similarity of the experimental benchmarks to the application is high. Unfortunately, few critical benchmarks have high similarity to the Hanford tanks. The waste in the tanks is highly dilute in plutonium and contains large masses of weakly neutron-absorbing elements like iron and manganese. Experimental benchmarks typically have low sensitivity to these absorbers because they are present as structural materials. Lacking similar benchmarks, new Thermal Epithermal eXperiment (TEX) configurations with high Pu content and interstitial iron absorbers have been designed for the criticality safety validation. The features of the design have been iterated upon to maximize the similarity between the experiment and different Hanford waste models. The similarity is quantified with sensitivity analysis and uncertainty quantification using the representativity coefficient, or c k . The representativity calculation requires nuclear data covariances, which may differ between nuclear data libraries and between library versions. Because of these variations, the optimal design may depend on the nuclear data covariances library. A scenario can be envisioned where an experiment is designed, and c k is maximized, with one set of covariance data. However, when the covariance data is changed, say from ENDF/B-VII.1 to ENDF/B-VIII.0, and the benchmark is used in a criticality safety evaluation, the experiment becomes suboptimal with respect to c k . In this paper, we present how the optimal design of the new TEX experiments varied depending on the nuclear data covariances used to calculate c k . We compare ENDF/B-VII.1 and ENDF/B-VIII.0, as if the library had been updated since the design of the experiment. Additionally, we use JEFF3.3 to simulate if the covariance data of a different library had been used. The results show that the covariances do have an important effect on the designs, less so for thermal systems (where the data are more consistent between evaluations) and more so for epithermal systems where more differences exist.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Summary of ORSphere Critical and Reactor Physics Measurements

In the early 1970s Dr. John T. Mihalczo (team leader), J. J. Lynn, and J. R. Taylor performed experiments at the Oak Ridge Critical Experiments Facility (ORCEF) with highly enriched uranium (HEU) metal (called Oak Ridge Alloy or ORALLOY) to recreate GODIVA I results with greater accuracy than those performed at Los Alamos National Laboratory in the 1950s. The purpose of the Oak Ridge ORALLOY Sphere (ORSphere) experiments was to estimate the unreflected and unmoderated critical mass of an idealized sphere of uranium metal corrected to a density, purity, and enrichment such that it could be compared with the GODIVA I experiments. This critical configuration has been evaluated. Preliminary results were presented at ND2013. Since then, the evaluation was finalized and judged to be an acceptable benchmark experiment for the International Criticality Safety Benchmark Experiment Project (ICSBEP). Additionally, reactor physics measurements were performed to determine surface button worths, central void worth, delayed neutron fraction, prompt neutron decay constant, fission density and neutron importance. These measurements have been evaluated and found to be acceptable experiments and are discussed in full detail in the International Handbook of Evaluated Reactor Physics Benchmark Experiments. The purpose of this paper is summary summarize all the critical and reactor physics measurements evaluations and, when possible, to compare them to GODIVA experiment results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

SFDS: The criticality assembly for the experimental research of the nuclear spent fuel dissolver in CIAE - 14401

SFDS is the criticality assembly for the experimental research of the spent fuel dissolver in China Institute of Atomic Energy. The spent fuel dissolver, as the bottleneck of spent fuel reprocessing, has so many characteristics such as the dynamic changes, heterogeneous distribution, complex compositions that it is hard to analysis by theoretical method. Without enough experiments, clear bias and uncertainty of the analysis tools the handling limits for criticality safety in dissolver can't be determined. The SFDS, physical designed by MONK 9A code, uses two kinds of nuclear fuels, 3% enrichment solid UO{sub 2} rods and 5.5% enrichment UO{sub 2}(NO{sub 3}){sub 2} solution, will meet the demand of the critical experiments about the dissolvers. Seven series of critical experiments will be present on it, those are on pitches of rods, uranium concentrations of solutions, nitric acid concentrations of solutions, fission products, void fractions, temperatures and dissolve phases. More kinds of experiments could be introduced with the flexible structures of SFDS in the future. The current work on it are testing and debugging with full systems by water and it will be first critical later in 2015. It will become the first benchmark assembly for critical experiments research in the nuclear fuel cycle system in China. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Comparison Study of Upper Subcritical Limits Derived Using Sensitivity/Uncertainty Tools: Case Studies of U233-SOL-THERM-001-001, MIX-COMP-THERM-001-001, IEU-MET-FAST-002-001, LEU-COMP-THERM-001-001, LEU-SOL-THERM-004-001

