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NASA NTRS2013

Goal-Function Tree Modeling for Systems Engineering and Fault Management

The draft NASA Fault Management (FM) Handbook (2012) states that Fault Management (FM) is a "part of systems engineering", and that it "demands a system-level perspective" (NASAHDBK- 1002, 7). What, exactly, is the relationship between systems engineering and FM? To NASA, systems engineering (SE) is "the art and science of developing an operable system capable of meeting requirements within often opposed constraints" (NASA/SP-2007-6105, 3). Systems engineering starts with the elucidation and development of requirements, which set the goals that the system is to achieve. To achieve these goals, the systems engineer typically defines functions, and the functions in turn are the basis for design trades to determine the best means to perform the functions. System Health Management (SHM), by contrast, defines "the capabilities of a system that preserve the system's ability to function as intended" (Johnson et al., 2011, 3). Fault Management, in turn, is the operational subset of SHM, which detects current or future failures, and takes operational measures to prevent or respond to these failures. Failure, in turn, is the "unacceptable performance of intended function." (Johnson 2011, 605) Thus the relationship of SE to FM is that SE defines the functions and the design to perform those functions to meet system goals and requirements, while FM detects the inability to perform those functions and takes action. SHM and FM are in essence "the dark side" of SE. For every function to be performed (SE), there is the possibility that it is not successfully performed (SHM); FM defines the means to operationally detect and respond to this lack of success. We can also describe this in terms of goals: for every goal to be achieved, there is the possibility that it is not achieved; FM defines the means to operationally detect and respond to this inability to achieve the goal. This brief description of relationships between SE, SHM, and FM provide hints to a modeling approach to provide formal connectivity between the nominal (SE), and off-nominal (SHM and FM) aspects of functions and designs. This paper describes a formal modeling approach to the initial phases of the development process that integrates the nominal and off-nominal perspectives in a model that unites SE goals and functions of with the failure to achieve goals and functions (SHM/FM). This methodology and corresponding model, known as a Goal-Function Tree (GFT), provides a means to represent, decompose, and elaborate system goals and functions in a rigorous manner that connects directly to design through use of state variables that translate natural language requirements and goals into logical-physical state language. The state variable-based approach also provides the means to directly connect FM to the design, by specifying the range in which state variables must be controlled to achieve goals, and conversely, the failures that exist if system behavior go out-of-range. This in turn allows for the systems engineers and SHM/FM engineers to determine which state variables to monitor, and what action(s) to take should the system fail to achieve that goal. In sum, the GFT representation provides a unified approach to early-phase SE and FM development. This representation and methodology has been successfully developed and implemented using Systems Modeling Language (SysML) on the NASA Space Launch System (SLS) Program. It enabled early design trade studies of failure detection coverage to ensure complete detection coverage of all crew-threatening failures. The representation maps directly both to FM algorithm designs, and to failure scenario definitions needed for design analysis and testing. The GFT representation provided the basis for mapping of abort triggers into scenarios, both needed for initial, and successful quantitative analyses of abort effectiveness (detection and response to crew-threatening events).

Patterson, Jonathan D.↗

DOE OSTI2025

Trade-offs among restored ecosystem functions are context-dependent in Mediterranean-type regions

