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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

The tensor-train stochastic finite volume method for uncertainty quantification

The stochastic finite volume method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimensionality when dealing with multiple stochastic variables. Here, we introduce the stochastic finite volume method within the tensor-train framework to counteract this limitation. This integration, however, comes with its own set of difficulties, mainly due to the propensity for shock formation in hyperbolic systems. To overcome these issues, we have developed a tensor-train-adapted stochastic finite volume method that employs a global WENO reconstruction, making it suitable for such complex systems. This approach represents the first step in designing tensor-train techniques for hyperbolic systems and conservation laws involving shocks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. In conclusion, we demonstrate the method's capabilities and performance characteristics using a standard benchmark test network.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

Here, we propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. Furthermore, we augment the existing SFV theory with a priori convergence results for statistical quantities, in particular push-forward densities, which we demonstrate through numerical experiments. By linking refinement indicators to regions of the physical and stochastic spaces, we drive anisotropic refinements of the discretizations, introducing new degrees of freedom where deemed profitable. To illustrate our proposed method, we consider a series of numerical examples for nonlinear hyperbolic PDEs based on Burgers’ and Euler’s equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

TT-SFV

The code uses tensor train decompositions to provide a low-rank framework for the stochastic finite volume method.

Walton, Steven↗
DOE OSTI2021

Few-nucleon matrix elements in pionless effective field theory in a finite volume

Here, pionless effective field theory in a finite volume (FVEFT $\notπ$ ) is investigated as a framework for the analysis of multinucleon spectra and matrix elements calculated in lattice QCD (LQCD). By combining FVEFT π with the stochastic variational method, the spectra of nuclei with atomic number A ∈ {2, 3} are matched to existing finite-volume LQCD calculations at heavier-than-physical quark masses corresponding to a pion mass m $\notπ$ = 806 MeV , thereby enabling infinite-volume binding energies to be determined using infinite-volume variational calculations. Based on the variational wave functions that are constructed in this approach, the finite-volume matrix elements of various local operators are computed in FVEFT $\notπ$ and matched to LQCD calculations of the corresponding QCD operators in the same volume, thereby determining the relevant one- and two-body effective field theory counterterms and enabling an extrapolation of the LQCD matrix elements to infinite volume. As examples, the scalar, tensor, and axial matrix elements are considered, in addition to the magnetic moments and the isovector longitudinal momentum fraction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Staggered scheme for the compressible fluctuating hydrodynamics of multispecies fluid mixtures

Here, we present a numerical formulation for the solution of nonisothermal, compressible Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical method is the use of staggered grid momenta along with a finite volume discretization of the thermodynamic variables to solve the resulting stochastic partial differential equations. The key advantages of the numerical scheme are that it significantly simplifies the discretization of diffusive and stochastic momentum fluxes into a more compact form, and it provides an unambiguous prescription of boundary conditions involving pressure. The staggered grid scheme more accurately reproduces the equilibrium static structure factor of hydrodynamic fluctuations in gas mixtures compared to a collocated scheme described previously by Balakrishnan et al. [Phys. Rev. E 89, 013017 (2014)1539-375510.1103/PhysRevE.89.013017]. The numerical method is tested for ideal noble gases mixtures under various nonequilibrium conditions, such as applied thermal and concentration gradients, to assess the role of cross-diffusion effects, such as Soret and Dufour, on the long-ranged correlations of hydrodynamic fluctuations, which are also more accurately reproduced compared to the collocated scheme. We numerically study giant nonequilibrium fluctuations driven by concentration gradients and fluctuation-driven Rayleigh-Taylor instability in gas mixtures. Wherever applicable, excellent agreement is observed with theory and measurements from the direct simulation Monte Carlo method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1984

Doppler lidar results from the San Gorgonio Pass experiments

During FY-84, the Doppler Lidar data from the San Gorgonio Pass experiments were analyzed, evaluated, and interpreted with regard to signal strength, signal width, magnitude and direction of velocity component and a goodness parameter associated with the expected noise level of the signal. From these parameters, a screening criteria was developed to eliminate questionable data. For the most part analysis supports the validity of Doppler Lidar data obtained at San Gorgonio Pass with respect to the mean velocity magnitude and direction. The question as to whether the Doppler width could be interpreted as a measure of the variance of the turbulence within the Doppler Lidar System (DLS) focal volume was not resolved. The stochastic nature of the Doppler broadening from finite residence time of the particles in the beam as well as other Doppler broadening phenomenon tend to mask the Doppler spread associated with small scale turbulence. Future tests with longer pulses may assist in better understanding.

