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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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At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Solving a two-electron quantum dot model in terms of polynomial solutions of a Biconfluent Heun equation

The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are investigated. In particular, it is shown that it is possible to determine exactly and in a closed form a finite portion of the energy spectrum and the associated eigenfunctions for the Schrödinger equation describing the relative motion of the electrons, by putting it into the form of a biconfluent Heun equation. In the same framework, another set of solutions of this type can be straightforwardly obtained for the case when the two electrons are submitted also to an external constant magnetic field. - Highlights: • Exact solution of a quantum dot model. • Determination of the energy levels. • Investigation of how the radial wave functions depend on the external excitation frequency. • Characteristic length between the two-electrons are found to be compatible with the semiconductor lattice parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Comment on: “Solving many-body Schrödinger equations with kinetic energy partition method”, Ann. Phys. 388 (2018) 54–68 by Y-H. Chen and S.D. Chao

We discuss a recent test of the performance of the kinetic energy partition method (KEP) through its application to two separable quantum-mechanical models. We argue that one of the benchmark models is exceedingly simple for testing any realistic approximate method and that almost any reasonable approach yields better results. In the second example our exact benchmark eigenvalues disagree considerably with those chosen by the authors for comparison, which casts doubts on the accuracy of their KEP approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Solving scattering problems in the half-line using methods developed for scattering in the full line

We reduce the solution of the scattering problem defined on the half-line [0,∞) by a real or complex potential v(x) and a general homogeneous boundary condition at x=0 to that of the extension of v(x) to the full line that vanishes for x<0. We find an explicit expression for the reflection amplitude of the former problem in terms of the reflection and transmission amplitudes of the latter. We obtain a set of conditions on these amplitudes under which the potential in the half-line develops bound states, spectral singularities, and time-reversed spectral singularities where the potential acts as a perfect absorber. We examine the application of these results in the study of the scattering properties of a δ-function potential and a finite barrier potential defined in [0,∞), discuss optical systems modeled by these potentials, and explore the configurations in which these systems act as a laser or perfect absorber. In particular, we derive an explicit formula for the laser threshold condition for a slab laser with a single mirror and establish the surprising fact that a nearly perfect mirror gives rise to a lower threshold gain than a perfect mirror. We also offer a nonlinear extension of our approach which allows for utilizing a recently developed nonlinear transfer matrix method in the full line to deal with finite-range nonlinear scattering interactions defined in the half-line.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

An adaptive local reduced basis method for solving PDEs with uncertain inputs and evaluating risk

Many physical systems are modeled using partial differential equations (PDEs) with uncertain or random inputs. For such systems, naively propagating a fixed number of samples of the input probability law (or an approximation thereof) through the PDE is often inadequate to accurately quantify the "risk" associated with critical system responses. In this paper, we develop a goal-oriented, adaptive sampling and local reduced basis approximation for PDEs with random inputs. Our method determines a set of samples and an associated (implicit) Voronoi partition of the parameter domain on which we build local reduced basis approximations of the PDE solution. The samples are selected in an adaptive manner using an a posteriori error indicator. A notable advantage of the proposed approach is that the computational cost of the approximation during the adaptive process remains constant. We provide theoretical error bounds for our approximation and numerically demonstrate the performance of our method when compared to widely used adaptive sparse grid techniques. In addition, we tailor our approach to accurately quantify the risk of quantities of interest that depend on the PDE solution. We demonstrate our method on an advection-diffusion example and a Helmholtz example. Keywords: stochastic partial differential equation, adaptive sampling, reduced basis, a posteriori error estimation, coherent risk measure, conditional value-at-risk.

42 ENGINEERING↗
DOE OSTI2021

On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit high-frequency or multi-scale features. Here in this work we investigate this limitation through the lens of Neural Tangent Kernel (NTK) theory and elucidate how PINNs are biased towards learning functions along the dominant eigen-directions of their limiting NTK. Using this observation, we construct novel architectures that employ spatio-temporal and multi-scale random Fourier features, and justify how such coordinate embedding layers can lead to robust and accurate PINN models. Numerical examples are presented for several challenging cases where conventional PINN models fail, including wave propagation and reaction–diffusion dynamics, illustrating how the proposed methods can be used to effectively tackle both forward and inverse problems involving partial differential equations with multi-scale behavior.

42 ENGINEERING↗
DOE OSTI2021

Solving inverse problems in stochastic models using deep neural networks and adversarial training

Inverse problems associated with stochastic models constitute a significant portion of scientific and engineering applications. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their demanding assumptions or prohibitive computational consumption; for example, maximum likelihood methods require closed-form density functions, and Markov Chain Monte Carlo needs a large number of simulations. We propose a new method that estimates the unknown distribution by matching the statistical properties between observed and simulated random processes. We leverage the expressive power of neural networks to approximate the unknown distribution and use a discriminative neural network for computing the statistical discrepancies between the observed and simulated random processes. Here we demonstrated numerically that the proposed methods can estimate both the model parameters and learn complicated unknown distributions.