Global biodiversity hotspots, including Mediterranean-type ecosystems worldwide, are highly threatened by global change that alters biodiversity, ecosystem functions, and services. Some restoration activities enhance ecosystem functions by reintroducing plant species based on known relationships between plant traits and ecosystem processes. Achieving multiple functions across different site conditions, however, requires understanding how abiotic factors like climate and soil, along with plant assemblages, influence ecosystem functions, including their trade-offs and synergies. We used the ModEST ecosystem simulation model, which integrates carbon, water, and nutrient processes with plant traits, to assess the relationships between restored plant assemblages and ecosystem functions in Mediterranean-type climates and soils. We investigated whether maximised carbon increment, water use efficiency, and nitrogen use efficiency, along with their trade-offs and synergies, varied across different abiotic contexts. Further, we asked whether assemblages that maximised functions varied across environments and among these functions. We found that maximised ecosystem carbon increment and nitrogen use efficiency occurred under moist, warm conditions, while water use efficiency peaked under drier conditions. Generally, the assemblage that maximised one function differed from those for other maximised functions. Synergies were rare, except between water and nitrogen use efficiencies in loam soils across most climates. Trade-offs among maximised functions were common, varying in strength with abiotic context and plant assemblages, and were more pronounced in sandy loam soils compared to clay-rich soils. Our findings suggest that due to variation in abiotic conditions within and across Mediterranean-type regions at the global scale, site-specific plant assemblages are required to maximise ecosystem functions. Thus, lessons from a single site cannot be transferred to another site, even where the same plant functional types are available for restoration. Our simulation results offer valuable insights into potential ecosystem performance under specific abiotic conditions following restoration with particular plant functional types, thereby informing local restoration efforts.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2009

Physiological Factors Contributing to Postflight Changes in Functional Performance

Astronauts experience alterations in multiple physiological systems due to exposure to the microgravity conditions of space flight. These physiological changes include sensorimotor disturbances, cardiovascular deconditioning and loss of muscle mass and strength. These changes might affect the ability of crewmembers to perform critical mission tasks immediately after landing on lunar and Martian surfaces. To date, changes in functional performance have not been systematically studied or correlated with physiological changes. To understand how changes in physiological function impact functional performance an interdisciplinary pre/postflight testing regimen (Functional Task Test, FTT) has been developed that systematically evaluates both astronaut postflight functional performance and related physiological changes. The overall objectives of the FTT are to: Develop a set of functional tasks that represent critical mission tasks for Constellation. Determine the ability to perform these tasks after flight. Identify the key physiological factors that contribute to functional decrements. Use this information to develop targeted countermeasures. The functional test battery was designed to address high priority tasks identified by the Constellation program as critical for mission success. The set of functional tests making up the FTT include the: 1) Seat Egress and Walk Test, 2) Ladder Climb Test, 3) Recovery from Fall/Stand Test, 4) Rock Translation Test, 5) Jump Down Test, 6) Torque Generation Test, and 7) Construction Activity Board Test. Corresponding physiological measures include assessments of postural and gait control, dynamic visual acuity, fine motor control, plasma volume, orthostatic intolerance, upper and lower body muscle strength, power, fatigue, control and neuromuscular drive. Crewmembers will perform both functional and physiological tests before and after short (Shuttle) and long-duration (ISS) space flight. Data will be collected on R+0 (Shuttle only), R+1, R+6 and R+30. Using a multivariate regression model we will identify which physiological systems contribute the most to impaired performance on each functional test. This will allow us to identify the physiological systems that play the largest role in decrement in functional performance. Using this information we can then design and implement countermeasures that specifically target the physiological systems most responsible for the altered functional performance associated with space flight.

Bloomberg, J. J.↗

DOE OSTI2025

Blocky Selective Postpolymerization C–H Functionalization of Polyolefins

C–H functionalization of commodity polyolefins affords functional materials derived from a high-volume, low-cost resource. However, current postpolymerization modification strategies result in randomly distributed functionalization along the length of the polymer backbone, which has a negative impact on the crystallinity of the resultant polymers, and thus the thermomechanical properties. Here, we demonstrate an amidyl radical mediated C–H functionalization of polyolefins to access blocky microstructures, which exhibit a higher crystalline fraction, larger crystallite size, and improved mechanical properties compared to their randomly functionalized analogues. Taking inspiration from the site-selective C–H functionalization of small molecules, we leverage the steric protection provided by crystallites and target polymer functionalization to amorphous domains in a semicrystalline polyolefin gel. The beneficial outcomes of blocky functionalization are independent of the identity of the pendant functional group that is installed through functionalization. Here, the decoupling of functional group incorporation and crystallinity highlights the promise in accessing nonrandom microstructures through selective functionalization to circumvent traditional tradeoffs in postpolymerization modification, with potential impact in advanced materials and upcycling plastic waste.

