Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “INTERPOLATION”

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 1,513 records · Page 84
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Experimental and theoretical study of rotationally inelastic diffraction of H{sub 2}(D{sub 2}) from methyl-terminated Si(111)

Fundamental details concerning the interaction between H{sub 2} and CH{sub 3}–Si(111) have been elucidated by the combination of diffractive scattering experiments and electronic structure and scattering calculations. Rotationally inelastic diffraction (RID) of H{sub 2} and D{sub 2} from this model hydrocarbon-decorated semiconductor interface has been confirmed for the first time via both time-of-flight and diffraction measurements, with modest j = 0 → 2 RID intensities for H{sub 2} compared to the strong RID features observed for D{sub 2} over a large range of kinematic scattering conditions along two high-symmetry azimuthal directions. The Debye-Waller model was applied to the thermal attenuation of diffraction peaks, allowing for precise determination of the RID probabilities by accounting for incoherent motion of the CH{sub 3}–Si(111) surface atoms. The probabilities of rotationally inelastic diffraction of H{sub 2} and D{sub 2} have been quantitatively evaluated as a function of beam energy and scattering angle, and have been compared with complementary electronic structure and scattering calculations to provide insight into the interaction potential between H{sub 2} (D{sub 2}) and hence the surface charge density distribution. Specifically, a six-dimensional potential energy surface (PES), describing the electronic structure of the H{sub 2}(D{sub 2})/CH{sub 3}−Si(111) system, has been computed based on interpolation of density functional theory energies. Quantum and classical dynamics simulations have allowed for an assessment of the accuracy of the PES, and subsequently for identification of the features of the PES that serve as classical turning points. A close scrutiny of the PES reveals the highly anisotropic character of the interaction potential at these turning points. This combination of experiment and theory provides new and important details about the interaction of H{sub 2} with a hybrid organic-semiconductor interface, which can be used to further investigate energy flow in technologically relevant systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

A reactant-coordinate-based approach to state-to-state differential cross sections for tetratomic reactions

A new algorithm is proposed to compute quantum mechanically state-to-state differential cross sections for reactions involving four atoms in full dimensionality. This algorithm, which is based on the propagation of an initial state specific wave packet exclusively in reactant coordinates, extracts the S-matrix elements in the product channel by first interpolating the time-dependent wave packet using a collocation method at selected time intervals on the product coordinate grid and then projecting out the contributions of all final product states. Here, this approach is efficient and accurate, particularly for reactions that are dominated by a product well or long-range interactions. Validation of this approach is demonstrated for the H 2 + OH → H + H 2 O reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems

Here, an explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as discrete differential form fields on a fixed mesh. With the assistance of Whitney interpolating forms, this scheme preserves the gauge symmetry of the electromagnetic field, and the pressure field is naturally derived from the discrete internal energy. The whole system is solved using the Hamiltonian splitting method discovered by He et al. [Phys. Plasmas 22, 124503 (2015)], which was been successfully adopted in constructing symplectic particle-in-cell schemes. Because of its structure preserving and explicit nature, this algorithm is especially suitable for large-scale simulations for physics problems that are multi-scale and require long-term fidelity and accuracy. The algorithm is verified via two tests: studies of the dispersion relation of waves in a two-fluid plasma system and the oscillating two-stream instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Efficient manifolds tracing for planar maps

Here, we present an exact calculation method and an approximation technique for tracing the invariant manifolds of unstable periodic orbits of planar maps. The exact approach relies on an adaptive refinement procedure that prevents redundant calculations occurring in other approaches, and the approximated method relies on a novel interpolation approach based on normal displacement functions. The resulting approximated manifold is precise when compared to the exact one, and its relative computational cost falls like the inverse of the manifold length. To present the tracing method, we obtain the invariant manifolds of the Chirikov-Taylor map, and as an application we illustrate the transition from homoclinic to heteroclinic chaos in the Duffing oscillator that leads from localized chaos to global chaotic motion.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2018

A new method for analyzing and visualizing plasma simulations using a phase-space tessellation

