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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 667 records · Page 37

Model Checker for Java Programs

Java Pathfinder (JPF) is a verification and testing environment for Java that integrates model checking, program analysis, and testing. JPF consists of a custom-made Java Virtual Machine (JVM) that interprets bytecode, combined with a search interface to allow the complete behavior of a Java program to be analyzed, including interleavings of concurrent programs. JPF is implemented in Java, and its architecture is highly modular to support rapid prototyping of new features. JPF is an explicit-state model checker, because it enumerates all visited states and, therefore, suffers from the state-explosion problem inherent in analyzing large programs. It is suited to analyzing programs less than 10kLOC, but has been successfully applied to finding errors in concurrent programs up to 100kLOC. When an error is found, a trace from the initial state to the error is produced to guide the debugging. JPF works at the bytecode level, meaning that all of Java can be model-checked. By default, the software checks for all runtime errors (uncaught exceptions), assertions violations (supports Java s assert), and deadlocks. JPF uses garbage collection and symmetry reductions of the heap during model checking to reduce state-explosion, as well as dynamic partial order reductions to lower the number of interleavings analyzed. JPF is capable of symbolic execution of Java programs, including symbolic execution of complex data such as linked lists and trees. JPF is extensible as it allows for the creation of listeners that can subscribe to events during searches. The creation of dedicated code to be executed in place of regular classes is supported and allows users to easily handle native calls and to improve the efficiency of the analysis.

Visser, Willem↗

Co-Benefits of Mitigating Aerosol Pollution to Future Solar and Wind Energy in China Toward Carbon Neutrality

The climate commitment to achieving carbon neutrality before 2060 in China has been announced recently. In the context of pursuing carbon neutrality, sharing similar sources as greenhouse gases, aerosol particle and precursor emissions are projected to substantially decrease in China, which can potentially have a great impact on climate. Here, we investigate the effects of future aerosol reductions, because of achieving carbon neutrality, on solar and wind energy in China by using an earth system model. We show that significant reductions in aerosol emissions, particularly in eastern China, lead to increases in the surface downwelling shortwave radiation, surface air temperature and wind speed, which can further enhance the potential of solar and wind energy production. The findings underline that the pursuit of carbon neutrality can yield co-benefits of not only mitigating climate change and air pollution but also fortifying the stability of renewable energy sources.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Reducing uncertainty of polar to midlatitude linkages using DOE’s E3SM in a coordinated model-experiment setting

This project brought DOE’s climate modeling effort with the Energy Exascale Earth System Model into the Polar Amplification Model Intercomparison Project (PAMIP), which is part of the sixth and latest Coupled Model Intercomparison Project, CMIP6. PAMIP examines the causes and consequences of polar amplification, when external forcing results in a larger temperature increase in high latitudes than the global average, in a coordinated set of model experiments with a common modeling protocol. Our teams from UC Irvine and the University of Toronto have designed, carried out, analyzed, and disseminated PAMIP output from the Energy Exascale Earth System Model (E3SM) and the Community Earth System Model (CESM). PAMIP’s ongoing stream of significant new results have advanced progress in the community’s understanding and led to new outstanding research questions that have motivated further work. PAMIP has led to improved consensus on the atmospheric response to sea ice loss. The important finding is that for a similar sea ice anomaly forcing, the simulated atmospheric response in the troposphere is remarkably consistent among the 16 models’ runs analyzed. The zonal-mean tropospheric response consists of a very robust equatorward shift of the westerly flow in mid-latitudes. However, while the multi-model mean response is robust, it has a weak amplitude relative to internal variability. We identified a weakness in the models (including E3SM) in terms of their response to sea-ice forcing that is related to eddy forcing (or nonlinear dynamical effects) at mid- to high latitudes. In fact, E3SM is an outlier in terms of the models participating, and in that sense, it turned out to be a vital participant model. We found that reductions in energy transport due sea-ice loss and involving dry air only are compensated by increases in moist energy transport from warmer sea surface temperature in midlatitudes. This leads to a large spread in energy transport into the Arctic and is a potential source of spread in Arctic amplification. We identified an important role that climate modes, including tropical modes of variability (El Nino and the Southern Oscillation (ENSO); the Quasi-biennial Oscillation (QBO)) play in the response to sea-ice anomalies, including in ocean coupled experiments. Similarly, we identified and quantified the contribution of sea-ice thickness to the atmospheric response compared to the response to sea-ice extent only. We found that it is important to run large ensembles and even with an ensemble size of 100 simulations the response is largely influenced by internal variability. We demonstrated convincingly that Ural blocking, not sea-ice loss, provides the weakening of the stratospheric polar vortex in fall/early winter and a negative phase of the North Atlantic Oscillation that can last for up to two months. However, sea-ice anomalies can influence the background flow so that the response to Ural blocking is more persistent under low sea-ice conditions in the Barents/Kara Sea than high sea ice Atmospheric model hierarchies that progressively add individual processes have a long history in providing dynamical insight for modeling the atmosphere. Similarly, coupled model hierarchies that progressively add individual ocean processes can provide insights into the workings of the coupled climate system, however such hierarchies have not been available except for a non-dynamical slab ocean model. Because of the missing processes, surface flux corrections must be added to produce a target climate. In this project, we managed to overcome this problem and develop a globally coupled ocean model hierarchy in CESM that can turn on and off the processes of mixed-layer entrainment and Ekman flow. We used the hierarchy to study the impact of Arctic sea-ice loss on the climate system. We find that the effect of mixed-layer entrainment on ocean heat uptake influences the atmospheric circulation by shifting the latitudinal positions of the mid-latitude westerly jet and the Intertropical Convergence Zone (ITCZ). In quadrupled CO 2 experiments, we studied how air-sea coupling affects the response of tropical rainfall under global warming. In order to identify the importance of individual ocean processes, we used the hierarchy of ocean models to separate the effects of seasonal mixed-layer entrainment, wind-driven Ekman flows, and frictional flows. We showed that including Ekman and frictional flows allows our simulation to produce the Pacific Ocean's enhanced equatorial warming pattern and equatorward ITCZ contraction noted in previous climate simulations. We also showed that the frictional flow, which has yet to receive much attention, is as important as the Ekman flow in generating equatorial heat convergence.

