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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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NASA NTRS1986

Self-regulated cooling flows in elliptical galaxies and in cluster cores - Is exclusively low mass star formation really necessary?

A self-consistent treatment of the heating by supernovae associated with star formation in a spherically symmetric cooling flow in a cluster core or elliptical galaxy is presented. An initial stellar mass function similar to that in the solar neighborhood is adopted. Inferred star-formation rates, within the cooling region - typically the inner 100 kpc around dominant galaxies at the centers of cooling flows in XD clusters - are reduced by about a factor of 2, relative to rates inferred when the heat input from star formation is ignored. Truncated initial mass functions (IMFs) are also considered, in which massive star formation is suppressed in accordance with previous treatments, and colors are predicted for star formation in cooling flows associated with central dominant elliptical galaxies and with isolated elliptical galaxies surrounded by gaseous coronae. The low inferred cooling-flow rates around isolated elliptical galaxies are found to be insensitive to the upper mass cutoff in the IMF, provided that the upper mass cutoff exceeds 2 M solar mass. Comparison with observed colors favors a cutoff in the IMF above 1 M solar mass in at least two well-studied cluster cooling flows, but a normal IMF cannot be excluded definitively. Models for NGC 1275 support a young (less than about 3 Gyr) cooling flow. As for the isolated elliptical galaxies, the spread in colors is consistent with a normal IMF. A definitive test of the IMF arising via star formation in cooling flows requires either UV spectral data or supernova searches in the cooling-flow-centered galaxies.

Silk, J.↗
NASA NTRS1990

Star formation in small globules - Bart Bok was correct

A large sample of optically selected, small molecular clouds (Bok globules) has been probed using IRAS coadded images to search for associated young stellar objects. The IRAS images were examined for point sources located within the boundaries of the optical and infrared extents of 248 clouds. A total of 57 of the globules (23 percent of the sample) show evidence for associated point sources. From a comparison of the 12- and 25-micron fluxes of these objects, a distribution of spectral indices consistent with the presence of circumstellar dust is found. Similar analysis of other point sources within the IRAS images, but far from the globule boundaries, shows only normal stellar spectral indices. All young stars more massive than 0.7 solar masses were likely found. However, extrapolation of a Miller-Scalo (1979) initial mass function to the hydrogen-burning limit indicates that only about 20 percent of the total number of stars were found. It is therefore likely that almost every Bok globule harbors a young star. The inferred star formation efficiency is about 6 percent, again based on the Miller-Scalo initial mass function. Interestingly, this is the best test in 43 years of the conjecture made by Bok, that dust globules could represent the earliest stage of star formation. His conjecture was correct.

Yun, Joao Lin↗
DOE OSTI2022

Constraining dark matter microphysics with the annihilation signal from subhalos

In the cold dark matter scenario, galactic dark matter halos are populated with a large number of smaller subhalos. Previous work has shown that dark matter annihilations in subhalos can generate a distinctive, non-Poisson signal in the gamma-ray photon counts probability distribution function (PDF). Here we show that the gamma-ray PDF also carries information about the velocity dependence of the dark matter annihilation cross section. After calculating the PDF assuming s-wave and Sommerfeld-enhanced annihilation, we perform a mock data analysis to illustrate how current and future observations can constrain the microphysics of the dark matter annihilation. We find that, with current Fermi data, and assuming a dark matter annihilation cross section roughly at the limit of current bounds from annihilation in dwarf spheroidal galaxies, one can potentially distinguish the non-Poissonian fluctuations expected from dark matter annihilation in subhalos from Poisson sources, as well as from dark matter models with an incorrect velocity-dependence. Here we explore how robust these results are to assumptions about the modeling of the galactic gamma-ray background, but further work is needed to determine the impact of realistic astrophysical source populations on our results. We also point out a four-parameter degeneracy between the velocity dependence of the dark matter annihilation, the minimum subhalo mass, the power law index of the subhalo mass function, and the normalization of the dark matter signal. This degeneracy can be broken with priors from N-body simulations or from observational constraints on the subhalo mass function.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

