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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Noncommutative Bohnenblust–Hille inequalities

Abstract Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree (Defant et al. in Math Ann 374(1):653–680, 2019). Such inequalities have found great applications in learning low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, 2022. arXiv preprint arXiv:2209.07279 ). The conjecture was resolved in Huang et al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894 ). In this paper, we give a new proof of these Bohnenblust–Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr’s radius phenomenon on quantum Boolean cubes.

Volberg, Alexander↗

DOE OSTI2022

A fast approximation to supershell partition functions

A formula for supershell partition functions, which play a major role in the Super Transition Array approach to radiative-opacity calculations, is derived as a functional of the distribution of energies within the supershell. It consists in an alternative expansion for an arbitrary number of electrons or holes which also allows for quick approximate evaluations with truncated number of terms in the expansion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Continuously bounds-preserving discontinuous Galerkin methods for hyperbolic conservation laws

For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are typically performed at discrete nodal locations, which is not sufficient to ensure the robustness of the scheme when the solution must be evaluated at arbitrary locations (e.g., for adaptive mesh refinement, remapping in arbitrary Lagrangian–Eulerian solvers, overset meshes, etc.). In this work, a novel limiting approach for discontinuous Galerkin methods is presented which ensures that the solution is continuously bounds-preserving (i.e., across the entire solution polynomial) for any arbitrary choice of basis, approximation order, and mesh element type. Through a modified formulation for the constraint functionals, the proposed approach requires only the solution of a single spatial scalar minimization problem per element for which a highly efficient numerical optimization procedure is presented. Here, the efficacy of this approach is shown in numerical experiments by enforcing continuous constraints in high-order unstructured discontinuous Galerkin discretizations of hyperbolic conservation laws, ranging from scalar transport with maximum principle preserving constraints to compressible gas dynamics with positivity-preserving constraints.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Recent Advances toward Efficient Calculation of Higher Nuclear Derivatives in Quantum Chemistry

In this article, we provide an overview of state-of-the-art techniques that are being developed for efficient calculation of second and higher nuclear derivatives of quantum mechanical (QM) energy. Calculations of nuclear Hessians and anharmonic terms incur high costs and memory and scale poorly with system size. Three emerging classes of methods—machine learning (ML), automatic differentiation (AD), and matrix completion (MC)—have demonstrated promise in overcoming these challenges. We illustrate studies that employ unsupervised ML methods to reduce the need for multiple Hessian calculations in dynamics simulations and those that utilize supervised ML to construct approximate potential energy surfaces and estimate Hessians and anharmonic terms at reduced cost. By extension, if electronic structure operations could be written in a manner similar to functions underlying ML methods, rapid differentiation or AD routines can be employed to inexpensively calculate higher arbitrary-order derivatives. While ML approaches are typically black-box, we describe methods such as compressed sensing (CS) and MC, which explicitly leverage problem-specific mathematical properties of higher derivatives such as sparsity and low-rank, to complete higher derivative information using only a small, incomplete sample. The three classes of methods facilitate reliable predictions of observables ranging from infrared spectra to thermal conductivity and constitute a promising way forward in accurately capturing otherwise intractable higher-order responses of QM energy to nuclear perturbations.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2020

Phase control of coherent acoustic phonons in gold bipyramids for optical memory and manipulating plasmon–exciton coupling

Recent efforts have targeted manipulation of nanomaterial vibrational modes in applications such as chemical/mass sensing, optical switching, and phonon-driven photochemistry. While impulsive photoexcitation can generate coherent phonons, multiple excitation pulses offer the prospect of control and manipulation of coherent phonon modes for functions of optical memory and logic. In this work, we use such an approach to inject an arbitrary coherent phonon phase into a colloidal ensemble of highly monodisperse gold bipyramids. We then demonstrate that this technique can be applied to a system that exhibits plasmon-exciton coupling to further manipulate the hybridization of the system. This ability to manipulate acoustic phonons and hybridization can enable optical logic applications of acoustic phonons in addition to optical memory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Laika BOSS (Binary Object Scanning System)

Laika BOSS (Binary Object Scanning System), often written as "Laikaboss", is an object scanner and intrusion detection system that strives to be scalable, flexible, and verbose. Its goal is to take arbitrary file input and extract all relevant subfiles and metadata for use in helping analysts determine the function and maliciousness of a file at a glance. This is an extension to the original code developed by Lockheed Martin.

Walkup, Gregory↗

NASA NTRS1980

An analytical transformation technique for generating uniformly spaced computational mesh

An analytical transformation method which can map arbitrary physical coordinate grid distribution into desired computational coordinate with uniform grid distribution is derived. The transformation function and its higher derivatives are differentiable. Salient features include; (1) precise control of grid sizes; (2) more than one location of clustered grids; (3) exact positioning of particular computational nodes in the physical plane; and (4) ensuring several patches of uniformly spaced grids in the physical plane for the higher accuracies (such as at the boundaries), etc., while keeping the variation of grid spacing continuous to avoid numerical instability.

