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DOE OSTI2020

Deeply uncertain: comparing methods of uncertainty quantification in deep learning algorithms

We present a comparison of methods for uncertainty quantification (UQ) in deep learning algorithms in the context of a simple physical system. Three of the most common uncertainty quantification methods - Bayesian Neural Networks (BNN), Concrete Dropout (CD), and Deep Ensembles (DE) - are compared to the standard analytic error propagation. We discuss this comparison in terms endemic to both machine learning ("epistemic" and "aleatoric") and the physical sciences ("statistical" and "systematic"). The comparisons are presented in terms of simulated experimental measurements of a single pendulum - a prototypical physical system for studying measurement and analysis techniques. Our results highlight some pitfalls that may occur when using these UQ methods. For example, when the variation of noise in the training set is small, all methods predicted the same relative uncertainty independently of the inputs. This issue is particularly hard to avoid in BNN. On the other hand, when the test set contains samples far from the training distribution, we found that no methods sufficiently increased the uncertainties associated to their predictions. This problem was particularly clear for CD. In light of these results, we make some recommendations for usage and interpretation of UQ methods.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1993

Computation of large-scale statistics in decaying isotropic turbulence

We have performed large-eddy simulations of decaying isotropic turbulence to test the prediction of self-similar decay of the energy spectrum and to compute the decay exponents of the kinetic energy. In general, good agreement between the simulation results and the assumption of self-similarity were obtained. However, the statistics of the simulations were insufficient to compute the value of gamma which corrects the decay exponent when the spectrum follows a k(exp 4) wave number behavior near k = 0. To obtain good statistics, it was found necessary to average over a large ensemble of turbulent flows.

Chasnov, Jeffrey R.↗

NASA NTRS2011

Precipitation Estimates for Hydroelectricity

Hydroelectric plants require precise and timely estimates of rain, snow and other hydrometeors for operations. However, it is far from being a trivial task to measure and predict precipitation. This paper presents the linkages between precipitation science and hydroelectricity, and in doing so it provides insight into current research directions that are relevant for this renewable energy. Methods described include radars, disdrometers, satellites and numerical models. Two recent advances that have the potential of being highly beneficial for hydropower operations are featured: the Global Precipitation Measuring (GPM) mission, which represents an important leap forward in precipitation observations from space, and high performance computing (HPC) and grid technology, that allows building ensembles of numerical weather and climate models.

Tapiador, Francisco J.↗

NASA NTRS2023

Using Random Hiveminds to Predict Solar Energetic Particles (SEPs)

The Problem: The use of conventional neural networks (CoNNs) to predict SEPs has become popular, but neural network models do not follow one-size-fits-all approaches and their chaotic natures can yield completely different results on identical data sets. Committees of neural networks identical in input features have been used to solve this problem by (Aminalragia et al., 2021), but they have the possibility of all agreeing together in lockstep and missing crucial information. The Solution: (O’Keefe et al., 2023) propose a solution consisting of neural network estimators in an ensemble, but with features randomly removed from them in a layout known as a random hivemind (RH). The decision weight, learning rate, and epoch count of each member in this ensemble are boosted in relation to how well its individual features perform in a chi-square test.

SMD↗

DOE OSTI2023

Comparison of Equilibrium and Nonequilibrium Approaches for Relative Binding Free Energy Predictions

Alchemical relative binding free energy calculations have recently found important applications in drug optimization. A series of congeneric compounds are generated from a preidentified lead compound, and their relative binding affinities to a protein are assessed in order to optimize candidate drugs. While methods based on equilibrium thermodynamics have been extensively studied, an approach based on nonequilibrium methods has recently been reported together with claims of its superiority. However, these claims pay insufficient attention to the basis and reliability of both methods. Here we report a comparative study of the two approaches across a large data set, comprising more than 500 ligand transformations spanning in excess of 300 ligands binding to a set of 14 diverse protein targets. Ensemble methods are essential to quantify the uncertainty in these calculations, not only for the reasons already established in the equilibrium approach but also to ensure that the nonequilibrium calculations reside within their domain of validity. If and only if ensemble methods are applied, we find that the nonequilibrium method can achieve accuracy and precision comparable to those of the equilibrium approach. Compared to the equilibrium method, the nonequilibrium approach can reduce computational costs but introduces higher computational complexity and longer wall clock times. There are, however, cases where the standard length of a nonequilibrium transition is not sufficient, necessitating a complete rerun of the entire set of transitions. This significantly increases the computational cost and proves to be highly inconvenient during large-scale applications. Our findings provide a key set of recommendations that should be adopted for the reliable implementation of nonequilibrium approaches to relative binding free energy calculations in ligand-protein systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Nuclear magnetic resonance dark-matter searches are sensitive to dark photons and the axion-photon coupling