Cliff, W. C.↗
DOE OSTI2025

QCD Predictions for Physical Multimeson Scattering Amplitudes

We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of 𝜋 + and 𝐾 + , at a lattice spacing 𝑎 = 0.063 fm, and in the isospin-symmetric limit. We also obtain accurate results for maximal-isospin two-meson amplitudes, with those for 𝜋 + ⁢𝐾 + and 2⁢𝐾 + being the first determinations at the physical point. Dense lattice spectra are obtained using the stochastic Laplacian-Heaviside method, and the analysis leading to scattering amplitudes is done using the relativistic finite-volume formalism. Results are compared to chiral perturbation theory and to phenomenological fits to experimental data, finding good agreement.

hadron-hadron interactions↗
DOE OSTI2022

Finite-volume pionless effective field theory for few-nucleon systems with differentiable programming

Finite-volume pionless effective field theory provides an efficient framework for the extrapolation of nuclear spectra and matrix elements calculated at finite volume in lattice QCD to infinite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wave functions optimized using differentiable programming and via solution of a generalized eigenvalue problem. This approach is shown to be significantly more efficient than a stochastic implementation of the variational method based on the same form of correlated Gaussian wave functions, yielding comparably accurate representations of the ground-state wave functions with an order of magnitude fewer terms. The efficiency of representation allows such calculations to be extended to larger systems than in previous work. Further, the method is demonstrated through calculations of the binding energies of nuclei with atomic number A ϵ {2,3,4} in finite volume, matched to lattice QCD calculations at quark masses corresponding to m π = 806 MeV, and infinite-volume effective field theory calculations of A ϵ {2,3,4,5,6} systems based on this matching.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Multiscale simulation of spatially correlated microstructure via a latent space representation

When deformation gradients act on the scale of the microstructure of a part due to geometry and loading, spatial correlations and finite-size effects in simulation cells cannot be neglected. We propose a multiscale method that accounts for these effects using a variational autoencoder to encode the structure–property map of the stochastic volume elements making up the statistical description of the part. In this paradigm the autoencoder can be used to directly encode the microstructure or, alternatively, its latent space can be sampled to provide likely realizations. Furthermore, we demonstrate the method on three examples using the common additively manufactured material AlSi10Mg in: (a) a comparison with direct numerical simulation of the part microstructure, (b) a push forward of microstructural uncertainty to performance quantities of interest, and (c) a simulation of functional gradation of a part with stochastic microstructure.

Elastoplasticity↗
DOE OSTI2021

Effects of as-received defects on ceramic matrix composites properties using high-fidelity microstructures with periodic boundary conditions

The presence of microstructural defects in as-received specimens of ceramic matrix composites (CMCs) significantly influences their constitutive response and damage, highlighting the importance of characterization and quantification of these defects for accurate assessment of damage and failure in the service environment. In a recent effort, the authors developed an algorithm to generate stochastic representative volume elements (SRVEs) of Carbon fiber Silicon-Carbide-Nitride matrix (C/SiNC) CMCs based on extensive multiscale material and defect characterization data. This paper implements this algorithm within a commercial finite element solver with periodic boundary conditions (PBCs) for high-fidelity micromechanics analysis and investigation of macroscopic material behavior of C/SiNC composites. Different loading directions are used to predict the global mechanical properties, and the results are in excellent agreement with theoretical (rule of mixture) predictions. Subsequently, the effects of as-received defects on the global and local responses are investigated. The results show that intratow porosity has pronounced degradation effects on the global elastic properties and results in complex stress localization patterns, which can be attributed to potential damage initiation sites.

Khafagy, Khaled H.↗
DOE OSTI2025

Two- and three-meson scattering amplitudes with physical quark masses from lattice QCD

We study systems of two and three mesons composed of pions and kaons at maximal isospin using four CLS ensembles with 𝑎 ≈ 0.063 fm, including one with approximately physical quark masses. Using the stochastic Laplacian-Heaviside method, we determine the energy spectrum of these systems including many levels in different momentum frames and irreducible representations. Using the relativistic two- and three-body finite-volume formalism, we constrain the two- and three-meson K matrices, including not only the leading 𝑠 wave, but also 𝑝 and 𝑑 waves. By solving the three-body integral equations, we determine, for the first time, the physical-point scattering amplitudes for 3⁢𝜋 + , 3⁢𝐾 + , 𝜋 + ⁢𝜋 + ⁢𝐾 + , and 𝐾 + ⁢𝐾 + ⁢𝜋 + systems. These are determined for total angular momentum 𝐽 𝑃 = 0 − , 1 + , and 2 − . We also obtain accurate results for 2⁢𝜋 + , 𝜋 + ⁢𝐾 + , and 2⁢𝐾 + phase shifts. We compare our results to chiral perturbation theory and to phenomenological fits.

FOS: Physical sciences↗
DOE OSTI2021

Interactions of two and three mesons including higher partial waves from lattice QCD

We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant s-wave interactions, but also those in d waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle d waves. We use three N f = 2 + 1 CLS ensembles with pion masses of 200, 280, and 340 MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1987

Mixing, transport and combustion in sprays

The state-of-the-art in analytical methods for sprays and drop/turbulence interactions in combustion processes is presented with reference to dilute sprays, and dilute dispersed flows, that contain well-defined dispersed-phase elements in volume fractions lower than 1 percent. Attention is given to the near-injector dense spray region. The methods tested are those of locally homogeneous flow, deterministic separated flow, and stochastic separated flow; the first of these was ineffective due to its ignoring finite interphase transport rates, and the second failed by ignoring turbulent dispersion. Stochastic separated flow methodology yielded encouraging results through its treatment of both finite interphase transport rates and dispersed-phase/turbulence interactions.