On the determination of the number of O stars in H II regions and starburst galaxies

The hot star population in H II regions, H II galaxies, and starburst galaxies is often described in terms of the number of 'equivalent' O stars of a single representative subtype and luminosity class needed to produce the ionizing luminosity deduced from the nebular recombination lines in the optical spectra. In this paper we define conversion factors eta(sub 0), eta(sub 1), and zeta(sub 5000) with which the total number of O V stars and their flux contribution at 5000 A can be derived from the number of these 'equivalent' stars. These quantities depend primarily on three parameters: the slope and upper mass limit of the stellar mass function and the metallicity of the region. Using the latest stellar atmosphere and evolution models, we calculate eta(sub 0), eta(sub 1), and zeta(sub 5000) for a large number of values of these parameters. The results are presented in tabular as well as graphical form. We apply our results to two H II regions for which the hot star population are known and find that the predicted numbers of O stars agree well the observed counts. In addition, we describe a method by which the values of eta(sub 0) and eta(sub 1) and the observed emission-line fluxes can be used to place constraints on the allowed values of the slope and upper mass limit of the stellar mass function in a region.

Vacca, William D.↗
DOE OSTI2020

Chemical Analysis of the Ultrafaint Dwarf Galaxy Grus II. Signature of High-mass Stellar Nucleosynthesis

We present a detailed abundance analysis of the three brightest member stars at the top of the giant branch of the ultrafaint dwarf (UFD) galaxy Grus II. All stars exhibit a higher than expected [Mg/Ca] ratio compared to metal-poor stars in other UFD galaxies and in the Milky Way (MW) halo. Nucleosynthesis in high-mass ( 20 M ⊙) core-collapse supernovae has been shown to create this signature. The abundances of this small sample (three) stars suggests the chemical enrichment of Grus II could have occurred through substantial high-mass stellar evolution, and is consistent with the framework of a top-heavy initial mass function. However, with only three stars it cannot be ruled out that the abundance pattern is the result of a stochastic chemical enrichment at early times in the galaxy. The most metal-rich of the three stars also possesses a small enhancement in rapid neutron-capture (r-process) elements. The abundance pattern of the r-process elements in this star matches the scaled r-process pattern of the solar system and r-process enhanced stars in other dwarf galaxies and in the MW halo, hinting at a common origin for these elements across a range of environments. All current proposed astrophysical sites of r-process element production are associated with high-mass stars, thus the possible top-heavy initial mass function of Grus II would increase the likelihood of any of these events occurring. The time delay between the α and r-process element enrichment of the galaxy favors a neutron star merger as the origin of the r-process elements in Grus II.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

A hydrodynamic approach to cosmology: The mixed dark matter cosmological scenario

