Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “generalized functions”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Land Use in Computable General Equilibrium Models

Constant Elasticity of Transformation (CET) functions are widely used to allocate land across uses in Computable General Equilibrium (CGE) models. These models fail to maintain area of land in balance. Several ways have been used or offered to fix this problem. This paper first examines the extent to which the CET approach may generate imbalances in area of land and identifies determinants of such imbalances. It then evaluates the merits, properties, and welfare impacts of the available approaches that restore area of land in balance. We show that heterogeneity in land prices (land rents) is the main source of imbalance in area of land, not the curvature of the CET function. Furthermore, we show that the available approaches that restore area of land in balance either introduce ad hoc adjustments in land allocation or undermine the conventional welfare assessments of the CET results and ignore the opportunity costs of land transformation. The CGE models which applied stochastic productivity distribution functions to allocate land among uses maintain area of land in balance, but they suffer from important limitations and ignore costs of land transformation.

Taheripour, Farzad↗
NASA NTRS1977

Correlated wave functions for three-particle systems with Coulomb interaction - The muonic helium atom

A computational procedure for calculating correlated wave functions is proposed for three-particle systems interacting through Coulomb forces. Calculations are carried out for the muonic helium atom. Variational wave functions which explicitly contain interparticle coordinates are presented for the ground and excited states. General Hylleraas-type trial functions are used as the basis for the correlated wave functions. Excited-state energies of the muonic helium atom computed from 1- and 35-term wave functions are listed for four states.

Huang, K.-N.↗
DOE OSTI2026

Ab Initio Modeling of Aqueous Methanol Mixtures at DFT-SCAN Level Using Machine Learning Interatomic Potentials

Abstract Methanol–water mixtures find use in many applications, particularly catalytic energy conversion processes. Their importance has motivated numerous computational studies, most of which employed molecular dynamics based on classical force fields. These enable simulations of large systems on long time scales but do not reliably describe reactive dynamics involving bond breaking and bond formation. In contrast, ab initio molecular dynamics (AIMD) based on density functional theory (DFT) is generally more reliable for such applications but has a high computational cost, which discourages systematic studies of alcohol-water mixtures. To remedy this, we trained a machine learning interatomic potential capable of probing the properties of aqueous methanol mixtures at the DFT level using the SCAN functional. Our results show that SCAN qualitatively reproduces multiple key experimental features arising from the amphiphilic nature of methanol, including density, diffusion coefficients, X-ray structure factors, and Kirkwood–Buff integrals. We also find that structural correlations between water molecules are somewhat overestimated, leading to a stronger preferential association than that predicted by experiments. However, increasing the temperature by 30 K mitigates this effect and also recovers the correct mobilities of both methanol and water. These results indicate that SCAN provides an accurate description of methanol–water mixtures, making it a reliable choice for investigating the reactive dynamics in such systems.

Park, Sanghyun J. [Princeton University , , , ,]↗
DOE OSTI2022

Closing the loop between microstructure and charge transport in conjugated polymers by combining microscopy and simulation

A grand challenge in materials science is to identify the impact of molecular composition and structure across a range of length scales on macroscopic properties. We demonstrate a unified experimental–theoretical framework that coordinates experimental measurements of mesoscale structure with molecular-level physical modeling to bridge multiple scales of physical behavior. Here we apply this framework to understand charge transport in a semiconducting polymer. Spatially-resolved nanodiffraction in a transmission electron microscope is combined with a self-consistent framework of the polymer chain statistics to yield a detailed picture of the polymer microstructure ranging from the molecular to device relevant scale. Using these data as inputs for charge transport calculations, the combined multiscale approach highlights the underrepresented role of defects in existing transport models. Short-range transport is shown to be more chaotic than is often pictured, with the drift velocity accounting for a small portion of overall charge motion. Local transport is sensitive to the alignment and geometry of polymer chains. At longer length scales, large domains and gradual grain boundaries funnel charges preferentially to certain regions, creating inhomogeneous charge distributions. While alignment generally improves mobility, these funneling effects negatively impact mobility. The microstructure is modified in silico to explore possible design rules, showing chain stiffness and alignment to be beneficial while local homogeneity has no positive effect. This combined approach creates a flexible and extensible pipeline for analyzing multiscale functional properties and a general strategy for extending the accesible length scales of experimental and theoretical probes by harnessing their combined strengths.