54 ENVIRONMENTAL SCIENCES↗

Future Climate Change Under SSP Emission Scenarios with GISS-E2.1

This paper presents the response to anthropogenic forcing in the GISS-E2.1 climate models for the 21st century Shared Socioeconomic Pathways emission scenarios within the Coupled Model Intercomparison Project Phase 6 (CMIP6). The experiments were performed using an updated and improved version of the NASA Goddard Institute for Space Studies (GISS) coupled general circulation model that includes two different versions for atmospheric composition: A non-interactive version (NINT) with prescribed composition and a tuned aerosol indirect effect and the One-Moment Aerosol model (OMA) version with fully interactive aerosols which includes a parameterized first indirect aerosol effect on clouds. The effective climate sensitivities are 3.0°C and 2.9°C for the NINT and OMA models, respectively. Each atmospheric version is coupled to two different ocean general circulation models: The GISS ocean model (E2.1-G) and HYCOM (E2.1-H). We describe the global mean responses for all future scenarios and spatial patterns of change for surface air temperature and precipitation for four of the marker scenarios: SSP1-2.6, SSP2-4.5, SSP4-6.0, and SSP5-8.5. By 2100, global mean warming ranges from 1.5°C to 5.2°C relative to 1,850–1,880 mean temperature. Two high-mitigation scenarios SSP1-1.9 and SSP1-2.6 limit the surface warming to below 2°C by the end of the 21st century, except for the NINT E2.1-H model that simulates 2.2°C of surface warming. For the high emission scenario SSP5-8.5, the range is 4.6–5.2°C at 2100. Due to about 15% larger effective climate sensitivity and stronger transient climate response in both NINT and OMA CMIP6 models compared to CMIP5 versions, there is a stronger warming by 2100 in the SSP emission scenarios than in the comparable Representative Concentration Pathway (RCP) scenarios in CMIP5. Changes in sea ice area are highly correlated to global mean surface air temperature anomalies and show steep declines in both hemispheres, with the largest sea ice area decreases occurring during September in the Northern Hemisphere in both E2.1-G (−1.21 × 106 km2/°C) and E2.1-H models (−0.94 × 106 km2/°C). Both coupled models project decreases in the Atlantic overturning stream function by 2100. The largest decrease of 56%–65% in the 21st century overturning stream function is produced in the warmest scenario SSP5-8.5 in the E2.1-G model, comparable to the reduction in the corresponding CMIP5 GISS-E2 RCP8.5 simulation. Both low-end scenarios SSP1-1.9 and SSP1-2.6 also simulate substantial reductions of the overturning (9%–37%) with slow recovery of about 10% by the end of the 21st century (relative to the maximum decrease at the middle of the 21st century).

