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At least 145 records · Page 8

Fuzzy Logic Controller Stability Analysis Using a Satisfiability Modulo Theories Approach

While many widely accepted methods and techniques exist for validation and verification of traditional controllers, at this time no solutions have been accepted for Fuzzy Logic Controllers (FLCs). Due to the highly nonlinear nature of such systems, and the fact that developing a valid FLC does not require a mathematical model of the system, it is quite difficult to use conventional techniques to prove controller stability. Since safety-critical systems must be tested and verified to work as expected for all possible circumstances, the fact that FLC controllers cannot be tested to achieve such requirements poses limitations on the applications for such technology. Therefore, alternative methods for verification and validation of FLCs needs to be explored. In this study, a novel approach using formal verification methods to ensure the stability of a FLC is proposed. Main research challenges include specification of requirements for a complex system, conversion of a traditional FLC to a piecewise polynomial representation, and using a formal verification tool in a nonlinear solution space. Using the proposed architecture, the Fuzzy Logic Controller was found to always generate negative feedback, but inconclusive for Lyapunov stability.

Fuzzy Logic Controller↗

Chapter 15: Potential Surprises: Compound Extremes and Tipping Elements

The Earth system is made up of many components that interact in complex ways across a broad range of temporal and spatial scales. As a result of these interactions the behavior of the system cannot be predicted by looking at individual components in isolation. Negative feedbacks, or self-stabilizing cycles, within and between components of the Earth system can dampen changes (Ch. 2: Physical Drivers of Climate Change). However, their stabilizing effects render such feedbacks of less concern from a risk perspective than positive feedbacks, or self-reinforcing cycles. Positive feedbacks magnify both natural and anthropogenic changes. Some Earth system components, such as arctic sea ice and the polar ice sheets, may exhibit thresholds beyond which these self-reinforcing cycles can drive the component, or the entire system, into a radically different state. Although the probabilities of these state shifts may be difficult to assess, their consequences could be high, potentially exceeding anything anticipated by climate model projections for the coming century.

Kopp, R. E.↗

Constraining the Climate and Ocean PH of the Early Earth with a Geological Carbon Cycle Model

The early Earth's environment is controversial. Climatic estimates range from hot to glacial, and inferred marine pH spans strongly alkaline to acidic. Better understanding of early climate and ocean chemistry would improve our knowledge of the origin of life and its coevolution with the environment. Here, we use a geological carbon cycle model with ocean chemistry to calculate self-consistent histories of climate and ocean pH. Our carbon cycle model includes an empirically justified temperature and pH dependence of seafloor weathering, allowing the relative importance of continental and seafloor weathering to be evaluated. We find that the Archean climate was likely temperate (0-50deg C) due to the combined negative feedbacks of continental and seafloor weathering. Ocean pH evolves monotonically from 6.6(sup + 0.6) (sub -0.4) (2 sigma) at 4.0 Ga to 7.0(sup +0.7) (sub-0.5) (2 sigma) at the Archean-Proterozoic boundary, and to 7.9(sup +0.1) (sub -0.2) (2 sigma) at the Proterozoic-Phanerozoic boundary. This evolution is driven by the secular decline of pCO2, which in turn is a consequence of increasing solar luminosity, but is moderated by carbonate alkalinity delivered from continental and seafloor weathering. Archean seafloor weathering may have been a comparable carbon sink to continental weathering, but is less dominant than previously assumed, and would not have induced global glaciation. We show how these conclusions are robust to a wide range of scenarios for continental growth, internal heat flow evolution and outgassing history, greenhouse gas abundances, and changes in the biotic enhancement of weathering.

Krissansen-Totton, Joshua↗

Fuzzy Logic Controller Stability Analysis Using a Satisfiability Modulo Theories Approach

While many widely accepted methods and techniques exist for validation and verification of traditional controllers, at this time no solutions have been accepted for Fuzzy Logic Controllers (FLCs). Due to the highly nonlinear nature of such systems, and the fact that developing a valid FLC does not require a mathematical model of the system, it is quite difficult to use conventional techniques to prove controller stability. Since safety-critical systems must be tested and verified to work as expected for all possible circumstances, the fact that FLC controllers cannot be tested to achieve such requirements poses limitations on the applications for such technology. Therefore, alternative methods for verification and validation of FLCs needs to be explored. In this study, a novel approach using formal verification methods to ensure the stability of a FLC is proposed. Main research challenges include specification of requirements for a complex system, conversion of a traditional FLC to a piecewise polynomial representation, and using a formal verification tool in a nonlinear solution space. Using the proposed architecture, the Fuzzy Logic Controller was found to always generate negative feedback, but inconclusive for Lyapunov stability.

