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NASA NTRS2017

Kepler Planet Detection Metrics: Window and One-Sigma Depth Functions for Data Release 25

This document describes the window and one-sigma depth functions relevant to the Transiting Planet Search (TPS) algorithm in the Kepler pipeline (Jenkins 2002; Jenkins et al. 2017). The window function specifies the fraction of unique orbital ephemeris epochs over which three transits are observable as a function of orbital period. In this context, the epoch and orbital period, together, comprise the ephemeris of an orbiting companion, and ephemerides with the same period are considered equivalent if their epochs differ by an integer multiple of the period. The one-sigma depth function specifies the depth of a signal (in ppm) for a given light curve that results in a one-sigma detection of a transit signature as a function of orbital period when averaged over all unique orbital ephemerides. These planet detection metrics quantify the ability of TPS to detect a transiting planet signature on a star-by-star basis. They are uniquely applicable to a specific Kepler data release, since they are dependent on the details of the light curves searched and the functionality of the TPS algorithm used to perform the search. This document describes the window and one-sigma depth functions relevant to Kepler Data Release 25 (DR25), where the data were processed (Thompson et al. 2016) and searched (Twicken et al. 2016) with the SOC 9.3 pipeline. In Section 4, we describe significant differences from those reported in Kepler Data Release 24 (Burke Seader 2016) and document our verification method.

Planet Detection Metrics↗

NASA NTRS2017

Comparison of Two Bioinformatics Tools Used to Characterize the Microbial Diversity and Predictive Functional Attributes of Microbial Mats from Lake Obersee, Antarctica

In this study, using NextGen sequencing of the collective 16S rRNA genes obtained from two sets of samples collected from Lake Obersee, Antarctica, we compared and contrasted two bioinformatics tools, PICRUSt and Tax4Fun. We then developed an R script to assess the taxonomic and predictive functional profiles of the microbial communities within the samples. Taxa such as Pseudoxanthomonas, Planctomycetaceae, Cyanobacteria Subsection III, Nitrosomonadaceae, Leptothrix, and Rhodobacter were exclusively identified by Tax4Fun that uses SILVA database; whereas PICRUSt that uses Greengenes database uniquely identified Pirellulaceae, Gemmatimonadetes A1-B1, Pseudanabaena, Salinibacterium and Sinibacteraceae. Predictive functional profiling of the microbial communities using Tax4Fun and PICRUSt separately revealed common metabolic capabilities, while also showing specific functional IDs not shared between the two approaches. Combining these functional predictions using a customized R script revealed a more inclusive metabolic profile, such as hydrolases, oxidoreductases, transferases; enzymes involved in carbohydrate and amino acid metabolisms; and membrane transport proteins known for nutrient uptake from the surrounding environment. Our results present the first molecular-phylogenetic characterization and predictive functional profiles of the microbial mat communities in Lake Obersee, while demonstrating the efficacy of combining both the taxonomic assignment information and functional IDs using the R script created in this study for a more streamlined evaluation of predictive functional profiles of microbial communities.

Hyunmin Koo↗

NASA NTRS2019

Experimentally-Derived Bidirectional Reflectance Distribution Function Data in Support of the Orbital Debris Program Office

The NASA Orbital Debris Program Office (ODPO) has used various optical assets to acquire photometric data of Earth-orbiting objects to define the orbital debris environment. To better characterize and model optical data acquired from ground-based telescopes, the Optical Measurements Center (OMC) at NASA Johnson Space Center emulates illumination conditions seen in space by using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. One of the OMC goals is to improve the size calculation used for optical data by developing an optical-based Size Estimation Model. The current size estimation requires applying a Lambertian phase function, a set albedo value, and range to the observed magnitude. The first step to improving the sampled brightness of laboratory targets is to remove aspect-angle dependencies. Then, the volume of possible object viewing angles is sampled at 21 combinations of azimuth and zenith angles for each solar phase angle. Finally, the acquired images are input into an image processing program that generates approximations for the object’s Bidirectional Reflectance Distribution Function (BRDF) and phase function. The BRDF is a radiometric concept that identifies an object’s material composition by matching a BRDF approximated with photometric data collected by ground-based telescopes with a BRDF generated experimentally from a known object in the laboratory. This paper discusses the validation of experimental BRDF and phase function approximations produced in the OMC and how the findings will be incorporated into ODPO models. A Lambertian sphere is imaged and the subsequent experimental functions are scrutinized to confirm that they correspond to an object that has an isotropic luminance. With the image processing algorithm validated, test objects with varying optical properties are then imaged to confirm that the produced photometric functions are both unique and repeatable. Once the validation is complete, the OMC will be used to evaluate a subset of fragments from a hypervelocity impact test of a mock-up satellite and assess the appropriate phase function and size estimates using BRDF measurements for a large volume of targets composed of various shapes, sizes, and materials.

