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NASA NTRS1976

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

Klimas, A. J.↗

NASA NTRS1984

FTIR-spectrometer-determined absorption coefficients of seven hydrazine fuel gases - Implications for laser remote sensing

The absorption spectra of three hydrazines and four of their air-oxidation products were measured in the 9-12-micron spectral region with a Fourier transform infrared (FTIR) spectrometer with a 0.05-kayser resolution to determine absorption coefficients at CO2 and tunable diode laser wavelengths. The measurements agreed well with published CO2 laser determinations for many of the absorption coefficients, except where the published values are thought to be in error. The coefficients were then used to estimate the sensitivity for remote detection of these gases using CO2 and tunable diode lasers in long-path differential absorption measurements.

Molina, L. T.↗

NASA NTRS2019

Frequency Control of Multi-Pulse 2-micron Laser Transmitter for Atmospheric Carbon Dioxide Measurement

Laser sources with highly stabilized emission wavelength is of paramount importance for a long term atmospheric carbon dioxide (CO2) measurement from a space platform. Integrated Path Differential Absorption (IPDA) lidar is a promising instrument for such a task. The design of a laser transmitter, with emphasis on the method used to control and select several wavelengths, is presented. This multi-pulsed, injection seeded, 2-μm transmitter uses a Ho:Tm:YLF laser crystal which has matching emission to the absorption of CO2 in the R30 spectroscopic area. The injection seeded laser produces triple single longitudinal mode transform limited line width pulses with a total of 80 mJ at a repetition rate of 50 Hz.

Petros, Mulugeta↗

DOE OSTI2025

Kinetics of amorphous defect phases measured through ultrafast nanocalorimetry

Recognition of the role of extended defects on local phase transitions has led to the conceptualization of the defect phase, localized thermodynamically stable interfacial states that have since been applied in a myriad of material systems to realize significant enhancements in material properties. Here, we explore the kinetics of grain boundary confined amorphous defect phases, utilizing the high temperature and scanning rates afforded by ultrafast differential scanning calorimetry to apply targeted annealing/quenching treatments at high rates capable of capturing the kinetic behavior. Four Al-based nanocrystalline alloys, including two binary systems, Al–Ni and Al–Y, and two ternary systems, Al–Mg–Y and Al–Ni–Y, are selected to probe the materials design space (enthalpy of mixing, enthalpy of segregation, chemical complexity) for amorphous defect phase formation and stability, with correlative transmission electron microscopy applied to link phase evolution and grain stability to nanocalorimetry signatures. A series of targeted isothermal annealing heat treatments is utilized to construct a Time–Temperature-Transformation curve for the Al–Ni system, from which a critical cooling rate of 2400 °C/s was determined for the grain boundary confined disordered-to-ordered transition. Finally, a thermal profile consisting of 1000 repeated annealing sequences was created to quantify the recovery of the amorphous defect phase following sequential annealing treatments, with results indicating remarkable microstructural stability after annealing at temperatures above 90% of the melting temperature. This work contributes to a deeper understanding of grain boundary localized thermodynamics and kinetics, with potential implications for the design and optimization of advanced materials with enhanced stability and performance.

Amorphous defect phases↗

DOE OSTI2021

Trigonometric Parallaxes of Two T Dwarfs With Keck and ShaneAO Astrometry

We present trigonometric parallax and proper motion measurements for two T-type brown dwarfs. We derive our measurements from infrared laser guide star adaptive optics observations spanning five years from the ShaneAO/SHARCS and NIRC2/medium-cam instruments on the Shane and Keck telescopes, respectively. To improve our astrometric precision, we measure and apply a distortion correction to our fields for both instruments. We also transform the Keck and ShaneAO astrometric reference frames onto the ICRS using five-parameter parallax and proper motion solutions for background reference stars from Gaia DR2. Fitting for parallax and proper motion, we measure parallaxes of 73.5 ± 9.2 mas and 70.1 ± 6.7 mas for WISEJ19010703+47181688 (WISE1901) and WISEJ21543294+59421370 (WISE2154), respectively. We utilize Monte Carlo methods to estimate the error in our sparse field methods, taking into account overfitting and differential atmospheric refraction. Comparing to previous measurements in the literature, all of our parallax and proper motion values fall within 2σ of the published measurements, and 4 of 6 measurements are within 1σ. These data are among the first parallax measurements of these T dwarfs and serve as precise measurements for calibrating stellar formation models. These two objects are the first results of an ongoing survey of T dwarfs with Keck/NIRC2 and the Shane Adaptive Optics system at Lick Observatory.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1988

Parallels between control PDE's and systems of ODE's

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differential equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