climate models↗

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING↗

Influence of Shear Stiffness Degradation on Crack Paths in Uni-Directional Composite Laminates

Influence of shear stiffness degradation in an element, due to damage, on crack paths in uni-directional laminates has been demonstrated. A new shear stiffness degradation approach to improve crack path prediction has been developed and implemented in an ABAQUS/Explicit frame work using VUMAT. Three progressive failure analysis models, built-in ABAQUS (TradeMark), original COmplete STress Reduction (COSTR) and the modified COSTR damage models have been utilized in this study to simulate crack paths in five unidirectional notched laminates, 15deg, 30deg, 45deg, 60deg and 75deg under uniaxial tension load. Results such as crack paths and load vs. edge displacement curves are documented in this report. Modified COSTR damage model shows better accuracy in predicting crack paths in all the uni-directional laminates compared to the ABAQUS (TradeMark) and the original COSTR damage models.

Satyanarayana, Arunkumar↗

Application of modern structural optimization to vibration reduction in rotorcraft

The helicopter rotor model consists of a four bladed hingeless rotor attached to a fuselage. The helicopter is assumed to be in trimmed forward flight. Each blade is assumed to have flap, lag, and torsional degrees of freedom. The fuselage degrees of freedom are not included in the analysis. Thus the aeroelastic stability and response analysis upon which this study is based is an isolated blade analysis. The helicopter rotor vibration reduction problem expressed as a general class of structural synthesis problems is given.

Friedmann, P. P.↗

Dynamic analysis of nonlinear rotor-housing systems

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.

Noah, Sherif T.↗

Unraveling membrane electrode assembly design for electrochemical conversion of carbon dioxide to formate/formic acid

This work presents a one-dimensional continuum modeling approach to investigate various cell architectures used for electrochemical conversion of CO 2 to formate/formic acid. Ion transport is simulated by a system of generalized modified Poisson–Nernst–Planck (GMPNP) equations that reflect the reactive transport phenomena including steric effects as the electrolyte solutions become concentrated. In the cathode catalyst layer, ionic current contributions from both the supporting electrolyte and solid-state ionomer are considered. Voltage and CO 2 utilization breakdowns are utilized to deconvolute the impacts of the cell architecture. The origins of (bi)carbonate formation in the cathode are explored, as the subsequent decrease in CO 2 availability is a key reason for low faradaic efficiencies to formate/formic acid. In addition, the role of a supporting electrolyte (KOH) is investigated to understand its tradeoffs: while the K + ions can improve both conductivity and electrochemically active surface area in the cathode, the presence of OH − ions raises the pH and leads to deleterious formation of (bi)carbonates. To this end, we also present parametric studies on the concentration and flow rate of supplied KOH to the cell, to establish a path towards eliminating the need for a supporting electrolyte.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enhancing Interpretability in Generative Modeling: Statistically Disentangled Latent Spaces Guided by Generative Factors in Scientific Datasets

This study addresses the challenge of statistically extracting generative factors from complex, high-dimensional datasets in unsupervised or semi-supervised settings. We investigate encoder-decoder-based generative models for nonlinear dimensionality reduction, focusing on disentangling low-dimensional latent variables corresponding to independent physical factors. Introducing Aux-VAE, a novel architecture within the classical Variational Autoencoder framework, we achieve disentanglement with minimal modifications to the standard VAE loss function by leveraging prior statistical knowledge through auxiliary variables. These variables guide the shaping of the latent space by aligning latent factors with learned auxiliary variables. We validate the efficacy of Aux-VAE through comparative assessments on multiple datasets, including astronomical simulations.