Fuzzy Logic Controller↗

Consequences of Prenatal Stress on Appetite Control and the Energy Expenditure Pathway

Established research has illustrated that moderate exposure to stress in the womb influences both adult phonotype and genotype for several physiological pathways, especially in males. Proposed explanations include adaptions made by the fetus resulting from a limited supply of nutrients, referred to as the thrifty phenotype. In this study, we examine this fetal programming effect on the appetite control and energy expenditure pathways in prenatally stressed adult male offspring. Subjects were male rats born from time-mated female rats exposed to unpredictable, variable prenatal stress (UVPS) throughout gestation. An analysis of the adult male rat offspring genetic expression of epididymal fat pads and the plasma concentrations of hormones involved in appetite control and energy expenditure pathways showed a significantly diminished expression of leptin and adiponectin compared to unstressed controls. Leptin and adiponectin are both major hormones involved in the appetite control and energy expenditure pathways, with leptin regulating energy balance due to its function as an inhibitor of hunger, and adiponectin modulating glucose levels and fatty acid breakdown. We observed higher leptin concentrations within the prenatally stressed male plasma, and lower expression of leptin (OB) and adiponectin (ADIPOQ) genes from the epididymal fat pads. We suggest that elevated leptin in the plasma elicited a negative feedback effect on OB expression levels, decreasing their quantification compared to control animals. Further analysis will include plasma quantification of insulin and glucose, as well as expression of ghrelin, a peptide which acts on the central nervous system and the bodys perception of hunger.

appetite control↗

Soil moisture-atmosphere feedbacks mitigate declining water availability in drylands

Global warming alters surface water availability (precipitation minus evapotranspiration, P–E) and hence freshwater resources. However, the influence of land–atmosphere feedbacks on future P–E changes and the underlying mechanisms remain unclear. Here we demonstrate that soil moisture (SM) strongly impacts future P–E changes, especially in drylands, by regulating evapotranspiration and atmospheric moisture inflow. Using modelling and empirical approaches, we find a consistent negative SM feedback on P–E, which may offset ~60% of the decline in dryland P–E otherwise expected in the absence of SM feedbacks. The negative feedback is not caused by atmospheric thermodynamic responses to declining SM; rather, reduced SM, in addition to limiting evapotranspiration, regulates atmospheric circulation and vertical ascent to enhance moisture transport into drylands. This SM effect is a large source of uncertainty in projected dryland P–E changes, underscoring the need to better constrain future SM changes and improve the representation of SM–atmosphere processes in models.

precipitation↗

CGILS: Results from the First Phase of an International Project to Understand the Physical Mechanisms of Low Cloud Feedbacks in Single Column Models

1] CGILS-the CFMIP-GASS Intercomparison of Large Eddy Models (LESs) and single column models (SCMs)-investigates the mechanisms of cloud feedback in SCMs and LESs under idealized climate change perturbation. This paper describes the CGILS results from 15 SCMs and 8 LES models. Three cloud regimes over the subtropical oceans are studied: shallow cumulus, cumulus under stratocumulus, and well-mixed coastal stratus/stratocumulus. In the stratocumulus and coastal stratus regimes, SCMs without activated shallow convection generally simulated negative cloud feedbacks, while models with active shallow convection generally simulated positive cloud feedbacks. In the shallow cumulus alone regime, this relationship is less clear, likely due to the changes in cloud depth, lateral mixing, and precipitation or a combination of them. The majority of LES models simulated negative cloud feedback in the well-mixed coastal stratus/stratocumulus regime, and positive feedback in the shallow cumulus and stratocumulus regime. A general framework is provided to interpret SCM results: in a warmer climate, the moistening rate of the cloudy layer associated with the surface-based turbulence parameterization is enhanced; together with weaker large-scale subsidence, it causes negative cloud feedback. In contrast, in the warmer climate, the drying rate associated with the shallow convection scheme is enhanced. This causes positive cloud feedback. These mechanisms are summarized as the "NESTS" negative cloud feedback and the "SCOPE" positive cloud feedback (Negative feedback from Surface Turbulence under weaker Subsidence-Shallow Convection PositivE feedback) with the net cloud feedback depending on how the two opposing effects counteract each other. The LES results are consistent with these interpretations

Single Column Models↗

Response to "The Iris Hypothesis: A Negative or Positive Cloud Feedback?"