We demonstrate that nuclear magnetic resonance based searches for dark matter (DM) have intrinsic and powerful sensitivity to dark photons and the axion-photon coupling. The reason is conceptually straightforward. An instrument such as CASPEr-Gradient begins with a large sample of nuclear spins polarized in a background magnetic field. In the presence of axion DM coupled to nucleons, the spin ensemble feels an effective magnetic field 𝐁 ∝ ∇𝑎 that tilts the spins, generating a potentially observable precession. If the magnetic field is real rather than effective, the system responds identically. A real field can be generated by a kinetically mixed dark photon within the shielded region the sample is placed or an axion coupled to photons through its interaction with the background magnetic field. We show that all three signals are detectable and distinguishable. If CASPEr-Gradient were to reach the QCD axion prediction of the axion-nucleon coupling, it would simultaneously be sensitive to kinetic mixings of 𝜀 ≃ 3 × 10 −16 and axion-photon couplings of 𝑔 𝑎⁢𝛾⁢𝛾 ≃ 2 × 10 −16 GeV −1 for 𝑚 ≃ 1 𝜇⁢eV. Our analysis demonstrates that CASPEr-Gradient has the tantalizing possibility of simultaneously measuring two separate couplings of axion dark matter, thereby providing a unique window into the axion’s UV completion.

Beadle, Carl [University of Geneva (Switzerland)] ↗

DOE OSTI2021

Adaptive resource allocation for surrogate modeling of systems comprised of multiple disciplines with varying fidelity

We present an adaptive algorithm for constructing surrogate models for integrated systems composed of a set of coupled components. With this goal we introduce ‘coupling’ variables with a priori unknown distributions that allow approximations of each component to be built independently. Once built, the surrogates of the components are combined and used to predict system-level quantities of interest (QoI) at a fraction of the cost of interrogating the full system model. We use a greedy experimental design procedure, based upon a modification of Multi-Index Stochastic Collocation (MISC), to minimize the error of the combined surrogate. This is achieved by refining each component surrogate in accordance with its relative contribution to error in the approximation of the system-level QoI. Our adaptation of MISC is a multi-fidelity procedure that can leverage ensembles of models of varying cost and accuracy, for one or more components, to produce estimates of system-level QoI. Several numerical examples demonstrate the efficacy of the proposed approach on systems involving feed-forward and feedback coupling. For a fixed computational budget, the proposed algorithm is able to produce approximations that are orders of magnitude more accurate than approximations that treat the integrated system as a black-box.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2019

Seasonal Forecasting of the Quasi-Biennial Oscillation

The ability to seasonally forecast the Quasi-Biennial Oscillation (QBO) was examined using NASA S2S (Sub-seasonal to Seasonal), 9-month, retrospective forecasts. Validation of these forecasts showed that the S2S retrospective QBO forecasts improved skill in predicting the QBO amplitude and phase over a simple QBO phase propagation model at forecast lead times of 1 to 3 months. Results from an initial assessment of whether more accurate QBO forecasts can improve Northern Hemisphere winter sea level pressure forecasts showed no significant forecast improvement at a 1-month lead time, indicating the need for improved stratosphere-troposphere QBO coupling metrics and pathway identification. Overall, these results suggest that future improvements in representing the QBO in global models can increase the ensemble fraction of valid 1 to 3 month QBO forecasts and potentially extend useful QBO forecasts beyond 3 months.