Neutron transport methods used to establish subcriticality require validation by comparison to critical experiments considered to be benchmarks. Whisper is a sensitivity/uncertainty analysis tool developed to assist with the task of validation in nuclear criticality safety. Details on the Whisper methodology can be found in References 1-3 on the MCNP® reference collection website at https://mcnp.lanl.gov. Whisper-1.0 was originally developed in 2014 and used to assist with nuclear criticality safety validation at Los Alamos National Laboratory. Whisper was upgraded in 2016 to Whisper-1.1 and prepared for release with MCNP6.2 [References 3-5]. Whisper contains a library of over 1100 critical experiment benchmarks and quantifies neutronic similarity of an application to benchmarks in the library. Using highest similarity benchmarks, Whisper computes a calculational margin (CM) encompassing of the worst-case bias and bias uncertainty at a 99% confidence level for each application. In addition, portions of the margin of subcriticality (MOS) for nuclear data uncertainty and potential code errors are computed. The baseline upper subcritical limit (USL) computed by Whisper is comprised of the CM, MOS nuclear data , and MOS code errors . The Whisper baseline USL is absent a portion of the MOS due to the area of application, which is applied based upon judgment by the criticality safety analyst. An objective of this paper is to present the baseline USL, CM and portions of the MOS as computed by Whisper for comparison with similar sensitivity/uncertainty tools, such as those used by IRSN and ORNL. An initial comparison involved four critical experiment benchmarks: HEU-MET-FAST-013-001, HEU-SOLTHERM-001-008, PU-MET-FAST-022-001, AND PU-SOL-THERM-001-001, which have been documented in References 10-13. This study extends the comparison to include cases U233-SOL-THERM-001-001, MIX-COMP-THERM-001-001, IEU-MET-FAST-002-001, LEU-COMP-THERM-001-001, LEU-SOL-THERM- 004-001.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Gaussian Process Optimization of Sensitivity-Based Similarity Metrics between New Nuclear Applications and New/Existing Benchmarks [Slides]

This presentation discusses Nuclear Criticality Safety (NCS) and how designing safe, new nuclear criticality experiments requires expert judgement, which could take years of experience. Sensitivity/uncertainty (S/U) analysis can be utilized by less experienced individuals to conservatively estimate uncertainties in important parameters, such as k eff , in newly proposed nuclear experiments. The presentation poses the question of how this analysis can be performed and states that the answer lies in matching new nuclear experiments with existing benchmark experiments using similarity metrics. By increasing the criticality safety of the application in this work, higher mass limits could be used in PF-4 operations. Additionally, the presentation discusses MCNP6.2®, Whisper-1.1, the software that can be used in this analysis. Also discussed is the fact that International Criticality Safety Benchmark Evaluation Project (ICSBEP) benchmarks rarely match new nuclear applications and that there are significant differences in given set of materials and/or geometry. If there are no benchmarks that match the application, the presentation discusses the possibility of creating new benchmarks. In conclusion, this work presents a Gaussian process (GP) optimization scheme that was used to generate new benchmarks with the highest sensitivity-based similarity metrics to user-defined nuclear applications. The Gaussian process optimization successfully designed 3 new experimental benchmarks that were highly correlated to the application of interest and had k eff values near critical. Optimization over c k,i-r has shown that investigating specific isotope reactions for different applications is crucial to designing benchmark experiments. Partial contribution from Pu dominates c k similarity metric. Future work includes testing new stand-alone similarity metrics or new combinations of similarity metrics as the design criterion of this optimization – design criterion is application dependent.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Evaluation of Sandia NCS Benchmark Suite Updates

