Investigation of Deep Learning-Based Filtered Density Function for Large Eddy Simulation of Turbulent Scalar Mixing

The present investigation focuses on the application of deep neural network (DNN) models to predict the filtered density function (FDF) of mixture fraction in large eddy simulation (LES) of variable density mixing layers with conserved scalar mixing. A systematic training method is proposed to select the DNN-FDF model training sample size and architecture via learning curves, thereby reducing bias and variance. Two DNN-FDF models are developed: one trained on the FDFs generated from direct numerical simulation (DNS), and another trained with low-fidelity simulations in a zero-dimensional pairwise mixing stirred reactor (PMSR). The accuracy and consistency of both DNN-FDF models are established by comparing their predicted scalar filtered moments with those of conventional LES, in which the transport equations corresponding to these moments are directly solved. Further, DNN-FDF approach is shown to perform better than the widely used $\beta$-FDF method, particularly for multi-modal FDF shapes and higher variances. Additionally, DNN-FDF results are also assessed via comparison with data obtained by DNS and the transported FDF method. The latter involves LES simulations coupled with the Monte Carlo (MC) methods which directly account for the mixture fraction FDF. The DNN-FDF results compare favorably with those of DNS and transported FDF method. Furthermore, DNN-FDF models exhibit good predictive capabilities compared to filtered DNS for filtering of highly non-linear functions, highlighting their potential for applications in turbulent reacting flow simulations. Overall, the DNN-FDF approach offers a more accurate alternative to the conventional presumed FDF method for describing turbulent scalar transport in a cost-effective manner

Optimal Fractional Dickey-Fuller Tests for Unit Roots

This article studies the fractional Dickey- Fuller (FDF) test for unit roots recently introduced by Dolado, Gonzalo and Mayoral (2002). Apart from the analogy with the Dickey-Fuller test, the main motivation for their method relies on simulations since these authors do not provide any justification for their particular implementation of the FDF test. In order to give additional rationale to the test, we frame the FDF test in a model where a nuisance or auxiliary parameter is not identified under the null hypothesis. Within this framework we investigate optimality aspects of the class of tests indexed by this auxiliary parameter and show that the test proposed by these authors is not optimal. In addition, we propose feasible FDF tests with good asymptotic and finite sample properties.

The results of the in-flight attitude sensor calibration for the Arthur Holly Compton Gamma Ray Observatory

The Arthur Holly Compton Gamma Ray Observatory (GRO) was launched by the shuttle Atlantis in April 1991. This paper presents the results of the attitude sensor calibration that was performed during the early mission. The GSFC Flight Dynamics Facility (FDF) performed an alignment calibration of the two fixed-head star trackers (FHST's) and two fine Sun sensors (FSS's) on board Compton GRO. The results show a 27-arcsecond shift between the bore sights of the FHST's with respect to prelaunch measurements. The alignments of the two FSS's shifted by 0.20 and 0.05 degree. During the same time period, the Compton GRO science teams performed an alignment calibration of the science instruments with respect to the attitude reported by the on board computer (OBC). In order to preserve these science alignments, FDF adjusted the overall alignments of the FHST's and FSS's, obtained by the FDF calibration, such that when up linked to the OBC, the shift in the OBC-determined attitude is minimized. FDF also calibrated the inertial reference unit (IRU), which consists of three dual-axis gyroscopes. The observed gyro bias matched the bias that was solved for by the OBC. This bias drifted during the first 6 days after release. The results of the FDF calibration of scale factor and alignment shifts showed changes that were of the same order as their uncertainties

Flicker-defined form stimuli are minimally affected by centre-surround lateral contrast interactions

Purpose: Flicker-defined form (FDF) stimuli have recently been adopted for visual field testing. A key difference between FDF and traditional perimetric stimuli is that the entire display background contains flickering dots. The purpose of this study was to determine whether the perception of FDF stimuli is influenced by lateral interactions involving regions beyond the stimulus border in young healthy observers. Methods: Experiment 1 measured the effect of surround size and retinal eccentricity on the detection of the FDF contour. Psychometric functions were collected for surround diameters of 20, 30 and 40°, and with stimuli centered at eccentricities of 0, 10 and 20°. Experiment 2 measured the effect of target-surround temporal phase difference on apparent temporal contrast (flicker strength) of the target for both the FDF stimulus and a solid-field stimulus. Psychometric functions were collected for target-surround phase differences of 0, 45, 90, 135 and 180°. Results: Our results show a mild surround-suppression effect for FDF stimuli that is independent of surround size. Magnitudes of FDF surround suppression were consistent with the reduced temporal contrast energy of the stimulus compared to solid-field stimuli. Conclusion: FDF stimuli necessarily have both flickering target and background. Our results suggest that visual field defects outside the target are unlikely to markedly influence the detection and perception of the FDF stimulus. Nevertheless, mild surround suppression of contrast arises for FDF stimuli, hence interactions between the background and the target area may influence FDF results in conditions that alter centre-surround perceptual effects

Experimental Assessment of ‘subgrid’ scale Probability Density Function Models for Large Eddy Simulation