Neidhart, Eliza K. [The University of North Caroli↗

DOE OSTI2025

Heterogeneous Mixtures of Dictionary Functions to Approximate Subspace Invariance in Koopman Operators: Why Deep Koopman Operators Work

Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.

Johnson, Charles A.↗

DOE OSTI2025

Massively parallel and universal approximation of nonlinear functions using diffractive processors

Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g., via a spatial light modulator (SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable. Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks, including the sigmoid, tanh, ReLU (rectified linear unit), and softplus. We numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.

Rahman, Md Sadman Sakib [University of California,↗

NASA NTRS2009

Defining the Physiological Factors that Contribute to Postflight Changes in Functional Performance

Astronauts experience alterations in multiple physiological systems due to exposure to the microgravity conditions of space flight. These physiological changes include sensorimotor disturbances, cardiovascular deconditioning and loss of muscle mass and strength. These changes might affect the ability of crewmembers to perform critical mission tasks immediately after landing on lunar and Martian surfaces. To date, changes in functional performance have not been systematically studied or correlated with physiological changes. To understand how changes in physiological function impact functional performance an interdisciplinary pre/postflight testing regimen (Functional Task Test, FTT) has been developed that systematically evaluates both astronaut postflight functional performance and related physiological changes. The overall objective of the FTT is to identify the key underlying physiological factors that contribute to performance of functional tests that are representative of critical mission tasks. This study will identify which physiological systems contribute the most to impaired performance on each functional test. This will allow us to identify the physiological systems that play the largest role in decrement in functional performance. Using this information we can then design and implement countermeasures that specifically target the physiological systems most responsible for the altered functional performance associated with space flight. The functional test battery was designed to address high priority tasks identified by the Constellation program as critical for mission success. The set of functional tests making up the FTT include the: 1) Seat Egress and Walk Test, 2) Ladder Climb Test, 3) Recovery from Fall/Stand Test, 4) Rock Translation Test, 5) Jump Down Test, 6) Torque Generation Test, and 7) Construction Activity Board Test. Corresponding physiological measures include assessments of postural and gait control, dynamic visual acuity, fine motor control, plasma volume, orthostatic intolerance, upper and lower body muscle strength, power, fatigue, control and neuromuscular drive. Crewmembers perform both functional and physiological tests before and after short (Shuttle) and long-duration (ISS) space flight. Data are collected on R+0 (Shuttle only), R+1, R+6 and R+30.