The Sandia Nuclear Criticality Safety (NCS) program’s benchmark suite was recently updated. This suite is used to ensure that NCS calculations using computer-based neutron transportation codes have an established baseline comparison of calculated versus known experimental results. The Evaluated Nuclear Data File (ENDF) version used for the MCNP models in the suite was changed from ENDF/B-VII.1 to ENDF/B-VIII.0. Additionally, relevant thermal scattering law data libraries (TSLs) were updated. The sensitivity of the calculational bias of each benchmark model to these changes is discussed. Implementation of the ENDF/B-VIII.0 library and updated TSLs results in improvements to bias distribution in the intermediate enriched uranium, plutonium, and mixed uranium–plutonium (IEU, PU, and MIX) fissionable material benchmark categories, but a small bias increase in low- and high-enriched uranium categories (LEU and HEU, respectively). The results also highlight the sensitivity of the benchmarks, with average lethargy of neutrons causing fission energies (EALF) in the intermediate energy range to ENDF/B library changes. The most numerous bias changes were observed in the thermal energy region when transitioning from ENDF/B-VII.1 to ENDF/B-VIII.0. In conclusion, most of the unique bias changes observed in MCNP 6.3.0 between the two nuclear data libraries were in the LEU-COMP-THERM evaluation subset.

ICSBEP↗
DOE OSTI2020

National Criticality Experiments Research Center (NCERC) - capabilities and recent measurements

The National Criticality Experiments Research Center (NCERC) located at the Device Assembly Facility (DAF) at the Nevada National Security Site (NNSS) and operated by Los Alamos National Laboratory (LANL) is home to four critical assemblies which are used to support of range of missions, including nuclear criticality safety and nuclear nonproliferation. Additionally, subcritical systems can also be assembled at NCERC. NCERC is providing critical and subcritical experiments valuable to the nuclear data community and experiments performed at NCERC are often published as benchmarks in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. This manuscript will give a broad overview of recent experiments performed at NCERC, upcoming experiments, and why integral measurements are important and useful to the nuclear data community. The four critical assemblies are GODIVA IV, FLATTOP, COMET, and PLANET. GODIVA IV is a cylindrical metal fast burst reactor, the fourth in the GODIVA series that dates back to the 1950’s. FLATTOP is an highly enriched uranium (HEU) or Pu core reflected by natural uranium. COMET and PLANET are vertical lift assemblies, where one half of the reactor can be lifted to the upper half of the reactor to create a critical system. Some recent experiments include various critical intermediate energy assemblies with lead, and subcritical measurements of plutonium reflected by copper, tungsten, and nickel. Work is also underway to make a better measurement of the critical mass of neptunium, using a neptunium sphere surrounded by nickel shells. Additionally, measurements will be performed next year with HEU shells from Rocky Flats. These HEU shells will be stacked together to make larger systems, allowing for a large range of criticality (from subcritical to delayed critical). Other upcoming measurements include an HEU critical assembly sensitive to intermediate energy neutrons.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2023

Verification and Validation of the New MCNP6.3 Criticality Features

The MCNP6® code, version 6.3, has been extensively verified and validated for many applications. The use of the same default capabilities existing in the MCNP6.2 code are also used in the verification and validation (V&V) of the MCNP6.3 code. In this paper, selected new features, code enhancements, and bug fixes in the MCNP6.3 code that impact criticality safety applications are described and investigated. More specifically, the changes within the MCNP6.3 code that are studied in this work include both the new fission matrix and the Doppler broadening resonance correction (DBRC) features. For nuclear criticality safety applications, the V&V benchmark problems within the criticality, extended criticality, and Rossi-α suites are used to study the upgrades within the MCNP6.3 code. Some additional investigations into benchmarks at elevated temperatures are used to showcase the impacts of the temperature-specific capabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Quantification of Uncertainties and Correlations in Criticality Experiments With SCALE