We compute the evolution of spatially flat, mixed cold and hot dark matter models containing both baryonic matter and two kinds of dark matter. Hydrodynamics is treated with a highly developed Eulerian hydrodynamic code (see Cen 1992). A standard particle-mesh (PM) code is also used in parallel to calculate the motion of the dark matter components. We adopt the following parameters: h equivalent to (sub 0)/100 km/s Mpc(exp -1) = 0.5, OMEGA(sub C) = 0.3, and OMEGA(sub B) = 0.06, with amplitude of the perturbation spectrum fixed by the Cosmic Background Explorer Satellite (COBE) Dark Matter Radiation (DMR) measurements (Smoot et al. 1992) being sigma (sub 8) = 0.67. Four different boxes are simulated with box sizes of L = (64, 16, 4, 1) h(exp -1) Mpc, respectively, the two small boxes providing good resolution but little valid information due to absence of large-scale power. We use 128(exp 3) approximate 10(exp 6.3) baryonic cells, 128(exp .3) cold dark matter particles, and 2 x 128(exp 3) hot dark matter particles. In addition to the dark matter we follow separately six baryonic species (H, H(+), He, He(+), He(++), e(-)) with allowance for both (nonequilibrium) collisional and radiative ionization in every cell. The background radiation field is also followed in detail with allowance made for both continuum and line processes, to allow nonequilibrium heating and cooling processes to be followed in detail. The mean final Zeldovich-Sunyaev y parameter is estimated to be y Bar = (5.4 + or - 2.7) x 10(exp -7) below currently attainable observations, with a rms fluctuation of approximately delta bar y = (0.6 + or - 3.0) x 10(exp -7) on arcminute scales. The rate of galaxy formation peaks at an even later epoch (z approximate 0.3) than in the standard (OMEGA = 1, sigma sub 8 = 0.67) cold dark matter (CDM) model (z approximate 0.5) and, at a redshift of z = 4, is nearly a factor of 100 lower than for the CDM model with the same value of sigma sub 8. With regard to mass function, the smallest objects are stabilized against collapse by thermal energy: the mass-weighted mass spectrum has a broad peak in the vicinity of M(sub B) = 10(exp 9.5) solar mass with a reasonable fit to the Schechter luminosity function if the ratio of baryon mass to blue light is approximately 4. In addition, one very large PM simulation was made in a box with size (320 h(exp - 1) Mpc) containing 3 x 200(exp 3) = 10(exp 7.4) particles. Utilizing this simulation we find that the model yields a cluster mass function which is about a factor of 4 higher than observed, but a cluster-cluster correlation length marginally lower than observed, but that both are closer to observations than in the (COBE) normalized CDM model. The one-dimensional pairwise velocity dispersion is 605 + or - 8 km/s at 1/h separation, lower than that of the DCM model normalized to COBE, but still significant higher than observations (Davis & Peebles 1983). A plausible velocity bias b(sub v) = 0.8 + or - 0.1 on this scale will reduce but not remove the discrepancy. The velocity auto-correlat ion function has a coherence length of 40/h Mpc, which is somewhat lower than the observed counterpart. In all these respects the model would be improved by decreasing the cold fraction of the dark OMEGA(sub CDM)/ (OMEGA(sub CDM) + OMEGA(sub HDB). But formation of galaxies and clusters of galaxies is much later in this model than in COBE-normalized CDM, perhaps too late. To improve on these constraints a larger ratio of OMEGA(sub CDM)/ (OMEGA(sub CDM) + OMEGA(sub HDM)) is required than the value of 0.67 adopted here. It does not seem possible to find a value for this ratio which would satisfy all tests. Overall, the model is similar both on large and intermediate scales to the standard CDM model normalized to the same value of sigma(sub B), but the problem with regard to late formation of galaxies is more severe in this model than in that CDM model. Adding hot dark matter, significantly improves the ability of the COBE-normalized CDM scenario to fit existing observations, but the model is in fact not as good as the CDM model with the same sigma(sub 8) and is still probably unsatisfactory with regard to several critical tests.

Cen, Renyue↗
DOE OSTI2021

Comparing galaxy formation in the L-GALAXIES semi-analytical model and the IllustrisTNG simulations

ABSTRACT We perform a comparison, object by object and statistically, between the Munich semi-analytical model, L-GALAXIES, and the IllustrisTNG hydrodynamical simulations. By running L-GALAXIES on the IllustrisTNG dark matter-only merger trees, we identify the same galaxies in the two models. This allows us to compare the stellar mass, star formation rate, and gas content of galaxies, as well as the baryonic content of subhaloes and haloes in the two models. We find that both the stellar mass functions and the stellar masses of individual galaxies agree to better than ${\sim} 0.2\,$dex. On the other hand, specific star formation rates and gas contents can differ more substantially. At z = 0, the transition between low-mass star-forming galaxies and high-mass quenched galaxies occurs at a stellar mass scale ${\sim} 0.5\,$dex lower in IllustrisTNG than that in L-GALAXIES. IllustrisTNG also produces substantially more quenched galaxies at higher redshifts. Both models predict a halo baryon fraction close to the cosmic value for clusters, but IllustrisTNG predicts lower baryon fractions in group environments. These differences are primarily due to differences in modelling feedback from stars and supermassive black holes. The gas content and star formation rates of galaxies in and around clusters and groups differ substantially, with IllustrisTNG satellites less star forming and less gas rich. We show that environmental processes such as ram-pressure stripping are stronger and operate to larger distances and for a broader host mass range in IllustrisTNG. We suggest that the treatment of galaxy evolution in the semi-analytic model needs to be improved by prescriptions that capture local environmental effects more accurately.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Indra: a public computationally accessible suite of cosmological N -body simulations