We apply a novel phase-space interpolation technique referred to as the simplex-in-cell (SIC) method to analyze two- and three-dimensional particle-in-cell (PIC) simulations of electromagnetic plasmas. SIC relies on a discretization of the initial phase-space distribution function into simplices, which allows an approximation to the full, continuously defined distribution function to be constructed at any later time in the simulation. This allows densities, currents, and even full momentum distribution functions to be measured at any point in the simulation domain without averaging over control volumes. The SIC approach applies to any PIC simulation for which a tessellation of the initial particle distribution can be constructed. In this study, we use outputs from standard PIC simulations of the Weibel instability and compare physical quantities such as charge and current densities calculated in postprocessing using SIC and standard particle deposits. Using 2D simulations with 1–65 536 particles-per-cell, we find that SIC eliminates discrete particle noise and in some cases can reach a given noise level using ~1000 times fewer simulation particles than with standard particle deposition schemes. In regions of low density, such as between current filaments, SIC is able to capture small amplitude features even with fewer particles than gridpoints due to the deformable nature of the SIC volume elements. Here, by calculating momentum distributions, we show how SIC can capture low density tails in the spectrum using far fewer particles than are necessary for standard particle deposits. We calculate the charge density on spatial grids of increasing resolution to demonstrate the ability of SIC to reveal fine-scale details that are not accessible with standard particle deposits. Finally, we show how SIC can be extended to 3D and give an example of its use to calculate the charge density from 3D PIC simulations of the Weibel instability. These results motivate the future implementation of SIC directly in the simulation force calculation for a novel low-noise electromagnetic plasma simulation method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Adaptive coupling of a deep neural network potential to a classical force field

An adaptive modeling method (AMM) that couples a deep neural network potential and a classical force field is introduced to address the accuracy-efficiency dilemma faced by the molecular simulation community. The AMM simulated system is decomposed into three types of regions. The first type captures the important phenomena in the system and requires high accuracy, for which we use the Deep Potential Molecular Dynamics (DeePMD) model in this work. The DeePMD model is trained to accurately reproduce the statistical properties of the ab initio molecular dynamics. The second type does not require high accuracy, and a classical force field is used to describe it in an efficient way. The third type is used for a smooth transition between the first and the second types of regions. By using a force interpolation scheme and imposing a thermodynamics force in the transition region, we make the DeePMD region embedded in the AMM simulated system as if it were embedded in a system that is fully described by the accurate potential. A representative example of the liquid water system is used to show the feasibility and promise of this method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Overlapped embedded fragment stochastic density functional theory for covalently-bonded materials

The stochastic density functional theory (DFT) is a valuable linear-scaling approach to Kohn-Sham DFT that does not rely on the sparsity of the density matrix. Linear (and often sub-linear) scaling is achieved by introducing a controlled statistical error in the density, energy, and forces. The statistical error (noise) is proportional to the inverse square root of the number of stochastic orbitals and thus decreases slowly; however, by dividing the system into fragments that are embedded stochastically, the statistical error can be reduced significantly. This has been shown to provide remarkable results for non-covalently-bonded systems; however, the application to covalently bonded systems had limited success, particularly for delocalized electrons. Here, we show that the statistical error in the density correlates with both the density and the density matrix of the system and propose a new fragmentation scheme that elegantly interpolates between overlapped fragments. In conclusion, we assess the performance of the approach for bulk silicon of varying supercell sizes (up to N e = 16 384 electrons) and show that overlapped fragments reduce significantly the statistical noise even for systems with a delocalized density matrix.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Checking the Salpeter enhancement of nuclear reactions at intermediate coupling in asymmetric mixtures

In this study, we investigate the plasma enhancement of nuclear reactions in the intermediate coupling regime using orbital free molecular dynamics (OFMD) simulations. Mixtures of H-Cu and H-Ag serve as prototypes of simultaneous weak and strong couplings due to the charge asymmetry. Of particular importance is the partial ionization of Cu and Ag and the free electron polarization captured by OFMD simulations. By comparing a series of OFMD simulations at various concentrations and constant pressure to multi-component hyper-netted chain (MCHNC) calculations of effective binary ionic mixtures, we set a general procedure for computing enhancement factors. The MCHNC procedure allows extension to very low concentrations (5% or less) and to very high temperatures (few keV) unreachable by the simulations. Lastly, enhancement factors for nuclear reaction rates extracted from the MCHNC approach are compared with the Salpeter theory in the weak and strong coupling regimes, and a new interpolation is proposed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Comparative collisionless alpha particle confinement in stellarator reactors with the XGC gyrokinetic code

