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Diagnosing ocean energy transports from earth radiation budget measurements

The maximum energy production (MEP) principle suggested by Paltridge (1975) is applied to separate the satellite-inferred required total transports into the atmospheric and the oceanic components within a two-dimensional (2D) framework. For this purpose, the required 2D energy transports (Sohn and Smith, 1991) are imposed on Paltridge's energy balance model which is then solved as a variational problem. The results provide separated atmospheric and oceanic transports on a 2D basis such that the total divergence is equal to the net radiation measured from a satellite.

Sohn, Byung-Ju↗

Detailed Comparison of Observed Dose-Time Profile of October 19-20, 1989 SPE on Mir with Model Calculations

The dose rate dynamics of the October 19-20,1989 solar energetic particle (SPE) event as observed by the Liulin instrument onboard the Mir orbital station was analyzed in light of new calculations of the geomagnetic cutoff and improved estimates of the less than 100 MeV energy spectra from the GOES satellite instrument. The new calculations were performed using the as-flown Mir orbital trajectory and includes time variations of the cutoff rigidity due to changes in the kappa (sub p) index. Although the agreement of total event integrated calculated dose to the measured dose is good, it results from some measured dose-time profile been higher and some lower than model calculations. They point to the need to include the diurnal variation of the geomagnetic cutoff and modifications of the cutoffs to variations in kappa (sub p) in model calculations. Understanding of such events in light of the upcoming construction of the International Space Station during the period of maximum solar activity needs to be vigorously pursued.

Badhwar, Gautam D.↗

A Variational Autoencoder Model Toward Molecular Structure Representation Learning of Fuels

Here, in this work, a Variational Autoencoder (VAE)-based data-driven modeling framework is developed with the overarching goal of enabling fuel design. The VAE model is trained on a large dataset with several chemical species to learn a compressed latent space molecular representation. Chemical structure in the form of Simplified Molecular Input Line Entry System (SMILES) string is fed as input, encoded into the VAE latent space, and decoded back to the SMILES string using Long Short-Term Memory (LSTM) networks. Complexities of the VAE training loss function are thoroughly examined by varying the weightage (beta (𝜷) parameter) of the latent space regularization term, thereby assessing the balance between reconstruction accuracy and validity, and focusing on both accurate molecular structure reconstruction and latent space consistency. Two different strategies for 𝜷 variation are evaluated: linear annealing and cyclic annealing. In addition, the impact of total correlation adjustment and hierarchical priors is also studied with regard to the balance between reconstruction fidelity and latent space regularization, and potential issues such as posterior collapse, over-regularization, and poor disentanglement of latent variables. Overall, the best performance of the model is achieved with hierarchical priors and incrementally increasing 𝜷 from 0 to a threshold value of 0.25 over 75 epochs. The generative VAE model can be readily coupled with Quantitative Structure–Property Relationship (QSPR) analysis to develop an integrated end-to-end framework for fuel-property prediction and molecular design of novel promising fuels.

