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NASA NTRS2006

Nonlinear consider covariance analysis using a sigma-point filter formulation

The research reported here extends the mathematical formulation of nonlinear, sigma-point estimators to enable consider covariance analysis for dynamical systems. This paper presents a novel sigma-point consider filter algorithm, for consider-parameterized nonlinear estimation, following the unscented Kalman filter (UKF) variation on the sigma-point filter formulation, which requires no partial derivatives of dynamics models or measurement models with respect to the parameter list. It is shown that, consistent with the attributes of sigma-point estimators, a consider-parameterized sigma-point estimator can be developed entirely without requiring the derivation of any partial-derivative matrices related to the dynamical system, the measurements, or the considered parameters, which appears to be an advantage over the formulation of a linear-theory sequential consider estimator. It is also demonstrated that a consider covariance analysis performed with this 'partial-derivative-free' formulation yields equivalent results to the linear-theory consider filter, for purely linear problems.

covariance↗

DOE OSTI2024

Spectral Analysis of Regular Material Point Method and its Application to Study High Pressure Reverse Osmosis Membrane Compaction and Embossing

Material Point Method (MPM) is gaining widespread interest in applied continuum mechanics. The fact that all the continuum properties are stored on the particles (or material points) and the governing equations are solved on these material points makes MPM extremely suited to problems involving severe material deformations, such as crack propagation, soil movement, and fluid flows. Despite its popularity, only a few studies have focused on the numerical properties of MPM. This presentation introduces a global spectral analysis of the regular material point method. Contrary to previous studies, the analysis focuses on the numerical properties of the method in the spectral space. The amplification factor is derived as a function of the non- dimensional wave numbers. It provides insights into the stability and dissipative properties of the method for various CFL and Fourier numbers. The effect of the grid shape functions, number of particles per cell and their locations inside the grid cell are also analyzed. The EXAGOOP MPM solver (https://github.com/NREL/Exagoop.git) is developed at the National Renewable Energy Laboratory as a part of the NAWI UHPRO project and is based on the AMReX framework. A single-level, uniform cartesian grid is used as the background mesh, while the particle class in AMReX is used to manage the material point operations. Linear hat and B-splines are used as grid shape functions, while the time integration is performed using explicit Euler time integration. EXAGOOP is both CPU and GPU compatible and has been demonstrated to work well on multiple compute architectures. The performance of EXAGOOP on various computing architectures is presented along with its application to study compaction and embossing of high-pressure reverse osmosis membranes. The MPM solution accurately reproduces the membrane deformation. The deformed pore size and structure simulated using MPM also agree well with experimental SEM images.

material point method↗

DOE OSTI2024

Methods to Evaluate Subcolumn Profiles Based on Two-Point Diagnostics

In atmospheric models, stochastic generation of subgrid-scale profiles or “subcolumns” has been used for a variety of purposes. Such subcolumns can be generated from subgrid probability density functions (PDFs) at different vertical levels, when such PDFs are available. To do so, the generator needs to decide how strongly points should be correlated in the vertical, that is, how much the values should be overlapped. This is sometimes called “PDF overlap.” To assess vertical correlation in a simplified, observable setting, here the vertical correlation of vertical velocity in subcloud layers is examined. Doppler lidar is used to evaluate the vertical profiles of vertical velocity produced by a large-eddy simulation (LES) model and the Subgrid Importance Latin Hypercube Sampler (SILHS) subcolumn generator. In order to diagnose unrealistic features in subcolumn profiles, various statistical diagnostics are examined here, including the bivariate PDF of vertical velocity at two separated points (i.e., altitudes), the two-point velocity correlation, the integral correlation length, the PDF of two-point velocity differences, and the skewness and kurtosis of two-point velocity differences. The profiles produced by LES match lidar well, except that they are too smooth at small scales. The profiles produced by SILHS exhibit sharp jumps from updraft to downdraft that are not observed in the lidar data. To reduce the generation of these unrealistically sharp jumps, the SILHS sampling method is revised. The diagnostics confirm that the revised sampling method reduces the overprediction of sharp jumps.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

A three-point velocity estimation method for two-dimensional coarse-grained imaging data