Whole volume simulations of stellarators are necessary to address a number of important physics and engineering issues, including turbulent transport prediction and optimising divertor operation. In this work, advances in development of a whole volume stellarator capability for the global gyrokinetic particle-in-cell code XGC are detailed. A 3D interpolation of the equilibrium magnetic eld to the last close flux surface, calculated using the VMEC ideal magnetohydrodynamic equilibrum code, has been implemented. Orbit tracing with the XGC code is verified for the Wendelstein 7-X stellarator by comparison with the BEAMS3D and EUTERPE codes. The XGC stellarator version has then been used to consider collisionless alpha particle con nement in representative quasi-isodynamic and quasi-axisymmetric designs. It has been shown that, at least without further optimisation for energetic particle confinement, the Wendelstein 7-X-like quasi-isodynamic reactor design exhibits better alpha particle confinement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Dynamically weighted multireference perturbation theory: Combining the advantages of multi-state and state-averaged methods

In this paper, we introduce two new approaches to compute near-degenerate electronic states based on the driven similarity renormalization group (DSRG) framework. The first approach is a unitary multi-state formalism based on the DSRG (MS-DSRG), whereby an effective Hamiltonian is built from a set of state-specific solutions. The second approach employs a dynamic weighting parameter to smoothly interpolate between the multi-state and the state-averaged DSRG schemes. The resulting dynamically weighted DSRG (DW-DSRG) theory incorporates the most desirable features of both multi-state approaches (ability to accurately treat many states) and state-averaged methods (correct description of avoided crossings and conical intersections). We formulate second-order perturbation theories (PT2) based on the MS- and DW-DSRG and study the potential energy curves of LiF, the conical intersection of the two lowest singlet states of NH 3 , and several low-lying excited states of benzene, naphthalene, and anthracene. The DW-DSRG-PT2 predicts the correct avoided crossing of LiF and avoids artifacts produced by the corresponding state-specific and multi-state theories. Excitation energies of the acenes computed with the DW-DSRG-PT2 are found to be more accurate than the corresponding state-averaged values, showing a small dependence on the number of states computed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

MPRAD: A Monte Carlo and ray-tracing code for the proton radiography in high-energy-density plasma experiments

Proton radiography is used in various high-energy-density (HED) plasma experiments. In this paper, we describe a Monte Carlo and raytracing simulation tool called multimegaelectronvolt proton radiography (MPRAD) that can be used for modeling the deflection of proton beams in arbitrary three dimensional electromagnetic fields as well as the diffusion of the proton beams by Coulomb scattering and stopping power. Specifically, the Coulomb scattering and stopping power models in cold matter and fully ionized plasma are combined using interpolation. We discuss the application of MPRAD in a few setups relevant to HED plasma experiments where the plasma density can play a role in diffusing the proton beams and affecting the prediction and interpretation of the proton images. It is shown how the diffusion due to plasma density can affect the resolution and dynamical range of the proton radiography.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Insulators at fractional fillings in twisted bilayer graphene partially aligned to hexagonal boron nitride

At partial fillings of its flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts a rich variety of competing correlated phases that show sample-to-sample variations. Divergent phase diagrams in MATBG are often attributed to the sublattice polarization energy scale, tuned by the degree of alignment of the hexagonal boron nitride (hBN) substrates typically used in van der Waals devices. Unaligned MATBG exhibits unconventional superconductor and correlated insulator phases, while nearly perfectly aligned MATBG/hBN exhibits zero-field Chern insulating phases and lacks superconductivity. Here we use scanning tunneling microscopy and spectroscopy (STM/STS) to observe gapped phases at partial fillings of the flat bands of MATBG in a new intermediate regime of sublattice polarization, observed when MATBG is only partially aligned (θ Gr-hBN ≈ 1.65°) to the underlying hBN substrate. Under this condition, MATBG hosts not only phenomena that naturally interpolate between the two sublattice potential limits, but also unexpected gapped phases absent in either of these limits. At charge neutrality, we observe an insulating phase with a small energy gap (Δ < 5 meV) likely related to weak sublattice symmetry breaking from the hBN substrate. In addition, we observe new gapped phases near fractional fillings ν = ±1/3 and ν = ±1/6, which have not been previously observed in MATBG. Importantly, energy-resolved STS unambiguously identifies these fractional filling states to be of single-particle origin, possibly a result of the super-superlattice formed by two moiré superlattices. Finally, our observations emphasize the power of STS in distinguishing single-particle gapped phases from many-body gapped phases in situations that could be easily confused in electrical transport measurements, and demonstrate the use of substrate engineering for modifying the electronic structure of a moiré flat-band material.