fuel design↗

Global Precipitation Means and Variations with the New Version of GPCP

Knowledge of global precipitation means, patterns and variations is essential for understanding the global water cycle. The observation-based global analysis of the Global Precipitation Climatology Project (GPCP) has been a key input to many such studies, including those related to means of the global (and regional) water and energy cycles. A new version (Version 3.1) of the GPCP monthly analysis is now available (1983-2019), with finer spatial resolution (0.5º latitude/longitude), updated satellite algorithms, latest gauge analysis over land from the Global Precipitation Climatology Center (GPCC), and with ocean climatologies adjusted using information from the Tropical Rainfall Measuring Mission (TRMM), the Global Precipitation Measurement (GPM) mission and CloudSat. The presentation will give key findings from the new analysis, compare with the previous version, link to studies of the water cycle and compare to CMIP6 climate model results. The GPCP Monthly V3.1 analysis uses a Tropical Composite Climatology (TCC) using 22 years (1998-2019) of TRMM and GPM-based surface precipitation estimates from passive microwave, radar and combined passive microwave and radar observations to adjust the long-term mean values in the tropics over ocean. At higher latitudes over ocean climatological values of merged CloudSat and GPM combined passive microwave and radar surface precipitation estimates are used. The result of the new algorithms and procedures is an ocean mean value 60º N to 60º S of 3.2 mm/d, an increase of 7% from the older V2.3. Over land the gauge analysis (from GPCC in Germany), combined with satellite estimates results in a small decrease (~ 0.5%) from the previous version, giving a total global precipitation mean of 2.81 mm/d for V3.1, an increase of 4.5%. Variations from inter-annual to trend scales over most of the ocean are driven by the Colorado State University (CSU) Goddard Profiling (GPROF) algorithm applied to SSMI/SSMIS satellite data. The new GPCP version retains a near zero trend of global precipitation, with significant positive trends in the deep tropics along the Pacific ITCZ and elsewhere, countered by middle latitude decreases, very similar to the previous version of the GPCP Monthly analysis. The pattern of trends is similar to that of AMIP climate model results, driven by observed SSTs for the period in question, but very different from results for “free-running” CMIP historical ensembles, likely due in part to the relatively short comparison period and effects of inter-decadal variations in the GPCP and AMIP results that are not in the “history” models. Interannual variations are also nearly the same in the new version, but with finer detail, although ENSO variations over the ocean have slightly larger amplitude than before, an effect likely related to the change in ocean satellite algorithm used in Version 3. For precipitation intensity (percentiles) at the monthly scale, especially in the tropics, GPCP shows a positive trend for the upper one third of the percentiles (Pct ≥ 70th) and a much weaker positive trend for the lowest percentiles (Pct ≤ 10th), while negative trends appear for the middle one-half percentiles (20th-65th). AMIP results agree with those from the GPCP in terms of the sign of the changes/trends for high and intermediate percentiles. The CMIP historical results also agree in the sign of the trends, but the trends are weaker. Comparisons with other types of CMIP historical simulations including the GHG-only, aerosol-only, and nature-only runs suggest that the observed changes/trends in precipitation amount and intensity during the GPCP period are dominated by a combination of the effects of the Pacific Decadal Oscillation (PDO) and anthropogenic GHG-related surface warming.

Robert Adler↗

Resonant behavior of MHD waves on magnetic flux tubes. IV - Total resonant absorption and MHD radiating eigenmodes

Resonant absorption of MHD waves on a nonuniform flux tube is investigated as a driven problem for a 1D cylindrical equilibrium. The variation of the fractional absorption is studied as a function of the frequency and its relation to the eigenvalue problem of the MHD radiating eigenmodes of the nonuniform flux tube is established. The optimal frequencies producing maximal fractional absorption are determined and the condition for total absorption is obtained. This condition defines an impedance matching and is fulfilled for an equilibrium that is fine tuned with respect to the incoming wave. The variation of the spatial wave solutions with respect to the frequency is explained as due to the variation of the real and imaginary parts of the dispersion relation of the MHD radiating eigenmodes with respect to the real driving frequency.

Goossens, Marcel↗

Sensitivity of Multiangle, Multispectral Polarimetric Remote Sensing Over Open Oceans to Water-Leaving Radiance: Analyses of RSP Data Acquired During the MILAGRO Campaign

For remote sensing of aerosol over the ocean, there is a contribution from light scattered underwater. The brightness and spectrum of this light depends on the biomass content of the ocean, such that variations in the color of the ocean can be observed even from space. Rayleigh scattering by pure sea water, and Rayleigh-Gans type scattering by plankton, causes this light to be polarized with a distinctive angular distribution. To study the contribution of this underwater light polarization to multiangle, multispectral observations of polarized reflectance over ocean, we previously developed a hydrosol model for use in underwater light scattering computations that produces realistic variations of the ocean color and the underwater light polarization signature of pure sea water. In this work we review this hydrosol model, include a correction for the spectrum of the particulate scattering coefficient and backscattering efficiency, and discuss its sensitivity to variations in colored dissolved organic matter (CDOM) and in the scattering function of marine particulates. We then apply this model to measurements of total and polarized reflectance that were acquired over open ocean during the MILAGRO field campaign by the airborne Research Scanning Polarimeter (RSP). Analyses show that our hydrosol model faithfully reproduces the water-leaving contributions to RSP reflectance, and that the sensitivity of these contributions to Chlorophyll a concentration [Chl] in the ocean varies with the azimuth, height, and wavelength of observations. We also show that the impact of variations in CDOM on the polarized reflectance observed by the RSP at low altitude is comparable to or much less than the standard error of this reflectance whereas their effects in total reflectance may be substantial (i.e. up to >30%). Finally, we extend our study of polarized reflectance variations with [Chl] and CDOM to include results for simulated spaceborne observations.