97 MATHEMATICS AND COMPUTING↗

Experiments on a vapor compression air conditioner with liquid desiccants for efficient dehumidification

Buildings require air conditioning systems that not only cool and dehumidify supply air but also provide sufficient ventilation to ensure indoor air quality and occupant comfort. However, standard recirculation systems-which introduce about a 10 % to 20 % fraction of outdoor air-often fail to deliver air that is precisely cooled and dry, particularly because 80-90 % of the ventilation cooling load is latent. Mixing humid ventilation air with recirculated indoor air increases the energy and costs required to condition the air to comfortable levels. Dedicated outdoor air systems (DOASs) are designed to handle this latent dominated ventilation load and thus need to have efficient humidity removal. Many cooling cycles can perform this task. Here we describe a liquid desiccant DOAS, which combines a vapor compression cycle and a liquid desiccant absorber and desorber pair. We present its performance at 26 operating conditions and a thermodynamic model which can accurately predict the moisture removal efficiency. The model's performance predictions have a mean percentage error of 2.5 % and a coefficient of variation of the root mean square error of 7.5 %. We also compare the performance of this vapor-compression-coupled liquid desiccant system with a standard vapor compression system with the same components but no liquid desiccant. For the 26 conditions tested in this study, this comparison shows that adding liquid desiccants lowers the required evaporator cooling load by 21 %, allows for 25 % lower compressor volumetric capacity, and 25 % lower electricity use. Future work will leverage this model to quantify the reduction in annual electricity use across different climates, including the need for a standard vapor compression system to reheat the air during some of the year.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Quantum fisher information reveals UV-IR mixing in the strange metal

The density-density response in optimally doped Bi 2 Sr 2 CaCu 2 O 8+$x$ has recently been shown to exhibit conformal symmetry. Using, the experimentally inferred conformal dynamic susceptibility, we compute the resultant quantum Fisher information (QFI), a witness to multi-partite entanglement. For a Fermi liquid, we find that the QFI grows quadratically as the temperature increases, consistent then with the phase space available for scattering in the standard theory of metals. By contrast, the QFI in a strange metal increases as a power law at as the temperature decreases, but ultimately extrapolates to a constant at T=0. The constant is of the form, ω$^{2Δ}_g$, where Δ is the conformal dimension and ω g is the UV cutoff which is on the order of the pseudogap. As this constant depends on both UV and IR properties, it illustrates that multipartite entanglement in a strange metal exhibits UV-IR mixing, a benchmark feature of doped Mott insulators as exemplified by dynamical spectral weight transfer. We conclude with a discussion of the implication of our results for low-energy reductions of the Hubbard model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Adsorption of Mixed Micelles of Polysorbate 80 and Oleic Acid to the Air–Water Interface

The solubilization of long chain amphiphiles with limited solubility into mixed micelles composed of highly soluble surfactants plays a crucial role in modulating the stability and functionality of formulations in pharmaceutical and food systems. Subsequently, the mixed micelles adsorb from solution to the air−water surface, defining the transport mechanism of the insoluble amphiphiles to the interface. We use X-ray reflectivity to measure the composition and provide insight into the structure of these mixed monolayers, and, alongside interfacial tension measurements, we provide an understanding of how the bulk composition determines the surface composition and the dynamics of tension reduction. We use a model system consisting of an insoluble fatty acid, oleic acid (OA), and a soluble micelle-forming surfactant, polysorbate 80 (PS80). PS80 forms spherical micelles, and, above the critical micelle concentration (cmc), OA is readily solubilized inside the micelles. We show that the adsorption of PS80/OA mixed micelles to the air−water interface rapidly reduces the tension and lowers the equilibrium tension in proportion to the OA concentration. X-ray reflectivity data, fit using Parratt-slab models, quantitively demonstrates that the monolayers become enriched with OA, and we show how the OA intercalates into the PS80 monolayers.

36 MATERIALS SCIENCE↗

Calibration and validation of the foundation for a multiphase strength model for tin

In this work, the Common Model of Multi-phase Strength and Equation of State (CMMP) model was applied to tin. Specifically, calibrations of the strength-specific elements of the CMMP foundation were developed with a combination of experiments and theory, and then the model was validated experimentally. The first element of the foundation is a multi-phase analytic treatment of the melt temperature and the shear modulus for the solid phases. These models were parameterized for each phase based on ab initio calculations using the software VASP (Vienna Ab initio Simulations Package) based on density functional theory. The shear modulus model for the ambient phase was validated with ultrasonic sound speed measurements as a function of pressure and temperature. The second element of the foundation is a viscoplastic strength model for the phase, upon which strength for inaccessible higher-pressure phases can be scaled as necessary. The stress–strain response of tin was measured at strain rates of 10 -3 to 3 x 10 3 s -1 and temperatures ranging from 87 to 373 K. The Preston–Tonks–Wallace (PTW) strength model was fit to that data using Bayesian model calibration. For validation, six forward and two reverse Taylor impact experiments were performed at different velocities to measure large plastic deformation of tin at strain rates up to ⁠10 5 s -1 . The PTW model accurately predicted the deformed shapes of the cylinders, with modest discrepancies attributed to the inability of PTW to capture the effects of twinning and dynamic recrystallization. Some material in the simulations of higher velocity Taylor cylinders reached the melting temperature, thus testing the multiphase model because of the presence of a second phase, the liquid. In simulations using a traditional modeling approach, the abrupt reduction of strength upon melt resulted in poor predictions of the deformed shape and non-physical temperatures. With CMMP, the most deformed material points evolved gradually to a mixed solid–liquid but never a fully liquid state, never fully lost strength, stayed at the melt temperature as the latent heat of fusion was absorbed, and predicted the deformed shape well.

