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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Modulation of lens cell adhesion molecules by particle beams

Cell adhesion molecules (CAMs) are proteins which anchor cells to each other and to the extracellular matrix (ECM), but whose functions also include signal transduction, differentiation, and apoptosis. We are testing a hypothesis that particle radiations modulate CAM expression and this contributes to radiation-induced lens opacification. We observed dose-dependent changes in the expression of beta 1-integrin and ICAM-1 in exponentially-growing and confluent cells of a differentiating human lens epithelial cell model after exposure to particle beams. Human lens epithelial (HLE) cells, less than 10 passages after their initial culture from fetal tissue, were grown on bovine corneal endothelial cell-derived ECM in medium containing 15% fetal bovine serum and supplemented with 5 ng/ml basic fibroblast growth factor (FGF-2). Multiple cell populations at three different stages of differentiation were prepared for experiment: cells in exponential growth, and cells at 5 and 10 days post-confluence. The differentiation status of cells was characterized morphologically by digital image analysis, and biochemically by Western blotting using lens epithelial and fiber cell-specific markers. Cultures were irradiated with single doses (4, 8 or 12 Gy) of 55 MeV protons and, along with unirradiated control samples, were fixed using -20 degrees C methanol at 6 hours after exposure. Replicate experiments and similar experiments with helium ions are in progress. The intracellular localization of beta 1-integrin and ICAM-1 was detected by immunofluorescence using monoclonal antibodies specific for each CAM. Cells known to express each CAM were also processed as positive controls. Both exponentially-growing and confluent, differentiating cells demonstrated a dramatic proton-dose-dependent modulation (upregulation for exponential cells, downregulation for confluent cells) and a change in the intracellular distribution of the beta 1-integrin, compared to unirradiated controls. In contrast, there was a dose-dependent increase in ICAM-1 immunofluorescence in confluent, but not exponentially-growing cells. These results suggest that proton irradiation downregulates beta 1-integrin and upregulates ICAM-1, potentially contributing to cell death or to aberrant differentiation via modulation of anchorage and/or signal transduction functions. Quantification of the expression levels of the CAMs by Western analysis is in progress.

NASA Discipline Radiation Health↗
DOE OSTI2024

Spectral scheme for atomic structure calculations in density functional theory

In this study, we present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial interpolation on a Chebyshev grid, with derivative operators approximated using the Chebyshev differentiation matrix, and integrations using Clenshaw-Curtis quadrature. We demonstrate the accuracy and efficiency of the scheme through spin-polarized and unpolarized calculations for representative atoms, while considering local, semilocal, and hybrid exchange-correlation functionals. In particular, we find that $\mathcal{O}$(200) grid points are sufficient to achieve an accuracy of 1 microhartree in the eigenvalues for optimized norm conserving Vanderbilt pseudopotentials spanning the periodic table from atomic number Ζ = 1 to 83.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1977

Some MACSYMA program for solving difference equations

A set of MACSYMA programs are described for finding closed form solutions to linear recurrence relations in equations having either constant or variable coefficients. In the homogenous case, a polymonial equation is obtained and the solution to the recurrence relation can be written as a linear combination of the roots of the polynomial. Exponential generating functions are used to solve variable coefficient relations. Taking successive derivatives and using the recurrence relation, an ordinary differential equation is obtained. Expanding the solution to the differential equation in a Taylor series, shows that the nth term of the series is the solution to the recurrence relation. For second order recurrences, a check is made for those that can be solved in terms of Bessel functions.

Ivie, J.↗
NASA NTRS2008

Expressions Module for the Satellite Orbit Analysis Program

The Expressions Module is a software module that has been incorporated into the Satellite Orbit Analysis Program (SOAP). The module includes an expressions- parser submodule built on top of an analytical system, enabling the user to define logical and numerical variables and constants. The variables can capture output from SOAP orbital-prediction and geometric-engine computations. The module can combine variables and constants with built-in logical operators (such as Boolean AND, OR, and NOT), relational operators (such as >, <, or =), and mathematical operators (such as addition, subtraction, multiplication, division, modulus, exponentiation, differentiation, and integration). Parentheses can be used to specify precedence of operations. The module contains a library of mathematical functions and operations, including logarithms, trigonometric functions, Bessel functions, minimum/ maximum operations, and floating- point-to-integer conversions. The module supports combinations of time, distance, and angular units and has a dimensional- analysis component that checks for correct usage of units. A parser based on the Flex language and the Bison program looks for and indicates errors in syntax. SOAP expressions can be built using other expressions as arguments, thus enabling the user to build analytical trees. A graphical user interface facilitates use.