Time delay and velocity estimation methods have been widely studied subjects in the context of signal processing, with applications in many different fields of physics. The velocity of waves or coherent fluctuation structures is commonly estimated as the distance between two measurement points divided by the time lag that maximizes the cross correlation function between the measured signals, but this is demonstrated to result in erroneous estimates for two spatial dimensions. We present an improved method to accurately estimate both components of the velocity vector, relying on three non-aligned measurement points. We introduce a stochastic process describing the fluctuations as a superposition of uncorrelated pulses moving in two dimensions. Using this model, we show that the three-point velocity estimation method, using time delays calculated through cross correlations, yields the exact velocity components when all pulses have the same velocity. The two- and three-point methods are tested on synthetic data generated from realizations of such processes for which the underlying velocity components are known. The results reveal the superiority of the three-point technique. Finally, we demonstrate the applicability of the velocity estimation on gas puff imaging data of strongly intermittent plasma fluctuations due to the radial motion of coherent, blob-like structures at the boundary of the Alcator C-Mod tokamak.

Materials Science↗

DOE OSTI2025

DESI 2024 II: sample definitions, characteristics, and two-point clustering statistics

We present the samples of galaxies and quasars used for DESI 2024 cosmological analyses, drawn from the DESI Data Release 1 (DR1). We describe the construction of largescale structure (LSS) catalogs from these samples, which include matched sets of synthetic reference ‘randoms’ and weights that account for variations in the observed density of the samples due to experimental design and varying instrument performance. We detail how we correct for variations in observational completeness, the input ‘target’ densities due to imaging systematics, and the ability to confidently measure redshifts from DESI spectra. We then summarize how remaining uncertainties in the corrections can be translated to systematic uncertainties for particular analyses. We describe the weights added to maximize the signalto-noise of DESI DR1 2-point clustering measurements. We detail measurement pipelines applied to the LSS catalogs that obtain 2-point clustering measurements in configuration and Fourier space. The resulting 2-point measurements depend on window functions and normalization constraints particular to each sample, and we present the corrections required to match models to the data. We compare the configuration- and Fourier-space 2-point clustering of the data samples to that recovered from simulations of DESI DR1 and find they are, generally, in statistical agreement to within 2% in the inferred real-space over-density field. The LSS catalogs, 2-point measurements, and their covariance matrices will be released publicly with DESI DR1.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

High-order cumulants and correlation functions near the critical point from molecular dynamics

We present a systematic investigation of particle-number fluctuations in the crossover region near the critical end point of a first-order phase transition using molecular dynamics simulations of the classical Lennard-Jones fluid. We extend our prior studies to third- and fourth-order cumulants in both coordinate- and momentum-space acceptances and integrated correlation functions (factorial cumulants). We find that, even near the critical point, non-Gaussian cumulants equilibrate on timescales comparable to those of the second-order cumulants, but show stronger finite-size effects. The presence of interactions and of the critical point leads to strong deviations of the cumulants from the ideal-gas baseline in coordinate space; these deviations are expected to persist in momentum space in the presence of collective expansion. In particular, the kurtosis becomes strongly negative, κσ 2 ≪ − 1 , on the crossover side of the critical point. However, this signal is significantly diluted once an efficiency cut used to distinguish protons from baryons is applied, leading to |κσ 2 | ≲ 1 even in the presence of the critical point. We discuss our results in the context of ongoing measurements of proton-number cumulants in heavy-ion collisions in RHIC-BES-II.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

A Quantum Approach for Implementing Fixed-Point Arithmetic in Solving Ordinary Differential Equations

Differential equations (DEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or computationally intensive problems. This study explores a quantum-inspired approach to solving DEs, combining quantum-inspired techniques with classical methods. It focuses on fixed-point arithmetic on quantum circuits, utilizing basic quantum gates to manipulate DE solutions. We expand upon the techniques introduced by Zanger et al. [Quantum, 5, 502 (2021)] by offering a precise computation for a fixed-point signed multiplication scheme, while also presenting a quantum circuit capable of executing the fixed-point division algorithm. We demonstrate the feasibility of our approach through the simulation of a linear Ordinary Differential Equation (ODE), where initial conditions and parameters are encoded into quantum circuits using fixed-point representation. By executing sequences of quantum gates mimicking numerical integration steps, we obtain approximate solutions to the ODE with specified fixed-point precision.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

A Quantum Approach for Implementing Fixed-Point Arithmetic in Solving Ordinary Differential Equations

