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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

The total neutron cross section of liquid and solid ammonia

Ammonia is a material of interest for future neutron moderators at high-power sources due to its high hydrogen density, low melting point, and resistance to polymerization in an intense radiation field. Its performance in such applications cannot currently be calculated due to the absence of suitable computer models for the interaction of neutrons with ammonia under relevant conditions. In an effort to develop suitable scattering kernels for computer simulations of moderator performance, we have conducted a series of Density Functional Theory and Molecular Dynamics calculations of the molecular-level thermal properties of ammonia at various temperatures within both the solid and liquid phases. In this paper, we compare computer calculations for the energy-dependent total neutron cross section of ammonia, based on these models, to experimental measurements of those cross sections at temperatures of 221 K, 180 K, and 35 K. The experimental data were collected over an energy range from 0.1 meV to 10 eV using time-of-flight techniques at the Low Energy Neutron Source (LENS) facility at Indiana University. This comparison provides a first validation in the development of thermal scattering libraries for Monte Carlo source design simulations based on liquid and solid ammonia. In conclusion, we also provide some insights into where additional development of tools for creating such models may be needed.

Ammonia↗
DOE OSTI2026

Integrated machine learning-molecular dynamics framework for electrolyte property prediction

Electrochemical stability windows determine the operating range of battery electrolytes, yet accurate prediction remains challenging because stability emerges from statistical ensembles of local solvation environments rather than single ground-state molecular structures. Traditional density functional theory calculations on energy-minimized clusters cannot capture the thermal variations in local coordination environments and geometries that govern decomposition, while SMILES-based machine learning methods lack explicit representation of three-dimensional solvation structure and ion pairing. Here, we introduce a structure-aware machine learning framework that predicts frontier orbital energies (HOMO and LUMO) directly from molecular dynamics-sampled solvation configurations, achieving sub-0.6 eV accuracy at computational costs 3–4 orders of magnitude lower than first-principles methods. Across twelve representative battery electrolytes, we demonstrate that solvent-separated and contact ion pairs exhibit strong size- and local chemistry dependent electronic stability, with variations in coordination shifts of HOMO or LUMO level by 2–3 eV, and that extended solvation structure and partially desolvated environment further modulate stability by up to 3 eV. By encoding the statistical nature of electrochemical failure through ensemble sampling of explicit solvation geometries, our approach enables high-throughput screening and rational design of next-generation battery electrolytes with mechanistic understanding of structure–property relationships.

Energy - Storage↗
DOE OSTI2024

Inter-Oligomer Interaction Influence on Photoluminescence in Cis-Polyacetylene Semiconductor Materials

Semiconducting conjugated polymers (CPs) are pivotal in advancing organic electronics, offering tunable properties for solar cells and field-effect transistors. Here, we carry out first-principle calculations to study individual cis-polyacetylene (cis-PA) oligomers and their ensembles. The ground electronic structures are obtained using density functional theory (DFT), and excited state dynamics are explored by computing nonadiabatic couplings (NACs) between electronic and nuclear degrees of freedom. We compute the nonradiative relaxation of charge carriers and photoluminescence (PL) using the Redfield theory. Our findings show that electrons relax faster than holes. The ensemble of oligomers shows faster relaxation compared to the single oligomer. The calculated PL spectra show features from both interband and intraband transitions. The ensemble shows broader line widths, redshift of transition energies, and lower intensities compared to the single oligomer. This comparative study suggests that the dispersion forces and orbital hybridizations between chains are the leading contributors to the variation in PL. It provides insights into the fundamental behaviors of CPs and the molecular-level understanding for the design of more efficient optoelectronic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Tuning chemical precompression: Theoretical design and crystal chemistry of novel hydrides in the quest for warm and light superconductivity at ambient pressures

Over the past decade, a combination of crystal structure prediction techniques and experimental synthetic work has thoroughly explored the phase diagrams of binary hydrides under pressure. The fruitfulness of this dual approach is demonstrated in the recent identification of several superconducting hydrides with T c s approaching room temperature. We start with an overview of the computational procedures for predicting stable structures and estimating their propensity for superconductivity. A survey of phases with high T c reveals some common structural features that appear conducive to the strong coupling of the electronic structure with atomic vibrations that leads to superconductivity. We discuss the stability and superconducting properties of phases containing two of these—molecular H 2 units mixed with atomic H and hydrogenic clathrate-like cages—as well as more unique motifs. Lastly, we argue that ternary hydride phases, whose exploration is still in its infancy, are a promising route to achieve simultaneous superconductivity at high temperatures and stability at low pressures. Several ternary hydrides arise from the addition of a third element to a known binary hydride structure through site mixing or onto a new site, and several more are based on altogether new structural motifs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Rendezvous algorithms for large-scale modeling and simulation