Orbital Debris Program Office (ODPO)↗

NASA NTRS2019

A Comparative Study on Computation of Cumulative Distribution Function in Predicting Time of Failure of Engineering Systems

Estimating accurate Time-of-Failure (ToF) of a system is key in making the decisions that impact operational safety and optimize cost. In this context, it is interesting to note that different approaches have been explored to tackle the problem of estimating ToF. The difference is in part characterized by different definitions of the hazard zones. The conventional definition for the cumulative distribution function (CDF) calculation is assumed to have well-defined hazard zones, that is, hazard zones defined as a function of the system state trajectory. An alternate method suggests the use of hazard zones defined as a function of the system state at time , instead of hazard zones defined as a function of system state up to and including time k (Acuna and Orchard 2018, 2017). This paper explores these differences and their impact on ToF estimation. Results for the conventional CDF definition indicated that, (i) the cumulative distribution function is always an increasing function of time, even when realizations of the degradation process are not monotonic, (ii) the sum of all probabilities is always 1 and does not need to be normalized, and (iii) all probabilities are positive and less than or equal to 1. Similar results are not observed for CDF calculation with hazard zones defined as a function only of the system state at time . Results for ToF estimation using Acuna's definition differ, suggesting that there is an underlying assumption of independence in the hazard zone definition. Therefore, we present an alternate definition of hazard zone which guarantees the properties of a well-defined CDF with a more straightforward ToF definition.

Hazard Zone↗

NASA NTRS2022

Further Development of a Function Generator Technique

Further features and properties of functions generated by generalization of the process originally uncovered to describe the evolution of pressure in a rigid volume due to outgassing or desorption are explored. Properties presented include development of a general Maclaurin series associated with these functions, a limitation in using integration by parts to produce asymptotic expansions, and a general description of an implicit Adams-Moulton method for numerical quadrature of transformed functions. These developments are then applied to develop and explore functions that solve the Sievert integral and the modified Bessel function of the first kind, order zero. Features of the error function and the incomplete lower gamma function are also considered.

Michael S. Woronowicz↗

NASA NTRSDate not supplied

Sampling Functions from Gaussian Processes and Structured Covariance Gaussian Networks

When learning aerodynamic models from data, it is critical to incorporate estimates of model uncertainty. This motivates the design of probabilistic aerodynamic databases which can be sampled to generate physically and statistically plausible aerodynamic models. In this talk we discuss how to sample deterministic functions from two different kinds of probabilistic models and demonstrate their use. First, Gaussian Process Regressors (GPRs) are a widely used probabilistic kernel-based model which can be thought of as Gaussian distributions over functions. GPRs are generally trained by maximizing the marginal likelihood of seeing the training data over the kernel parameter space. Sample functions are easily generated by drawing points from the Gaussian distribution at desired input points. However, when the points are not known ahead of time, the classical sampling approach is not possible since successive function samples will generate different function realizations. We present an approach for sampling consistent function evaluations from a GPR over multiple samples. Second, we describe a neural network architecture which learns a conditional Gaussian distribution by maximizing the marginal likelihood at each point in the input space. We then discuss and compare several options for generating sample functions which match this distribution. Finally, we demonstrate the use of these probabilistic aerodynamic models in an atmospheric reentry simulation.

Gaussian process regression↗

DOE OSTI2023

Elastic functional changepoint detection of climate impacts from localized sources

Detecting changepoints in functional data has become an important problem as interest in monitoring of climate phenomenon has increased, where the data is functional in nature. Here, the observed data often contains both amplitude (y-axis) and phase (x-axis) variability. If not accounted for properly, true changepoints may be undetected, and the estimated underlying mean change functions will be incorrect. In this article, an elastic functional changepoint method is developed which properly accounts for these types of variability. The method can detect amplitude and phase changepoints which current methods in the literature do not, as they focus solely on the amplitude changepoint. This method can easily be implemented using the functions directly or can be computed via functional principal component analysis to ease the computational burden. We apply the method and its nonelastic competitors to both simulated data and observed data to show its efficiency in handling data with phase variation with both amplitude and phase changepoints. We use the method to evaluate potential changes in stratospheric temperature due to the eruption of Mt. Pinatubo in the Philippines in June 1991. Using an epidemic changepoint model, we find evidence of a increase in stratospheric temperature during a period that contains the immediate aftermath of Mt. Pinatubo, with most detected changepoints occurring in the tropics as expected.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Exact constraints and appropriate norms in machine-learned exchange-correlation functionals

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human-designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently, efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to de-orbitalize the strongly constrained and appropriately normed (SCAN) functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding the use of the orbital-dependent kinetic energy density. The performance and transferability of the machine-learned functional are demonstrated for molecular and periodic systems.