ABSTRACT Indra is a suite of large-volume cosmological N-body simulations with the goal of providing excellent statistics of the large-scale features of the distribution of dark matter. Each of the 384 simulations is computed with the same cosmological parameters and different initial phases, with 10243 dark matter particles in a box of length 1 h−1 Gpc, 64 snapshots of particle data and halo catalogues, and 505 time-steps of the Fourier modes of the density field, amounting to almost a petabyte of data. All of the Indra data are immediately available for analysis via the SciServer science platform, which provides interactive and batch computing modes, personal data storage, and other hosted data sets such as the Millennium simulations and many astronomical surveys. We present the Indra simulations, describe the data products and how to access them, and measure ensemble averages, variances, and covariances of the matter power spectrum, the matter correlation function, and the halo mass function to demonstrate the types of computations that Indra enables. We hope that Indra will be both a resource for large-scale structure research and a demonstration of how to make very large data sets public and computationally accessible.

Falck, Bridget↗
DOE OSTI2025

Constraints on f ( R ) gravity from thermal-Sunyaev-Zel’dovich-effect-selected SPT galaxy clusters and weak lensing mass calibration from DES and HST

We present constraints on the f ( R ) gravity model using a sample of 1005 galaxy clusters in the redshift range 0.25–1.78 that have been selected through the thermal Sunyaev-Zel’dovich effect from South Pole Telescope data and subjected to optical and near-infrared confirmation with the multicomponent matched filter algorithm. We employ weak gravitational lensing mass calibration from the Dark Energy Survey Year 3 data for 688 clusters at z < 0.95 and from the Hubble Space Telescope for 39 clusters with 0.6 < z < 1.7 . Our cluster sample is a powerful probe of f ( R ) gravity, because this model predicts a scale-dependent enhancement in the growth of structure, which impacts the halo mass function (HMF) at cluster mass scales. To account for these modified gravity effects on the HMF, our analysis employs a semianalytical approach calibrated with numerical simulations. Combining calibrated cluster counts with primary cosmic microwave background temperature and polarization anisotropy measurements from the Planck 2018 release, we derive robust constraints on the f ( R ) parameter f R 0 . Our results, log 10 | f R 0 | < − 5.32 at the 95% credible level, are the tightest current constraints on f ( R ) gravity from cosmological scales. This upper limit rules out f ( R ) -like deviations from general relativity that result in more than a ∼ 20 % enhancement of the cluster population on mass scales M 200 c > 3 × 10 14 M ⊙ . Published by the American Physical Society 2025

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Practical Probabilistic Programming

Recent advances in probabilistic programming languages (PPLs) have provided the capability for exact inference: computing a closed-form probability distribution for a given probabilistic program. In particular, the new language Roulette uses a language oriented programming (LOP) approach, wherein analysts build new programming languages on top of a set of primitives provided by Roulette, which then translates these structures into a weighted model counting problem which can be solved by automated reasoning tools. However, because Roulette provides few convenience features, developing these new languages is challenging even for expert users. We developed a standard library of common probability functions for Roulette with the goal of improved usability. This included approximation of continuous probability density functions using discrete probability mass functions. We demonstrated this approach by modeling a cosmic ray striking a RAM controller. We found that Roulette provides a powerful interface for highly expressive probabilistic programs to be generated. In collaboration with the NNSA Advanced Simulation and Computing program, which resulted in development of a tool called Circulette, we were able to model complex circuits expressed in Verilog using probabilistic programs with an expressivity not previously possible. Our research question that motivated the development of a Roulette standard library was to determine whether non-experts could use a PPL to model relevant problems regarding radiation effects on microelectronics. This standard library improved the expressivity of Roulette by implementing common probability density functions, mathematical operators on distributions, and support for empirical distributions. While Roulette is a powerful modeling language, the untyped, LOP approach makes error messages difficult to understand and requires expert aid. We recommend further research on Roulette, especially with its error messages, to enable improved usability. At the same time, this project demonstrated that for users familiar with Roulette and the LOP approach, Roulette provides powerful new capabilities that can be integrated with other Sandia modeling capabilities.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Discovery of a massive unseen star in LMC X-3