Based on radiance measurements of Japan's Geostationary Meteorological Satellite, Lindzen et al. found that the high-level cloud cover averaged over the tropical western Pacific decreases with increasing sea surface temperature. They further found that the response of high-level clouds to the sea surface temperature had an effect of reducing the magnitude of climate change, which is referred as a negative climate feedback. Lin et al. reassessed the results found by Lindzen et al. by analyzing the radiation and clouds derived from the Tropical Rainfall Measuring Mission Clouds and the Earth's Radiant Energy System measurements. They found a weak positive feedback between high-level clouds and the surface temperature. We have found that the approach taken by Lin et al. to estimating the albedo and the outgoing longwave radiation is incorrect and that the inferred climate sensitivity is unreliable.

Chou, Ming-Dah↗

Causes of Reduced Climate Sensitivity in E3SM From Version 1 to Version 2

The effective climate sensitivity in the Department of Energy's Energy Exascale Earth System Model (E3SM) has decreased from 5.3 K in version 1 to 4.0 K in version 2. This reduction is mainly due to a weaker positive cloud feedback that leads to a stronger negative radiative feedback. Present-day atmosphere-only experiments with uniform 4 K sea surface temperature warming are used to separate the contributions of individual model modifications to the reduced cloud feedback. We find that the reduced cloud feedback is mostly driven by changes over the tropical marine low cloud regime, mainly related to a new trigger function for the deep convection scheme and modifications in the cloud microphysics scheme. The new trigger function helps weaken the low cloud reduction by increasing the cloud water detrainment at low levels from deep convection under warming. Changes to the formula of autoconversion rate from liquid to rain and an introduced minimum cloud droplet number concentration threshold in cloud microphysical calculations help sustain clouds against dissipation by suppressing precipitation generation with warming. In the midlatitudes, the increased Wegener-Bergeron-Findeisen (WBF) efficiency strongly reduces present-day liquid water and leads to a stronger negative cloud optical depth feedback. The reduced trade cumulus cloud feedback in v2 is closer to estimates from recent observational and large-eddy modeling studies but might not be due to the right physical reasons. The reduced mid-latitude cloud feedback may be more plausible because more realistic present-day mixed-phase clouds are produced through the change in the WBF efficiency.

54 ENVIRONMENTAL SCIENCES↗

Psychophysiological Control of Acognitive Task Using Adaptive Automation

The major focus of the present proposal was to examine psychophysiological variables related to hazardous states of awareness induced by monitoring automated systems. With the increased use of automation in today's work environment, people's roles in the work place are being redefined from that of active participant to one of passive monitor. Although the introduction of automated systems has a number of benefits, there are also a number of disadvantages regarding worker performance. Byrne and Parasuraman have argued for the use of psychophysiological measures in the development and the implementation of adaptive automation. While both performance based and model based adaptive automation have been studied, the use of psychophysiological measures, especially EEG, offers the advantage of real time evaluation of the state of the subject. The current study used the closed-loop system, developed at NASA-Langley Research Center, to control the state of awareness of subjects while they performed a cognitive vigilance task. Previous research in our laboratory, supported by NASA, has demonstrated that, in an adaptive automation, closed-loop environment, subjects perform a tracking task better under a negative than a positive, feedback condition. In addition, this condition produces less subjective workload and larger P300 event related potentials to auditory stimuli presented in a concurrent oddball task. We have also recently shown that the closed-loop system used to control the level of automation in a tracking task can also be used to control the event rate of stimuli in a vigilance monitoring task. By changing the event rate based on the subject's index of arousal, we have been able to produce improved monitoring, relative to various control groups. We have demonstrated in our initial closed-loop experiments with the the vigilance paradigm that using a negative feedback contingency (i.e. increasing event rates when the EEG index is low and decreasing event rates when the EEG index is high) results in a marked decrease of the vigilance decrement over a 40 minute session. This effect is in direct contrast to performance of a positive feedback group, as well as a number of other control groups which demonstrated the typical vigilance decrement. Interestingly, however, the negative feedback group performed at virtually the same level as a yoked control group. The yoked control group received the same order of changes in event rate that were generated by the negative feedback subjects using the closed-loop system. Thus it would appear to be possible to optimize vigilance performance by controlling the stimuli which subjects are asked to process.

