SEARCH · Search NASA

Results for “Real 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.

SourceResearch connectionFrom yearThrough year

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

At least 307 records · Page 17

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Real-space visualization of short-range antiferromagnetic correlations in a magnetically enhanced thermoelectric

Short-range magnetic correlations can significantly increase the thermopower of magnetic semiconductors, representing a noteworthy development in the decades-long effort to develop high-performance thermoelectric materials. Here, we reveal the nature of the thermopower-enhancing magnetic correlations in the antiferromagnetic semiconductor MnTe. Using magnetic pair distribution function analysis of neutron scattering data, we obtain a detailed, real-space view of robust, nanometer-scale, antiferromagnetic correlations that persist into the paramagnetic phase above the Neel temperature $T_N$ = 307 K. In this work, the magnetic correlation length in the paramagnetic state is significantly longer along the crystallographic c axis than within the ab plane, pointing to anisotropic magnetic interactions. Ab initio calculations of the spin-spin correlations using density functional theory in the disordered local moment approach reproduce this result with quantitative accuracy. These findings constitute the first real-space picture of short-range spin correlations in a magnetically enhanced thermoelectric and inform future efforts to optimize thermoelectric performance by magnetic means.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A Nonlocal-Gradient Descent Method for Inverse Design in Nanophotonics

Local-gradient-based optimization approaches lack nonlocal exploration abilityrequired for escaping from local minima when searching non-convex landscapes.A directional Gaussian smoothing (DGS) approach was recently proposed in [29]and used to define a truly nonlocal gradient, referred to as the DGS gradient, inorder to enable nonlocal exploration in high-dimensional black-box optimization.Promising results show that replacing the traditional local gradient with the nonlocalDGS gradient can significantly improve the performance of gradient-based methodsin optimizing highly multi-modal loss functions. However, the current DGS methodis designed for unbounded and uncontrained optimization problems, making itinapplicable to real-world engineering optimization problems where the tuningparameters are often bounded and the loss function is usually constrained byphysical processes. In this work, we propose to extend to the DGS approachto the constrained inverse design framework in order to find better optima ofmulti-modal loss functions. A series of adaptive strategies for smoothing radiusand learning rate updating are developed to improve the computational efficiencyand robustness. Our methodology is demonstrated by an example of designing ananoscale wavelength demultiplexer, and shows superior performance compared tothe state-of-the-art approaches. By incorporating volume constraints, the optimizeddesign achieves an equivalently high performance but significantly reduces theamount of material usage.

Bi, Sirui↗

DOE OSTI2024

Human-in-the-Loop: The Future of Machine Learning in Automated Electron Microscopy

Machine learning (ML) methods are progressively gaining acceptance in the electron microscopy community for de-noising, semantic segmentation, and dimensionality reduction of data post-acquisition. The introduction of the application programming interfaces (APIs) by major instrument manufacturers now allows the deployment of ML workflows in microscopes, not only for data analytics but also for real-time decision-making and feedback for microscope operation. However, the number of use cases for real-time ML remains remarkably small. Furthermore, we discuss some considerations in designing ML-based active experiments and pose that the likely strategy for the next several years will be human-in-the-loop automated experiments (hAE). In this paradigm, the ML learning agent directly controls beam position and image and spectroscopy acquisition functions, and a human operator monitors experiment progression in real and feature space of the system and tunes the policies of the ML agent to steer the experiment toward specific objectives.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Skew-Symmetric adjacency matrices for clustering directed graphs

Graph clustering methods often critically rely on the symmetry of graph matrices. Developing analogous methods for digraphs often proves more challenging, because digraph matrices are typically asymmetric and not orthogonally diagonalizable. However, researchers have recently proposed several complex-valued Hermitian digraph matrices. In particular, one such representation has been utilized as an input to an algorithm for finding imbalanced cuts. In this work, we establish an algebraic relationship between this matrix and an associated real-valued matrix. We show using this real-valued matrix for imbalanced cut-finding algorithms is not only sufficient but advantageous. Our algorithm uses less memory and asymptotically less computation while provably preserving solution quality. We also show our method can be easily implemented using standing computational building blocks, possesses better numerical properties, and loans itself to a natural interpretation via an objective function relaxation argument. We empirically demonstrate these advantages on real world data sets and show how our algorithm can uncover meaningful cluster structure.