42 ENGINEERING↗
DOE OSTI2022

Dynamical electron correlation and the chemical bond. I. Covalent bonds in AH and AF (A = B–F)

Dynamical electron correlation has a major impact on the computed values of molecular properties and the energetics of molecular processes. This study focused on the effect of dynamical electron correlation on the spectroscopic constants ($R$ e , $ω$ e , $D$ e ), and potential energy curves, Δ$E$($R$), of the covalently bound AH and AF molecules, A = B–F. The changes in the spectroscopic constants (Δ$R$ e , Δ$ω$ e , Δ$D$ e ) caused by dynamical correlation are erratic and, at times, even surprising. These changes can be understood based on the dependence of the dynamical electron correlation energies of the AH and AF molecules as a function of the bond distance, i.e., Δ$E$ DEC ($R$). At large $R$, the magnitude of Δ$E$ DEC ($R$) increases nearly exponentially with decreasing $R$, but this increase slows as $R$ continues to decrease and, in many cases, even reverses at very short $R$. The changes in Δ$E$ DEC ($R$) in the region around $R$ e were as unexpected as they were surprising, e.g., distinct minima and maxima were found in the curves of Δ$E$ DEC ($R$) for the most polar molecules. The variations in Δ$E$ DEC ($R$) for $R$ ≲ $R$ e are directly correlated with major changes in the electronic structure of the molecules as revealed by a detailed analysis of the spin-coupled generalized valence bond wave function. In conclusion, the results reported here indicate that we have much to learn about the nature of dynamical electron correlation and its effect on chemical bonds and molecular properties and processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1973

Rapid iterative reanalysis for automated design

A method for iterative reanalysis in automated structural design is presented for a finite-element analysis using the direct stiffness approach. A basic feature of the method is that the generalized stiffness and inertia matrices are expressed as functions of structural design parameters, and these generalized matrices are expanded in Taylor series about the initial design. Only the linear terms are retained in the expansions. The method is approximate because it uses static condensation, modal reduction, and the linear Taylor series expansions. The exact linear representation of the expansions of the generalized matrices is also described and a basis for the present method is established. Results of applications of the present method to the recalculation of the natural frequencies of two simple platelike structural models are presented and compared with results obtained by using a commonly applied analysis procedure used as a reference. In general, the results are in good agreement. A comparison of the computer times required for the use of the present method and the reference method indicated that the present method required substantially less time for reanalysis. Although the results presented are for relatively small-order problems, the present method will become more efficient relative to the reference method as the problem size increases. An extension of the present method to static reanalysis is described, ana a basis for unifying the static and dynamic reanalysis procedures is presented.

Bhatia, K. G.↗
NASA NTRS1993

The analytical representation of viscoelastic material properties using optimization techniques

This report presents a technique to model viscoelastic material properties with a function of the form of the Prony series. Generally, the method employed to determine the function constants requires assuming values for the exponential constants of the function and then resolving the remaining constants through linear least-squares techniques. The technique presented here allows all the constants to be analytically determined through optimization techniques. This technique is employed in a computer program named PRONY and makes use of commercially available optimization tool developed by VMA Engineering, Inc. The PRONY program was utilized to compare the technique against previously determined models for solid rocket motor TP-H1148 propellant and V747-75 Viton fluoroelastomer. In both cases, the optimization technique generated functions that modeled the test data with at least an order of magnitude better correlation. This technique has demonstrated the capability to use small or large data sets and to use data sets that have uniformly or nonuniformly spaced data pairs. The reduction of experimental data to accurate mathematical models is a vital part of most scientific and engineering research. This technique of regression through optimization can be applied to other mathematical models that are difficult to fit to experimental data through traditional regression techniques.

Hill, S. A.↗
DOE OSTI2021

Cluster Configuration Spaces of Finite Type

For each Dynkin diagram $D$, we define a ''cluster configuration space'' ${\mathcal{M}}_D$ and a partial compactification ${\widetilde {\mathcal{M}}}_D$. For $D = A_{n-3}$, we have ${\mathcal{M}}_{A_{n-3}} = {\mathcal{M}}_{0,n}$, the configuration space of $n$ points on ${\mathbb P}^1$, and the partial compactification ${\widetilde {\mathcal{M}}}_{A_{n-3}}$ was studied in this case by Brown. The space ${\widetilde {\mathcal{M}}}_D$ is a smooth affine algebraic variety with a stratification in bijection with the faces of the Chapoton-Fomin-Zelevinsky generalized associahedron. The regular functions on ${\widetilde {\mathcal{M}}}_D$ are generated by coordinates $u_\gamma$, in bijection with the cluster variables of type $D$, and the relations are described completely in terms of the compatibility degree function of the cluster algebra. As an application, we define and study cluster algebra analogues of tree-level open string amplitudes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Nonadiabatic transition paths from quantum jump trajectories