Freeman, Frederick↗

Midlatitude cyclone processes as a key to understanding climate sensitivity

Global climate models (GCMs) differ greatly in their shortwave cloud feedback. One feature that is consistent across GCMs is a positive shortwave cloud feedback in the subtropics, and a negative shortwave cloud feedback across the midlatitudes. Confidence has grown in the mechanisms that lead to, and the strength of, the subtropical shortwave cloud feedback, but the midlatitude negative shortwave cloud feedback is not well-constrained or well-understood. It is critical to reduce uncertainty in midlatitude shortwave cloud feedback. A more positive midlatitude shortwave cloud feedback in the sixth coupled model intercomparison project (CMIP6) has been found to be one of the primary causes of the increased climate sensitivity of CMIP6 models relative to CMIP5. We show that changes in midlatitude cyclones in future climates are the primary cause of the negative shortwave cloud feedback and are thus key to understanding the high climate sensitivity in the most recent GCMs. Warming-induced changes in cloud liquid water path in midlatitude cyclones can almost entirely be explained by Clausius-Clapeyron increasing moisture convergence into cyclones. One concern with simulating midlatitude cyclones is the lack of predictive skill at low resolution. A more realistic relationship between moisture flux and cyclone liquid content is found at high horizontal resolution (∆x<25km), but the cloud feedback within cyclones can be explained by increased moisture convergence across low- and high-resolution models. Observations and models agree that the extratropical shortwave cloud feedback is moderated by precipitation processes in cyclones. This rules out a large contribution from ice-to-liquid transitions, as has been hypothesized in previous studies. Understanding and constraining these precipitation processes is crucial to constraining the response of midlatitude cyclones to warming and by extension climate sensitivity.

Cyclones↗

Significance of the organic aerosol driven climate feedback in the boreal area

Aerosol particles cool the climate by scattering solar radiation and by acting as cloud condensation nuclei. Higher temperatures resulting from increased greenhouse gas levels have been suggested to lead to increased biogenic secondary organic aerosol and cloud condensation nuclei concentrations creating a negative climate feedback mechanism. Here, we present direct observations on this feedback mechanism utilizing collocated long term aerosol chemical composition measurements and remote sensing observations on aerosol and cloud properties. Summer time organic aerosol loadings showed a clear increase with temperature, with simultaneous increase in cloud condensation nuclei concentration in a boreal forest environment. Remote sensing observations revealed a change in cloud properties with an increase in cloud reflectivity in concert with increasing organic aerosol loadings in the area. The results provide direct observational evidence on the significance of this negative climate feedback mechanism.

54 ENVIRONMENTAL SCIENCES↗

Metal fuel relocation experiments with pressure injection

A pool-type sodium-cooled fast reactor (SFR) using metal fuels has a number of inherent safety features that can support benign consequences for design basis accidents (DBAs). Even in postulated severe accident conditions, the core is designed to remain under sub-critical condition in a passive coolable geometry. In case of the postulated severe accidents in SFRs, fuel relocation in the core region along the coolant channel is an important negative reactivity feedback factor that lowers the reactor power level and consequently eliminates the possibility of recriticality. Therefore, understanding the relocation behavior of fuels and the coolability of the relocated fuels in the postulated severe accident is one of the most important factors in the safety assessment of SFRs. In the present study, the relocation behavior of the metal fuel in a pin bundle geometry was investigated by injecting the metal fuels into the coolant channels with pressure. The first metal fuel relocation with pressure injection (RPI-1) experiment showed that many of the metal fuels levitated to upper plenum. In case of RPI-2 experiment, the Real Time X-ray Video System (RTXVS) was constructed and used to obtain a real time X-ray video of the experiment. This real time X-ray video clearly showed the relocation behavior of the pressure injected metallic uranium in the sodium coolant channel. Through this video, it was confirmed that part of the fuel was dispersed downward and part of the fuel was dispersed upward, and the relocation behavior of the injected fuel proceeded simultaneously in the downward and upward directions. So, it can be concluded that in case of pressure injection of the metallic fuel, there is a possibility that the metallic fuel can be quickly removed from the core region, resulting in a negative reactivity feedback effect.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Contributions to Polar Amplification in CMIP5 and CMIP6 Models