Rendezvous algorithms encode a communication pattern that is useful when processors sending data do not know who the receiving processors should be, or vice versa. The idea is to define an intermediate decomposition where datums from different sending processors can ”rendezvous” to perform a computation, in a manner that both the senders and eventual receivers of the results can identify the appropriate rendezvous processor. Though they were originally designed for interpolating between overlaid grids with independent parallel decompositions (Plimpton et al., 2004), we have recently found rendezvous algorithms useful for a variety of operations in particle- or grid-based simulation codes when running large problems on large numbers of processors. In particular, we show they can perform well when a load-balanced intermediate decomposition is randomized and not spatial, requiring all-to-all communication to move data between processors. In this case rendezvous algorithms leverage the large bisection communication bandwidths which parallel machines provide. We describe how rendezvous algorithms work in a scientific computing context and give specific examples for molecular dynamics and Direct Simulation Monte Carlo codes which result in dramatic performance improvements versus simpler algorithms which do not scale as well. We explain how a generic rendezvous algorithm can be implemented, and also point out similarities with the MapReduce paradigm popularized by Google and Hadoop.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Ion Pairing and Molecular Orientation at Liquid/Liquid Interfaces: Self-Assembly and Function

We report that molecular orientation plays a pivotal role in defining the functionality and chemistry of interfaces, yet accurate measurements probing this important feature are few, due, in part, to technical and analytical limitations in extracting information from molecular monolayers. For example, buried liquid/liquid interfaces, where a complex and poorly understood balance of inter- and intramolecular interactions impart structural constraints that facilitate the formation of supramolecular assemblies capable of new functions, are difficult to probe experimentally. Here, we use vibrational sum-frequency generation spectroscopy, numerical polarization analysis, and atomistic molecular dynamics simulations to probe molecular orientations at buried oil/aqueous interfaces decorated with amphiphilic oligomers. We show that the orientation of self-assembled oligomers changes upon the addition of salts in the aqueous phase. The evolution of these structures can be described by competitive ion effects in the aqueous phase altering the orientations of the tails extending into the oil phase. These specific anionic effects occur via interfacial ion pairing and associated changes in interfacial solvation and hydrogen-bonding networks. These findings provide more quantitative insight into orientational changes encountered during self-assembly and pave the way for the design of functional interfaces for chemical separations, neuromorphic computing applications, and related biomimetic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Single-Site Carbon-Supported Metal-Oxo Complexes in Heterogeneous Catalysis: Structure, Reactivity, and Mechanism

When early transition metal complexes are molecularly grafted onto catalyst supports, well-defined, surface-bound species are created, which are highly active and selective single-site heterogeneous catalysts (SSHCs) for diverse chemical transformations. Further, in this minireview, we analyze and summarize a less conventional type of SSHC in which molybdenum dioxo species are grafted onto unusual carbon-unsaturated scaffolds, such as activated carbon, reduced graphene oxide, and carbon nanohorns. The choice of earth-abundant, low-toxicity, versatile metal constituents, and various carbon supports illustrates “catalyst by design” principles and yields insights into new catalytic systems of both academic and technological interest. Here, we summarize experimental and computational investigations of the bonding, electronic structure, reaction scope, and mechanistic pathways of these unusual catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

AI-Accelerated Design of Targeted Covalent Inhibitors for SARS-CoV-2

Direct-acting antivirals for the treatment of the COVID-19 pandemic caused by the SARS-CoV-2 virus are needed to complement vaccination efforts. Given the ongoing emergence of new variants, automated experimentation, and active learning based fast workflows for antiviral lead discovery remain critical to our ability to address the pandemic’s evolution in a timely manner. While several such pipelines have been introduced to discover candidates with noncovalent interactions with the main protease (M pro ), here we developed a closed-loop artificial intelligence pipeline to design electrophilic warhead-based covalent candidates. Here, this work introduces a deep learning-assisted automated computational workflow to introduce linkers and an electrophilic “warhead” to design covalent candidates and incorporates cutting-edge experimental techniques for validation. Using this process, promising candidates in the library were screened, and several potential hits were identified and tested experimentally using native mass spectrometry and fluorescence resonance energy transfer (FRET)-based screening assays. We identified four chloroacetamide-based covalent inhibitors of M pro with micromolar affinities (K I of 5.27 μM) using our pipeline. Experimentally resolved binding modes for each compound were determined using room-temperature X-ray crystallography, which is consistent with the predicted poses. The induced conformational changes based on molecular dynamics simulations further suggest that the dynamics may be an important factor to further improve selectivity, thereby effectively lowering KI and reducing toxicity. These results demonstrate the utility of our modular and data-driven approach for potent and selective covalent inhibitor discovery and provide a platform to apply it to other emerging targets.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