Spectroscopic observations of the optical counterpart of LMC X-3 show it to be a spectroscopic binary in the Large Magellanic Cloud with an orbital period of 1.70 days. The B3 main-sequence primary has a large radial velocity amplitude indicating a mass function of 2.3 solar masses. LMC X-3 is an extremely luminous and variable X-ray source, but no 1.7 day X-ray periodicity has been detected. The lack of optical and X-ray eclipses limits the inclination to less than 70 degrees and implies a mass for the unseen star of more than 9.0 solar masses, if the B star has a normal mass. The system now appears to be the strongest evidence for the existence of a stellar mass black hole and is the first extragalactic example.

Remillard, R.↗
NASA NTRS1988

Cepheid binaries with large mass ratios (M1/M2)

The IUE observations of 3 Cepheid systems (Polaris, FF Aql, and S Sge) are used to derive, or set limits on, the temperatures and masses of the companions. Light from the companions of FF Aql and S Sge from 1700 to 2000 A is consistent with an A5 to A7 main sequence companion for both Cepheids, with a mass of 1.8 solar mass. This mass for the companion of S Sge is smaller than required by the orbital mass function and an evolutionary mass of the Cepheid, suggesting that the companion may itself be a binary. For Polaris, the mass of the companion must be less than 1.8 solar mass.

Evans, Nancy Remage↗
NASA NTRS1990

Meteorite infall as a function of mass - Implications for the accumulation of meteorites on Antarctic ice

Antarctic meteorites are considerably smaller, on average, than those recovered elsewhere in the world, and seem to represent a different portion of the mass distribution of infalling meteorites. When an infall rate appropriate to the size of Antarctic meteorites is used (1000 meteorites 10 grams or larger/sq km/1 million years), it is found that direct infall can produce the meteorite accumulations found on eight ice fields in the Allan Hills region in times ranging from a few thousand to nearly 200,000 years, with all but the Allan Hills Main and Near Western ice fields requiring less than 30,000 years. Meteorites incorporated into the ice over time are concentrated on the surface when the ice flows into a local area of rapid ablation. The calculated accumulation times, which can be considered the average age of the exposed ice, agree well with terrestrial ages for the meteorites and measured ages of exposed ice. Since vertical concentration of meteorites through removal of ice by ablation is sufficient to explain the observed meteorite accumulations, there is no need to invoke mechanisms to bring meteorites from large areas to the relatively small blue-ice patches where they are found. Once a meteorite is on a bare ice surface, freeze-thaw cycling and wind break down the meteorite and remove it from the ice. The weathering lifetime of a 100-gram meteorite on Antarctic ice is on the order of 10,000 + or - 5,000 years.

Huss, Gary R.↗
NASA NTRS1991

Maximum-entropy probability distributions under Lp-norm constraints

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

Dolinar, S.↗
NASA NTRS1992

Evidence for a black hole in the X-ray binary Nova Muscae 1991

Optical photometry and spectroscopy of the X-ray Nova Muscae 1991 in quiescence reveal an orbital period of 10.398 +/- 0.014 hr and an absorption-line velocity curve consistent with a sinusoidal modulation at a half-amplitude of 409 +/- 18 km/s. The spectral type of the secondary star is in the range K0 V to K4 V. The value of the mass function, 3.1 +/- 0.4 solar mass, is a conservative lower limit on the mass of the compact primary and suggests that the primary is a black hole. Further considerations of the binary inclination angle and the mass of the secondary strengthen the black hole model. The folded light curves in the I band and the B + V band resemble ellipsoidal variations, with an additional brightening near one of the maxima in the B + V band. The orbital period is 1.4 percent shorter than the photometric period observed during outburst, as expected if the outburst modulations are analogs of 'superhumps' in dwarf novae. In quiescence, the optical properties of the X-ray binary Nova Muscae 1991 bear a striking resemblance to the black hole binary A0620-00, which extends the basis of similarity that was demonstrated during outburst at X-ray and optical wavelengths.