We present a means of studying rare reactive pathways in open quantum systems using transition path theory and ensembles of quantum jump trajectories. This approach allows for the elucidation of reactive paths for dissipative, nonadiabatic dynamics when the system is embedded in a Markovian environment. Here, we detail the dominant pathways and rates of thermally activated processes and the relaxation pathways and photoyields following vertical excitation in a minimal model of a conical intersection. We find that the geometry of the conical intersection affects the electronic character of the transition state as defined through a generalization of a committor function for a thermal barrier crossing event. Similarly, the geometry changes the mechanism of relaxation following a vertical excitation. Relaxation in models resulting from small diabatic coupling proceeds through pathways dominated by pure dephasing, while those with large diabatic coupling proceed through pathways limited by dissipation. The perspective introduced here for the nonadiabatic dynamics of open quantum systems generalizes classical notions of reactive paths to fundamentally quantum mechanical processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

Fault Management Algorithm Risk Assessment for the NASA Space Launch System

This paper presents the false positive (FP) and false negative (FN) risk assessment process currently being conducted for the Space Launch System (SLS) Artemis II Fault Management (FM) detection functions. The analysis scope, general assumptions and guide rules, and key modeling concepts were discussed to establish the basis of the risk assessments conducted. Initial analyses indicated a dominance in the total risk by software and firmware failures. This paper presents efforts applied to refine the software risks and the overall impact of implementing those modifications. Current analyses conducted on the detection functions implemented for the SLS Artemis II mission indicate primary risk drivers for the individual FM detection functions are flight software failures, firmware design failures, and hardware Common Cause Failures (CCFs). There still remains issues of how to account for time and redundancy in the software risk estimations.

probability risk analysis↗
NASA NTRSDate not supplied

Fault Management Algorithm Risk Assessment for the NASA Space Launch System

This presentation describes the false positive (FP) and false negative (FN) risk assessment process currently being conducted for the Space Launch System (SLS) Artemis II Fault Management (FM) detection functions. The analysis scope, general assumptions and guide rules, and key modeling concepts were discussed to establish the basis of the risk assessments conducted. Initial analyses indicated a dominance in the total risk by software and firmware failures. This paper presents efforts applied to refine the software risks and the overall impact of implementing those modifications. Current analyses conducted on the detection functions implemented for the SLS Artemis II mission indicate primary risk drivers for the individual FM detection functions are flight software failures, firmware design failures, and hardware Common Cause Failures (CCFs). There still remains issues of how to account for time and redundancy in the software risk estimations.

probability risk analysis↗
DOE OSTI2026

Thermal exchange-correlation functionals: Capturing quantum electron behavior in warm, dense plasmas

We summarize and give perspective upon recent progress in developing non-empirical constraint-based thermal (i.e., free energy) exchange-correlation (XC) density functionals essential for accurate description of the quantum behavior of electrons in warm, dense plasmas. After delineating the critical role of ground-state functionals for zero-temperature, time-dependent DFT, we outline the underpinnings of local density approximation, generalized gradient approximation (GGA), and meta-GGA XC free-energy functionals. Two basic thermalization principles for upgrading ground-state XC functionals to successful thermal ones are emphasized. Then, we turn to a long-standing challenge, assessment of the accuracy of well-founded functionals. Unlike the ground state, there are a few exact results for large T and P. An exception is path integral Monte Carlo (PIMC) data for dense H/D and He plasmas. For those, we did ab initio molecular dynamics simulations under selected thermodynamic conditions employing five thermal XC functionals: two approximate thermal GGAs, fully thermal GGA, an approximate meta-GGA, and fully thermal meta-GGA. Comparisons with the PIMC data show that functionals thermalized by augmenting a non-thermal functional with a lower-level thermal contribution are inferior to functionals with thermal XC and spatial inhomogeneity effects taken into account at the same level of refinement. We believe this and similar evidence should be convincing to the high-energy density physics community of the necessity of use of proper thermal XC functionals in simulation studies of finite-temperature quantum effects in warm, dense plasmas.