42 ENGINEERING↗
DOE OSTI2025

Solving high-dimensional inverse problems using amortized likelihood-free inference with noisy and incomplete data

Here, we present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates samples of the approximate posterior distribution of the model parameters based on these summary features. The posterior samples are produced in a deep generative fashion by sampling from a latent Gaussian distribution and passing these samples through an invertible transformation. We construct this invertible transformation by sequentially alternating conditional invertible neural network and conditional neural spline flow layers. The summary and inference networks are trained simultaneously. We apply the proposed method to an inversion problem in groundwater hydrology to estimate the posterior distribution of the log-conductivity field conditioned on spatially sparse time-series observations of the system’s hydraulic head responses. The conductivity field is represented with 706 degrees of freedom in the considered problem. Comparison with the likelihood-based iterative ensemble smoother PEST-IES method demonstrates that the proposed method accurately estimates the parameter posterior distribution and the observations’ predictive posterior distribution at a fraction of the inference time of PEST-IES.

conditional invertible neural network↗
DOE OSTI2022

KSSOLV 2.0: An efficient MATLAB toolbox for solving the Kohn-Sham equations with plane-wave basis set

KSSOLV (Kohn-Sham Solver) is a MATLAB toolbox for performing Kohn-Sham density functional theory (DFT) calculations with a plane-wave basis set. KSSOLV 2.0 preserves the design features of the original KSSOLV software to allow users and developers to easily set up a problem and perform ground-state calculations as well as to prototype and test new algorithms. Furthermore, it includes new functionalities such as new iterative diagonalization algorithms, k-point sampling for electron band structures, geometry optimization and advanced algorithms for performing DFT calculations with local, semi-local, and hybrid exchange-correlation functionals. It can be used to study the electronic structures of both molecules and solids. So, we describe these new capabilities in this work through a few use cases. We also demonstrate the numerical accuracy and computational efficiency of KSSOLV on a variety of examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Liquid lithium applications for solving challenging fusion reactor issues and NSTX-U contributions

Steady-state fusion reactor operation presents major divertor technology challenges, including high divertor heat flux both steady-state and transients. In addition to those issues, there are unresolved issues of long term dust accumulation and associated tritium inventory and safety issues. It has been suggested that radiative liquid lithium divertor concepts with a modest lithium-loop could provide a possible solution for these outstanding fusion reactor technology issues while potentially improving the reactor plasma performance. The application of lithium (Li) in NSTX resulted in improved H-mode confinement, H-mode power threshold reduction, and reduction in the divertor peak heat flux while maintaining essentially Li-free core plasma operation even during H-modes. These promising results in NSTX and related modeling calculations motivated the radiative liquid lithium divertor (RLLD) concept and its variant, the active liquid lithium divertor concept (ARLLD), taking advantage of the enhanced Li radiation in relatively poorly confined divertor plasmas. It was estimated that only a few moles/sec of lithium injection would be needed to significantly reduce the divertor heat flux in a tokamak fusion power plant. By operating at lower temperatures ≤ 500°C than the first wall ~ 600 – 700°C, the LL-covered divertor chamber wall surfaces can serve as an effective particle pump, as impurities generally migrate toward lower temperature LL divertor surfaces. To maintain the LL purity, a closed LL loop system with a modest circulating capacity of ~ 1 liter/second (l/sec) is envisioned to sustain the steady-state operation of a 1 GW-electric class fusion power plant. By running the Li loop continuously, it can carry the dust particles and impurities generated in the vacuum vessel to outside where the dust / impurities are removed by relatively simple filter and cold/hot trap systems. Using a cold trap system, it can recover in tritium (T) in real time from LL at a rate of ~ 0.5 g / sec needed to sustain the fusion reaction while minimizing the T inventory issue. With an expected T fraction of ≤ 0.7 %, an acceptable level of T inventory can be achieved. In NSTX-U, preparations are now underway to elucidate the physics of Li plasma interactions with a number of Li application tools and Li radiation spectroscopic instruments. The NSTX-U Li evaporator which provides Li coating over the lower divertor plate, can offer important information on the RLLD concept, and the Li granule injector will test some of the key physics issue on the ARLLD concept. A LL-loop is also being prepared off line for prototyping future use on NSTX-U.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Solving the strength-ductility tradeoff in the medium-entropy NiCoCr alloy via interstitial strengthening of carbon

Interstitial solid strengthening is an effective strategy to harden metallic materials, however, it usually deteriorates the ductility. In this work, we report that addition of carbon into the medium-entropy NiCoCr alloy successfully enhances the strength at no expense of ductility. It was found that up to 0.75 at.% carbon was completely solid-solutionized in (NiCoCr )100-x C x (x = 0, 0.10, 0.25, 0.50 and 0.75 at.%) without formation of any carbides. With the increase of carbon content from 0 to 0.75 at.%, the yield and fracture strength were increased from 242 to 347 MPa to 727 and 862 MPa, respectively, whilst the ductility kept as high as about 75%. It is noteworthy that the integral of the stress over strain for the alloy with 0.75 at.% carbon reaches a value of 59 GPa %, surmounting the level of many reported multi-principal elements alloys. Our analysis indicates that carbon addition increases stacking fault energy, thus delaying occurrence of twinning and decreasing the thickness of twin lamellas. At the early deformation stage, carbon decreases the stress localization and stimulates dislocation multiplication. After occurrence of deformation twinning, finer twinning structure in the alloys added with carbon not only can obstacle and trigger more dislocations, but also transfer plastic deformation more efficiently, thus promoting the twinning process, postponing the plastic instability and eventually giving rise to a more pronounced work-hardening. Our conclusions not only have important implications for understanding the solid solution strengthening mechanism in medium-entropy alloys, but also shed lights on developing advanced metallic alloys with a unique combination of strength and ductility.

36 MATERIALS SCIENCE↗