Faeth, G. M.↗
DOE OSTI2023

Interactions of πK, ππK and KKπ systems at maximal isospin from lattice QCD

We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specifically $π^+K^+, π^+π^+K^+$ and $K^+K^+π^+$. Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLS $N_f$ = 2 + 1 ensembles with pion masses of 200 MeV and 340 MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up to p waves. This requires also results for the $π^+π^+$ and $K^+K^+$ spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit twoparticle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix in $π^+π^+K^+$ and $K^+K^+π^+$ systems, finding statistically significant nonzero results in most cases. We include s and $\textit{p}$ waves in the K matrix for $π^+K^+$ scattering, finding evidence for an attractive p-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2007

High-LET Patterns of DSBs in DNA Loops, the HPRT Gene and Phosphorylation Foci

We present new results obtained with our model based on the track structure and chromatin geometry that predicts the DSB spatial and genomic distributions in a cell nucleus with the full genome represented. The model generates stochastic patterns of DSBs in the physical space of the nucleus filled with the realistic configuration of human chromosomes. The model was re-used to find the distribution of DSBs in a physical volume corresponding to a visible phosphorylation focus believed to be associated with a DSB. The data shows whether there must more than one DSB per foci due to finite size of the visible focus, even if a single DSB is radiochemically responsible for the phosphorylation of DNA in its vicinity. The same model can predict patterns of closely located DSBs in a given gene, or in a DNA loop, one of the large-scale chromatin structures. We demonstrated for the example of the HPRT gene, how different sorts of radiation lead to proximity effect in DSB locations, which is important for modeling gene deletions. The spectrum of intron deletions and total gene deletions was simulated for the HPRT gene. The same proximity effect of DSBs in a loop can hinder DSB restitutions, as parts of the loop between DSBs is deleted with a higher likelihood. The distributions of DSBs and deletions of DNA in a loop are presented.

Ponomarev, Artem L.↗
DOE OSTI2023

Multi-fidelity Uncertainty Quantification for Homogenization Problems in Structure-Property Relationships from Crystal Plasticity Finite Elements

Crystal plasticity finite element method (CPFEM) has been an integrated computational materials engineering (ICME) workhorse to study materials behaviors and structure-property relationships for the last few decades. These relations are mappings from the microstructure space to the materials properties space. Due to the stochastic and random nature of microstructures, there is always some uncertainty associated with materials properties, for example, in homogenized stress-strain curves. For critical applications with strong reliability needs, it is often desirable to quantify the microstructure-induced uncertainty in the context of structure-property relationships. However, this uncertainty quantification (UQ) problem often incurs a large computational cost because many statistically equivalent representative volume elements (SERVEs) are needed. In this article, we apply a multi-level Monte Carlo (MLMC) method to CPFEM to study the uncertainty in stress-strain curves, given an ensemble of SERVEs at multiple mesh resolutions. By using the information at coarse meshes, we show that it is possible to approximate the response at fine meshes with a much reduced computational cost. We focus on problems where the model output is multi-dimensional, which requires us to track multiple quantities of interest (QoIs) at the same time. In conclusion, our numerical results show that MLMC can accelerate UQ tasks around 2.23x, compared to the classical Monte Carlo (MC) method, which is widely known as ensemble average in the CPFEM literature.

36 MATERIALS SCIENCE↗
NASA NTRS2005

Lifetime Reliability Prediction of Ceramic Structures Under Transient Thermomechanical Loads

An analytical methodology is developed to predict the probability of survival (reliability) of ceramic components subjected to harsh thermomechanical loads that can vary with time (transient reliability analysis). This capability enables more accurate prediction of ceramic component integrity against fracture in situations such as turbine startup and shutdown, operational vibrations, atmospheric reentry, or other rapid heating or cooling situations (thermal shock). The transient reliability analysis methodology developed herein incorporates the following features: fast-fracture transient analysis (reliability analysis without slow crack growth, SCG); transient analysis with SCG (reliability analysis with time-dependent damage due to SCG); a computationally efficient algorithm to compute the reliability for components subjected to repeated transient loading (block loading); cyclic fatigue modeling using a combined SCG and Walker fatigue law; proof testing for transient loads; and Weibull and fatigue parameters that are allowed to vary with temperature or time. Component-to-component variation in strength (stochastic strength response) is accounted for with the Weibull distribution, and either the principle of independent action or the Batdorf theory is used to predict the effect of multiaxial stresses on reliability. The reliability analysis can be performed either as a function of the component surface (for surface-distributed flaws) or component volume (for volume-distributed flaws). The transient reliability analysis capability has been added to the NASA CARES/ Life (Ceramic Analysis and Reliability Evaluation of Structures/Life) code. CARES/Life was also updated to interface with commercially available finite element analysis software, such as ANSYS, when used to model the effects of transient load histories. Examples are provided to demonstrate the features of the methodology as implemented in the CARES/Life program.

Nemeth, Noel N.↗