Remillard, Ronald A.↗
NASA NTRS1993

Dynamics of the young binary LMC cluster NGC 1850

BV CCD images and echelle spectra of 52 supergiants are used to examine the age and internal dynamics of the young binary LMC cluster NGC 1850. A color-magnitude diagram was constructed and found to contain three distinct populations of stars. Using star-subtracted, median filtered BV images, attempts were made to determine ellipticity parameters, BV luminosity profiles were constructed to project radii greater than 40. A power law model was applied to test for the presence of a tidal cutoff in the luminosity profile. Of the 52 stars with echelle spectra, a subset of 36 were used to study the cluster dynamics. A rotational signal in the radial velocities has been detected at the 93-percent confidence level, implying a rotation axis at a position angle of 100 +/- 40 deg. Values for the slope of the mass function were determined using mass luminosity relationships and different forms for the IMF. The current cluster age is similar to its central relaxation time.

Fischer, Philippe↗
NASA NTRS1993

The orbit and companion of the Cepheid S Sge - A probable triple system

New radial velocities for the classical Cepheid S Sge have been obtained and combined with previous observations to derive a new orbit. The revised orbital elements are: gamma, -10.3 +/- 0.4 km/s; K, 15.5 +/- 0.2 km/s; e, 0.23 +/- 0.02; omega, 203.1 +/- 4.2 deg; T0, 39902.3 +/- 6.6 JD; P, 675.79 +/- 0.18 days; f(m), 0.239 +/- 0.010 solar masses; a sin i, 0.935 AU = 139.9 +/- 2.0 x 10 exp 6 km; s.e., 1.2 km/s. The revised elements differ very little from the orbit determined by Herbig and Moore (1952). We have also obtained low resolution IUE spectra to search for the companion. The IUE spectra show excess flux at 1800 A when compared with spectra of the single Cepheid Delta Cep at the same (B-V)0. The spectral type of the companion determined from this flux excess is A7 V to F0 V. However, the mass of such a companion (1.7 to 1.5 solar masses) is smaller than the minimum mass (2.8 solar masses) required by the mass function and an evolutionary mass of the Cepheid. We infer that the companion is itself a short period binary.

Evans, Nancy R.↗
NASA NTRS2001

Filtered Mass Density Function for Design Simulation of High Speed Airbreathing Propulsion Systems

The objective of this research is to develop and implement new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. We have just completed two (2) years of Phase I of this research. This annual report provides a brief and up-to-date summary of our activities during the period: September 1, 2000 through August 31, 2001. In the work within the past year, a methodology termed "velocity-scalar filtered density function" (VSFDF) is developed and implemented for large eddy simulation (LES) of turbulent flows. In this methodology the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function (PDF) of all of the components of the velocity and scalar vectors. An exact transport equation is derived for the VSFDF in which the effects of the unresolved SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source terms appear in closed form. The remaining unclosed terms in this equation are modeled. A system of stochastic differential equations (SDEs) which yields statistically equivalent results to the modeled VSFDF transport equation is constructed. These SDEs are solved numerically by a Lagrangian Monte Carlo procedure. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed by comparison with results obtained by an Eulerian LES procedure in which the corresponding transport equations for the first two SGS moments are solved. The unclosed SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source in the Eulerian LES are replaced by corresponding terms from VSFDF equation. The consistency of the results is then analyzed for a case of two dimensional mixing layer.

Drozda, T. G.↗