Oh, Y. H.↗

NASA NTRS1981

Aerodynamic mathematical modeling - basic concepts

This lecture is a review of the basic concepts involved In the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers. The review leads from Bryan's original formulation through the concepts of linear aerodynamic indicial functions and superposition to the extension of these concepts into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well-defined characteristic motions, reproducible in principle either in wind-tunnel experiments or flow-field computations. A further generalization leads to a torn, accommodating the discontinuous and double-valued behavior characteristic of hysteresis in the steady-state aerodynamic response

Murray Tobak↗

NASA NTRS1985

Magnetic optical activity in intense laser fields. I - Self-rotation and Verdet constant

The paper is concerned with the Faraday rotation and circular dichroism of dilute gases in longitudinal magnetic fields subject to strong radiation fields. In particular, magnetic fields are considered which produce Zeeman shifts much smaller than inverse collision times but which may be greater or smaller then the multipole relaxation times. Doppler broadening is considered, and explicit expressions are given for dipole transitions in a two-level system with arbitrary angular momentum for strong and weak magnetic fields. The same system is then studied as a function of the external magnetic-field strength with a fixed laser frequency. It is shown that this experimental arrangement, referred to as forward scattering, has certain advantages that are not present in the more usual magnetic rotation spectroscopy.

Giraud-Cotton, S.↗

NASA NTRS1992

Electromagnetic scattering by coated convex surfaces and wedges simulated by approximate boundary conditions

Asymptotic/high-frequency solutions are developed for analyzing the non-specular scattering mechanisms associated with coated convex surfaces and edges simulated by approximate boundary conditions. In particular, the standard impedance boundary conditions (SIBC's) and the second order generalized impedance boundary conditions (GIBC's) are employed for a characterization of the edge diffraction, creeping wave, and surface diffracted wave contributions. To study the creeping wave and surface diffracted wave mechanisms, rigorous UTD (uniform geometrical theory of diffraction) diffraction coefficients are developed for a convex coated cylinder simulated with SIBC's and GIBC's. The ray solutions obtained remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficient for a convex cylinder are obtained via a generalization of the corresponding ones of the circular cylinder. To validate the asymptotic/high-frequency solution, integral equations are derived for both E and H-polarization and solved numerically using the method of moments. Results are presented for a single and three layered coated convex cylinder. Some insights are also provided on the accuracy of the employed GIBC's versus SIBC's for application to curved surfaces. To characterize the scattering by impedance wedges illuminated at skew incidence, diffraction coefficients are derived from an approximate solution of the governing functional difference equations. This solution exactly recovers the known ones for an impedance half plane or an arbitrary wedge at normal incidence, and to validate it for other wedge angles, a moment method code was used. Finally, to test the usefulness of the approximate skew incidence impedance wedge diffraction coefficient for three dimensional structures, equivalent currents are derived in the context of the physical theory of diffraction (PTD) for a finite length impedance wedge of arbitrary internal angles. These are incorporated in a standard general purpose PTD code and results are presented for a number of different impedance structures.

Syed, H. H.↗

NASA NTRS1992

A satellite anemometer

We present the conceptual design of an instrument that can provide a continuous analog measure of the pitch and yaw angles of a low altitude satellite in the frame of the neutral atmosphere. The device, which uses pressure sensor orientation to provide its signal, can function in an attitude control loop and/or be used to measure atmospheric winds or wave motions. Any arbitrary angle of attack (pitch and yaw) less than +/- 45 deg can be selected for a heading. The sensitivity of the device is 0.1 deg but this would be limited by low ambient pressure at high altitudes and by multiple particle collisions in and below the slip flow region. The development of a prototype flight unit is in progress.

Hanson, W. B.↗

NASA NTRS2000

Evolution of Rotor Wake in Swirling Flow

A theory is presented for modeling the evolution of rotor wakes as a function of axial distance in swirling mean flows. The theory, which extends an earlier work to include arbitrary radial distributions of mean swirl, indicates that swirl can significantly alter the wake structure of the rotor especially at large downstream distances (i.e., for moderate to large rotor-stator spacings). Using measured wakes of a representative scale model fan stage to define the mean swirl and initial wake perturbations, the theory is used to predict the subsequent evolution of the wakes. The results indicate the sensitivity of the wake evolution to the initial profile and the need to have complete and consistent initial definition of both velocity and pressure perturbations.

El-Haldidi, Basman↗

NASA NTRS1947

On the Theory of the Unsteady Motion of an Airfoil

The paper presents a systematical analysis of the problem of the determination of the unsteady motion about an airfoil moving in an infinite fluid that contains a system of vortices and the determination of the hydrodynamical forces acting on the airfoil. The hydrodynamical problem is reduced to the determination of the function f (xi) which transforms conformally the external region of the airfoil into the interior of a circle. The proposed methods of determining the irrotational motion of a fluid that is produced by any motion of the airfoil are especially simple and effective if the function f (xi) is rational. As an example the flow is determined for the case of an arbitrary motion of an airfoil of the Joukowsky type. The formulas obtained for the determination of the hydrodynamical forces by means of contour integration are similar to those given by S. Chaplygin. These formulas are used to determine the force acting on the airfoil in the cases where the unsteady motion is potential throughout and the circulation about the airfoil is constant and also when the fluid contains a system of vortices. A full discussion is given of the concept of virtual masses together with practical formulas for computing the virtual mass coefficients.