Chowdhary, Jacek↗

Energy, greenhouse gas, and water life cycle analysis of synthetic graphite anode production in the United States

This study presents a comprehensive life cycle analysis of potential synthetic graphite battery anode material (BAM) production in the U.S. based on industrial-scale data. The analysis focuses on three impacts: greenhouse gas (GHG) emissions, total energy use, and water consumption. We also conducted sensitivity analyses to evaluate the effect of variation in process parameters and energy sources used for synthetic graphite BAM production on its life cycle GHG emissions. A detailed supply chain analysis of graphite BAM in the U.S. was also undertaken, along with a study of its associated GHG emissions. The results show GHG emissions of 29.7 kg CO 2 -eq. per kg BAM, total energy use of 580 MJ kg −1 BAM, and water consumption of 121 L kg −1 BAM for the baseline condition. The graphitization step is a major process hotspot, contributing to over 74% of all impacts. This is attributed to the energy and material input requirements for this step, particularly through the use of crucibles. Across the entire synthetic graphite production process, electricity is the primary contributor, followed by crucibles used in graphite block production, and then calcined petroleum coke. Sensitivity analyses indicate that improvement in micronization yield, reuse of crucibles, and use of low-carbon nuclear energy can significantly reduce GHG emissions of potential domestic graphite production (by ∼70%). Supply chain analysis identified major graphite BAM sources in the U.S. and showed that the U.S. has a competitive advantage in domestic production of synthetic graphite BAM in terms of reduced life cycle GHG emissions compared to present-day imported sources (by ∼20%).

Battery anode↗

Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 2

Two families of parametrized mixed variational principles for linear electromagnetodynamics are constructed. The first family is applicable when the current density distribution is known a priori. Its six independent fields are magnetic intensity and flux density, magnetic potential, electric intensity and flux density and electric potential. Through appropriate specialization of parameters the first principle reduces to more conventional principles proposed in the literature. The second family is appropriate when the current density distribution and a conjugate Lagrange multiplier field are adjoined, giving a total of eight independently varied fields. In this case it is shown that a conventional variational principle exists only in the time-independent (static) case. Several static functionals with reduced number of varied fields are presented. The application of one of these principles to construct finite elements with current prediction capabilities is illustrated with a numerical example.

Felippa, Carlos A.↗

Monitoring Degradation of Nuclear Cable Insulation Subjected To Sequential and Simultaneous Thermal and Radiation Aging

Predicting useful remaining life of cables in nuclear power plants is a topic of growing interest as plant continue to age. A typical electrical cable consists of polymeric materials, such as the cable jacket and insulation, which are susceptible to degradation due to exposure to both elevated temperatures and gamma irradiation over decades of service. In this work two insulation materials, crosslinked polyethylene (XLPE) and ethylene propylene diene (EPDM) elastomer, were characterized to quantify aging using total color difference and indenter modulus. Since the effects of thermal and gamma radiation are not additive but coupled, the effects of different aging scenarios including sequential and simultaneous aging were also evaluated. In the case of sequential aging, two aging scenarios were explored where the order in which thermal and gamma radiation received were altered. Total color difference of XLPE showed that sequentially aged insulation specimens, which received radiation first, degraded slightly more at maximum exposure than specimens which received thermal first. Similarly, in the case of EPDM, the extent of degradation evaluated using total color difference was found to be most severe in the case of sequentially aged insulation specimens which received radiation first. Indenter modulus was found to be insensitive to aging for XLPE but trended for EPDM. The largest variations were observed for the sequentially aged insulation specimens which received radiation first, similar to what was observed for total color difference.