Hunt, L. R.↗

NASA NTRS2003

Performance of the NASA Digitizing Core-Loss Instrumentation

The standard method of magnetic core loss measurement was implemented on a high frequency digitizing oscilloscope in order to explore the limits to accuracy when characterizing high Q cores at frequencies up to 1 MHz. This method computes core loss from the cycle mean of the product of the exciting current in a primary winding and induced voltage in a separate flux sensing winding. It is pointed out that just 20 percent accuracy for a Q of 100 core material requires a phase angle accuracy of 0.1 between the voltage and current measurements. Experiment shows that at 1 MHz, even high quality, high frequency current sensing transformers can introduce phase errors of a degree or more. Due to the fact that the Q of some quasilinear core materials can exceed 300 at frequencies below 100 kHz, phase angle errors can be a problem even at 50 kHz. Hence great care is necessary with current sensing and ground loops when measuring high Q cores. Best high frequency current sensing accuracy was obtained from a fabricated 0.1-ohm coaxial resistor, differentially sensed. Sample high frequency core loss data taken with the setup for a permeability-14 MPP core is presented.

Schwarze, Gene E.↗

DOE OSTI2025

Towards AI Based Data Classification for Decision Making During Testing

During the development of high-consequence items, test systems should be capable of differentiating between test failures resulting from narrowly missing requirements versus those indicating potentially catastrophic faults. In many instances, classifying the data corresponds to simply identifying whether measured waveforms have approximately the anticipated shape. Cast in this light, the problem reduces to converting raw data into a form optimal for use with neural network classifiers. This manuscript investigates different means of representing raw data for image classification. Raw data plots and Short Time Fourier Transform (STFT) spectrograms are classified by both custom built, small-scale, Convolution Neural Networks (CNN) and open-source, multi-million parameter, pre-trained deep CNNs. In the case of time varying frequency content, the STFTs provide images with greater detail and can be accurately classified with simpler networks. This requires less memory and runs faster than classifying the raw data using the more sophisticated options—making STFTs optimal for applications with memory constraints. STFTs are not a panacea. In some cases the time-domain signal contains useful information that should not be discarded. Rather than using raw data or STFTs, the images can be constructed from both by using red and green channels of an RGB image to visualize the real and imaginary components of the transform, with the raw data occupying the blue channel.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1976

Prolongation structures of nonlinear evolution equations. II

The prolongation structure of a closed ideal of exterior differential forms is further discussed, and its use illustrated by application to an ideal (in six dimensions) representing the cubically nonlinear Schroedinger equation. The prolongation structure in this case is explicitly given, and recurrence relations derived which support the conjecture that the structure is open - i.e., does not terminate as a set of structure relations of a finite-dimensional Lie group. We introduce the use of multiple pseudopotentials to generate multiple Baecklund transformation, and derive the double Baecklund transformation. This symmetric transformation concisely expresses the (usually conjectured) theorem of permutability, which must consequently apply to all solutions irrespective of asymptotic constraints.

Estabrook, F. B.↗

NASA NTRS1984

Variational objective analyses for cyclone studies

The basic analysis equations, i.e., the two horizontal momentum equations, the hydrostatic equation, and the integrated continuity equation were derived for the nonlinear vertical coordinate, nondimensionalized, and expressed in finite differences on a staggered grid. Special care was taken to transform the hydrostatic equation and the pressure gradient terms of the horizontal momentum equations to nearly eliminate truncation error over steeply sloping terrain. This formulation also eliminated explicit reference to orographically induced variations in the thermodynamic variables so that the variational adjustments are on the scale of the meteorological perturbations. The analysis equations were subjected to the Euler-Lagrange operations as expressed for finite differences and an additional set of five partial differential equations was derived, bringing to nine the number of equations in Model I. Higher order terms, terms containing observed quantities, and terms containing none of the variables to be adjusted were grouped into forcing functions and the equations were solved for the zero order terms. Zero order variables were eliminated between these equations and there resulted two diagnostic equations which take the form of general linear second order partial differential equations with nonconstant coefficients.