Bloomberg, J. J.↗

NASA NTRS2013

Goal-Function Tree Modeling for Systems Engineering and Fault Management

Johnson, Stephen B.↗

NASA NTRS2016

Exercise Effects on the Brain and Sensorimotor Function in Bed Rest

Long duration spaceflight microgravity results in cephalad fluid shifts and deficits in posture control and locomotion. Effects of microgravity on sensorimotor function have been investigated on Earth using head down tilt bed rest (HDBR). HDBR serves as a spaceflight analogue because it mimics microgravity in body unloading and bodily fluid shifts. Preliminary results from our prior 70 days HDBR studies showed that HDBR is associated with focal gray matter (GM) changes and gait and balance deficits, as well as changes in brain functional connectivity. In consideration of the health and performance of crewmembers we investigated whether exercise reduces the effects of HDBR on GM, functional connectivity, and motor performance. Numerous studies have shown beneficial effects of exercise on brain health. We therefore hypothesized that an exercise intervention during HDBR could potentially mitigate the effects of HDBR on the central nervous system. Eighteen subjects were assessed before (12 and 7 days), during (7, 30, and ~70 days) and after (8 and 12 days) 70 days of 6-degrees HDBR at the NASA HDBR facility in UTMB, Galveston, TX, US. Each subject was randomly assigned to a control group or one of two exercise groups. Exercise consisted of daily supine exercise which started 20 days before the start of HDBR. The exercise subjects participated either in regular aerobic and resistance exercise (e.g. squat, heel raise, leg press, cycling and treadmill running), or aerobic and resistance exercise using a flywheel apparatus (rowing). Aerobic and resistance exercise intensity in both groups was similar, which is why we collapsed the two exercise groups for the current experiment. During each time point T1-weighted MRI scans and resting state functional connectivity scans were obtained using a 3T Siemens scanner. Focal changes over time in GM density were assessed using voxel based morphometry (VBM8) under SPM. Changes in resting state functional connectivity was assessed using both a region of interest (ROI, or seed-to-voxel) approach as well as a whole brain intrinsic connectivity (i.e., voxel-to-voxel) analysis. For the ROI analysis we selected 11 ROIs of brain regions that are involved in sensorimotor function (i.e., L. Insular C., L. Putamen, R. Premotor C., L.+R. Primary Motor C., R. Vestibular C., L. Posterior Cingulate G., R. Cerebellum Lobule V + VIIIb + Crus I, and the R. Superior Parietal G.) and correlated their time course of brain activation during rest with all other voxels in the brain. The whole brain connectivity analysis tests changes in the strength of the global connectivity pattern between each voxel and the rest of the brain. Functional mobility was assessed using an obstacle course. Vestibular contribution to balance was measured using Neurocom Sensory Organization Test 5. Behavioral measures were assessed pre-HDBR, and 0, 8 and 12 days post-HDBR. Linear mixed models were used to test for effects of time, group, and group-by-time interactions. Family-wise error corrected VBM revealed significantly larger increases in GM volume in the right primary motor cortex in bed rest control subjects than in bed rest exercise subjects. No other significant group by time interactions in gray matter changes with bed rest were observed. Functional connectivity MRI revealed that the increase in connectivity during bed rest of the left putamen with the bilateral midsagittal precunes and the right cingulate gyrus was larger in bed rest control subjects than in bed rest exercise subjects. Furthermore, the increase in functional connectivity with bed rest of the right premotor cortex with the right inferior frontal gyrus and the right primary motor cortex with the bilateral premotor cortex was smaller in bed rest control subjects than in bed rest exercise subjects. Functional mobility performance was less affected by HDBR in exercise subjects than in control subjects and post HDBR exercise subjects recovered faster than control subjects. The group performance differences and GM changes were not related. Exercise in HDBR partially mitigates the adverse effect of HDBR on functional mobility, particularly during the post-bed rest recovery phase. In addition, exercise appears to result in differential brain structural and functional changes in motor regions such as the primary motor cortex, the premotor cortex and the putamen. Whether these central nervous system changes are related to motor behavioral changes including gait and balance warrants further research.

Koppelmans, V.↗

NASA NTRS2020

Evaluation of Fatigue Damage Accumulation Functions for Delamination Initiation and Propagation

The present report follows on the cohesive fatigue damage model methodology proposed in NASA-TP-2018-219838. In that report, an empirical function describing the incremental damage due to cyclic loading was used to calculate fatigue damage within a cohesive formulation. The form of the function was developed such that, when integrated at a constant stress amplitude from no damage to failure, it produces a life versus load response that is consistent with an S-N diagram. Therefore, the parameters of the damage model could be obtained by fitting the model predictions to an S-N diagram. The finite element analyses performed demonstrate that the cohesive fatigue accumulation function provides a link between the S-N diagram that describes crack initiation, and the Paris law that characterizes the rate of crack propagation. However, when the model was proposed, it was not known whether the form of the damage accumulation function associated with a desired S-N diagram is unique and, if not, if the link between S-N and the Paris law is unique and independent of the fatigue function selected. In the effort described herein, several alternative forms of the damage function that reproduce the desired features of S-N diagrams were found and evaluated. The effects of each of these functions on the predicted parameters of the Paris law and the propagation threshold are discussed. The results indicate that the predicted exponent m of the Paris law is indeed independent of the damage accumulation function. However, different functions predict different values for the pre-factor C of the Paris law. Therefore, the proper damage accumulation function must be selected by comparison with experiments. One of the new damage accumulation functions proposed herein was found to be particularly useful for analysis because of the ease with which the model parameters can be determined with a minimal amount of experimental information. The effectiveness of the proposed methodology and damage function was demonstrated by conducting analyses of a double cantilever beam test, a mixed-mode bending test, and a three-point bending test of a skin/doubler specimen. The results indicate that the same set of model parameters can provide accurate predictions of the rate of fatigue crack propagation for a variety of material interfaces, mode mixities, load levels, and stress ratios.