Uncertainties in benchmark keff values due to uncertainties in individual components, such as geometry and material compositions, are rigorously quantified and documented in evaluations provided in the International Handbook of Evaluated Criticality Safety Benchmark Experiments (IHECSBE). Correlations between the uncertainties may affect not only the overall uncertainty for a series of benchmarks but also the magnitude of computational biases and bias uncertainties quantified by validation methods. The impact of the correlations in experimental uncertainties is especially important in the use of advanced validation methods such as Generalized Linear Least Squares (GLLS), as implemented in the SCALE TSURFER code. In a recent study, it was demonstrated that biases computed with GLLS procedures vary by as much as 75%, depending on the selection of the experimental uncertainty correlation value. of the >4000 benchmarks documented in the IHECSBE; experimental correlation data are only available in the DICE database tool for ~60 benchmarks. Additional data are available in DICE to identify the potential for correlations between evaluations, but the values of correlations are not quantified. The new Sampler module of SCALE provides stochastic capabilities to quantify uncertainties and correlations in keff or any other measured value for one or more benchmark experiments due to uncertainties in individual sources of uncertainty, such as geometry and material composition. The values for individual parameters in the input model are randomly modified within the reported uncertainty, and a distribution function and a series of perturbed keff values are obtained. Where sufficient samples are made, the distribution of the perturbed keff values is used to determine the uncertainty in the keff due to uncertainties in the input parameters. In cases where the same uncertainty parameters influence multiple experiments, such as where the same fissile solution or fuel rods are used for many critical measurements, the simultaneous perturbation of an uncertain parameter for multiple cases provides the correlation in keff uncertainties between the different configurations. The parametric uncertainty capabilities of Sampler for a single system are demonstrated for a benchmark exercise from the Organization for Economic Cooperation and Development (OECD) Nuclear Energy Agency (NEA) Working Party on Nuclear Criticality Safety (WPNCS) Expert Group on Uncertainty Analysis for Criticality Safety Assessment (UACSA) Phase II benchmark. Sampler is further applied to quantify correlations among benchmarks from a series of highly enriched uranium (HEU) solution (SOL) thermal spectrum (THERM) systems, through the analysis of the 10 cases from HEU-SOL-THERM-001 from the IHECSBE.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Verification of MCNP6.1, MCNP6.1.1, and MCNP6.2-pre for Criticality Safety Applications

Several suites of verification/validation benchmark problems were run in early 2016 to verify that MCNP6.1, MCNP6.1.1, and MCNP6.2-pre are performing correctly for nuclear criticality safety (NCS) applications. MCNP6.1 is the production version of MCNP{sup R} released in 2013; MCNP6.1.1 is the update released in 2014; MCNP6.2-pre is the pre-release development version of MCNP6.2, which is targeted for release in the near future. All versions of MCNP6 include all of the standard features for NCS calculations that have been available for the past 15 years, along with new features for sensitivity-uncertainty based methods for NCS validation. Results from the benchmark suites were compared with results from previous verification testing. Several standard criticality benchmark suites were used for the verification calculations: - VERIFICATION-KEFF - A suite of criticality problems for which exact analytical results are available, - VALIDATION-CRITICALITY - 31 ICSBEP problems, using ENDF/B-VII.1, - VALIDATION-CRIT-EXPANDED - 119 ICSBEP problems, using ENDF/B-VII.1. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Gaussian Process Optimization of Sensitivity-Based Similarity Metrics between New Nuclear Applications and New/Existing Benchmarks

Confidently designing safe, new nuclear criticality experiments requires expert judgement, which could take years of experience. Sensitivity/uncertainty (S/U) analysis can be utilized by less experienced individuals to conservatively estimate uncertainties in important parameters, such as k eff , in newly proposed nuclear applications. This type of analysis relies on matching new nuclear applications with existing benchmark experiments. The Whisper-1.1 software package included in MCNP6.2 ®1 contains more than 1,100 International Criticality Safety Benchmark Evaluation Project (ICSBEP) benchmarks. These benchmarks however rarely match new nuclear applications. The number of benchmarks available to match a given set of materials or geometric configurations varies significantly. Furthermore, recently performed benchmark experiments may not have had enough time to be properly documented and published. Benchmarks are vital for determining the accuracy of nuclear data and can assist nuclear physics and evaluators in improving nuclear data libraries. Exhaustively exploring the parameter space using simulations with software such as MCNP is too computationally expensive. In this work, Gaussian process optimization was implemented to reduce the number of simulations needed for optimization over multiple parameters. This optimization scheme was designed to selectively generate new benchmarks with high sensitivity-based similarity metrics to user-defined nuclear applications. Two benchmark models of spherically nested shells containing plutonium, uranium, tantalum, and water were used in the optimization to match an application containing plutonium plates, stacked in a tantalum reflector, surrounded by water.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Updates to the n+ 63,65 Cu RRR+URR Evaluations [Slides]

This work updates neutron reactions on 63,65 Cu. It also discusses the motivations of the research which is to correct deficiencies in benchmark performance since critical assembly configurations use Cu as a reflector. This presentation discusses the incorporation of URR parameters fit to 2017 63 Cu(n, γ) measurement by Weigand et al., as well as preliminary work on angular distributions and states that validation against copper-sensitive ICSBEP benchmarks is ongoing. The presentation concludes by stating that R -matrix analysis coupled to consistent average parameters used in the URR have been performed for 63,65 Cu isotopes, that future work will focus on the angular distributions, and that an analysis of additional data measured on natural Cu sample is in progress.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2020

Sulfur Pellets Responses to a Bare and Steel Reflected Pulse of the Oak Ridge National Laboratory Health Physics Research Reactor

The experiments analyzed in this report were conducted at the Health Physics Research Reactor (HPRR), also known as the $\textit{Fast Burst Reactor}$. The reactor was designed and built at Oak Ridge National Laboratory (ORNL) in 1961. The HPRR was an unmoderated, unshielded fast reactor that used highly enriched uranium and molybdenum alloy as fuel. The reactor was initially sent to the Nevada Test Site in 1962, where it was used to evaluate radiation doses received as a result of the Hiroshima and Nagasaki bombings during World War II. A few years later, the reactor was sent back to ORNL to be part of the Dosimetry Application Research (DOSAR) facility shown in Figure 1, which included a reactor building shown on the left (west) of the picture and a control and laboratory building in the upper right corner (northeast). The critical assembly was used for numerous technical studies, including systems calibration, dosimetry, radiobiology of plants and animals, testing of radiation alarms, as well as teaching and training in radiation dosimetry and nuclear engineering. Between 1963 and 1987, the HPRR was operated for thousands of hours, achieving criticality close to 10,000 times and motivating many publications. The HPRR was decommissioned in 1987. The goal of this effort was to use historical data from operation of the HPRR to create a criticality accident alarm system (CAAS) benchmark to be included in the $\textit{International Handbook of Evaluated Criticality Safety Benchmark Experiments}$ (ICSBEP Handbook). A thorough inspection was performed of all available documentation and information available. The most promising experiments that were selected for evaluation were those described in the 1987 ORNL report entitled $\textit{Health Physics Research Reactor Reference Dosimetry}$, ORNL-6240. The report includes reference dosimetry results of the shielded and unshielded configurations of the HPRR after burst operations. Because of changes to the reactor positioning and storage systems that were made in 1985, the previous dosimetry reports became obsolete, and the newly designed experiments were needed to create the HPRR’s adjusted dosimetry data. The various results reported in ORNL-6240 include reference doses and dose equivalents from different conventions at different distances and elevations as determined using the detected neutron fluence and conversion factors. The HPRR neutron fluence was obtained through different methods, including sulfur pellet analysis and threshold detector unit data. Information about the HPRR spectrum was also obtained through Bonner sphere measurements. This benchmark is focused on a part of the measured sulfur fluences reported in Appendix H of ORNL-6240. Standard commercial sulfur pellets were placed at different distances from the HPRR centerline during burst operation and were activated due to the 32 S(n,p) 32 P reaction. The resulting 32 P activity was then measured and the information about the corresponding sulfur fluence and/or neutron dose could be extracted. Many of those measurements have 7 been performed with the HPRR in its bare configuration or with different shields (combinations of Lucite, concrete, steel). All the necessary, precise information about material and/or dimensions of the different shields was not found, so it was decided to focus only on the unshielded and steel-shielded configurations to minimize the benchmark uncertainty. A total of 31 cases (24 unshielded and 7 shielded cases at different positions) of sulfur fluence were selected before evaluation to develop the benchmark.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2026