Physics↗
DOE OSTI2023

Eulerian finite element simulations of the drop weight impact test with a dislocation Density-based continuum model

During a drop weight impact test, the kinetic energy of the falling weight is transferred into the sample resting on the anvil. The plastic deformation in the sample is an important mechanism for the dissipation of the input kinetic energy. We use Eulerian finite element analysis to simulate the deformation and temperature evolution in a 1,3,5-trinitro-1,3,5-triazine (RDX) sample consisting of multiple crystals. In Eulerian finite element simulations, the mesh moves relative to the material. After every change of position between the mesh and the material, the state variables are interpolated to the new mesh position, i.e., advection. In an effort to reduce the advection errors, we use a rate form of a dislocation density-based continuum model by Luscher et al. Here, the simulations predict localization of plastic deformation, and plastic dissipation as a significant source of heat generation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Data-driven recovery of hidden physics in reduced order modeling of fluid flows

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Furthermore, our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

42 ENGINEERING↗
DOE OSTI2020

Computational modeling of charge hopping dynamics along a disordered one-dimensional wire with energy gradients in quantum environments

This computational study investigates the effects of energy gradients on charge hopping dynamics along a one-dimensional chain of discrete sites coupled to quantum bath, which is modeled at the level of Pauli master equation (PME). This study also assesses the performance of different approximations for the hopping rates. Three different methods for solving the PME, a fourth order Runge–Kutta method, numerical diagonalization of the rate matrix followed by analytic propagation, and kinetic Monte Carlo simulation method, are tested and confirmed to produce virtually identical values of time dependent mean square displacement, diffusion constant, and mobility. Five different rate expressions, exact numerical evaluation of Fermi’s Golden Rule (FGR) rate, stationary phase interpolation (SPI) approximation, semiclassical approximation, classical Marcus rate, and Miller–Abrahams rate, are tested to help understand the effects of approximations in representing quantum environments in the presence of energy gradients. The results based on direct numerical evaluation of FGR rate exhibit transition from diffusive to non-diffusive behavior with the increase in the gradient and show that the charge transport in the quantum bath is more sensitive to the magnitude of the gradient and the disorder than in the classical bath. Among all the four approximations for the hopping rates, the SPI approximation is confirmed to work best overall. A comparison of two different methods to calculate the mobility identifies drift motion of the population distribution as the major source of non-diffusive behavior and provides more reliable information on the contribution of quantum bath.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Phase behavior of continuous-space systems: A supervised machine learning approach

The phase behavior of complex fluids is a challenging problem for molecular simulations. Supervised machine learning (ML) methods have shown potential for identifying the phase boundaries of lattice models. In this work, we extend these ML methods to continuous-space systems. We propose a convolutional neural network model that utilizes grid-interpolated coordinates of molecules as input data of ML and optimizes the search for phase transitions with different filter sizes. We test the method for the phase diagram of two off-lattice models, namely, the Widom–Rowlinson model and a symmetric freely jointed polymer blend, for which results are available from standard molecular simulations techniques. The ML results show good agreement with results of previous simulation studies with the added advantage that there is no critical slowing down. We find that understanding intermediate structures near a phase transition and including them in the training set is important to obtain the phase boundary near the critical point. The method is quite general and easy to implement and could find wide application to study the phase behavior of complex fluids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Improved accuracy and transferability of molecular-orbital-based machine learning: Organics, transition-metal complexes, non-covalent interactions, and transition states

We report molecular-orbital-based machine learning (MOB-ML) provides a general framework for the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. The application of Nesbet’s theorem makes it possible to recast a typical extrapolation task, training on correlation energies for small molecules and predicting correlation energies for large molecules, into an interpolation task based on the properties of orbital pairs. We demonstrate the importance of preserving physical constraints, including invariance conditions and size consistency, when generating the input for the machine learning model. Numerical improvements are demonstrated for different datasets covering total and relative energies for thermally accessible organic and transition-metal containing molecules, non-covalent interactions, and transition-state energies. MOB-ML requires training data from only 1% of the QM7b-T dataset (i.e., only 70 organic molecules with seven and fewer heavy atoms) to predict the total energy of the remaining 99% of this dataset with sub-kcal/mol accuracy. This MOB-ML model is significantly more accurate than other methods when transferred to a dataset comprising of 13 heavy atom molecules, exhibiting no loss of accuracy on a size intensive (i.e., per-electron) basis. It is shown that MOB-ML also works well for extrapolating to transition-state structures, predicting the barrier region for malonaldehyde intramolecular proton-transfer to within 0.35 kcal/mol when only trained on reactant/product-like structures. Finally, the use of the Gaussian process variance enables an active learning strategy for extending the MOB-ML model to new regions of chemical space with minimal effort. We demonstrate this active learning strategy by extending a QM7b-T model to describe non-covalent interactions in the protein backbone–backbone interaction dataset to an accuracy of 0.28 kcal/mol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