Coy, Lawrence↗

NASA NTRSDate not supplied

Automated Tracking of Shallow Maritime Clouds on Geostationary Imagery to Extract Lifecycle Characteristics

Shallow moist convection is ubiquitous throughout the tropics and represents a key player in boundary layer processes. Satellites have provided valuable insight on shallow clouds, such as size, structure, and geographical coverage, from static views of recurring cloud fields. But determining why certain cloud features appear and persist for different periods requires a time-evolving view of their behaviors. Geostationary satellites provide a unique opportunity to follow the time evolution of individual convective features, given their enhanced spatial and temporal sampling. A cloud-tracking tool was developed to identify properties of cloud lifecycle from the NASA Cloud, Aerosol, and Monsoon Processes Philippines Experiment (CAMP2EX) field campaign of 2019. The mission conducted intensive sampling of shallow cumulus in the West Pacific Ocean, in tandem with Rapid Scan imagery from the Advanced Himawari Imager (AHI) on the Japan Meteorological Agency’s (JMA) Himawari-8 satellite. Shallow cumulus were segmented according to thresholds in 0.5-km visible reflectance and with blurring techniques. Despite being limited to daytime hours, the segmentations yielded the best resolution available for capturing cloud initiation, growth, and decay. The tracking procedure is based on a computer vision package that includes Kalman filters for motion prediction, object overlap search, and the Hungarian (or Kuhn-Munkres) matching algorithm for track designation. AHI radiances available within the tracked cloud boundaries are assembled to form individual spectral histories. The resulting catalog provides thousands of cloud histories for domains measuring only a few degrees in latitude and longitude. We present an overview of the cloud-tracking tool and its results for cloud fields sampled throughout CAMP2EX by the airborne P-3. Cloud tracks were selected from about 10 flights to form ensembles, specific groups of tracks occurring in a region with airborne sampling. Cloud lifecycle properties, including duration and maximum area, are calculated for all ensemble members, and analyzed for cloud behavior and P-3 coincidences. By following this strategy, we quantitatively assess the degree of airborne sampling for specific cloud classes defined by the lifecycle calculations. We can summarize which cloud classes had more sampling, the stage of development during sampling, and general differences in character (e.g., isolated congestus vs. cold-pool producer).

Cloud Tracking↗

NASA NTRS2023

Importance of Internal Variability for Climate Model Assessment

Benchmarking climate model simulations against observations of the climate is core to the process of building realistic climate models and developing accurate future projections. However, in many cases, models do not match historical observations, particularly on regional scales. If there is a mismatch between modeled and observed climate features, should we necessarily conclude that our models are deficient? Using several illustrative examples, we emphasize that internal variability can easily lead to marked differences between the basic features of the model and observed climate, even when decades of model and observed data are available. This can appear as an apparent failure of models to capture regional trends or changes in global teleconnections, or simulation of extreme events. Despite a large body of literature on the impact of internal variability on climate, this acknowledgment has not yet penetrated many model evaluation activities, particularly for regional climate. We emphasize that using a single or small ensemble of simulations to conclude that a climate model is in error can lead to premature conclusions on model fidelity. A large ensemble of multidecadal simulations is therefore needed to properly sample internal climate variability in order to robustly identify model deficiencies and convincingly demonstrate progress between generations of climate models.

Climate and Earth system modelling↗

DOE OSTI2022

Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties

Abstract Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We use a convolutional adversarial autoencoder (CAAE) to parameterize a heterogeneous non‐Gaussian conductivity field via a low‐dimensional latent representation. A three‐dimensional dense convolutional encoder‐decoder (DenseED) network serves as a forward surrogate of the flow and transport model. The CAAE‐DenseED surrogate is fed into the ensemble smoother with multiple data assimilation (ESMDA) algorithm to sample from the Bayesian posterior distribution of the unknown parameters, forming a CAAE‐DenseED‐ESMDA inversion framework. The resulting CAAE‐DenseED‐ESMDA inversion strategy is used to identify a three‐dimensional contaminant source and conductivity field. A comparison of the inversion results from CAAE‐ESMDA with physical flow and transport simulator and from CAAE‐DenseED‐ESMDA shows that the latter yields accurate reconstruction results at the fraction of the computational cost of the former.

Zhou, Zitong↗

DOE OSTI2025

Overestimated natural biological nitrogen fixation translates to an exaggerated CO 2 fertilization effect in Earth system models