Pallaka, Madhusudhan Reddy↗

A Method for Projecting Cloud Shadows Onto a Central Receiver Field to Predict Receiver Damage

This work demonstrates methods of mapping high-spatial-resolution direct normal irradiance (DNI) data from satellites, Total Sky Imagers (TSIs), and analogous data sources onto a heliostat field for characterizing the spatial and temporal variation of the incident flux on a central receiver tower during cloud transient events. The mapping methods are incorporated into an optical software module that interfaces with CoPylot–SolarPILOT’s python API– to provide computationally efficient optical simulation of the heliostat field and the solar power tower. Eventually, this optical model will be incorporated into optimization models whereby a plant operator can understand the effects of cloud transient events on overall power production and receiver lifetime due to creep-fatigue damage and therefore make better informed decisions about receiver shutdown events. By more accurately modelling the effects of cloud events on receiver flux maps, this work may determine the magnitude and frequency of thermal cycling on receiver tubes and panels using actual or realistic cloud shapes instead of averaged DNI values–which may undercount the total cycle number. This work may also prevent unnecessary plant shutdowns due to overly precautionary control strategies and characterize the relative impact of various cloud types on receiver life. We plan to eventually integrate this methodology into the System Advisor Model (SAM) to improve performance model accuracy during periods of cloudiness. In this paper, we demonstrate generating DNI maps and mapping them to a solar field in CoPylot using 10 m resolution data from publicly available Sentinel-2 satellite data over the Crescent Dunes plant.

Mullin, Matthew↗

Effects of sound level fluctuations on annoyance caused by aircraft-flyover noise

A laboratory experiment was conducted to determine the effects of variations in the rate and magnitude of sound level fluctuations on the annoyance caused by aircraft-flyover noise. The effects of tonal content, noise duration, and sound pressure level on annoyance were also studied. An aircraft-noise synthesis system was used to synthesize 32 aircraft-flyover noise stimuli representing the factorial combinations of 2 tone conditions, 2 noise durations, 2 sound pressure levels, 2 level fluctuation rates, and 2 level fluctuation magnitudes. Thirty-two test subjects made annoyance judgements on a total of 64 stimuli in a subjective listening test facility simulating an outdoor acoustic environment. Variations in the rate and magnitude of level fluctuations were found to have little, if any, effect on annoyance. Tonal content, noise duration, sound pressure level, and the interaction of tonal content with sound pressure level were found to affect the judged annoyance significantly. The addition of tone corrections and/or duration corrections significantly improved the annoyance prediction ability of noise rating scales.

Mccurdy, D. A.↗

Enhanced Performance of Streamline-Traced External-Compression Supersonic Inlets

A computational design study was conducted to enhance the aerodynamic performance of streamline-traced, external-compression inlets for Mach 1.6. Compared to traditional external-compression, two-dimensional and axisymmetric inlets, streamline-traced inlets promise reduced cowl wave drag and sonic boom, but at the expense of reduced total pressure recovery and increased total pressure distortion. The current study explored a new parent flowfield for the streamline tracing and several variations of inlet design factors, including the axial displacement and angle of the subsonic cowl lip, the vertical placement of the engine axis, and the use of porous bleed in the subsonic diffuser. The performance was enhanced over that of an earlier streamline-traced inlet such as to increase the total pressure recovery and reduce total pressure distortion.

performance↗

Invited Talks at Naples and Coimbra

Prior to observations of the solar irradiance from space that began in 1979 there was no hope of obtaining even rough estimates of the solar irradiance variation over a solar cycle, since the space observations made since showed that the magnitude of the variation over a cycle to date is less than 0.1 %, a value too small to measure from the ground. At the same time, it would be useful to know the cycle-dependent variation over more than just the two recent cycles. Lacking a complete theory for the solar dynamo responsible for this variation, the current hope is to determine what proxy might yield the best values. Because there is an excellent database on sunspot umbral and penumbral areas from the Greenwich Observatory for the years 1874-1976 (but not beyond), the possibility exists that these data could be used. This talk will summarize results of a joint study in which satellite measurements of the solar irradiance variation are compared with ground-based measurements from the Coimbra Observatory of sunspot number, umbral area, and total sunspot area to determine which would serve as the best proxy for using the Greenwich observations back to 1874. From the near constancy of sunspot umbral magnetic fields upon which the useful parameter photometric sunspot index is based, we expected that umbral area would yield the beat proxy. To our surprise, after performing a statistical study of the observations over the period 1980-1990, preliminary indications are that sunspot number (a parameter available back into the 18th century) may be just as useful as the umbral area. As expected, both are quite superior as proxies to total sunspot area, which includes the penumbral area. This conclusion is consistent with earlier work of Hop and Schatten, who sought a proxy by studies of the umbral-penumbral area ratio. A second motivation for pursuing this work is the possibility that relatively small variations in the solar irradiance may induce larger responses in Earth's climate than would occur from simply introducing the corresponding heat differential into the terrestrial atmosphere. The talk will conclude with a description of why some climatologists are beginning to explore this possibility, which is suggest by some of the space observations used in the above search for a solar irradiance variation proxy.