36 MATERIALS SCIENCE↗

Quantum error mitigation for Fourier moment computation

Hamiltonian moments in Fourier space—expectation values of the unitary evolution operator under a Hamiltonian at different times—provide a convenient framework to understand quantum systems. They offer insights into the energy distribution, higher-order dynamics, response functions, correlation information, and physical properties. This paper focuses on the computation of Fourier moments within the context of a nuclear effective field theory on superconducting quantum hardware. The study integrates echo verification and noise renormalization into Hadamard tests using control reversal gates. These techniques, combined with purification and error suppression methods, effectively address quantum hardware decoherence. The analysis, conducted using noise models, reveals a significant reduction in noise strength by two orders of magnitude. Moreover, quantum circuits involving up to 266 gates over five qubits demonstrate high accuracy under these methodologies when run on IBM superconducting quantum devices. Published by the American Physical Society 2025

Kiss, Oriel (ORCID:0000000174613342)↗

Accelerating particle-in-cell kinetic plasma simulations via reduced-order modeling of space-charge dynamics using dynamic mode decomposition

We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. Here, we demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Calibration and validation of the foundation for a multiphase strength model for tin

In this work, the Common Model of Multi-phase Strength and Equation of State (CMMP) model was applied to tin. Specifically, calibrations of the strength-specific elements of the CMMP foundation were developed with a combination of experiments and theory, and then the model was validated experimentally. The first element of the foundation is a 10 multi-phase analytic treatment of the melt temperature and the shear modulus for the solid phases. These models were parameterized for each phase based on ab initio calculations using the software VASP (Vienna Ab initio Simulations Package) based on density functional theory (DFT). The shear modulus model for the ambient β phase was validated with ultrasonic sound speed measurements as a function of pressure and temperature. The second element of the foundation is a viscoplastic strength model for the β phase, upon which strength for inaccessible higher-pressure phases can be scaled as necessary. The stress-strain response of tin was measured at strain rates of 10 -3 to 3 x 10 3 s -1 and temperatures ranging from 87 to 373 K. The Preston-Tonks-Wallace (PTW) strength model was fit to that data using Bayesian model calibration. For validation, six forward and two reverse Taylor impact experiments were performed at different velocities to measure large plastic deformation of tin at strain rates up to 10 5 s -1 . The PTW model accurately predicted the deformed shapes of the cylinders, with modest discrepancies attributed to the inability 20 of PTW to capture the effects of twinning and dynamic recrystallization. Some material in the simulations of higher velocity Taylor cylinders reached the melting temperature, thus testing the multiphase model because of the presence of a second phase, the liquid. In simulations using a traditional modeling approach, the abrupt reduction of strength upon melt resulted in poor predictions of the deformed shape and non-physical temperatures. With CMMP, the most deformed material points evolved gradually to a mixed solid-liquid but never fully liquid state, never fully lost strength, 25 stayed at the melt temperature as the latent heat of fusion was absorbed, and predicted the deformed shape well.

36 MATERIALS SCIENCE↗

A new upper limit to the local population II density.

An upper limit to the local population II density is derived, in terms of the mass-luminosity ratio, on the basis of U, B, and V photometric observations of several thousand stars with V magnitudes between 12 and 18 in a region near the North Galactic Pole. The photographic and photoelectric photometry and the reduction procedures are discussed. Models of the density distribution and luminosity function of the population II stars are used to predict their distribution in color and apparent magnitude. The derived local density of population II is found to be significantly lower than previous estimates. Possible causes for this discrepancy are considered.

Weistrop, D.↗