Artificial neural networks↗

DOE OSTI2023

The Predictive Power of Exact Constraints and Appropriate Norms in Density Functional Theory

Ground-state Kohn-Sham density functional theory provides, in principle, the exact ground-state energy and electronic spin densities of real interacting electrons in a static external potential. In practice, the exact density functional for the exchange-correlation (xc) energy must be approximated in a computationally efficient way. About 20 mathematical properties of the exact xc functional are known. In this work, we review and discuss these known constraints on the xc energy and hole. By analyzing a sequence of increasingly sophisticated density functional approximations (DFAs), we argue that (a) the satisfaction of more exact constraints and appropriate norms makes a functional more predictive over the immense space of many-electron systems and (b) fitting to bonded systems yields an interpolative DFA that may not extrapolate well to systems unlike those in the fitting set. We discuss both how the class of well-described systems has grown along with constraint satisfaction and the possibilities for future functional development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Hierarchical Self‐Assembly of Multidimensional Functional Materials from Sequence‐Defined Peptoids

Abstract Hierarchical self‐assembly represents a powerful strategy for the fabrication of functional materials across various length scales. However, achieving precise formation of functional hierarchical assemblies remains a significant challenge and requires a profound understanding of molecular assembly interactions. In this study, we present a molecular‐level understanding of the hierarchical assembly of sequence‐defined peptoids into multidimensional functional materials, including twisted nanotube bundles serving as a highly efficient artificial light harvesting system. By employing synchrotron‐based powder X‐ray diffraction and analyzing single crystal structures of model compounds, we elucidated the molecular packing and mechanisms underlying the assembly of peptoids into multidimensional nanostructures. Our findings demonstrate that incorporating aromatic functional groups, such as tetraphenyl ethylene (TPE), at the termini of assembling peptoid sequences promotes the formation of twisted bundles of nanotubes and nanosheets, thus enabling the creation of a highly efficient artificial light harvesting system. This research exemplifies the potential of leveraging sequence‐defined synthetic polymers to translate microscopic molecular structures into macroscopic assemblies. It holds promise for the development of functional materials with precisely controlled hierarchical structures and designed functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Assessing the Performance of Exchange‐Correlation Density Functionals in Describing the Iron‐Catalyzed Ammonia Synthesis System

Density functional theory (DFT) has been widely employed for elucidating mechanistic aspects of heterogeneous catalysis. However, the accuracy of DFT calculations relies heavily on selecting an exchange-correlation (XC) functional that correctly describes the electronic structure of materials involved in the reactions. This study assesses the accuracy of several XC density functionals for modeling the iron-catalyzed ammonia synthesis system. In the assessment of functional accuracy, experimental references are compared to DFT-calculated values for the formation energy of gas-phase ammonia and nitrogen, bulk Fe/Fe-nitride (γ′-Fe 4 N) lattice constants and cohesive/formation energies, and nitrogen and ammonia binding energies on Fe(100), Fe(111), Fe(110), and γ′-Fe 4 N(111). It is observed that the experimental value for each of these descriptors is accurately modeled by at least one functional. RPBE alone provides reliable estimates for both the lattice constant and cohesive energy of Fe and γ′-Fe 4 N. Temperature-programmed desorption experiments led to estimates for N and NH 3 adsorption across several Fe-based facets that are best captured by RPBE. These results highlight the importance of choosing an appropriate XC functional that accurately describes experimental systems and offer insights into effectively modeling the interactions between nitrogen and ammonia on Fe-based surfaces.

adsorption↗

DOE OSTI2025

Functional but not taxonomic diversity increases productivity of Populus in the southeastern United States

