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DOE OSTI2026

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential applications in specialized areas such as segmented inverse beta decay neutrino detectors, astronomy, machine learning, and more. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Physics↗

NASA NTRS1998

Time-resolved diffusion tomographic imaging in highly scattering turbid media

A method for imaging objects in highly scattering turbid media. According to one embodiment of the invention, the method involves using a plurality of intersecting source/detectors sets and time-resolving equipment to generate a plurality of time-resolved intensity curves for the diffusive component of light emergent from the medium. For each of the curves, the intensities at a plurality of times are then inputted into the following inverse reconstruction algorithm to form an image of the medium: X.sup.(k+1).spsp.T =?Y.sup.T W+X.sup.(k).spsp.T .LAMBDA.!?W.sup.T W+.LAMBDA.!.sup.-1 wherein W is a matrix relating output at detector position r.sub.d, at time t, to source at position r.sub.s, .LAMBDA. is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, to fluctuations in the absorption (or diffusion) X.sub.j that we are trying to determine: .LAMBDA..sub.ij =.lambda..sub.j .delta..sub.ij with .lambda..sub.j = /<.DELTA.Xj.DELTA.Xj> Here Y is the data collected at the detectors, and X.sup.k is the kth iterate toward the desired absoption information.

Alfano, Robert R.↗

NASA NTRS2007

Lightning Charge Retrievals: Dimensional Reduction, LDAR Constraints, and a First Comparison w/ LIS Satellite Data

A "dimensional reduction" (DR) method is introduced for analyzing lightning field changes whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight to just four. The four unknowns are found by performing a numerical minimization of a chi-squared goodness-of-fit function. At each step of the minimization, an Overdetermined Fixed Matrix (OFM) method is used to immediately retrieve the best "residual source". In this way, all 8 parameters are found, yet a numerical search of only 4 parameters is required. The inversion method is applied to the understanding of lightning charge retrievals. The accuracy of the DR method has been assessed by comparing retrievals with data provided by the Lightning Detection And Ranging (LDAR) instrument. Because lightning effectively deposits charge within thundercloud charge centers and because LDAR traces the geometrical development of the lightning channel with high precision, the LDAR data provides an ideal constraint for finding the best model charge solutions. In particular, LDAR data can be used to help determine both the horizontal and vertical positions of the model charges, thereby eliminating dipole ambiguities. The results of the LDAR-constrained charge retrieval method have been compared to the locations of optical pulses/flash locations detected by the Lightning Imaging Sensor (LIS).

Koshak, William↗

DOE OSTI2025

Photoredox Catalysis with Spin Magnetic Field Effects: A Scheme for Chiral Resolution

Quantities that break both mirror symmetry and time-reversal symmetry, such as the orbital angular momentum, are known to connect molecular chirality with an applied magnetic field. This concept has led to observations such as magneto-chiral dichroism and chirality-induced spin selectivity (CISS). However, being small, these effects often require additional amplification procedures such as flow chemistry to achieve bulk enantioseparation. In this work, we demonstrate how the magnetic field effect on photogenerated radical pairs, which also breaks time-reversal symmetry, can be harnessed for enantiopurification. Fundamental to this process is the collective decay of the singlet and triplet radical-pair states made possible by an applied magnetic field. Because opposite enantiomers exhibit spin-orbit coupling matrix elements of opposite signs, the singlet and triplet decay channels interfere constructively in one enantiomer. Meanwhile, molecules of the other enantiomer are funnelled into the first enantiomer through excited-state chirality inversion, achieving (dynamic kinetic) chiral resolution. Using an axially chiral binaphthyl derivative and a borane photosensitizer as prototype, we predict an appreciable enantiomeric excess (e.e.) of 90% to be possible at steady state, attained within hundreds of milliseconds when irradiated by a laser. Importantly, our analytical results showcase regimes of perfect enantioselectivity (100% e.e.), accessible by further chemical optimization of the photosensitizer for which general strategies are discussed. Altogether, this work illustrates a so-far untapped but powerful control knob for photoredox catalysis based on spin chemistry principles.