Jordan, Stuart↗

Glauber-theory analysis of nuclear reactions on a 12 C target with variational Monte Carlo wave functions

The application of Glauber theory has been playing an increasingly important role with the study of unstable or exotic nuclei. Its adaptation to medium and high-energy nucleus-nucleus collisions is severely limited because one has to evaluate the matrix elements of multiple-scattering operators. The extraction of physical observables has been done using ‘approximate’ Glauber theory whose validity is hard to evaluate. Here, we perform a full calculation of the matrix elements using Monte Carlo integration and analyze the elastic differential cross sections and the total reaction cross sections for p+¹²C, ⁴,⁶He+¹²C, and ¹²C+¹²C collisions. We use the variational Monte Carlo wave functions for ⁴,⁶He and ¹²C obtained by using realistic two- and three-nucleon potentials. We demonstrate the performance of the Glauber-theory calculations by comparing with available experimental data. We further discuss the accuracy of the conventional approximate methods in the light of the cumulant expansion for Glauber’s phase-shift function.

Horiuchi, W. [Osaka Metropolitan University (Japan↗

The Value Proposition of Multi-Megawatt Electric Power/Propulsion for the Human Exploration of Mars

NASA and other space agencies have been offering stakeholders an architecture for the human exploration of Mars that has remained essentially unchanged since the 1960's. The mission duration and launch mass are the two first order figures of merit that drive the total cost of such an architecture. The options studied to date center on the "conjunction class" or "Long Stay" mission, in which surface infrastructure elements are sent ahead on uncrewed, slow trajectories requiring a minimum amount of propellant, and the crewed elements are sent at the synotic cycle's shortest trajectory, stay on Mars until the next close alignment, and then return to Earth. Total crewed mission durations for these architectures range from 900 to 1100 days, with variations driven primarily by trades between the amount of propellant launched and the effective specific mass of the propulsion technology assumed (e.g., chemical, nuclear thermal, solar electric, nuclear electric). Mars transit propulsion systems assumed in mission architectures studied to date have all resulted in architectural figures of merit that drive the cost to a level of "too much." However, nuclear electric propulsion (NEP) technology offers a "knob" that might be turned to enable a radically different Mars architecture, whose launch mass and mission duration may enable a value proposition more palatable to mission stakeholders. Mars architectures studied to date have assumed an NEP system providing 2.5 MWe at a specific mass of no less than 20 kg/kWe. This has often been seen as obtainable with a moderately high temperature fission reactor. An NEP system providing 15 MWe at specific mass of ~1 kg/kWe, though, could enable a short stay (30 days on surface) Mars mission, requiring only two or three SLS-class launch vehicles and a total mission duration of under one calendar year. However, turning this NEP "knob" would require a high risk development program driving innovation on the order of that delivered by the Manhattan Project, but for a fraction of the cost. Any technology option that might offer such a capability at such a development cost now stands at a low Technology Readiness Level (TRL) 3, would be based on a nuclear energy source (likely fusion), and would require an extremely high risk (and rapid) development effort. The aggressive, parallel path project management paradigm exemplified by the original Manhattan Project might have the best chance of success. An energy source developed in this manner may also have a major impact on the terrestrial power industry.

power↗

Airborne Measurements of Scale‐Dependent Latent Heat Flux Impacted by Water Vapor and Vertical Velocity Over Heterogeneous Land Surfaces During the CHEESEHEAD19 Campaign