Differential equations (DEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or computationally intensive problems. This study explores a quantum-inspired approach to solving DEs, combining quantum- inspired techniques with classical methods. It focuses on fixed- point arithmetic on quantum circuits, utilizing basic quantum gates to manipulate DE solutions. We expand upon the techniques introduced by Zanger et al. [Quantum, 5, 502 (2021)] by offering a precise computation for a fixed-point signed multiplication scheme, while also presenting a quantum circuit capable of executing the fixed-point division algorithm. We demonstrate the feasibility of our approach through the simulation of a linear Ordinary Differential Equation (ODE), where initial conditions and parameters are encoded into quantum circuits using fixed- point representation. By executing sequences of quantum gates mimicking numerical integration steps, we obtain approximate solutions to the ODE with specified fixed-point precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

All-sky Neutrino Point-source Search with IceCube Combined Track and Cascade Data

Despite extensive efforts, discovery of high-energy astrophysical neutrino sources remains elusive. We present an event-level simultaneous maximum likelihood analysis of tracks and cascades using IceCube data collected from 2008 April 6 to 2022 May 23 to search the whole sky for neutrino sources, and using a source catalog, for coincidence of neutrino emission with gamma-ray emission. This is the first time a simultaneous fit of different detection channels is used to conduct a time-integrated all-sky scan with IceCube. Combining all-sky tracks, with superior pointing power and sensitivity in the northern sky, with all-sky cascades, with good energy resolution and sensitivity in the southern sky, we have developed the most sensitive point-source search to date by IceCube that targets the entire sky. The most significant point in the northern sky aligns with NGC 1068, a Seyfert II galaxy, which, from the catalog search, shows a 3.5σ excess over background after accounting for trials. The most significant point in the southern sky does not align with any source in the catalog and is not significant after accounting for trials. A search for the single most significant Gaussian flare at the locations of NGC 1068, PKS 1424+240, and the southern highest-significance point shows results consistent with expectations for steady emission. Notably, this is the first time that a flare shorter than four years has been excluded as being responsible for NGC 1068’s emergence as a neutrino source. Our results show that combining tracks and cascades when conducting neutrino source searches improves sensitivity and can lead to new discoveries.

Abbasi, R. [Loyola University, Chicago, IL (United↗

NASA NTRS1973

Effects of certain control-system nonlinearities on stability and pointing of an attached double-gimbal experiment package in presence of random crew-motion disturbances

The effects of two types of control-system nonlinearities, sensor deadband and actuator breakout torque, on the pointing capability of a Apollo Telescope Mount (ATM) double-gimbal experiment isolation and control system are investigated. A composite structural model of a flexible experiment package connected through frictionless double gimbals to a flexible carrier vehicle is used for this investigation. Contributions of the primary carrier control system to experiment pointing are neglected. Pointing errors onboard the experiment package due to random crew-motion input into the carrier vehicle are computed. A stability investigation is performed to verify control-system stability with nominal nonlinearities and gains. Indications are that there is no stability problem due to the nonlinearities. A nonlinearity sensitivity study is carried out to determine the effects on pointing accuracy. Its results indicate that nominal ATM control system nonlinearities limit the pointing accuracy to approximately 0.4 arc second in the presence of crew motion. Methods of reducing the error to less than 0.1 arc second are discussed.

Shaughnessy, J. D.↗

NASA NTRS1974

Tricritical points in multicomponent fluid mixtures

In view of experimental considerations, we give a model-independent argument that the novel tricritical points in multicomponent fluid mixtures, where three phases simultaneously become critical, are points on the boundary of a single two-dimensional surface of critical points. This result is corroborated by the Landau model suggested by Griffiths. The relationship between these tricritical points and the complex 'higher-order' critical points proposed to exist in certain magnetic systems is elucidated.

Hankey, A.↗

NASA NTRS1974

Determination of dynamic corrections to point coordinates of photographs obtained by the Zond 6 and Zond 8 spacecraft

The linear and angular motions of the Zond 6 and Zond 8 spacecraft imaging camera during the exposure cause displacements of the optical image points. In the case of instantaneous exposure of each individual point and the nonsimultaneous exposure of the complete frame, this leads to finite geometric shifts of the points without causing blurring of the photographic image. Therefore, when measuring the resulting photographic pictures, the problem arises of reducing the picture point positions to a common instant of time. This reduction is performed by means of dynamic corrections to the measured picture point coordinates. These corrections are found by using formulas of dynamic photogrammetry. Their use with the Zond space probe photographs is described.