As a step towards understanding the fundamental drivers of polar climate change, we evaluate contributions to polar warming and its seasonal and hemispheric asymmetries in Coupled Model Intercomparison Project phase 6 (CMIP6) as compared with CMIP5. CMIP6 models broadly capture the observed pattern of surface- and winter-dominated Arctic warming that has outpaced both tropical and Antarctic warming in recent decades. For both CMIP5 and CMIP6, CO 2 quadrupling experiments reveal that the lapse-rate and surface albedo feedbacks contribute most to stronger warming in the Arctic than the tropics or Antarctic. The relative strength of the polar surface albedo feedback in comparison to the lapse-rate feedback is sensitive to the choice of radiative kernel, and the albedo feedback contributes most to intermodel spread in polar warming at both poles. By separately calculating moist and dry atmospheric heat transport, we show that increased poleward moisture transport is another important driver of Arctic amplification and the largest contributor to projected Antarctic warming. Seasonal ocean heat storage and winter-amplified temperature feedbacks contribute most to the winter peak in warming in the Arctic and a weaker winter peak in the Antarctic. In comparison with CMIP5, stronger polar warming in CMIP6 results from a larger surface albedo feedback at both poles, combined with less-negative cloud feedbacks in the Arctic and increased poleward moisture transport in the Antarctic. However, normalizing by the global-mean surface warming yields a similar degree of Arctic amplification and only slightly increased Antarctic amplification in CMIP6 compared to CMIP5.

54 ENVIRONMENTAL SCIENCES↗

Sea ice pattern effect on Earth’s energy budget is characterized by hemispheric asymmetry

Earth’s energy budget is sensitive to the spatial distribution of sea surface temperature and sea ice concentration (SIC) change, but the global radiative effect of changes in SIC spatial distribution has not been quantified. We show that SIC-induced radiation anomalies at the top of the atmosphere are sensitive to the location of SIC reduction in each season, which qualitatively explains how and why the effect of sea ice loss on Earth’s energy budget is determined by its spatial pattern. Idealized experiments indicate that SIC-induced surface warming is greater in the Arctic regions, resulting in a more negative Planck feedback. Global low-level cloud cover responses to Arctic and Antarctic SIC reduction are also distinct, leading to more negative SIC-cloud feedback in Arctic regions. SIC-induced albedo feedback is sensitive to latitude due to inhomogeneous solar radiation at the surface. As a result, the simulated radiative effect of SIC anomalies during 1980–2019 is dominated by variations in the spatial pattern of SIC.

54 ENVIRONMENTAL SCIENCES↗

Assessment of MOOSE-Based Tools for Calculating Radial Core Expansion

Radial core expansion in liquid-metal cooled fast reactor systems is a well-known phenomenon that produces strong reactivity feedback effects. An inherently safe reactor design takes advantage of negative reactivity feedback in accident scenarios by utilizing a core restraint system which produces a bowed shape that allows for radial expansion of the fuel regions. Detailed modeling and simulation of core radial expansion itself as well as subsequent reactivity feedback is a challenging task involving contact of many fuel assembly elements and physics feedback from neutronics, thermal hydraulics, and thermal mechanical response. A variety of physics codes have been developed to model aspects of radial core expansion but in general invoke geometrical or physics approximations. No code system currently exists which tightly and robustly couples these physics with enough detail to fully resolve the complex core radial expansion reactivity feedback effects. The future availability of such a code system is of vital importance to fully understanding the reactivity feedback effects that occur due to radial expansion, and consequently to optimizing the design of the core restraint system. A high-fidelity code will also be used to benchmark existing lower fidelity, faster running models to understand their benefits, limitations, and range of applications. A code development path using MOOSE-based tools is proposed in order to leverage the detailed geometry capabilities and natural tight coupling and robustness of MOOSE-based applications for modeling this complex phenomena. While simulation of the full phenomenon involves several physics, an assessment has been initiated on the capabilities and readiness of the currently available Tensor Mechanics module within MOOSE for calculation of the structural mechanical responses which occur within the reactor core. This report focuses on modeling the force-deformation response which mimics the physics of a duct contact deformation, as well as differential thermal expansion which produces a thermal bowed shaped for the fuel assemblies in a core. Simple examples were initially performed such as simple supported beam bending under load. The complexity of examples was progressively increased to better mimic the duct behavior by including a differential thermal example and inclusion of hexagonal cross-sections in the geometry. Further assessment of the structural mechanical response simulation capability is still required for modeling duct contact interactions and irradiation creep and swelling. Companion thermal hydraulic and neutronics assessments will also be required; these activities are planned for future years. Finally, integration of the multiple physics components through MOOSE is required to predict the core radial expansion and subsequent feedback effects.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Strong Dependence of Atmospheric Feedbacks on Mixed-Phase Microphysics and Aerosol-Cloud Interactions in HadGEM3