Cohesive elements↗

NASA NTRS1971

A table of integrals of the error function. II - Additions and corrections.

Integrals of products of error functions with other functions are presented, taking into account a combination of the error function with powers, a combination of the error function with exponentials and powers, a combination of the error function with exponentials of more complicated arguments, definite integrals from Laplace transforms, and a combination of the error function with trigonometric functions. Other integrals considered include a combination of the error function with logarithms and powers, a combination of two error functions, and a combination of the error function with other special functions.

Geller, M.↗

NASA NTRS2000

R-Function Relationships for Application in the Fractional Calculus

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

Lorenzo, Carl F.↗

NASA NTRS2013

Arctic Tundra Vegetation Functional Types Based on Photosynthetic Physiology and Optical Properties

Non-vascular plants (lichens and mosses) are significant components of tundra landscapes and may respond to climate change differently from vascular plants affecting ecosystem carbon balance. Remote sensing provides critical tools for monitoring plant cover types, as optical signals provide a way to scale from plot measurements to regional estimates of biophysical properties, for which spatial-temporal patterns may be analyzed. Gas exchange measurements were collected for pure patches of key vegetation functional types (lichens, mosses, and vascular plants) in sedge tundra at Barrow, AK. These functional types were found to have three significantly different values of light use efficiency (LUE) with values of 0.013 plus or minus 0.0002, 0.0018 plus or minus 0.0002, and 0.0012 plus or minus 0.0001 mol C mol (exp -1) absorbed quanta for vascular plants, mosses and lichens, respectively. Discriminant analysis of the spectra reflectance of these patches identified five spectral bands that separated each of these vegetation functional types as well as nongreen material (bare soil, standing water, and dead leaves). These results were tested along a 100 m transect where midsummer spectral reflectance and vegetation coverage were measured at one meter intervals. Along the transect, area-averaged canopy LUE estimated from coverage fractions of the three functional types varied widely, even over short distances. The patch-level statistical discriminant functions applied to in situ hyperspectral reflectance data collected along the transect successfully unmixed cover fractions of the vegetation functional types. The unmixing functions, developed from the transect data, were applied to 30 m spatial resolution Earth Observing-1 Hyperion imaging spectrometer data to examine variability in distribution of the vegetation functional types for an area near Barrow, AK. Spatial variability of LUE was derived from the observed functional type distributions. Across this landscape, a fivefold variation in tundra LUE was observed. LUE calculated from the functional type cover fractions was also correlated to a spectral vegetation index developed to detect vegetation chlorophyll content. The concurrence of these alternate methods suggest that hyperspectral remote sensing can distinguish functionally distinct vegetation types and can be used to develop regional estimates of photosynthetic LUE in tundra landscapes.

VEGETATION↗

NASA NTRS2015

NASA's Functional Task Test: Providing Information for an Integrated Countermeasure System