CO 2 fertilization of the terrestrial biosphere is limited by nitrogen. Biological nitrogen fixation (BNF) is the dominant natural nitrogen source to the terrestrial biosphere and can alleviate nitrogen limitation but is poorly constrained in Earth system models (ESMs). Here, in this study, we compare terrestrial BNF from an ensemble of ESMs of the 6th Coupled Model Intercomparison Project to a new global synthesis of observations across natural and agricultural biomes. We find that compared to observations, ESMs underestimate agricultural BNF but overestimate natural BNF in the present day by over 50%. Natural BNF is overestimated in the most productive ecosystems that contribute most to the terrestrial carbon sink (forests and grasslands). ESMs with different BNF representations yield a range of BNF responses to CO 2 enrichment. Some ESMs with phenomenological representations of BNF predict a natural BNF increase in response to a doubling of CO 2 that aligns with a meta-analysis of CO 2 enrichment experiments (31% increase) but fail to account for the substantial carbon cost of BNF. In contrast, ESMs with mechanistic representations of BNF account for its carbon cost as well as its regulation by nitrogen limitation but overestimate the BNF response to a doubling of CO 2 (135% increase). Overall, all current BNF representations in ESMs fall short of fully capturing its response to rising atmospheric CO 2 . Finally, we find a positive correlation between modeled present-day natural BNF and the CO 2 fertilization effect across ESMs, suggesting that overestimated natural BNF translates to an exaggerated CO 2 fertilization effect of approximately 11% in ESMs.

Biological nitrogen fixation↗

NASA NTRS2022

Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis

There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.

Uncertainty quantification↗

DOE OSTI2022

High-throughput screening of tribological properties of monolayer films using molecular dynamics and machine learning

Monolayer films have shown promise as a lubricating layer to reduce friction and wear of mechanical devices with separations on the nanoscale. These films have a vast design space with many tunable properties that can affect their tribological effectiveness. For example, terminal group chemistry, film composition, and backbone chemistry can all lead to films with significantly different tribological properties. This design space, however, is very difficult to explore without a combinatorial approach and an automatable, reproducible, and extensible workflow to screen for promising candidate films. Here, using the Molecular Simulation Design Framework (MoSDeF), a combinatorial screening study was performed to explore 9747 unique monolayer films (116 964 total simulations) and a machine learning (ML) model using a random forest regressor, an ensemble learning technique, to explore the role of terminal group chemistry and its effect on tribological effectiveness. The most promising films were found to contain small terminal groups such as cyano and ethylene. The ML model was subsequently applied to screen terminal group candidates identified from the ChEMBL small molecule library. Approximately 193 131 unique film candidates were screened with approximately a five order of magnitude speed-up in analysis compared to simulation alone. The ML model was thus able to be used as a predictive tool to greatly speed up the initial screening of promising candidate films for future simulation studies, suggesting that computational screening in combination with ML can greatly increase the throughput in combinatorial approaches to generate in silico data and then train ML models in a controlled, self-consistent fashion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Optical anisotropy of CsPbBr3 perovskite nanoplatelets

Abstract The two-dimensional CsPbBr 3 nanoplatelets have a quantum well electronic structure with a band gap tunable with sample thicknesses in discreet steps based upon the number of monolayers. The polarized optical properties of CsPbBr 3 nanoplatelets are studied using fluorescence anisotropy and polarized transient absorption spectroscopies. Polarized spectroscopy shows that they have absorption and emission transitions which are strongly plane-polarized. In particular, photoluminescence excitation and transient absorption measurements reveal a band-edge polarization approaching 0.1, the limit of isotropic two-dimensional ensembles. The degree of anisotropy is found to depend on the thickness of the nanoplatelets: multiple measurements show a progressive decrease in optical anisotropy from 2 to 5 monolayer thick nanoplatelets. In turn, larger cuboidal CsPbBr 3 nanocrystals, are found to have consistently positive anisotropy which may be attributed to symmetry breaking from ideal perovskite cubes. Optical measurements of anisotropy are described with respect to the theoretical framework developed to describe exciton fine structure in these materials. The observed planar absorption and emission are close to predicted values at thinner nanoplatelet sizes and follow the predicted trend in anisotropy with thickness, but with larger anisotropy than theoretical predictions. Dominant planar emission, albeit confined to the thinnest nanoplatelets, is a valuable attribute for enhanced efficiency of light-emitting devices.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2021

Modular hybrid modeling to increase efficiency, explore structural uncertainty, and allow multidimensional complexity scaling in land surface models

Land surface models (LSMs) are indispensable tools for predicting hydrologic extremes, as well as a particularly uncertain component of Earth system models that has stubbornly resisted the convergence in projections over several successive generations of model intercomparisons. This uncertainty in LSMs is poorly quantified and poorly attributed to specific processes, which has hampered efforts to focus research in reducing uncertainty. This has resulted from sparse sampling of the possible uncertainty space—which is high-dimensional and has contributions from parametric, structural, initial, and boundary condition uncertainties—as an artifact of CMIP-type ensembles of opportunity and limitations inherent in observational benchmarks. A new approach is needed to understand and reduce this uncertainty, based around individual LSMs that can represent the breadth of assumptions represented in current CMIP-type efforts, while at the same time exploring that uncertainty in a systematic way, confronting multiple types of observations, and where justified, replacing process representations with ML-driven emulators. We propose an approach of modular hybrid modeling to address these challenges.