Edmonds, Karina↗
DOE OSTI2025

Fermi Velocity Dependent Critical Current in Ballistic Bilayer Graphene Josephson Junctions

We perform transport measurements on proximitized, ballistic, bilayer graphene Josephson junctions (BGJJs) in the intermediate-to-long junction regime (L > ξ). We measure the device’s differential resistance as a function of bias current and gate voltage for a range of different temperatures. The extracted critical current IC follows an exponential trend with temperature: exp(−k B T/δE). Here δE = ħν F /2πL: an expected trend for intermediate-to-long junctions. From δE, we determine the Fermi velocity of the bilayer graphene, which is found to increase with gate voltage. Simultaneously, we show the carrier density dependence of δE, which is attributed to the quadratic dispersion of bilayer graphene. This is in contrast to single layer graphene Josephson junctions, where δE and the Fermi velocity are independent of the carrier density. The carrier density dependence in BGJJs allows for additional tuning parameters in graphene-based Josephson junction devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1982

Numerical computation of exponential matrices using the Cayley-Hamilton theorem

A method for computing exponential matrices, which often arise naturally in the solution of systems of linear differential equations, is developed. An exponential matrix is generated as a linear combination of a finite number (equal to the matrix order) of matrices, the coefficients of which are scalar infinite sums. The method can be generalized to apply to any formal power series of matrices. Attention is focused upon the exponential function, and the matrix exponent is assumed tri-diagonal in form. In such cases, the terms in the coefficient infinite sums can be extracted, as recursion relations, from the characteristic polynomial of the matrix exponent. Two numerical examples are presented in some detail: (1) the three dimensional infinitesimal rotation rate matrix, which is skew symmetric, and (2) an N-dimensional tri-diagonal and symmetric finite difference matrix which arises in the numerical solution of the heat conduction partial differential equation. In the second example, the known eigenvalues and eigenvectors of the finite difference matrix permit an analytical solution for the exponential matrix, through the theory of diagonalization and similarity transformations, which is used for independent verification. The convergence properties of the scalar infinite summations are investigated for finite difference matrices of various orders up to ten, and it is found that the number of terms required for convergence increases slowly with the order of the matrix.

Walden, H.↗
DOE OSTI2023

Real-time spin systems from lattice field theory

We construct a lattice field theory method for computing the real-time dynamics of spin systems in a thermal bath. This is done by building on previous work of Takano with Schwinger-Keldysh and functional differentiation techniques. We derive a Schwinger-Keldysh path integral for generic spin Hamiltonians, then demonstrate the method on a simple system. Our path integral has a sign problem, which generally requires exponential run time in the system size, but requires only linear storage. The latter may place this method at an advantage over exact diagonalization, which is exponential in both. Our path integral is amenable to contour deformations, a technique for reducing sign problems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1994

A note on the accuracy of spectral method applied to nonlinear conservation laws

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

Shu, Chi-Wang↗
NASA NTRS1985

Legendre-tau approximation for functional differential equations. III - Eigenvalue approximations and uniform stability

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A characteristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

Ito, K.↗
NASA NTRS1998

A Solution to the Fundamental Linear Fractional Order Differential Equation

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Hartley, Tom T.↗
NASA NTRS1984

Legendre-Tau approximation for functional differential equations. Part 3: Eigenvalue approximations and uniform stability

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

Ito, K.↗
DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2012

The Ground Flash Fraction Retrieval Algorithm Employing Differential Evolution: Simulations and Applications

The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error plots are provided for both the simulations and actual data analyses.

Koshak, William↗
DOE OSTI2020

Gauges, loops, and polynomials for partition functions of graphical models

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is #P-hard that is of an exponential complexity with respect to the number of variables. Here, aimed at approximating the partition function, we consider multi-graph models where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge function technique from Chertkov and Chernyak with the technique developed in Anari and Oveis Gharan 2017 arXiv:1702.02937; Gurvits 2011 arXiv:1106.2844; Straszak and Vishnoi 2017 55th Annual Allerton Conf. on Communication, Control, and Computing, based on the recent progress in the field of real stable polynomials. We show that the Gauge function, representing a single-out term in a finite sum expression for the partition function which achieves extremum at the so-called belief-propagation gauge, has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, Gauge function can be used to recover the partition function through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists of the application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination/contraction of edges resulting in multi-graph models on decreasing in size (number of edges) graphs with the same partition function as in the original multi-graph model. Even though the complexity of computing factors in the sequence of the derived multi-graph models and respective Gauge functions grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that BP estimations in the sequence do not decrease, each low-bounding the partition function.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Hadamard products and BPS networks

We study examples of fourth-order Picard-Fuchs operators that are Hadamard products of two second-order Picard-Fuchs operators. Each second-order Picard-Fuchs operator is associated with a family of elliptic curves, and the Hadamard product computes period integrals on the fibred product of the two elliptic surfaces. We construct 3-cycles on this geometry as the union of 2-cycles in the fibre over contours on the base. We then use the special Lagrangian condition to constrain the contours on the base. This leads to a construction that is reminiscent of spectral networks and exponential networks that have previously appeared in string theory literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

ORMATEX

The Oak Ridge Matrix Exponential (ORMATEX) software library contains methods to compute the matrix exponential and the action of the matrix exponential on a vector. Additionally, this package contains the related methods for the phi-functions which commonly appear in a wide class of exponential time integration methods. Krylov methods are provided to evaluate the matrix exponential-vector and phi-vector products for cases where the matrix is large and sparse. Utilizing these methods, ORMATEX implements performant exponential integrators for large systems of coupled ordinary differential equations (ODEs). The exponential time integration routines in ORMATEX are particularly suitable to large, stiff systems of equations. These routines may be utilized as a competitive alternative to classical implicit and explicit time integration schemes for certain classes of differential equations where the problem stiffness can be predominately explained by the linear terms.

Gurecky, William [Oak Ridge National Laboratory (O↗