We analyze the atmospheric processes that explain the large changes in radiative feed-backs between the two latest climate configurations of the Hadley Centre Global Environmental model. We use a large set of atmosphere-only climate-change simulations (amip and amip-p4K) to separate the contributions to the differences in feedback parameter from all the atmospheric model developments between the two latest model configurations. We show that the differences are mostly driven by changes in the shortwave cloud radiative feedback in the midlatitudes, mainly over the Southern Ocean. Two new schemes explain most of the differences: the introduction of a new aerosol scheme; and the development of a new mixed-phase cloud scheme. Both schemes reduce the strength of the pre-existing shortwave negative cloud feedback in the midlatitudes. The new aerosol scheme dampens a strong aerosol-cloud interaction, and it also suppresses a negative clear-sky shortwave feedback. The mixed-phase scheme increases the amount of cloud liquid water path (LWP) in the present-day, thereby reducing the radiative effciency of the increase of LWP in the warmer climate. It also enhances a strong, pre-existing, positive cloud fraction feedback. We assess the realism of the changes by comparing present-day simulations against observations, and discuss avenues that could help constrain the relevant processes.

HadGEM3↗

A Burst Mode, Ultrahigh Temperature UF4 Vapor Core Reactor Rankine Cycle Space Power System Concept

Static and dynamic neutronic analyses have been performed on an innovative burst mode (100's of MW output for a few thousand seconds) Ulvahigh Temperature Vapor Core Reactor (UTVR) space nuclear power system. The NVTR employs multiple, neutronically-coupled fissioning cores and operates on a direct, closed Rankine cycle using a disk Magnetohydrodynamic (MHD) generater for energy conversion. The UTVR includes two types of fissioning core regions: (1) the central Ultrahigh Temperature Vapor Core (UTVC) which contains a vapor mixture of highly enriched UF4 fuel and a metal fluoride working fluid and (2) the UF4 boiler column cores located in the BeO moderator/reflector region. The gaseous nature of the fuel the fact that the fuel is circulating, the multiple coupled fissioning cores, and the use of a two phase fissioning fuel lead to unique static and dynamic neutronic characteristics. Static neutronic analysis was conducted using two-dimensional S sub n, transport theory calculations and three-dimensional Monte Carlo transport theory calculations. Circulating-fuel, coupled-core point reactor kinetics equations were used for analyzing the dynamic behavior of the UTVR. In addition to including reactivity feedback phenomena associated with the individual fissioning cores, the effects of core-to-core neutronic and mass flow coupling between the UTVC and the surrounding boiler cores were also included in the dynamic model The dynamic analysis of the UTVR reveals the existence of some very effectlve inherent reactivity feedback effects that are capable of quickly stabilizing this system, within a few seconds, even when large positive reactivity insertions are imposed. If the UTVC vapor fuel density feedback is suppressed, the UTVR is still inherently stable because of the boiler core liquid-fuel volume feedback; in contrast, suppression of the vapor fuel density feedback in 'conventional" gas core cavity reactors causes them to become inherently unstable. Due to the strength of the negative reactivity feedback in the UTVR, it is found that external reactivity insertions alone are inadequate for bringing about significant power level changes during normal reactor operations. Additional methods of reactivity control such as variations in the gaseous fuel mass flow rate, are needed to achieve the desired power level oontrol.

Dugan, E. T.↗