Plant interactions like competition and facilitation impact ecosystem function and resilience. Improving our understanding of the relationships between these interactions and community productivity has important implications for managers of production systems in forestry and agriculture as well as conservation science. Populus spp. are an excellent model system for exploring how inter‐ and intraspecific interactions impact ecosystem functions, such as productivity, in forest plantations. In this study, we compared aboveground productivity of six Populus clones from three different taxa grown in monoclonal and mixed‐clonal plots. The different mixture treatments were intended to experimentally test aboveground biomass response to contrasting levels of taxonomic diversity and functional diversity based on nitrogen use characteristics of Populus clones. We hypothesize that functional diversity would be more important than taxonomic diversity in increasing aboveground productivity of mixed‐clonal plantings compared to monocultures. In addition, a subset of treatments was carried out on additional sites representing a productivity gradient in order to determine if the relationship between biodiversity and productivity in these systems diminished at more productive sites as suggested by the stress‐gradient hypothesis. We found that functionally diverse mixtures of clones had greater yield of aboveground biomass than the average of their constituent monocultures, while more taxonomically diverse mixes of clones did not differ from the average of their constituent monocultures. However, when reestablished on sites with extremely high or low productivity, the best performing clone mixture also did not differ from the average of its constituent monocultures. Our results suggest that intimate clone mixtures of Populus have the potential to significantly increase productivity, but results vary by mixture and by site. To capitalize on positive biodiversity effects on yield in production systems, targeted mixtures based on divergent functional traits linked to different use and acquisition strategies for site‐specific limiting resources are most likely to be successful.

BEF↗

DOE OSTI2022

Microbial communities and biogeochemical functioning across peatlands in the Athabasca Oil Sands region of Canada: Implications for reclamation and management

Abstract Peatlands play an important role in global biogeochemical cycles and are essential for multiple ecosystem functions. Understanding the environmental drivers of microbial functioning and community structure can provide insights to enable effective and evidence‐based management. However, it remains largely unknown how microbial diversity contributes to the functioning of belowground processes. Addressing this gap in knowledge will provide a better understanding of microbial‐mediated processes in peatlands that are undergoing restoration or reclamation. This study assessed the changes in microbial community diversity and structure as well as soil function by measuring microbial respiration on a range of substrates from three natural fen types found in the Athabasca Oil Sands region of Alberta, Canada (a poor fen, a hypersaline fen, and a tree‐rich fen) and a nearby constructed fen undergoing reclamation following open pit mining. Overall, substrate induced respiration was significantly higher in the constructed fen. Alpha diversity of fungi and prokaryotes was highest in the tree‐rich fen, and the composition of microbial communities was significantly different between fens. Both fungal and prokaryotic communities were strongly related to pore water pH and temperature, with plant richness also contributing to the shape of fungal communities. In summary, microbial community structure reflects the underlying differences in soil condition across different fens but plays essential roles in the ecological functions of soil. These findings provide a new outlook for the management of peatlands undergoing post‐mining reclamation. Future research on peatland reclamation should consider the dynamic interaction between communities and ecosystem functionality, for which this study forms a useful baseline.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Visualisation and outlier detection for probability density function ensembles

Abstract Exploratory data analysis (EDA) for functional data—data objects where observations are entire functions—is a difficult problem that has seen significant attention in recent literature. This surge in interest is motivated by the ubiquitous nature of functional data, which are prevalent in applications across fields such as meteorology, biology, medicine and engineering. Empirical probability density functions (PDFs) can be viewed as constrained functional data objects that must integrate to one and be nonnegative. They show up in contexts such as yearly income distributions, zooplankton size structure in oceanography and in connectivity patterns in the brain, among others. While PDF data are certainly common in modern research, little attention has been given to EDA specifically for PDFs. In this paper, we extend several methods for EDA on functional data for PDFs and compare them on simulated data that exhibit different types of variation, designed to mimic that seen in real‐world applications. We then use our new methods to perform EDA on the breakthrough curves observed in gas transport simulations for underground fracture networks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Efficient Pd on carbon catalyst for ammonium formate dehydrogenation: Effect of surface oxygen functional groups

Formate solution is one of a kind promising liquid organic hydrogen carrier but suffers from kinetic challenges. This study investigates the kinetics of the surfacefunctionalized Pd on carbon catalysts for formate dehydrogenation and the impact of O-functional groups. Here, the fraction of the distinguished O-functional groups was modulated by the different concentrated HNO 3 solutions treatment or by H 2 reduction. This study shows that the O-functional groups play critical roles in dispersing Pd nanoparticles and decreasing the activation energy for dehydrogenation. Density functional theory (DFT) calculation reveals that most O-functional groups enhance formate adsorption on the Pd active site. However, the existence of C=O groups consumes reducing agents and hinders the formation of metallic Pd. The electron transfer from Pd to oxygen functional groups is unfavorable to dehydrogenation. The as-prepared Pd5/re-ACA (reduced activated carbon washed by acid) exhibited significant activity with a higher turnover frequency of 13,511 h -1 than commercial Pd/C.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Deep learning-enhanced design for functionally graded auxetic lattices