Abstract The water vapor transport associated with latent heat flux (LE) in the planetary boundary layer (PBL) is critical for the atmospheric hydrological cycle, radiation balance, and cloud formation. The spatiotemporal variability of LE and water vapor mixing ratio ( r v ) are poorly understood due to the scale‐dependent and nonlinear atmospheric transport responses to land surface heterogeneity. Here, airborne in situ measurements with the wavelet technique are utilized to investigate scale‐dependent relationships among LE, vertical velocity ( w ) variance (), and r v variance () over a heterogeneous surface during the Chequamegon Heterogeneous Ecosystem Energy‐balance Study Enabled by a High‐density Extensive Array of Detectors 2019 (CHEESEHEAD19) field campaign. Our findings reveal distinct scale distributions of LE, , and at 100 m height, with a majority scale range of 120 m–4 km in LE, 32 m–2 km in , and 200 m–8 km in . The scales are classified into three scale ranges, the turbulent scale (8–200 m), large‐eddy scale (200 m–2 km), and mesoscale (2–8 km) to evaluate scale‐resolved LE contributed by and . The large‐eddy scale in PBL contributes over 70% of the monthly mean total LE with equal parts (50%) of contributions from and . The monthly temporal variations mainly come from the first two major contributing classified scales in LE, , and . These results confirm the dominant role of the large‐eddy scale in the PBL in the vertical moisture transport from the surface to the PBL, while the mesoscale is shown to contribute an additional ∼20%. This analysis complements published scale‐dependent LE variations, which lack detailed scale‐dependent vertical velocity and moisture information.

54 ENVIRONMENTAL SCIENCES↗

Simulation of the NuScale SMR and Investigation of the Effect of Load-Following on Component Lifetimes

The NuScale SMR has been modelled using the Virtual Environment for Reactor Applications (VERA) multiphysics environment and the results compared with the publicly reported data in the Design Certification Application (DCA). The results show an excellent agreement for the compared axial and radial power distributions, temperature coefficients of reactivity, boron and control rod worths, and fast neutron flux. This NuScale model is then used to investigate the effect of different operational modes on reactor components to determine how flexible load-following operation may affect control rod and reactor pressure vessel (RPV) lifetimes. The control rod degradation is confirmed to primarily affect the silver-indium-cadmium (AIC) rod tip. The degradation rate is observed to follow a non-linear function of core power level where the increase in degradation decreases with insertion depth. For the variation in core power levels expected with current load-following schemes, the total control rod degradation is found to be mild, at 5-10% of usable life per cycle for a reactor operating at <80% power. Nonetheless, this enables load following strategies to be confirmed and/or modified to ensure that control rods do not need to be replaced during the 60+ year life of the reactor. The RPV degradation was found to be almost directly proportional to the core power level and was not overly sensitive to flux shape perturbations. Future work is planned using these damage functions to optimize operation over multiple NuScale SMR units and develop strategies for prognostics and health management.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

The population of galaxies that contribute to the H i mass function

ABSTRACT We look at the contribution of different galaxy populations to the atomic hydrogen (H i) mass function (HIMF) and the H i density parameter, ΩH i, in the local Universe. Our analysis is based on a sample of 7857 H i selected galaxies selected from a volume common to the Sloan Digital Sky Survey (SDSS) and Arecibo Fast Legacy ALFA (40 per cent catalogue – α.40) surveys. We define different populations of galaxies in the colour (u − r)–magnitude (Mr) plane and compute the HIMF for each of them. Additionally we compute the HIMF for dark galaxies; these are undetected in SDSS and represent $\sim 2{{\ \rm per\ cent}}$ of the total sample. We find that the luminous red population dominates the total HIMF for $\log _{10}(M_{\rm{H\,{\small I}}}h^2_{70}/M_{\odot }) \ge 10.4$. The full red population – luminous and faint – represents about $\sim 17{{\ \rm per\ cent}}$ of the ΩH i budget, while that of the dark population is $\sim 3{{\ \rm per\ cent}}$. The HIMF about the knee, $\log _{10}(M_{\rm{H\,{\small I}}}h^2_{70}/M_{\odot }) \in [8,10.4]$, is dominated by the faint and luminous blue populations, the latter dominating at larger masses in this interval. Their total contribution to ΩH i is $\sim 55\!-\!70{{\ \rm per\ cent}}$, the variation depending on the definition of population. The dominant populations at the low-mass end, $\log _{10}(M_{\rm{H\,{\small I}}}h^2_{70}/M_{\odot }) \le 8.0$ are the faint blue and faint bluer populations, the latter’s dominance being sensitive to its definition. The full blue (blue–bluer luminous and faint) population represents $\sim 80{{\ \rm per\ cent}}$ of ΩH i. A bimodal HIMF suggested by our results is however not seen since the amplitude of the HIMF of the luminous red population is small compared to that of the luminous blue population.

Dutta, Saili↗