Hayashi, Koby↗

DOE OSTI2024

Swarm Intelligence Based Optimal Design of Local Volt/Var Control Function for Distributed Energy Resources

The increasing penetration of renewable based distributed energy resources (DERs) in distribution network (DN) leads to larger and more frequent voltage variation in distributions network (DN), thus posing challenges on voltage control. Real-time local voltage control method is a promising solution for the above issue. However, the local voltage control function needs to be customized and optimized according to real distribution system condition. In this paper, a swarm intelligence based Volt/Var control optimal design method (SO-VVC) is proposed to optimize the control function. Compared with existing approaches, the proposed method can not only represent the nonlinear behaviour of power flow but is also computation efficient. The performance of the proposed SO-VVC is demonstrated by case studies on a modified IEEE-123 bus system.

Zhang, Zhengfa [University of Tennessee, Knoxville↗

DOE OSTI2023

Real-space solution to the electronic structure problem for nearly a million electrons

We report a Kohn–Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix–vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh–Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Chemistry↗

DOE OSTI2023

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree–Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree–Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Imaging real-space flat band localization in kagome magnet FeSn

Kagome lattices host flat bands due to their frustrated lattice geometry, which leads to destructive quantum interference of electron wave functions. Here, we report imaging of the kagome flat band localization in real-space using scanning tunneling microscopy. We identify both the Fe 3 Sn kagome lattice layer and the Sn 2 honeycomb layer with atomic resolution in kagome antiferromagnet FeSn. On the Fe 3 Sn lattice, at the flat band energy determined by the angle resolved photoemission spectroscopy, tunneling spectroscopy detects an unusual state localized uniquely at the Fe kagome lattice network. We further show that the vectorial in-plane magnetic field manipulates the spatial anisotropy of the localization state within each kagome unit cell. Our results are consistent with the real-space flat band localization in the magnetic kagome lattice. We further discuss the magnetic tuning of flat band localization under the spin–orbit coupled magnetic kagome lattice model.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Enhancing Early Systems R&D Capabilities with Systems —Theoretic Process Analysis

Systems engineering today faces a wide array of challenges, ranging from new operational environments to disruptive technological — necessitating approaches to improve research and development (R&D) efforts. Yet, emphasizing the Aristotelian argument that the “whole is greater than the sum of its parts” seems to offer a conceptual foundation creating new R&D solutions. Invoking systems theoretic concepts of emergence and hierarchy and analytic characteristics of traceability, rigor, and comprehensiveness is potentially beneficial for guiding R&D strategy and development to bridge the gap between theoretical problem spaces and engineering-based solutions. In response, this article describes systems–theoretic process analysis (STPA) as an example of one such approach to aid in early-systems R&D discussions. STPA—a ‘top-down’ process that abstracts real complex system operations into hierarchical control structures, functional control loops, and control actions—uses control loop logic to analyze how control actions (designed for desired system behaviors) may become violated and drive the complex system toward states of higher risk. By analyzing how needed controls are not provided (or out of sequence or stopped too soon) and unneeded controls are provided (or engaged too long), STPA can help early-system R&D discussions by exploring how requirements and desired actions interact to either mitigate or potentially increase states of risk that can lead to unacceptable losses. This article will demonstrate STPA's benefit for early-system R&D strategy and development discussion by describing such diverse use cases as cyber security, nuclear fuel transportation, and US electric grid performance. Together, the traceability, rigor, and comprehensiveness of STPA serve as useful tools for improving R&D strategy and development discussions. In conclusion, leveraging STPA as well as related systems engineering techniques can be helpful in early R&D planning and strategy development to better triangulate deeper theoretical meaning or evaluate empirical results to better inform systems engineering solutions.