Exposure to the microgravity conditions of spaceflight causes astronauts to experience alterations in multiple physiological systems. These physiological changes include sensorimotor disturbances, cardiovascular deconditioning, and loss of muscle mass and strength. Some or all of these changes might affect the ability of crewmembers to perform critical mission tasks immediately after landing on a planetary surface. The goals of the Functional Task Test (FTT) study were to determine the effects of spaceflight on functional tests that are representative of critical exploration mission tasks and to identify the key physiological factors that contribute to decrements in performance. The FTT was comprised of seven functional tests and a corresponding set of interdisciplinary physiological measures targeting the sensorimotor, cardiovascular and muscular changes associated with exposure to spaceflight. Both Shuttle and ISS crewmembers participated in this study. Additionally, we conducted a supporting study using the FTT protocol on subjects before and after 70 days of 6 head-down bed rest. The bed rest analog allowed us to investigate the impact of body unloading in isolation on both functional tasks and on the underlying physiological factors that lead to decrements in performance, and then to compare them with the results obtained in our spaceflight study. Spaceflight data were collected on three sessions before flight, on landing day (Shuttle only) and 1, 6 and 30 days after landing. Bed rest subjects were tested three times before bed rest and immediately after getting up from bed rest as well as 1, 6, and 12 days after reambulation. We have shown that for Shuttle, ISS and bed rest subjects, functional tasks requiring a greater demand for dynamic control of postural equilibrium (i.e. fall recovery, seat egress/obstacle avoidance during walking, object translation, jump down) showed the greatest decrement in performance. Functional tests with reduced requirements for postural stability (i.e. hatch opening, ladder climb, manual manipulation of objects and tool use) showed little reduction in performance. These changes in functional performance were paralleled by similar decrements in sensorimotor tests designed to specifically assess postural equilibrium and dynamic gait control. Bed rest subjects experienced similar deficits both in functional tests with balance challenges and in sensorimotor tests designed to evaluate postural and gait control as spaceflight subjects indicating that body support unloading experienced during spaceflight plays a central role in post-flight alteration of functional task performance. To determine how differences in body-support loading experienced during in-flight treadmill exercise affect postflight functional performance, the loading history for each subject during in-flight treadmill (T2) exercise was correlated with postflight measures of performance. ISS crewmembers who walked on the treadmill with higher pull-down loads had enhanced post-flight performance on tests requiring mobility. Taken together the spaceflight and bed rest data point to the importance of supplementing inflight exercise countermeasures with balance and sensorimotor adaptability training. These data also support the notion that inflight treadmill exercise performed with higher body loading provides sensorimotor benefits leading to improved performance on functional tasks that require dynamic postural stability and mobility.

Bloomberg, J. J.↗

NASA NTRS2018

Modified Geometric Truncation of the Scattering Phase Function

Phase function of light scattering on large atmospheric particles has very strong peak in forward direction constituting a challenge for accurate numerical calculations of radiance required in remote sensing problems. Scaling transformation replaces original phase function with a sum of the delta function and a new regular smooth phase function. Geometric truncation is one of the ways to construct such a smooth function. The replacement phase function coincides with the original one outside the forward cone and preserves the asymmetry parameter. It has discontinuity at the cone. Another simple functional form of the replacement phase function within the cone is suggested. It enables continuity and allows for a number of modifications. Three of them are considered in this study: preserving asymmetry parameter, providing continuity of the 1st derivative of the phase function, and preserving mean scattering angle. Yet another problem addressed in this study is objective selection of the width of the forward cone. That angle affects truncation fraction and values of the phase function within the cone. A heuristic approach providing unambiguous criterion of selection of the truncation angle is proposed. The approach has easy numerical implementation. Suggested modifications were tested on cloud phase function using discrete ordinates and Monte Carlo methods. It was shown that the modifications provide better accuracy of the radiance computation compare to the original geometric truncation with discrete ordinates while continuous derivative approach provides significant gain in computer time with Monte Carlo simulations.

Alexander Radkevich↗

DOE OSTI2026

Thermal exchange-correlation functionals: Capturing quantum electron behavior in warm, dense plasmas

We summarize and give perspective upon recent progress in developing non-empirical constraint-based thermal (i.e., free energy) exchange-correlation (XC) density functionals essential for accurate description of the quantum behavior of electrons in warm, dense plasmas. After delineating the critical role of ground-state functionals for zero-temperature, time-dependent DFT, we outline the underpinnings of local density approximation, generalized gradient approximation (GGA), and meta-GGA XC free-energy functionals. Two basic thermalization principles for upgrading ground-state XC functionals to successful thermal ones are emphasized. Then, we turn to a long-standing challenge, assessment of the accuracy of well-founded functionals. Unlike the ground state, there are a few exact results for large T and P. An exception is path integral Monte Carlo (PIMC) data for dense H/D and He plasmas. For those, we did ab initio molecular dynamics simulations under selected thermodynamic conditions employing five thermal XC functionals: two approximate thermal GGAs, fully thermal GGA, an approximate meta-GGA, and fully thermal meta-GGA. Comparisons with the PIMC data show that functionals thermalized by augmenting a non-thermal functional with a lower-level thermal contribution are inferior to functionals with thermal XC and spatial inhomogeneity effects taken into account at the same level of refinement. We believe this and similar evidence should be convincing to the high-energy density physics community of the necessity of use of proper thermal XC functionals in simulation studies of finite-temperature quantum effects in warm, dense plasmas.