Kiselev, V. V.↗

NASA NTRS1975

Multiple scattered radiation emerging from continental haze layers. 1: Radiance, polarization, and neutral points

The complete radiation field is calculated for scattering layers of various optical thicknesses. Results obtained for Rayleigh and haze scattering are compared. Calculated radiances show differences as large as 23% compared to the approximate scalar theory of radiative transfer, while the same differences are approximately 0.1% for a continental haze phase function. The polarization of reflected and transmitted radiation is given for various optical thicknesses, solar zenith angles, and surface albedos. Two types of neutral points occur for aerosol phase functions. Rayleigh-like neutral points arise from zero polarization that occurs at scattering angles of 0 deg and 180 deg. For Rayleigh phase functions, the position of these points varies with the optical thickness of the scattering layer. Non-Rayleigh neutral points are associated with the zeros of polarization which occur between the end points of the single scattering curve, and are found over a wide range of azimuthal angles.

Kattawar, G. W.↗

NASA NTRS1977

Triple point determinations of monomethylhydrazine and nitrogen tetroxide, 2.2 percent by weight nitric oxide

A series of tests was performed to ascertain the triple points of monomethylhydrazine and nitrogen tetroxide. A laboratory method indicated a triple point for monomethylhydrazine, but tests in a large vacuum chamber indicated that a triple point does not occur in spacelike conditions because the mono-methylhydrazine tends to supercool. Instead, an effective freezing point (with agitation) was obtained. New experimental values for liquid monomethylhydrazine vapor pressure were determined for temperatures from 275.2 to 207.6 K. The values were used to derive vapor pressure equations. Tentative values were obtained for the effective freezing point of nitrogen tetroxide spacelike conditions.

Smith, Irwin D.↗

NASA NTRS1979

Dependence of the pour point of diesel fuels on the properties of the initial components

An analytical expression is obtained for the dependence of the pour point of diesel fuels on the pour point and weight relationship of the initial components. For determining the pour point of a multicomponent fuel mixture, it is assumed that the mixture of two components has the pour point of a separate equivalent component, then calculating the pour point of this equivalent component mixed with a third component, etc.

Ostashov, V. M.↗

NASA NTRS1979

Magnetic suspension and pointing system

Apparatus for providing accurate pointing of instruments on a carrier vehicle and for providing isolation of the instruments from the vehicle's motion disturbances is presented. The apparatus includes two assemblies, with connecting interfaces, each assembly having a separate function. The first assembly is attached to the carrier vehicle and consists of an azimuth gimbal and an elevation gimbal which provide coarse pointing of the instruments by allowing two rotations of the instruments relative to the carrier vehicle. The second or vernier pointing assembly is made up of magnetic suspension and fine pointing actuators, roll motor segments, and an instrument mounting plate around which a continuous annular rim is attached which provides appropriate magnetic circuits for the actuators and the roll motor segments. The vernier pointing assembly provides six degree-of-freedom isolation from carrier motion disturbances.

Anderson, W. W.↗

NASA NTRS1979

Optimal nodal point distribution for improved accuracy in computational fluid dynamics

In applying finite-difference techniques to flow field problems, the accuracy attained for a fixed number of node points can be improved using unequally-spaced node points. The distribution of these node points is chosen here by minimizing a measure of local truncation error with respect to the parameters which define a transformation between the computational space of equally-spaced node points and the physical space of unequally-spaced node points. The problem then becomes a nonlinear programming problem. Numerical results are presented for two one-dimensional test problems: the Blasius boundary layer problem and the inviscid Burgers' equation.

Pierson, B. L.↗

NASA NTRS1980

Backward deletion to minimize prediction errors in models from factorial experiments with zero to six center points

Population model coefficients were chosen to simulate a saturated 2 to the 4th fixed-effects experiment having an unfavorable distribution of relative values. Using random number studies, deletion strategies were compared that were based on the F-distribution, on an order statistics distribution of Cochran's, and on a combination of the two. The strategies were compared under the criterion of minimizing the maximum prediction error, wherever it occurred, among the two-level factorial points. The strategies were evaluated for each of the conditions of 0, 1, 2, 3, 4, 5, or 6 center points. Three classes of strategies were identified as being appropriate, depending on the extent of the experimenter's prior knowledge. In almost every case the best strategy was found to be unique according to the number of center points. Among the three classes of strategies, a security regret class of strategy was demonstrated as being widely useful in that over a range of coefficients of variation from 4 to 65%, the maximum predictive error was never increased by more than 12% over what it would have been if the best strategy had been used for the particular coefficient of variation. The relative efficiency of the experiment, when using the security regret strategy, was examined as a function of the number of center points, and was found to be best when the design used one center point.

Holms, A. G.↗