Magnetic properties↗

NASA NTRS1983

Global transformations of nonlinear systems

Necessary and sufficient conditions for a nonlinear system of equations to be locally equivalent, in a neighborhood of the origin in the real number system, to a controllable linear system are combined with several versions of the global inverse function theorem to define sufficient conditions for transforming the nonlinear system into a linear system. Additionally, a technique is introduced for developing a transformation under the assumptions that the columns of a controllability matrix span an n-dimensional space. Finally, the n-l form of the controllability matrix columns is demonstrated to be involutive

Hunt, L. R.↗

NASA NTRS1987

Simultaneous stochastic inversion for geomagnetic main field and secular variation. I - A large-scale inverse problem

The method of stochastic inversion is extended to the simultaneous inversion of both main field and secular variation. In the present method, the time dependency is represented by an expansion in Legendre polynomials, resulting in a simple diagonal form for the a priori covariance matrix. The efficient preconditioned Broyden-Fletcher-Goldfarb-Shanno algorithm is used to solve the large system of equations resulting from expansion of the field spatially to spherical harmonic degree 14 and temporally to degree 8. Application of the method to observatory data spanning the 1900-1980 period results in a data fit of better than 30 nT, while providing temporally and spatially smoothly varying models of the magnetic field at the core-mantle boundary.

Bloxham, Jeremy↗

NASA NTRS2017

Inverse Force Determination on a Small Scale Launch Vehicle Model Using a Dynamic Balance

A launch vehicle can experience large unsteady aerodynamic forces in the transonic regime that, while usually only lasting for tens of seconds during launch, could be devastating if structural components and electronic hardware are not designed to account for them. These aerodynamic loads are difficult to experimentally measure and even harder to computationally estimate. The current method for estimating buffet loads is through the use of a few hundred unsteady pressure transducers and wind tunnel test. Even with a large number of point measurements, the computed integrated load is not an accurate enough representation of the total load caused by buffeting. This paper discusses an attempt at using a dynamic balance to experimentally determine buffet loads on a generic scale hammer head launch vehicle model tested at NASA Ames Research Center's 11' x 11' transonic wind tunnel. To use a dynamic balance, the structural characteristics of the model needed to be identified so that the natural modal response could be and removed from the aerodynamic forces. A finite element model was created on a simplified version of the model to evaluate the natural modes of the balance flexures, assist in model design, and to compare to experimental data. Several modal tests were conducted on the model in two different configurations to check for non-linearity, and to estimate the dynamic characteristics of the model. The experimental results were used in an inverse force determination technique with a psuedo inverse frequency response function. Due to the non linearity, the model not being axisymmetric, and inconsistent data between the two shake tests from different mounting configuration, it was difficult to create a frequency response matrix that satisfied all input and output conditions for wind tunnel configuration to accurately predict unsteady aerodynamic loads.

testing↗

NASA NTRS1988

The Jacobi Matrix Technique in Computational Fluid Dynamics

The Jacobi matrix technique was applied to the direct calculation of inviscid supersonic flow about two dimensional airfoils of varying thickness, angle of attack and camber and axisymmetric bodies of varying thickness and taper; and the design (inverse) calculation of inviscid supersonic flow past airfoils described by a given family of pressure distributions and axisymmetric bodies described by a given family of pressure distributions. The method was also applied to subsonic potential flow about two dimensional airfoils by modifying Jameson's FLO36. Results are discussed.

Sharp, H. Thomas↗

NASA NTRS1998

Accelerated Training for Large Feedforward Neural Networks

In this paper we introduce a new training algorithm, the scaled variable metric (SVM) method. Our approach attempts to increase the convergence rate of the modified variable metric method. It is also combined with the RBackprop algorithm, which computes the product of the matrix of second derivatives (Hessian) with an arbitrary vector. The RBackprop method allows us to avoid computationally expensive, direct line searches. In addition, it can be utilized in the new, 'predictive' updating technique of the inverse Hessian approximation. We have used directional slope testing to adjust the step size and found that this strategy works exceptionally well in conjunction with the Rbackprop algorithm. Some supplementary, but nevertheless important enhancements to the basic training scheme such as improved setting of a scaling factor for the variable metric update and computationally more efficient procedure for updating the inverse Hessian approximation are presented as well. We summarize by comparing the SVM method with four first- and second- order optimization algorithms including a very effective implementation of the Levenberg-Marquardt method. Our tests indicate promising computational speed gains of the new training technique, particularly for large feedforward networks, i.e., for problems where the training process may be the most laborious.