58 GEOSCIENCES↗

DOE OSTI2025

WRF-ELM v1.0: a regional climate model to study land–atmosphere interactions over heterogeneous land use regions

Abstract. The Energy Exascale Earth System Model (E3SM) Land Model (ELM) is a state-of-the-art land surface model that simulates the intricate interactions between the terrestrial land surface and other components of the Earth system. Originating from the Community Land Model (CLM) version 4.5, ELM has been under active development, with added new features and functionality, including plant hydraulics, radiation–topography interaction, subsurface multiphase flow, and more explicit land use and management practices. This study integrates ELM v2.1 with the Weather Research and Forecasting (WRF; WRF-ELM) model through a modified Lightweight Infrastructure for Land Atmosphere Coupling (LILAC) framework, enabling affordable high-resolution regional modeling by leveraging ELM's innovative features alongside WRF's diverse atmospheric parameterization options. This framework includes a top-level driver for variable communication between WRF and ELM and Earth System Modeling Framework (ESMF) caps for the WRF atmospheric component and ELM workflow control, encompassing initialization, execution, and finalization. Importantly, this LILAC–ESMF framework demonstrates a more modular approach compared to previous coupling efforts between WRF and land surface models. It maintains the integrity of ELM's source code structure and facilitates the transfer of future developments in ELM to WRF-ELM. To test the ability of the coupled model to capture land–atmosphere interactions over regions with a variety of land uses and land covers, we conducted high-resolution (4 km) WRF-ELM ensemble simulations over the Great Lakes region (GLR) in the summer of 2018 and systematically compared the results against observations, reanalysis data, and WRF-CTSM (WRF coupled with the Community Terrestrial Systems Model). In general, the coupled WRF-ELM model has reasonably captured the spatial distribution of surface state variables and fluxes across the GLR, particularly over the natural vegetation areas. The evaluation results provide a baseline reference for further improvements in ELM in the regional application of high-resolution weather and climate predictions. Our work serves as an example to the model development community for expanding an advanced land surface model's capability to represent fully-coupled land–atmosphere interactions at fine spatial scales. The development and release of WRF-ELM marks a significant advancement for the ELM user community, providing opportunities for fine-scale regional representation, parameter calibration in coupled mode, and examination of new schemes with atmospheric feedback.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1992

The compositional structure and the effects of exothermicity in an unpremixed planar jet flame

Results are presented of direct numerical simulations (DNS) of a randomly perturbed compressible, spatially developing planar jet under the influence of a finite rate Arrhenius chemical reaction of the type F + O yields Product + Heat. The objectives of the simulations are to assess the compositional structure of the flame and to determine the influence of reaction exothermicity by means of statistical sampling of the data generated by DNS. It is shown that even with this idealized kinetics model, the simulated results exhibit features in accordance with experimental data. These results indicate that the Damkoehler number is an important parameter in determining the statistical composition of the reacting field, and that the results are insensitive to the mechanism by which this parameter is varied. It is demonstrated that as the intensity of mixing is increased and the effect of finite rate chemistry is more pronounced, the magnitudes of the ensemble mean and rms of the product mass fraction decrease, and those of the reactants mass fraction increase. Also, at higher mixing rates the joint probability density functions of the reactants' mass fractions shift towards higher values within the composition domain indicating a lower reactedness. These trends are consistent with those observed experimentally and are very useful in portraying the statistical structure of non-equilibrium diffusion flames. The DNS generated data are also utilized to examine the applicability of the 'laminar diffusion flamelet model' in predicting the rate of the reactant conversion with finite rate chemistry. This examination indicates that the bounds of the product formation scale reasonably well with those obtained by the flamelet model. However, in the range of the relatively low values of the Damkoehler numbers considered, the scatter of the results is substantially more than that to be completely determined by the closure.

Steinberger, C. J.↗