Ab-initio molecular dynamics↗
DOE OSTI2023

Efficient Reliability Analysis using Generalized Multifidelity Modeling and Explainable Active Learning

To assess the reliability of critical technologies like nuclear plants and infrastructure systems and improve the robustness of design, engineers have to quantify the uncertainties surrounding the system behavior accurately. However, the complexity of the problem can make standard reliability analysis algorithms prohibitively expensive, primarily due to the high computational cost of estimating the system response at each iteration. This cost can be greatly reduced by using multi-fidelity modeling and machine learning to build a surrogate model to replace the expensive response function. We propose a general and robust method for building surrogates from multiple Low Fidelity (LF) models coupled with machine learning to retain accuracy. Our framework first constructs “Corrected Low Fidelity models” (CLFs) by coupling a High Fidelity (HF) model inferred Gaussian Process correction term with each of the LF models. It then uses the correction terms to assign model probabilities to each of these CLFs in an explainable way before using them to assemble the final surrogate. No assumptions are made about the type of the LF models or their correlation with the HF model. The proposed surrogate modeling framework is used within the subset simulation algorithm (a variance-reduced MCMC-based reliability analysis algorithm) for enhanced efficiency. Additionally, an active learning step is added to the algorithm to adaptively decide when the surrogate is not sufficiently accurate, at which point the HF model is called and used to refine the surrogate. Through a frame buckling example, our method is shown to be highly efficient at reducing the expensive HF model calls while accurately estimating the failure probability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. Here, this study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A minimum assumption approach to MEG sensor array design

Objective. Our objective is to formulate the problem of the magnetoencephalographic (MEG) sensor array design as a well-posed engineering problem of accurately measuring the neuronal magnetic fields. This is in contrast to the traditional approach that formulates the sensor array design problem in terms of neurobiological interpretability the sensor array measurements. Approach. We use the vector spherical harmonics (VSH) formalism to define a figure-of-merit for an MEG sensor array. We start with an observation that, under certain reasonable assumptions, any array of m perfectly noiseless sensors will attain exactly the same performance, regardless of the sensors' locations and orientations (with the exception of a negligible set of singularly bad sensor configurations). We proceed to the conclusion that under the aforementioned assumptions, the only difference between different array configurations is the effect of (sensor) noise on their performance. We then propose a figure-of-merit that quantifies, with a single number, how much the sensor array in question amplifies the sensor noise. Main results. We derive a formula for intuitively meaningful, yet mathematically rigorous figure-of-merit that summarizes how desirable a particular sensor array design is. We demonstrate that this figure-of-merit is well-behaved enough to be used as a cost function for a general-purpose nonlinear optimization methods such as simulated annealing. We also show that sensor array configurations obtained by such optimizations exhibit properties that are typically expected of 'high-quality' MEG sensor arrays, e.g. high channel information capacity. Significance. Our work paves the way toward designing better MEG sensor arrays by isolating the engineering problem of measuring the neuromagnetic fields out of the bigger problem of studying brain function through neuromagnetic measurements.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Transition Metal Dichalcogenide MoS 2 : Oxygen and Fluorine Functionalization for Selective Plasma Processing

Low-temperature plasma processing is a promising technique for tailoring transition metal dichalcogenides (TMDs). For chalcogen substitution processing, a key challenge is to identify the ion energy window that enables selective chalcogen removal while preserving the metal lattice. Using ab initio molecular dynamics (AIMD), we demonstrate that oxygen and fluorine functionalization widen the processing window by significantly lowering the sulfur sputtering energy threshold (E sputt,S ) of MoS 2 from ∼30 to ∼10 eV via formation of sputtering products such as SO 2 and SF n . Additionally, we show that experimentally relevant cryogenic temperatures strongly affect E sputt,S (T). The dependence is confirmed via AIMD and also predicted by a mechanistic parameter-free theory, suggesting that E sputt (T) generalizes to other TMDs, functionalizations, and surface impact conditions. Our results highlight oxygen/fluorine functionalization, ionic impact angle, and material temperature to be key control parameters for selective, damage-controlled chalcogen removal in TMD processing.