Stepniewski, Slawomir W.↗

NASA NTRS1971

Inversion of very large matrices encountered in large scale problems of photogrammetry and photographic astrometry

The simultaneous adjustment of very large nets of overlapping plates covering the celestial sphere becomes computationally feasible by virtue of a twofold process that generates a system of normal equations having a bordered-banded coefficient matrix, and solves such a system in a highly efficient manner. Numerical results suggest that when a well constructed spherical net is subjected to a rigorous, simultaneous adjustment, the exercise of independently established control points is neither required for determinancy nor for production of accurate results.

Brown, D. C.↗

NASA NTRS1991

Analysis and design of a six-degree-of-freedom Stewart platform-based robotic wrist

The kinematic analysis and implementation of a six degree of freedom robotic wrist which is mounted to a general open-kinetic chain manipulator to serve as a restbed for studying precision robotic assembly in space is discussed. The wrist design is based on the Stewart Platform mechanism and consists mainly of two platforms and six linear actuators driven by DC motors. Position feedback is achieved by linear displacement transducers mounted along the actuators and force feedback is obtained by a 6 degree of freedom force sensor mounted between the gripper and the payload platform. The robot wrist inverse kinematics which computes the required actuator lengths corresponding to Cartesian variables has a closed-form solution. The forward kinematics is solved iteratively using the Newton-Ralphson method which simultaneously provides a modified Jacobian Matrix which relates length velocities to Cartesian translational velocities and time rates of change of roll-pitch-yaw angles. Results of computer simulation conducted to evaluate the efficiency of the forward kinematics and Modified Jacobian Matrix are discussed.

Nguyen, Charles C.↗

NASA NTRS1992

Top-of-atmosphere radiative fluxes - Validation of ERBE scanner inversion algorithm using Nimbus-7 ERB data

The ERBE algorithm is applied to the Nimbus-7 earth radiation budget (ERB) scanner data for June 1979 to analyze the performance of an inversion method in deriving top-of-atmosphere albedos and longwave radiative fluxes. The performance is assessed by comparing ERBE algorithm results with appropriate results derived using the sorting-by-angular-bins (SAB) method, the ERB MATRIX algorithm, and the 'new-cloud ERB' (NCLE) algorithm. Comparisons are made for top-of-atmosphere albedos, longwave fluxes, viewing zenith-angle dependence of derived albedos and longwave fluxes, and cloud fractional coverage. Using the SAB method as a reference, the rms accuracy of monthly average ERBE-derived results are estimated to be 0.0165 (5.6 W/sq m) for albedos (shortwave fluxes) and 3.0 W/sq m for longwave fluxes. The ERBE-derived results were found to depend systematically on the viewing zenith angle, varying from near nadir to near the limb by about 10 percent for albedos and by 6-7 percent for longwave fluxes. Analyses indicated that the ERBE angular models are the most likely source of the systematic angular dependences. Comparison of the ERBE-derived cloud fractions, based on a maximum-likelihood estimation method, with results from the NCLE showed agreement within about 10 percent.

Suttles, John T.↗

NASA NTRS1980

Atmospheric particulate analysis using angular light scattering

Using light scattering matrix elements measured by a polar nephelometer, a procedure for estimating the characteristics of atmospheric particulates was developed. A theoretical library data set of scattering matrices derived from Mie theory was tabulated for a range of values of the size parameter and refractive index typical of atmospheric particles. Integration over the size parameter yielded the scattering matrix elements for a variety of hypothesized particulate size distributions. A least squares curve fitting technique was used to find a best fit for the experimental measurements. This was used as a first guess for a nonlinear iterative inversion of the size distribution. A real index of 1.50 and an imaginary index of -0.005 are representative of the smoothed inversion results for the near ground level atmospheric aerosol in Tucson.