Ab-initio molecular dynamics↗

DOE OSTI2025

Fully thermal meta-GGA exchange correlation free-energy density functional

The application of density functional theory to materials in the warm dense matter regime has motivated the development of exchange-correlation functionals which incorporate proper, explicit temperature dependence. Previous work has yielded fully-thermal exchange-correlation free energy functionals at the local density approximation (LDA) and generalized gradient approximation (GGA) levels of refinement. Recently an additive thermal correction scheme was utilized to construct a meta-GGA exchange-correlation (XC) functional in which thermal effects are treated at the GGA level. Here, the f TSCAN free-energy XC functional presented here includes thermal effects through the meta-GGA level in the context of the SCAN (strongly constrained and appropriately normed) ground-state functional. The f TSCAN functional provides generality while achieving similar performance to a thermal GGA functional at high temperatures, e.g. pressures within 1% of path integral Monte Carlo simulations of warm dense hydrogen, and a significant improvement over ground-state functionals. At low temperatures, f TSCAN demonstrates improvements in accuracy relative to lower-level and deorbitalized functionals, indicating that calculations using f TSCAN may be expected to perform well across experimentally relevant densities and pressures.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Transfer Function Models and Sensitivity Analysis

In many situations, real or induced flaws such as tight cracks with known morphology cannot be manufactured in part configuration specimens or in real parts. Typically, fatigue cracks are manufactured in simple geometry specimens such as flat plates, dog-bone shaped flat or round specimens. If a nondestructive evaluation (NDE) technique is required to provide a reliably detectable target flaw size denoted as α_(90/95) for induced flaws in real part, then the direct method for qualifying the NDE procedure is to use the appropriate induced flaw specimens and perform probability of detection analysis using these flaws. This can be described as direct POD demonstration testing, which may follow guidelines of MIL-HDBK-1823. This paper considers a case, where induced flaws are not available in part configuration specimens. Therefore, a direct POD demonstration study cannot be undertaken. In such situation, general practice for NDE procedure qualification is to use artificial flaws in simple geometry and part configuration specimens, and induced flaws in the chosen simple geometry specimens. Signal response data is taken on all sets of artificial and induced flaws. NDE procedure testing on induced flaw in simple geometry specimen is called NDE demonstration testing here. A transfer function NDE procedure qualification method for forward case calculates predicted induced flaw size for demonstration using a chosen target flaw size. Another transfer function method for inverse case, calculates the target flaw size using a given demonstration flaw size. The transfer function analysis assumes relationship of artificial flaw signal responses in real parts and simple geometry specimens; and induced flaw responses in simple geometry specimens to induced flaws in real parts. The signal response transfer relationships model should be defined before transfer function models can be devised. Assuming that the signal response transfer relationships model is valid, forward and inverse case transfer function methods have been devised. Because of lack of signal response data from induced flaws in real part, 90/95% POD/confidence (P/C) cannot be demonstrated directly. However, the transfer function method may be assessed using simulation to evaluate whether the resulting target flaw size or demonstration flaw size provides adequate confidence to the assumed signal response transfer relationships model. Therefore, the transfer function approach is a risk assessment approach. Both the signal response transfer relationships model and the transfer function model are important in managing risk in results provided by the transfer function NDE technique qualification or assessment. The signal response transfer relationships model needs to be validated with empirical data and then transfer function model needs to be validated for desired P/C on case-by-case basis.

Nondestructive evaluation↗