Auxetic materials with counterintuitive negative Poisson’s ratio have been of significant interest due to potential applications across diverse engineering fields. Functionally grading such auxetics further enables customization of the structural response and harnesses the potential for multi-functional applications. However, a critical challenge in designing functionally graded lattices is to efficiently determine the spatial variation of the functional gradient and the corresponding geometric designs to achieve the desired response. In this paper, a highly efficient deep learning-based inverse design framework for functionally graded tetra-petal auxetics with spatially tailored properties is presented. This framework significantly improves the efficiency of tailoring functionally graded auxetics where many unit cells need to be tailor-designed. The graded tetra-petal auxetics obtained from the inverse design framework are additively manufactured and subjected to impact tests. The results show superior impact performance compared with uniform designs, demonstrating the effectiveness of the proposed inverse design framework, which can be inspirable to promote advanced structures/materials with enhanced impact resistance.

42 ENGINEERING↗

DOE OSTI2023

Functional variability in specific root respiration translates to autotrophic differences in soil respiration in a temperate deciduous forest

CO 2 release from forest soils (R s ) is a prominent flux in the global carbon cycle. Rs is derived from roots (autotrophic respiration, R a ) and microbial (heterotrophic) respiration and is highly dynamic, as it depends on edaphic and environmental conditions as well as root functional traits and microbial community composition. It is unclear how root functional traits affect root and microbial respiration rates; however, their consideration may help parse out the relative contributions of root and microbial respiration to R s . At a temperate forest site, root systems of 3–4 functional root orders and their surrounding surface soil were carefully excavated and placed into custom trays designed to repeatedly measure R s in situ on eight temperate tree species that varied in their root functional strategies and mycorrhizal affinity. R s was measured bi-weekly to monthly for nearly one year using a custom chamber attached to a gas exchange system. R s varied over time, ranging from 0.3 to 12 µmol m -2 s -1 . Comparable root systems of the same species were excised from the soil and specific root respiration rates (R r ) were measured. Rr ranged from 2.5 to 9.0 nmol g -1 s -1 and was negatively correlated with root tissue density and positively related to root tissue nitrogen concentration. Using R r to estimate R a , we estimate that R a accounts for <10%, on average 2–3%, of R s for individual root systems (averaging 1.2 g dry biomass) housed in surrounding soil (average 1.3 kg dry mass) in situ; thus, Ra was roughly 20 times greater than Rh per unit mass. The contribution of R a peaked in the fall and coincided with leaf senescence of the forest canopy. A soil-sterilizing experimental treatment designed to help isolate R a in situ reduced bacterial biomass and shifted fungal community composition, but there was no reduction in Rs of the in-situ root-soil tray systems. The relative R a to R s ratio increased with root functional strategies characterized by greater specific root length and tip abundance, but also to greater root tissue density. The ratio of R a to R s also increased with warmer soil temperatures and decreased slightly with increasing soil moisture. We discuss how incorporating root functional traits as modulators of the autotrophic contribution to R s could be considered when modeling total soil CO 2 efflux from forests.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

On the convexity of phase-field fracture formulations: Analytical study and comparison of various degradation functions

Efficient and accurate fracture modeling is of great importance in applications where catastrophic outcomes under extreme scenarios are possible. The phase-field (PF) approach to fracture received significant attention over the past decade, due to its capability to capture complicated fracture patterns (e.g., crack merging and branching). Specifically, crack initiation and propagation are modeled via minimization of the total energy functional, which is regularized with the aid of a phase field. Despite the promising results and modeling capabilities of the PF method in many applications, the solution of fracture problems remains computationally challenging mainly due to the non-convexity of the total energy functional with respect to the combined unknown (phase field and displacement) fields. Understanding the effects of their coupling on convexity is crucial in order to address frequently encountered hurdles in fracture modeling (e.g., inefficient solvers and non-physical crack nucleation). In this paper, we develop convexity criteria for a wide class of PF fracture formulations. For this class of formulations, the second variation of the total energy functional is expressed in terms of Hessian matrices (evaluated at individual material points). Depending on the choice of geometric crack functions and degradation functions, we classify the formulations into three categories and analytically study each one separately. To study the sign of the second variation, we derive inequalities which are satisfied at material points when the Hessian matrix is locally positive semi-definite. These inequalities provide objective criteria for comparing degradation functions. Finally, the applicability of the proposed convexity criteria is demonstrated in the context of a one-dimensional problem, solved using a conventional monolithic solver.

97 MATHEMATICS AND COMPUTING↗