Achtemeier, G. L.↗

NASA NTRS2001

Using EEG To Detect and Monitor Mental Fatigue

This project aims to develop EEG-based methods for detecting and monitoring mental fatigue. Mental fatigue poses a serious risk, even when performance is not apparently degraded. When such fatigue is associated with sustained performance of a single type of cognitive task it may be related to the metabolic energy required for sustained activation of cortical areas specialized for that task. The objective of this study was to adapt EEG to monitor cortical energy over a long period of performance of a cognitive task. Multielectrode event related potentials (ERPs) were collected every 15 minutes in nine subjects who performed a mental arithmetic task (algebraic sum of four randomly generated negative or positive digits). A new problem was presented on a computer screen 0.5 seconds after each response; some subjects endured for as long as three hours. ERPs were transformed to a quantitative measure of scalp electrical field energy. The average energy level at electrode P3 (near the left angular gyrus), 100-300 msec latency, was compared over the series of ERPs. For most subjects, scalp energy density at P3 gradually fell over the period of task performance and dramatically increased just before the subject was unable to continue the task. This neural response can be simulated for individual subjects using, a differential equation model in which it is assumed that the mental arithmetic task requires a commitment of metabolic energy that would otherwise be used for brain activities that are temporarily neglected. Their cumulative neglect eventually requires a reallocation of energy away from the mental arithmetic task.

Montgomery, Leslie↗

NASA NTRS2013

Low Temperature Creep of Hot-Extruded Near-Stoichiometric NiTi Shape Memory Alloy: Effect of Thermal Cycling - Part 2

This paper is the first report on the effect prior low temperature creep on the thermal cycling behavior of NiTi. The isothermal low temperature creep behavior of near-stoichiometric NiTi between 300 and 473 K was discussed in Part I. The effect of temperature cycling on its creep behavior is reported in the present paper (Part II). Temperature cycling tests were conducted between either 300 or 373 K and 473 K under a constant applied stress of either 250 or 350 MPa with hold times lasting at each temperature varying between 300 and 700 h. Each specimen was pre-crept either at 300 or at 473 K for several months under an identical applied stress as that used in the subsequent thermal cycling tests. Irrespective of the initial pre-crept microstructures, the specimens exhibited a considerable increase in strain with each thermal cycle so that the total strain continued to build-up to 15 to 20 percent after only 5 cycles. Creep strains were immeasurably small during the hold periods. It is demonstrated that the strains in the austenite and martensite are linearly correlated. Interestingly, the differential irrecoverable strain, in the material measured in either phase decreases with increasing number of cycles, similar to the well-known Manson-Coffin relation in low cycle fatigue. Both phases are shown to undergo strain hardening due to the development of residual stresses. Plots of true creep rate against absolute temperature showed distinct peaks and valleys during the cool-down and heat-up portions of the thermal cycles, respectively. Transformation temperatures determined from the creep data revealed that the austenitic start and finish temperatures were more sensitive to the pre-crept martensitic phase than to the pre-crept austenitic phase. The results are discussed in terms of a phenomenological model, where it is suggested that thermal cycling between the austenitic and martensitic phase temperatures or vice versa results in the deformation of the austenite and a corresponding development of a back stress due to a significant increase in the dislocation density during thermal cycling.

Raj, S. V.↗

DOE OSTI2025

Design and Development of Novel Equiatomic Refractory Multi Principal elemental Alloys Based on MoNbTi System for Use in Irradiation Environments

Multi Principal Elemental Alloys (MPEA) have emerged as promising materials for next-generation nuclear reactors due to their exceptional irradiation resistance. Eight equiatomic MPEA based on the MoNbTi system, comprising of elements with low thermal neutron absorption cross-sections were explored using a combined approach employing empirical parameter estimations, and CALPHAD simulations by which the phases and elemental segregation observed in all the alloys in the as-cast state were predicted. Solution heat treatment at 1500°C transformed five alloys into single-phase matrix materials, enhancing homogeneity and reducing hardness. The densities of the alloys ranged between 6.47 to 7.68 g/cm3, hardness between 472 and 656 VHN, Young’s modulus between 142 GPa to 169 GPa, shear modulus between 54 GPa and 62 GPa, bulk modulus between 117 GPa to 194 GPa and Poisson’s ratio between 0.3 to 0.35. The in-situ high temperature Xray diffraction results, differential scanning calorimetry and dilatometry results up to 1000°C suggested the high temperature phase stability of the MPEA. Subsequent ageing heat treatment at 800 and 1000 oC for 96 hours revealed significant secondary phase precipitation in MoNbTiZr, MoNbTiZrV, and MoNbTiCrA. Oxidation studies at 800 oC for 24 hours in air revealed superior oxidation resistance and cubic rate law dependence in Cr containing MPEA especially in MoNbTiCrAl, while severe mass gain resulting in total disintegration and exfoliation in MoNbTiZr and MoNbTiZrV. This comprehensive study underscores the potential of novel MPEA as promising materials for advanced nuclear reactor applications, shedding light on their microstructural control, mechanical properties, thermal stability, and oxidation resistance.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1981

Advantages of multigrid methods for certifying the accuracy of PDE modeling

Numerical techniques for assessing and certifying the accuracy of the modeling of partial differential equations (PDE) to the user's specifications are analyzed. Examples of the certification process with conventional techniques are summarized for the three dimensional steady state full potential and the two dimensional steady Navier-Stokes equations using fixed grid methods (FG). The advantages of the Full Approximation Storage (FAS) scheme of the multigrid technique of A. Brandt compared with the conventional certification process of modeling PDE are illustrated in one dimension with the transformed potential equation. Inferences are drawn for how MG will improve the certification process of the numerical modeling of two and three dimensional PDE systems. Elements of the error assessment process that are common to FG and MG are analyzed.