Hansen, M. Z.↗

NASA NTRS2020

Line shape parameters of PH3 transitions: Theoretical studies of self-broadened widths and line mixing effects

Line mixing effects have been calculated in various parallel and perpendicular bands of self-broadened PH3 lines and compared with recent experimental data. The theoretical approach is an extension to symmetric tops with high inversion barrier of the formalism previously developed for NH3 [Q. Ma and C. Boulet, J. Chem. Phys. 144, 224303 (2016)]. The model takes into account the non-diagonality of the scattering operator within the line space as well as, in a correct way, the double degeneracy of the j, k levels when k ≠ 0. Transitions between such levels should be considered as doublets whose components may be coupled by the line mixing process. It has been shown that, at low pressure, the inversion of the experimental data will strongly depend on the splitting between the two components of a doublet. When it is significant, one can measure independently both the width of one component and the intra-doublet coupling matrix element. Otherwise, one can only measure the sum of these two elements. Comparisons with measurements show that the present formalism leads to accurate predictions of the experimental line shapes.

Remote sensing↗

NASA NTRS1989

Application of recursive manipulator dynamics to hybrid software/hardware simulation

Computer simulations of robotic mechanisms have traditionally solved the dynamic equations of motion for an N degree of freedom manipulator by formulating an N dimensional matrix equation combining the accelerations and torques (forces) for all joints. The use of an alternative formulation that is strictly recursive is described. The dynamic solution proceeds on a joint by joint basis, so it is possible to perform inverse dynamics at arbitrary joints. The dynamic formulation is generalized with respect to both rotational and translational joints, and it is also directly extendable to branched manipulator chains. A hardware substitution test is described in which a servo drive motor was integrated with a simulated manipulator arm. The form of the dynamic equation permits calculation of acceleration given torque or vice versa. Computing torque as a function of acceleration is required for the hybrid software/hardware simulation test described. For this test, a joint servo motor is controlled in conjunction with the simulation, and the dynamic torque on the servo motor is provided by a load motor on a common driveshaft.

Hill, Christopher J.↗

NASA NTRS1990

Luminescent barometry in wind tunnels

A flexible and relatively inexpensive method and apparatus are described for continuous pressure mapping of aerodynamic surfaces using photoluminescence and imaging techniques. Platinum octaethylporphyrin (PtOEP) has a phosphorescence known to be quenched by oxygen. When dissolved in a silicone matrix, PtOEP may be distributed over a surface as a thin, uniform film. When the film is irradiated with ultraviolet light, the luminescence intensity provides a readily detectable, qualitative surface flow visualization. Moreover, since the luminescence intensity is found to be inversely proportional to the partial pressure of oxygen, a quantitative measure of pressure change may be obtained using a silicon target vidicon or a charge-coupled device video sensor to measure intensity. Luminescent images are captured by a commercial frame buffer board. Images taken in wind tunnels during airflow are ratioed to images taken under ambient 'wind-off' conditions. The resulting intensity ratio information is converted to pressure using calibration curves of I0/I vs p/p0, where I0 is the intensity at ambient pressure p0 and I is the intensity at any other pressure p.

Kavandi, Janet↗

NASA NTRS1999

Inversion of Gravity Fields From the Spacecraft Orbital Data Using an Adjoint Operator Approach

In perturbation approximation, the forward problem of orbital dynamics (equations with initial conditions) is linear with respect to variations of coordinates and/or velocities of the spacecraft and to corresponding variations of the gravity field in the models used. The linear operator adjoint to the linear operator of such forward problem turns out to be instrumental in inversion of differences between observed and predicted coordinates/velocities in terms of the updates of harmonics in the initial gravity field model. Based on this approach, the solution of resulting adjoint problem of orbital dynamics can be used to directly evaluate the matrix of partial derivatives of observable differences with respect to the gravity field harmonics. General discussion of the adjoint problem of orbital dynamics is given and an example of a mathematical formalism for the practical retrieval algorithm is presented.

Ustinov, E. A.↗

NASA NTRS1980

Atmospheric particulate analysis using angular light scattering

Using the light scattering matrix elements measured by a polar nephelometer, a procedure for estimating the characteristics of atmospheric particulates was developed. A theoretical library data set of scattering matrices derived from Mie theory was tabulated for a range of values of the size parameter and refractive index typical of atmospheric particles. Integration over the size parameter yielded the scattering matrix elements for a variety of hypothesized particulate size distributions. A least squares curve fitting technique was used to find a best fit from the library data for the experimental measurements. This was used as a first guess for a nonlinear iterative inversion of the size distributions. A real index of 1.50 and an imaginary index of -0.005 are representative of the smoothed inversion results for the near ground level atmospheric aerosol in Tucson.

Hansen, M. Z.↗