Sedov, L. I.↗

NASA NTRS1996

(abstract) Radiometric Calibration of the Multi-angle Imaging Spectro-Radiometer

The EOS/MISR instrument has completed preflight calibration and characterization of its nine cameras. The radiometric calibration requirements includes absolute radiometric accuracy to 3 percent. To meet this challenging requirement MISR has employed detector based calibration methodology. The source, a 1.65 m integrating sphere, is spatially and spectrally featureless. Thus, when viewing scenes that are likewise homogeneous, the sensor incident radiance is easily retrieved to high accuracy. To enhance the radiance product for arbitrary scene types, however, MISR is planning to incorporate spectral out-of-band, point-spread function deconvolution, and pixel nonuniformity of response corrections. A summary of the preflight calibration is presented in this paper, as well as the error uncertainties for specific scene types with and without these processing corrections.

radiometric calibration EOS MISR↗

NASA NTRS2018

PYSAT: Python Satellite Data Analysis Toolkit

A common problem in space science data analysis is combining complementary data sources that are provided and analyzed in different formats and programming languages. The Python Satellite Data Analysis Toolkit (pysat) addresses this issue by providing an open source toolkit that implements the general process of space science data analysis, from beginning to end, in an instrumentindependent manner. This toolkit uses an Instrument object that enables systematic analysis of science data from a variety of platforms within a single interface. Basic functions such as downloading, loading, and cleaning are included for all supported instruments. Common analysis routines are also included, which are instrument and data source independent. A nanokernel is used to provide instrument independence, it is attached to the Instrument object and mediates the systematic and arbitrary modification of loaded data. Pysat uses the nanokernel to improve the rigor of time series analysis, support onthefly orbit determination, and cleanly span file breaks. Pysat's functions and higherlevel scientific analysis features are validated through the use of unit testing. Further adoption by the community provides a set of scientific results produced by a common core, constituting a distributed heritage that supports the validity of the underlying processing and scientific output. These features are used to demonstrate consistency between derived electron density profiles and measured ion drifts, particularly downward ion drifts in the afternoon hours during extreme solar minimum. Pysat builds upon open source Python software that is freely available and encourages communitydriven development.

Stoneback, R.A.↗

DOE OSTI2025

Kernel Manifolds: Nonlinear‐Augmentation Dimensionality Reduction Using Reproducing Kernel Hilbert Spaces

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. In conclusion, we compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.

kernel methods↗

DOE OSTI2020

Process optimization of complex geometries using feed forward control for laser powder bed fusion additive manufacturing

Additive manufacturing (AM) enables the fabrication of complex designs that are difficult to create by other means. Metal parts manufactured by laser powder bed fusion (LPBF) can incorporate intricate design features and demonstrate desirable mechanical properties. However, printing a part that is qualified for its intended application often involves reprinting and discarding many parts to eliminate defects, improve dimensional accuracy, and increase repeatability. The process of iteratively converging on the appropriate build parameters increases the time and cost of creating functional LPBF manufactured parts. This work describes a fast, scalable method for part-scale process optimization of arbitrary geometries. Additionally, the computational approach uses feature extraction to identify scan vectors in need of parameter adaptation and applies results from simulation-based feed forward control models. This method provides a framework to quickly optimize complex parts through the targeted application of models with a range of fidelity and by automating the transfer of optimization strategies to new part designs. The computational approach and algorithmic framework are described, a software package is implemented, the method is applied to parts with complex features, and parts are printed on a customized open architecture LPBF machine.

3D printing↗

DOE OSTI2020

Laser writing of nitrogen-doped silicon carbide for biological modulation

Conducting or semiconducting materials embedded in insulating polymeric substrates can be useful in biointerface applications; however, attainment of this composite configuration by direct chemical processes is challenging. Laser-assisted synthesis has evolved as a fast and inexpensive technique to prepare various materials, but its utility in the construction of biophysical tools or biomedical devices is less explored. Here, we use laser writing to convert portions of polydimethylsiloxane (PDMS) into nitrogen-doped cubic silicon carbide (3C-SiC). The dense 3C-SiC surface layer is connected to the PDMS matrix via a spongy graphite layer, facilitating electrochemical and photoelectrochemical activity. We demonstrate the fabrication of arbitrary two-dimensional (2D) SiC-based patterns in PDMS and freestanding 3D constructs. To establish the functionality of the laser-produced composite, we apply it as flexible electrodes for pacing isolated hearts and as photoelectrodes for local peroxide delivery to smooth muscle sheets.

59 BASIC BIOLOGICAL SCIENCES↗