Polyachenko, Yury [Princeton Plasma Physics Labora↗
DOE OSTI2024

Magnetism in the two-dimensional dipolar XY model

Here, motivated by a recent experiment on a square-lattice Rydberg atom array realizing a long-range dipolar XY model [C. Chen et al., Nature (London) 616, 691 (2023)], we numerically study the model's equilibrium properties. We obtain the phase diagram, critical properties, entropies, variance of the magnetization, and site-resolved correlation functions. We consider both ferromagnetic and antiferromagnetic interactions and apply quantum Monte Carlo and pseudo-Majorana functional renormalization group techniques, generalizing the latter to a U⁡(1) symmetric setting. Our simulations perform extensive thermometry in dipolar Rydberg atom arrays and establish conditions for adiabaticity and thermodynamic equilibrium. On the ferromagnetic side of the experiment, we determine the entropy per particle S/N≈0.5, close to the one at the critical temperature, S c /N=0.585⁢(15). The simulations suggest the presence of an out-of-equilibrium plateau at large distances in the correlation function, thus motivating future studies on the nonequilibrium dynamics of the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Atomic Layer Deposition for Materials-Based H2 Storage: Opportunities and Limitations

The transportation demands in our growing hydrogen (H2) economy requires robust storage systems. The current commercially implemented technology in fuel cell cars relies on the well-established technology of hydrogen gas compressed to 350-700 bar, depending on the application. The compressed gas tanks in use today are bulky and cost intensive. To address this challenge, material-based storage is one of the long-term alternatives considered and constitutes the focus of this talk. Material-based storage is broadly defined as hydrogen bound to solid materials, with its binding strength varying from physisorption to porous materials, such as zeolites and metal organic frameworks, to chemisorption in (complex) metal hydrides. The ultimate targets set by the U.S. Department of Energy for this technology include a system gravimetric capacity of 6.5 wt% and volumetric capacity of 40 g/L at 100 bar, operating temperatures ranging between -40 C and +40 C and adsorption/desorption timescales of < 5 min. Storage in the form of physisorbed or chemisorbed hydrogen has guided the materials research, which metal- organic framework and (complex) metal hydrides being the most promising materials classes. A variety of these materials have met one or more of the targets, but it has remained elusive for a single material system to meet all these stringent requirements. Nano-encapsulation and low-concentration chemical additives have previously been employed separately to overcome such challenges. Functionalization via atomic layer deposition (ALD), however, offers unique characteristics that make it suitable for both, nano-encapsulation and "doping" with low-concentration additives. This deposition technique has sub-monolayer thickness control, is highly conformal in high-surface area materials and is self-limiting, i.e., once the gas-phase precursor reacts with the available surface sites, the surface reactions stop. In this presentation, we will showcase examples where ALD, more generally vapor-phase functionalization, on (complex) metal hydrides and organic frameworks has improved the material properties for H2 storage. In our first study, Al2O3 was deposited on magnesium borohydride, Mg(BH4)2, at room temperature using trimethylaluminum (TMA) and water. From our findings, encouraging initial results were obtained: the H2 desorption temperature was lowered by 60-120 degrees C, the desorbed gravimetric H2 capacity at temperatures < 250 degrees C was doubled, and the desorption kinetics increased by a factor of ~6 compared to uncoated Mg(BH4)2. However, hydrolysis reactions caused by residual surface -OH groups from the ALD water-pulse degraded the sample substantially. Through this study, the use of TMA was observed to be highly reactive with the Mg(BH4)2 surface species, leading to the strategy of exposing the sample only to TMA. The relative mole fraction of the vapor-phase additive can be precisely controlled with the number of TMA pulses and pulse duration. By tuning these parameters, we show in our second study that 10 pulses of TMA at ambient conditions were able to decrease the H2 desorption temperature by ~100 degrees C while retaining <95 % of its H2 capacity. We applied this approach with other additives such as BBr3, TiCl4 and tetrahydrofuran, and demonstrate that this unique approach opens the door to a new class of molecular additives and catalysts which cannot easily be introduced with conventional mechano-chemical or solvent-based techniques for (complex) metal-hydrides. In the case of metal organic frameworks, ALD is a promising technique to functionalize the pores with metal atoms or functional groups able to tune the gas selectivity and binding energy, for which ~15 kJ/mol has been established as the optimal value for H2 storage in sorbent materials. Vapor-phase techniques such as ALD have numerous benefits over other functionalization tools for H2 storage materials opening innumerable opportunities to the field. To exploit these opportunities, the current limitations on room temperature and water-less ALD processes needs to be overcome which will greatly expand the possibilities of encapsulation and incorporation of additives for organic frameworks and (complex) metal hydrides.

atomic layer deposition↗