New Methods for Predicting Non-Born-Oppenheimer Chemistry

Current methods for modeling non-adiabatic molecular dynamics face fundamental limitations when treating geometric phase effects: quantum mechanical phenomena where nuclear wavepackets acquire phase shifts when encircling conical intersections. Existing approaches either neglect these effects entirely or rely on potential energy surfaces arising from the Born-Oppenheimer approximation, which introduce artificial singularities and can overestimate geometric phase contributions. This project developed a new theoretical framework based on exact factorization (XF) methods to overcome these limitations. We derived mathematical formulations for hybrid quantum-classical XF dynamics that selectively treat critical nuclear degrees of freedom quantum mechanically while propagating others classically. This approach addresses the computational intractability that has previously limited exact methods to toy systems. Key innovations include a new approach to systematically identifying nuclear coordinates requiring quantum treatment, as well as novel implementation strategies that interface with existing quantum chemistry codes. The project also developed a proof-of-concept code for treating Jahn-Teller systems and creation of educational materials on non-adiabatic dynamics geared at the graduate level. The theoretical framework developed will enable future systematically improvable calculations of nuclear quantum effects in realistic molecular systems, filling a critical gap in non-adiabatic dynamics methods. This foundation supports future development of predictive tools for designing energy-relevant photochemical processes where quantum coherence effects may be exploited to control reaction outcomes.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2023

A multiscale phase field fracture approach based on the non-affine microsphere model for rubber-like materials

Rubber-like materials have a broad scope of applications due to their unique properties like high stretchability and increased toughness. Hence, computational models for simulating their fracture behavior are paramount for designing them against failures. In this study, the phase field fracture approach is integrated with a multiscale polymer model for predicting the fracture behavior in elastomers. At the microscale, damaged polymer chains are modeled to be made up of a number of elastic chain segments pinned together. Using the phase field approach, the damage in the chains is represented using a continuous variable. Both the bond stretch internal energy and the entropic free energy of the chain are assumed to drive the damage, and the advantages of this assumption are expounded. A framework for utilizing the non-affine microsphere model for damaged systems is proposed here by considering the minimization of a hypothetical undamaged free energy, ultimately connecting the chain stretch to the macroscale deformation gradient. At the macroscale, a thermodynamically consistent formulation is derived in which the total dissipation is assumed to be mainly due to the rupture of molecular bonds. Using a monolithic scheme, the proposed model is numerically implemented and the resulting three-dimensional simulation predictions are compared with existing experimental data. The capability of the model to qualitatively predict the propagation of complex crack paths and quantitatively estimate the overall fracture behavior is verified. Additionally, the effect of the length scale parameter on the predicted fracture behavior is studied for an inhomogeneous system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Harnessing the Spin-Flip Radiative Lifetimes of Optically Addressable Molecular Qubits

Optically addressable molecular qubits based on spin-flip (SF) emissive transitions are promising candidates for quantum technologies due to their sharp luminescence lines and tunable optical-spin interfaces. Yet, the microscopic mechanisms controlling the spin-flip radiative lifetime of SF emitters, a key property for efficient spin readout, remain largely unexplored. Here, we present a computational study of several Cr 4+ and Mo 4+ pseudotetrahedral molecular qubits, and we identify chemical and structural features that influence the transition dipole moment associated with the SF emission, which, in turn, governs the SF radiative lifetime. We find that the magnitude of the dipole moment is governed by the multireference character of the spin-flip excited-state wave function, which can be modulated by tuning the energy separation between the d orbitals of the metal and the spin-pairing energy. Both parameters are sensitive to molecular symmetry, metal–ligand bond covalency, and bond anisotropy and leave room for modulation via ligand and metal design, as well as applied strain, which is relevant for sensing applications. Our findings provide a mechanistic framework for understanding and tuning the spin-flip radiative behavior of molecular qubits and SF emitters that may guide future advances in quantum information science.

molecular qubits↗
DOE OSTI2020

D3R grand challenge 4: blind prediction of protein–ligand poses, affinity rankings, and relative binding free energies

The Drug Design Data Resource (D3R) aims to identify best practice methods for computer aided drug design through blinded ligand pose prediction and affinity challenges. