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Marginalizing Instrument Systematics in HST WFC3 Transit Light Curves

Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) infrared observations at 1.1-1.7 microns probe primarily the H2O absorption band at 1.4 microns, and have provided low-resolution transmission spectra for a wide range of exoplanets. We present the application of marginalization based on Gibson to analyze exoplanet transit light curves obtained from HST WFC3 to better determine important transit parameters such as "ramp" probability (R (sub p)) divided by "ramp" total (R (sub asterisk)), which are important for accurate detections of H2O. We approximate the evidence, often referred to as the marginal likelihood, for a grid of systematic models using the Akaike Information Criterion. We then calculate the evidence-based weight assigned to each systematic model and use the information from all tested models to calculate the final marginalized transit parameters for both the band-integrated and spectroscopic light curves to construct the transmission spectrum. We find that a majority of the highest weight models contain a correction for a linear trend in time as well as corrections related to HST orbital phase. We additionally test the dependence on the shift in spectral wavelength position over the course of the observations and find that spectroscopic wavelength shifts delta (sub lambda) times lambda) best describe the associated systematic in the spectroscopic light curves for most targets while fast scan rate observations of bright targets require an additional level of processing to produce a robust transmission spectrum. The use of marginalization allows for transparent interpretation and understanding of the instrument and the impact of each systematic evaluated statistically for each data set, expanding the ability to make true and comprehensive comparisons between exoplanet atmospheres.

Wakeford, H. R.↗

AC Power Flow Based DLMP Calculation and Decomposition Method to Smooth Power Fluctuation of Distributed Renewable Energy Sources

As the penetration of renewable energy sources increases, the growing renewable power variability brings ramping issues to power systems. Meanwhile, the development of distributed energy resources (DERs) makes the distribution systems to provide both energy and ancillary services. To incentivise individual resources and customers to alleviate ramping issues on the demand side, a two-stage distribution locational marginal price (DLMP) calculation and decomposition method is developed to formulate the marginal power ramping price for DERs. In the first stage of the proposed method, a distribution system operator market scheduling model based on AC optimal power flow is designed to estimate the optimal operating point of the distribution system. Subsequently, the voltage and power flow constraints are linearised in stage two to calculate DLMP. Finally, based on the Lagrange function and sensitivity factors, DLMP is decomposed to the marginal costs for active/reactive power, voltage management, power loss and power variability. Case studies demonstrate that the proposed model can effectively smooth the power fluctuation and reduce the ramping flexibility requirements of distribution systems.

AC optimal power flow↗

MSR Fuel Salt Qualification Methodology

This report documents the continuing activities at Oak Ridge National Laboratory (ORNL) in support of the US Nuclear Regulatory Commission (NRC) efforts to develop an efficient, appropriate process for liquid fuel salt system qualification. Fuel qualification for salt-cooled molten salt reactors (MSRs) is part of the ongoing coated particle fuel qualification effort. Fuel qualification is a process which provides high confidence that physical and chemical behavior of fuel is sufficiently understood so that it can be adequately modeled for both normal and accident conditions, reflecting the role of the fuel design in the overall safety of the facility. Uncertainties are defined so that calculated fission product releases include the appropriate margins to ensure conservative calculation of radiological dose consequences. The initial phase of ORNL’s activities is documented in ORNL/LTR-2018/1045 Molten Salt Reactor Fuel Qualification Considerations and Challenges.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Fuel Salt Qualification and Associated Fuel Cycle Opportunities & Issues

NRC staff have defined fuel qualification as a process which provides high confidence that the physical and chemical behavior of fuel is sufficiently understood so that it can be adequately modeled for both normal and accident conditions, reflecting the role of the fuel design in the overall safety of the facility. Uncertainties are defined so that calculated fission product releases include the appropriate margins to ensure conservative calculation of radiological dose consequences. The Advisory Committee on Reactor Safeguards (ACRS) has accepted the methodology described in NUREG/CR-7299 as an acceptable method for fuel qualification for molten salt reactors. The fuel salt qualification process described in NUREG/CR-7299 is based upon understanding the role that the fuel salt plays in achieving the fundamental safety functions, which in-turn is based on the fuel salt thermophysical and thermochemical properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Thrust stand evaluation of engine performance improvement algorithms in an F-15 airplane

Results are presented from the evaluation of the performance seeking control (PSC) optimization algorithm developed by Smith et al. (1990) for F-15 aircraft, which optimizes the quasi-steady-state performance of an F100 derivative turbofan engine for several modes of operation. The PSC algorithm uses onboard software engine model that calculates thrust, stall margin, and other unmeasured variables for use in the optimization. Comparisons are presented between the load cell measurements, PSC onboard model thrust calculations, and posttest state variable model computations. Actual performance improvements using the PSC algorithm are presented for its various modes. The results of using PSC algorithm are compared with similar test case results using the HIDEC algorithm.

Conners, Timothy R.↗

Cellular and dendritic growth in a binary melt - A marginal stability approach

A simple model for the constrained growth of an array of cells or dendrites in a binary alloy in the presence of an imposed positive temperature gradient in the liquid is proposed, with the dendritic or cell tip radius calculated using the marginal stability criterion of Langer and Muller-Krumbhaar (1977). This approach, an approach adopting the ad hoc assumption of minimum undercooling at the cell or dendrite tip, and an approach based on the stability criterion of Trivedi (1980) all predict tip radii to within 30 percent of each other, and yield a simple relationship between the tip radius and the growth conditions. Good agreement is found between predictions and data obtained in a succinonitrile-acetone system, and under the present experimental conditions, the dendritic tip stability parameter value is found to be twice that obtained previously, possibly due to a transition in morphology from a cellular structure with just a few side branches, to a more fully developed dendritic structure.

Laxmanan, V.↗

Probabalistic Risk Analysis and Thermal Margin Process for an Inflatable Aeroshell

Uncertainties always exist in atmospheric entry aeroheating environments and the thermal response of thermal protection system (TPS) material. These uncertainties are mitigated in the design by ap-plying margin and factors of safety to the TPS. Entry vehicle TPS is often conservatively over-sized for the heat loads that are experienced along the entry trajectory by stacking worst-case scenarios together. Additionally, the current TPS design and margin process used by NASA offers very little insight into the risk of over-temperature during flight and the reliability of the heat shield performance [1,3]. A probabilistic margin process can be used to calculate the amount of TPS margin necessary to survive a given entry heat load at a specified level of risk [2,3,4]. The vehicle’s initial entry state (entry velocity, flight path angle, and entry mass) determines the expected atmospheric entry environmental conditions and resulting heat load that the entry vehicle will experience. If there is flexibility in the entry state, then this process can be used to select an appropriate combination of entry state parameters and TPS size to target a desired reentry reliability. This probabilistic margin process allows engineers to make informed aeroshell design, entry-trajectory design, and TPS performance risk trades while preventing excessive TPS margin from being applied. The probabilistic TPS margin process has been performed to determine TPS thickness and entry heating constraints given an acceptable risk level for the Low Earth Orbit Flight Experiment of an Inflatable Decelerator (LOFTID) flight project. The process is used in a manner to size the entry heat load for a given flexible TPS (FTPS) thickness so that it meets project reliability standards while allowing the FTPS and the underlying inflatable structure (IS) to be pushed to adequately high temperatures. Since the LOFTID project is an experimental flight demonstration, it is de-sired to drive the FTPS and IS to temperatures that cover a large range of their thermal response models’ applicability. This will allow the thermal response models to be better improved and validated post-flight using LOFTID’s extensive instrumentation embedded within the aeroshell. The presentation demonstrates how uncertainty analysis is carried out using an end-to-end Monte Carlo process where three separate Monte Carlo simulations are run in sequence. The first Monte Carlo simulation operates on the entry trajectory model to generate trajectory parameter dispersions that are fed into the second Monte Carlo simulation. The second Monte Carlo simulation operates on the aerothermodynamics model to generate aeroheating parameter dispersions that are fed into the third Monte Carlo simulation. The third Monte Carlo simulation operates on the FTPS material thermal response model to generate the final FTPS/IS thermal response dispersions. The end-to-end Monte Carlo simulation propagates the uncertainties of each model into the next to quantify the resulting uncertainty of the FTPS/IS thermal response. The fractional contributions of the uncertain parameters in the trajectory, aerothermal, and thermal response models to the variance in the FTPS/IS thermal response is determined as a byproduct of the Monte Carlo analysis. The structural uncertainty of the FTPS thermal response model is evaluated by flight relevant ground testing and model error analysis using test measurements. This probabilistic TPS margin process had never been applied to an entry vehicle and it is one of the LOFTID project’s goals to demonstrate its merits.

Steven A. Tobin↗

Design of a Torque Current Generator for Strapdown Gyroscopes

The design, analysis, and experimental evaluation of an optimum performance torque current generator for use with strapdown gyroscopes, is presented. Among the criteria used to evaluate the design were the following: (1) steady-state accuracy; (2) margins of stability against self-oscillation; (3) temperature variations; (4) aging; (5) static errors drift errors, and transient errors, (6) classical frequency and time domain characteristics; and (7) the equivalent noise at the input of the comparater operational amplifier. The DC feedback loop of the torque current generator was approximated as a second-order system. Stability calculations for gain margins are discussed. Circuit diagrams are shown and block diagrams showing the implementation of the torque current generator are discussed.

Mcknight, R. D.↗

A method to account for variation of average compressor inlet pressure during instantaneous distortion analyses

Instantaneous distortion analyses compare a time-varying value of an index (or 'surge margin used up') with a critical level (or 'available surge margin' of the compressor) to determine inlet-engine compatibility. Unless freestream conditions or propulsion system controls are changing, it is generally assumed that the available surge margin of the compressor is accurately determined from the steady-state operating point. Results are presented which show that variations of average compressor inlet pressure may occur without changes in freestream conditions or propulsion system controls. The volume dynamics of the compressor will cause these pressure variations to be attenuated and delayed by the time they reach the exit. This will cause the compressor pressure ratio (and available surge margin) to vary with time. A method is presented to calculate the available surge margin as a function of time and incorporate it into an instantaneous distortion analysis. Results show that inlet pressure variations which cause only a small change at the compressor exit can cause a significant variation in the available surge margin.

Burstadt, P. L.↗

Thrust stand evaluation of engine performance improvement algorithms in an F-15 airplane

An investigation is underway to determine the benefits of a new propulsion system optimization algorithm in an F-15 airplane. The performance seeking control (PSC) algorithm optimizes the quasi-steady-state performance of an F100 derivative turbofan engine for several modes of operation. The PSC algorithm uses an onboard software engine model that calculates thrust, stall margin, and other unmeasured variables for use in the optimization. As part of the PSC test program, the F-15 aircraft was operated on a horizontal thrust stand. Thrust was measured with highly accurate load cells. The measured thrust was compared to onboard model estimates and to results from posttest performance programs. Thrust changes using the various PSC modes were recorded. Those results were compared to benefits using the less complex highly integrated digital electronic control (HIDEC) algorithm. The PSC maximum thrust mode increased intermediate power thrust by 10 percent. The PSC engine model did very well at estimating measured thrust and closely followed the transients during optimization. Quantitative results from the evaluation of the algorithms and performance calculation models are included with emphasis on measured thrust results. The report presents a description of the PSC system and a discussion of factors affecting the accuracy of the thrust stand load measurements.

Conners, Timothy R.↗

The quantum p -spin glass model: a user manual for holographers

We study a large-N bosonic quantum mechanical sigma-model with a spherical target space subject to disordered interactions, more colloquially known as the p-spin spherical model. Replica symmetry is broken at low temperatures and for sufficiently weak quantum fluctuations, which drives the system into a spin glass (SG) phase. The first half of this paper is dedicated to a discussion of this model's thermodynamics, with particular emphasis on the marginally stable SG. This phase exhibits an emergent conformal symmetry in the strong coupling regime, which dictates its thermodynamic properties. It is associated with an extensive number of nearby states in the free energy landscape. We discuss in detail an elegant approximate solution to the SG equations, which interpolates between the conformal regime and an ultraviolet-complete short distance solution. In the second half of this paper we explore the real-time dynamics of the model and uncover quantum chaos as measured by out-of-time-order four-point functions, both numerically and analytically. We find exponential Lyapunov growth, which intricately depends on the model's couplings and becomes strongest in the quantum critical regime. We emphasize that the SG phase also exhibits quantum chaos, albeit with parametrically smaller Lyapunov exponent than in the replica symmetric phase. An analytical calculation in the marginal SG phase suggests that this Lyapunov exponent vanishes in a particular infinite coupling limit. Finally, we comment on the potential meaning of these observations from the perspective of holography.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Nuclear Safety [Vol. 35, No. 2, July-December 1994]

Nuclear Safety is a journal that covers significant issues in the field of nuclear safety. Its primary scope is safety in the design, construction, operation, and decommissioning of nuclear power reactors worldwide and the research and analysis activities that promote this goal, but it also encompasses the safety aspects of the entire nuclear fuel cycle, including fuel fabrication, spent-fuel processing and handling, and nuclear waste disposal, the handling of fissionable materials and radioisotopes, and the environmental effects of all these activities. Table of Contents for this issue follows. GENERAL SAFETY CONSIDERATIONS: 179 Consideration of Postaccident Consequences in the Determination of Safety Objectives for Future Nuclear Power Plants in France, D. Queniart, A. Sugier, and J. Lochard; ACCIDENT ANALYSIS: 187 Nuclear Safety Research: The Phebus FP Severe Accident Experimental Program, P. von der Hardt, A. V. Jones, C. Lecomte, and A. Tattegrain; 205 Containment Performance Analysis of the Advanced Neutron Source Reactor at the Oak Ridge National Laboratory, S. H. Kim, R. P. Taleyarkhan, and V. Georgevich; 213 Assessment of Fission Product Deposits in the Reactor Coolant System: The DEVAP Program, G. Le Marois and M. Megnin; 222 Erratum to “A Review of the Available Information on the Triggering Stage of a Steam Explosion," Vol. 35, No. 1, CONTROL AND INSTRUMENTATION: 223 Effects of Normal Aging on Calibration and Response Time of Nuclear Plant Resistance Temperature Detectors and Pressure Sensors, H. M. Hashemian; DESIGN FEATURES: 235 Defense in Depth Against the Hydrogen Risk—A European Research Program, F. Fineschi; ENVIRONMENTAL EFFECTS: 246 Technical Note: A Preliminary Analysis of the Risks to Hong Kong Resulting from Potential Accidents of Daya Bay Nuclear Power Plant, Z. Shi and X. Wei; OPERATING EXPERIENCES: 253 Reactor Shutdown Experience, Compiled by J. W. Cletcher; SPECIAL SECTION ON TMI-2 VESSEL INVESTIGATION PROJECT: 256 Three Mile Island—New Findings 15 Years After the Accident A. M. Rubin and E. Beckjord; 269 Relocation of Molten Material to the TMI-2 Lower Head, J. R. Wolf, D. W. Akers, and L. A. Neimark; 280 Insight Into the TMI-2 Core Material Relocation Through Examination of Instrument Tube Nozzles, L. A. Neimark; 288 Physical and Radiochemical Examinations of Debris from the TMI-2 Lower Head, D. W. Akers and B. K. Schuetz; 301 Results of Metallographic Examinations and Mechanical Tests of Pressure Vessel Samples from the TMI-2 Lower Head, D. R. Diercks and G. E. Korth; 313 Margin-to-Failure Calculations for the TMI-2 Vessel, J. Rempe, L. Stickler, S. Chavez, G. Thinnes, R. Witt, and M. Corradini; U.S. NUCLEAR REGULATORY COMMISSION INFORMATION AND ANALYSES: 328 1993 Accident Sequence Precursor (ASP) Program Results, L. N. Vanden Heuvel, J. W. Cletcher, D. A. Copinger, J. W. Minarick, B. W. Dolan, and P. D. O’Reilley; RECENT DEVELOPMENTS: 339 Reports, Standards, and Safety Guides, D. S. Queener; 345 Proposed Rule Changes as of June 30, 1994; ANNOUNCEMENTS: 234 Thirty-First Annual Meeting of the National Council on Radiation Protection and Measurements; 356 1995 International Incineration Conference; 358 Fifth International Controls and Instrumentation Conference; 359 ANS International Topical Meeting on Safety of Operating Reactors; 359 Fifth International Conference on Nuclear Criticality Safety; 360 International Conference on Probabilistic Safety Assessment Methodology and Applications; 351 The Authors; 357 Reviewers of Nuclear Safety, Vol. 35.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Status of Multiple Channel Fuel Performance Capabilities Within the SAS4A/SASSYS-1 Safety Analysis Software

SAS4A/SASSYS-1 (SAS) is a fast-running simulation tool used to perform deterministic analysis of anticipated events as well as design basis and beyond design basis accidents for advanced liquid-metal-cooled nuclear reactors. It is a critical element of safety analysis capabilities for the U.S. Department of Energy and is utilized within industry to perform the transient safety analyses required to support the licensing of Liquid Metal-cooled Fast Reactors (LMFRs). Although SAS is exceptionally fast for most transient scenarios, fuel performance calculations, along with the associated pre-transient characterization of the fuel pin, may be required for transient scenarios where fuel pin failure is hypothesized. Both the pre-transient characterization and the transient fuel performance calculation are necessary to properly quantify margins to potential fuel failure and assess the time spent potentially exceeding such margins during events. While safety analysis calculations with fuel performance models provide a more detailed characterization of the reactor during a transient, the pre-transient characterization can be time-consuming and computationally expensive. Often, large numbers of fuel pins have been exposed to similar pre-transient irradiation conditions. Similarly, the same pre-transient fuel characterization may be applicable to numerous transient conditions. This provides an opportunity to optimize the SAS computational framework such that pre-transient fuel characterization can be shared across multiple channels (fuel pins) and across multiple simulations, thus dramatically reducing overall computational costs. This report summarizes progress toward enhancing the SAS computational framework to support shared, multiple channel fuel performance characterizations intended to significantly reduce computational costs. Preliminary testing has shown that the computational time saved by using the pre-transient sharing capability is approximately equal to the time it takes to perform the pre-transient characterization.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Flight Testing and Real-Time System Identification Analysis of a UH-60A Black Hawk Helicopter with an Instrumented External Sling Load

Helicopter external air transportation plays an important role in today's world. For both military and civilian helicopters, external sling load operations offer an efficient and expedient method of handling heavy, oversized cargo. With the ability to reach areas otherwise inaccessible by ground transportation, helicopter external load operations are conducted in industries such as logging, construction, and fire fighting, as well as in support of military tactical transport missions. Historically, helicopter and load combinations have been qualified through flight testing, requiring considerable time and cost. With advancements in simulation and flight test techniques there is potential to substantially reduce costs and increase the safety of helicopter sling load certification. Validated simulation tools make possible accurate prediction of operational flight characteristics before initial flight tests. Real time analysis of test data improves the safety and efficiency of the testing programs. To advance these concepts, the U.S. Army and NASA, in cooperation with the Israeli Air Force and Technion, under a Memorandum of Agreement, seek to develop and validate a numerical model of the UH-60 with sling load and demonstrate a method of near real time flight test analysis. This thesis presents results from flight tests of a U.S. Army Black Hawk helicopter with various external loads. Tests were conducted as the U.S. first phase of this MOA task. The primary load was a container express box (CONEX) which contained a compact instrumentation package. The flights covered the airspeed range from hover to 70 knots. Primary maneuvers were pitch and roll frequency sweeps, steps, and doublets. Results of the test determined the effect of the suspended load on both the aircraft's handling qualities and its control system's stability margins. Included were calculations of the stability characteristics of the load's pendular motion. Utilizing CIFER(R) software, a method for near-real time system identification was also demonstrated during the flight test program.

McCoy, Allen H.↗

Effects of Defects Analysis and Sizing Framework for Efficient Design of Composite Structures

Design of large composite structures requires striking a balance between permitted flaw size,strength margins, weight, and production rate. Stringent requirements manufacturing flaws can result in a lightweight structure because the strength properties are assumed to be closer to pristine. However, these stringent requirements can lead to production delays due to increased inspection and rework needed during the layup and rejection of parts after cure. Conversely, permitting larger flaws can reduce production delays, but will likely result in a heavier structure due to increased conservatism needed to maintain acceptable structural margins. The tradeoff between these criteria can vary between different structures and material systems, so the balance between manufacturing and design requirements is always a moving target. Assessment of this tradeoff requires having the ability to quickly evaluate the impact of flaw size on strength margin across an entire structure for a large number of load cases. The approach taken in this work is to implement an effects of defects analysis and sizing framework within HyperX. HyperX performs optimization of composite structures; this capability has been enhanced to include structural flaw data in the margin of safety calculations performed during optimization. Both the flaw import process and analysis of flaws have been generalized such that any flaw type from any source can be considered. The resulting tool enables rapid assessment of the impact of defects both at a vehicle and part level.