Filtered density functions (FDFs) of mixture fraction are quantified by analyzing experimental data obtained from two-dimensional planar laser-induced fluorescence scalar measurements in the isothermal swirling flow of a combustor operating at a Reynolds number of 28,662 for three different swirl numbers (0.3, 0.58 and 1.07). Two-dimensional filtering using a box filter was performed on the measured scalar to obtain the filtered variables used for presumed FDF for Large Eddy Simulations (LES). A dependant variable from the measured scalar, which was a pre-computed temperature, was integrated over the experimentally obtained FDF as well as over the presumed beta or top-hat FDFs and a relative error in temperature prediction was calculated. The experimentally measured FDFs depended on swirl numbers and axial and radial positions in the flow. The FDFs were unimodal in the regions of low variance and bimodal in the regions of high variance. The influence of the filter spatial dimension on the measured FDF was evaluated and consequences for subgrid modeling for LES discussed

Progress in the Prediction of Entropy Generation in Turbulent Reacting Flows Using Large Eddy Simulation

An overview is presented of the recent developments in the application of large eddy simulation (LES) for prediction and analysis of local entropy generation in turbulent reacting flows. A challenging issue in such LES is subgrid-scale (SGS) modeling of filtered entropy generation terms. An effective closure strategy, recently developed, is based on the filtered density function (FDF) methodology with inclusion of entropy variations. This methodology, titled entropy FDF (En-FDF), is the main focus of this article. The En-FDF has been introduced as the joint velocity-scalar-turbulent frequency-entropy FDF and the marginal scalar-entropy FDF. Both formulations contain the chemical reaction and its entropy generation effects in closed forms. The former constitutes the most comprehensive form of the En-FDF and provides closure for all of the unclosed terms in LES transport equations. The latter is the marginal En-FDF and accounts for entropy generation effects, as well as scalar-entropy statistics. The En-FDF methodologies are described, and some of their recent predictions of entropy statistics and entropy generation in turbulent shear flows are presented

Evolution and Reengineering of NASA's Flight Dynamics Facility (FDF)

The NASA Goddard Space Flight Center's Flight Dynamics Facility (FDF) is a multimission support facility that performs ground navigation and spacecraft trajectory design services for a wide range of scientific satellites. The FDF also supports the NASA Space Network by providing orbit determination and tracking data evaluation services for the Tracking Data Relay Satellite System (TDRSS). The FDF traces its history to early NASA missions in the 1960's, including navigation support to the Apollo lunar missions. Over its 40 year history, the FDF has undergone many changes in its architecture, services offered, missions supported, management approach, and business operation. As a fully reimbursable facility (users now pay 100% of all costs for FDF operations and sustaining engineering activities), the FDF has faced significant challenges in recent years in providing mission critical products and services at minimal cost while defining and implementing upgrades necessary to meet future mission demands. This paper traces the history of the FDF and discusses significant events in the past that impacted the FDF infrastructure and/or business model, and the events today that are shaping the plans for the FDF in the next decade. Today's drivers for change include new mission requirements, the availability of new technology for spacecraft navigation, and continued pressures for cost reduction from FDF users. Recently, the FDF completed an architecture study based on these drivers that defines significant changes planned for the facility. This paper discusses the results of this study and a proposed implementation plan. As a case study in how flight dynamics operations have evolved and will continue to evolve, this paper focuses on two periods of time (1992 and the present) in order to contrast the dramatic changes that have taken place in the FDF. This paper offers observations and plans for the evolution of the FDF over the next ten years. Finally, this paper defines the mission model of the future for the FDF based on NASA's current mission list and planning for the Constellation Program. As part of this discussion the following are addressed: the relevance and benefits of a multi-mission facility for NASA's navigation operations in the future; anticipated technologies affecting ground orbit determination; continued incorporation of Commercial Off-the-shelf (COTS) software into the FDF; challenges of a business model that relies entirely on user fees to fund facility upgrades; anticipated changes in flight dynamics services required; and considerations for defining architecture upgrades given a set of cost drivers

The star formation rate history in the FORS Deep and GOODS South Fields

We measure the star formation rate (SFR) as a function of redshift z up to z \~4.5, based on B, I and (I+B) selected galaxy catalogues from the FORS Deep Field (FDF) and the K-selected catalogue from the GOODS-South field. Distances are computed from spectroscopically calibrated photometric redshifts accurate to (Delta_z / (z_spec+1)) ~0.03 for the FDF and ~0.056 for the GOODS-South field. The SFRs are derived from the luminosities at 1500 Angstroem. We find that the total SFR estimates derived from B, I and I+B catalogues agree very well (\lsim 0.1 dex) while the SFR from the K catalogue is lower by ~0.2 dex. We show that the latter is solely due to the lower star-forming activity of K-selected intermediate and low luminosity (L<L_*) galaxies. The SFR of bright (L>L_*) galaxies is independent of the selection band, i.e. the same for B, I, (I+B), and K-selected galaxy samples. At all redshifts, luminous galaxies (L>L_*) contribute only ~1/3 to the total SFR. There is no evidence for significant cosmic variance between the SFRs in the FDF and GOODs-South field, ~0.1 dex, consistent with theoretical expectations. The SFRs derived here are in excellent agreement with previous measurements provided we assume the same faint-end slope of the luminosity function as previous works (alpha ~ -1.6). However, our deep FDF data indicate a shallower slope of alpha=-1.07, implying a SFR lower by ~0.3 dex. We find the SFR to be roughly constant up to z ~4 and then to decline slowly beyond, if dust extinctions are assumed to be constant with redshift.Comment: 6 pages, 2 figures, Accepted for publication in ApJ