Multi‐Model Ensembles in Ecosystem Modeling: Challenges and Best Practices for Decision‐Making

Ecosystem models are increasingly central to the decision-making for environmental policy, conservation planning, and climate-related investments. Yet, the growing reliance on Multi-Model Ensembles (MMEs) of ecosystem models by practitioners and policymakers, sometimes under tight timelines and imperfect information, has frequently outpaced the scientific rigor required to ensure ensemble reliability. Here, MMEs refer to approaches that combine targeted predictions from multiple models with the expectation of improving robustness and quantifying predictive uncertainty. Poorly designed MMEs may create a false sense of confidence and lead to suboptimal policy and market decisions. This perspective argues that robust decision-making-relevant MMEs must be grounded on two pillars: (1) rigorous Model Intercomparison Projects (MIPs), which identify inter-model agreement and disagreement, characterize model uncertainties, and evaluate robustness with observationally based benchmarks—MIPs' diagnostic evaluation is so critical that it must be needed to drive MME's decision in model selection and weighting, especially when only a limited number of models available; and (2) co-design by both stakeholders and scientists to ensure that scenarios, metrics and uncertainty requirements provide decision-relevant information. Building upon the past success and lessons from the existing MIPs-MMEs efforts (e.g., climate/Earth system/crop), we derived the theoretical basis for MMEs, addressed their specific challenges in ecosystem modeling, and highlighted proper consideration of model numbers and diversity, risk of model inter-dependence, effective calibration of model parameters, possible overdue of some ecosystem model development, critical roles of open benchmark data across a wide range of conditions, and suggested use of Artificial Intelligence to support MIPs-MMEs. We highlighted the under-recognized opportunity for MIPs and MMEs to drive scientific progress and innovation through identifying better performing models, systematic benchmarking, feedback loops, and targeted model improvement. By following actionable best practice guidelines, MMEs can evolve from ad hoc aggregation of models into a trusted backbone of environmental policy and decision-making.

ecosystem modeling↗
NASA NTRS2010

Assessment of Static Delamination Propagation Capabilities in Commercial Finite Element Codes Using Benchmark Analysis

With capabilities for simulating delamination growth in composite materials becoming available, the need for benchmarking and assessing these capabilities is critical. In this study, benchmark analyses were performed to assess the delamination propagation simulation capabilities of the VCCT implementations in Marc TM and MD NastranTM. Benchmark delamination growth results for Double Cantilever Beam, Single Leg Bending and End Notched Flexure specimens were generated using a numerical approach. This numerical approach was developed previously, and involves comparing results from a series of analyses at different delamination lengths to a single analysis with automatic crack propagation. Specimens were analyzed with three-dimensional and two-dimensional models, and compared with previous analyses using Abaqus . The results demonstrated that the VCCT implementation in Marc TM and MD Nastran(TradeMark) was capable of accurately replicating the benchmark delamination growth results and that the use of the numerical benchmarks offers advantages over benchmarking using experimental and analytical results.

Orifici, Adrian C.↗