Effects of defects↗

Effects of Defects Analysis and Sizing Framework for Efficient Design of Composite Structures

Design of large composite structures requires striking a balance between permitted flaw size,strength margins, weight, and production rate. Stringent requirements manufacturing flaws can result in a lightweight structure because the strength properties are assumed to be closer to pristine. However, these stringent requirements can lead to production delays due to increased inspection and rework needed during the layup and rejection of parts after cure. Conversely, permitting larger flaws can reduce production delays, but will likely result in a heavier structure due to increased conservatism needed to maintain acceptable structural margins. The tradeoff between these criteria can vary between different structures and material systems, so the balance between manufacturing and design requirements is always a moving target. Assessment of this tradeoff requires having the ability to quickly evaluate the impact of flaw size on strength margin across an entire structure for a large number of load cases. The approach taken in this work is to implement an effects of defects analysis and sizing framework within HyperX. HyperX performs optimization of composite structures; this capability has been enhanced to include structural flaw data in the margin of safety calculations performed during optimization. Both the flaw import process and analysis of flaws have been generalized such that any flaw type from any source can be considered. The resulting tool enables rapid assessment of the impact of defects both at a vehicle and part level.

Effects of defects↗

ON THE LANGUAGE OF RELIABILITY: A SYSTEM ENGINEER PERSPECTIVE

In its classical definition, risk is defined by three elements: what can go wrong, what are its consequences and how likely is it to occur. While this definition makes sense in a regulatory based framework to estimate risk associated to power plants (in terms of core damage frequency and large early release frequency), this approach does not provide a useful snapshot of the health of the plant. A possible alternate path can start by redefining the word “risk” to a broader meaning that better reflects the needs of a system health and asset management decision making process. Rather than asking how likely an event can occur (in probabilistic terms), we can ask how far this event is from occurring. We will show how, given the data available from plant equipment reliability and monitoring/diagnostic/prognostic centers, a margin can be described and determined for all type of maintenance approaches (e.g., corrective or predictive maintenance). We will show how to link SSC margin-based reliability models to system reliability models (i.e., fault trees) in order to assess system/plant health and how to perform margin-based system calculations. These calculations are not solved using classical probabilistic calculations applied to sets (as performed by any PRA code) but, instead, through metric spaces operations (i.e., distance/margin based approach).

97 - MATHEMATICS AND COMPUTING↗

ARDP Natrium Neutronic Methodology: Argonne Neutronic Assessment of ABR-1000

The Natrium Sodium-cooled Fast Reactor (SFR) concept developed by TerraPower, LLC was selected as one of the advanced reactor designs for demonstration under the Advanced Reactor Demonstration Program Natrium Demo project. In collaboration with TerraPower, the Argonne National Laboratory (ANL) team provide independent reviews of the neutronic methodology being used for the Natrium design. As part of this activity, both the TerraPower and ANL teams agreed to perform independent neutronics analyses of the ABR-1000 reactor problem as a demonstration on the usage of the neutronics methodologies. Comparison of the results from TerraPower and ANL would expose any methodological differences in the modeling approaches. This report describes and presents the Argonne analysis work on the ABR-1000, and will be provided to TerraPower, along with data files, to complete the comparison study. The comparison will cover the methodology to evaluate the reactivity coefficients for a safety analysis, the shutdown margin, and the reconstructed pin power distribution. The methods and models used to calculate the kinetic parameters and the reactivity coefficients (density, Doppler, axial/radial expansion, etc.) are described in detail with recommendations of specific method options and modelling techniques. The control system reactivity worth and the excess reactivity due to temperature defect are calculated for the shutdown margin analysis. The method to evaluate the excess reactivity is discussed in detail. The pin power reconstruction methodology used in SE2ANL, SE2RCT, and DASSH are discussed in this report. The pin power distribution evaluated by different methods are compared and discussed in the report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