Forester, C. K.↗

DOE OSTI2021

A VR-based volumetric medical image segmentation and visualization system with natural human interaction

Volume rendering produces informative two-dimensional (2D) images from a 3-dimensional (3D) volume. It highlights the region of interest and facilitates a good comprehension of the entire data set. However, volume rendering faces a few challenges. First, a high-dimensional transfer function is usually required to differentiate the target from its neighboring objects with subtle variance. Unfortunately, designing such a transfer function is a strenuously trial-and-error process. Second, manipulating/visualizing a 3D volume with a traditional 2D input/output device suffers dimensional limitations. To address all the challenges, we design NUI-VR 2 , a natural user interface-enabled volume rendering system in the virtual reality space. NUI-VR 2 marries volume rendering and interactive image segmentation. It transforms the original volume into a probability map with image segmentation. A simple linear transfer function will highlight the target well in the probability map. More importantly, we set the entire image segmentation and volume rendering pipeline in an immersive virtual reality environment with a natural user interface. NUI-VR 2 eliminates the dimensional limitations in manipulating and perceiving 3D volumes and dramatically improves the user experience.

42 ENGINEERING↗

DOE OSTI2026

Deep-ultraviolet ptychographic pocket-scope (DART): mesoscale lensless molecular imaging with label-free spectroscopic contrast

The mesoscale characterization of biological specimens has traditionally required compromises between resolution, field-of-view, depth-of-field, and molecular specificity, with most approaches relying on external labels. Here we present the Deep-ultrAviolet ptychogRaphic pockeT-scope (DART), a handheld platform that transforms label-free molecular imaging through intrinsic deep-ultraviolet spectroscopic contrast. By leveraging biomolecules’ natural absorption fingerprints and combining them with lensless ptychographic microscopy, DART resolves down to 308-nm linewidths across centimeter-scale areas while maintaining millimeter-scale depth-of-field. The system’s virtual error-bin methodology effectively eliminates artifacts from limited temporal coherence and other optical imperfections, enabling high-fidelity molecular imaging without lenses. Through differential spectroscopic imaging at deep-ultraviolet wavelengths, DART quantitatively maps nucleic acid and protein distributions with femtogram sensitivity, providing an intrinsic basis for explainable virtual staining. We demonstrate DART’s capabilities through imaging of tissue sections, cytopathology specimens, blood cells, and neural populations, revealing detailed molecular contrast without external labels. The combination of high-resolution molecular mapping and broad mesoscale imaging in a portable platform opens new possibilities from rapid clinical diagnostics, tissue analysis, to biological characterization in space exploration.

60 APPLIED LIFE SCIENCES↗

NASA NTRSDate not supplied

Obtaining Accurate Derivatives Across Adaptive-Step Integration

Obtaining derivatives through the integration of a set of ordinary differential equations is of interest to a number of fields of research. Approaches for doing so that are available in the literature, however, do not account for details associated with variable step integrator that cause inaccuracies in the total derivatives. In this paper, we explore the causes of the accumulation of derivative error in adaptive-step Runge-Kutta integration schemes and propose a solution to eliminate them. The new algorithm proposed is a transformation of each step of a Runge-Kutta integration into a set of residual equations. This work demonstrates the improvement in accuracy of total derivatives when the new algorithm is utilized.

Kaushik Ponnapalli↗

NASA NTRS1991

Accuracy and speed in computing the Chebyshev collocation derivative

We studied several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed accurately. A subtle cause is is found to account for the poor accuracy when computing the derivative by the matrix-vector multiplication method. Methods for accurately computing the elements of the matrix are presented, and we find that if the entities of the matrix are computed accurately, the roundoff error of the matrix-vector multiplication is as small as that of the transform-recursion algorithm. Results of CPU time usage are shown for several different algorithms for computing the derivative by the Chebyshev collocation method for a wide variety of two-dimensional grid sizes on both an IBM and a Cray 2 computer. We found that which algorithm is fastest on a particular machine depends not only on the grid size, but also on small details of the computer hardware as well. For most practical grid sizes used in computation, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.

Don, Wai-Sun↗