42 ENGINEERING↗

DOE OSTI2024

Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms

We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty; which most functional alignment methods cannot handle. A pair of functions can also have multiple optimal alignment solutions, which is not addressed in current literature. In this paper, a flexible Bayesian approach to functional alignment is presented, which appropriately accounts for noise in the data without any pre-smoothing required. Additionally, by running parallel MCMC chains, the method can account for multiple optimal alignments via the multi-modal posterior distribution of the warping functions. To most efficiently sample the warping functions, the approach relies on a modification of the standard Hamiltonian Monte Carlo to be well-defined on the infinite-dimensional Hilbert space. In this work, this flexible Bayesian alignment method is applied to both simulated data and real data sets to show its efficiency in handling noisy functions and successfully accounting for multiple optimal alignments in the posterior; characterizing the uncertainty surrounding the warping functions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Density Functional Tight-Binding Enables Tractable Studies of Quantum Plasmonics

Routine investigations of plasmonic phenomena at the quantum level present a formidable computational challenge due to the large system sizes and ultrafast time scales involved. This Feature Article highlights the use of density functional tight-binding (DFTB), particularly its real-time time-dependent formulation (RT-TDDFTB), as a tractable approach to study plasmonic nanostructures from a quantum mechanical purview. We begin by outlining the theoretical framework and limitations of DFTB, emphasizing its efficiency in modeling systems with thousands of atoms over picosecond time scales. Applications of RT-TDDFTB are then explored in the context of optical absorption, nonlinear harmonic generation, and plasmon-mediated photocatalysis. We demonstrate how DFTB can reconcile classical and quantum descriptions of plasmonic behavior, capturing key phenomena such as size-dependent plasmon shifts and plasmon coupling in nanoparticle assemblies. Lastly, we showcase DFTB’s ability to model hot carrier generation and reaction dynamics in plasmon-driven H2 dissociation, underscoring its potential to model photocatalytic processes. Collectively, these studies establish DFTB as a powerful, yet computationally efficient tool to probe the emergent physics of materials at the limits of space and time.

Electrical energy↗

DOE OSTI2021

An Observationally Trained Markov Model for MJO Propagation

A Markovian stochastic model is developed for studying the propagation of the Madden-Julian Oscillation (MJO). This model represents the daily changes in real time multivariate MJO (RMM) indices as random functions of their current state and background conditions. The probability distribution function of the RMM changes is obtained using a machine learning algorithm trained to maximize MJO forecast skills using observed daily indices of RMM and different modes of variability. Skillful forecasts are obtained for lead times between 8 and 27 days. Large ensemble simulations by the stochastic model show that with monsoonal changes in the background state, MJO propagation across the Maritime Continent (MC) is most likely to be disrupted in boreal spring and summer when MJO events propagate from favorable conditions over the Indian Ocean to unfavorable ones over the MC, and predictability is higher during spring and summer when MJO activity is away from the MC region.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Enhancing nanoscale charged colloid crystallization near a metastable liquid binodal

Achieving predictive control over crystallization using non-classical nucleation while avoiding kinetic traps would be a step towards designing materials with new functionalities. We address these challenges by inducing the bottom-up assembly of nanocrystals into ordered arrays, or superlattices. Using electrostatics—rather than density—to tune the interactions between particles, we watch self-assembly proceed through a metastable liquid phase. Here, we systematically investigate the phase behaviour as a function of quench conditions in situ and in real time using small-angle X-ray scattering. By fitting to colloid, liquid and superlattice models, we extract the time evolution of each phase and the system phase diagram, which we find to be consistent with short-range attractive interactions. Using the predictive power of the phase diagram, we establish control of the self-assembly rate over three orders of magnitude, and we identify one- and two-step self-assembly regimes, with only the latter implicating the metastable liquid as an intermediate. The presence of the metastable liquid increases the superlattice formation rate relative to the equivalent one-step pathway, and the superlattice order increases with the rate, revealing a generalizable kinetic strategy for promoting and enhancing ordered assembly.

Tanner, Christian P. N. [University of California,↗

DOE OSTI2021

Noise reduction in X-ray photon correlation spectroscopy with convolutional neural networks encoder–decoder models

Abstract Like other experimental techniques, X-ray photon correlation spectroscopy is subject to various kinds of noise. Random and correlated fluctuations and heterogeneities can be present in a two-time correlation function and obscure the information about the intrinsic dynamics of a sample. Simultaneously addressing the disparate origins of noise in the experimental data is challenging. We propose a computational approach for improving the signal-to-noise ratio in two-time correlation functions that is based on convolutional neural network encoder–decoder (CNN-ED) models. Such models extract features from an image via convolutional layers, project them to a low dimensional space and then reconstruct a clean image from this reduced representation via transposed convolutional layers. Not only are ED models a general tool for random noise removal, but their application to low signal-to-noise data can enhance the data’s quantitative usage since they are able to learn the functional form of the signal. We demonstrate that the CNN-ED models trained on real-world experimental data help to effectively extract equilibrium dynamics’ parameters from two-time correlation functions, containing statistical noise and dynamic heterogeneities. Strategies for optimizing the models’ performance and their applicability limits are discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Intercalation–exfoliation processes during ionic exchange reactions from sodium lepidocrocite-type titanate toward a proton-based trititanate structure

Topochemical reactions involving ionic exchange have been used to assess a large number of metastable compositions, particularly in layered metal oxides. This method encompasses complex reactions that are poorly explored, yet are of prime importance to understand and control the materials’ properties. In this work, we embark on investigating the reactions involved during the ionic exchange between a layered Na-titanate (lepidocrocite-type structure) and an acidic solution (HCl), leading to a protonic (H 3 O + ) titanate (trititanate structure). The reactions involve an ionic exchange provoking a structural change from the lepidocrocite-type to the trititanate structure as shown by real-space refinements of ex situ pair distribution function data. Mobile Na + ions are exchanged by hydronium ions inducing high proton mobility in the final structure. Moreover, the reaction was followed by ex situ 23 Na and 1 H solid-state MAS NMR which allowed, among other things, confirming that the Na + ions are in the interlayer space and specifying their local environment. Strikingly, the ionic exchange reaction induces progressive exfoliation of the Na-titanate particles leading to 2–5 nm thin elongated crystallites. To further understand the different steps associated with the ionic exchange, the evolution of the electrolytic conductivity, using conductimetric titration, has been monitored upon HCl addition, enabling characterization of the intercalation(H + )/de-intercalation(Na + ) reactions and assessing kinetic parameters. Accordingly, it is hypothesized that the exfoliation of the particles is due to the accumulation of charges at the particle level in relation to the rapid intercalation of protons. This work provides novel insights into ionic exchange reactions involved in layered oxide compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

DESC: A stellarator equilibrium solver

In this paper, the new code DESC is presented to solve for fixed-boundary ideal magnetohydrodynamic equilibria in stellarators. The approach directly solves the equilibrium force balance as a system of nonlinear equations in the form f(x) = 0. The independent variables x represent nested magnetic flux surfaces expressed in the inverse representation with toroidal flux coordinates, and the equations f(x) quantify equilibrium force balance errors at discrete points in real space. Discretizing with global Fourier–Zernike basis functions properly treats the magnetic axis and minimizes the number of coefficients needed to describe the flux surfaces. The pseudospectral method provides great flexibility in where the errors are evaluated, and the system of equations is efficiently solved with a Newton–Raphson iteration. Equilibria are computed and compared against VMEC for both axisymmetric and non-axisymmetric examples. The results show fast convergence rates and solutions with low errors throughout the plasma volume.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

A new method for solving the linearized 1D Vlasov–Poisson system yielding a new class of solutions

We describe a new method for solving the linearized 1D Vlasov–Poisson system by using properties of Cauchy-type integrals. Our method remedies critical flaws of the two standard methods, reveals a previously unrecognized Gaussian-in-time-like decay, and can also account for an externally applied electric field. The Landau approximation involves deforming the Bromwich contour around the poles closest to the real axis due to the analytically continued dielectric function, finding the long-time behavior for a stable system: Landau damping. Jackson's generalization encircles all poles while sending the contour to infinity, assuming its contribution vanishes, which is not true in general. This gives incorrect solutions for physically reasonable configurations and can exhibit pathological behavior, of which we show examples. The van Kampen method expresses the solution for a stable equilibrium as a continuous superposition of waves, resulting in an opaque integral. Case's generalization includes unstable systems and predicts a decaying discrete mode for each growing discrete mode, an apparent contradiction to both the Jackson solution and ours. We show, without imposing additional constraints, that the decaying modes are never present in the time evolution due to an exact cancellation with part of the continuum. Our solution is free of integral expressions, is obtained using algebra and Laurent series expansions, does not rely on analytic continuations, and results in a correct asymptotically convergent form in the case of infinite sums. The analysis used can be readily applied in higher-dimensional, electromagnetic systems and also provides a new technique for evaluating certain inverse Laplace transforms.

Physics↗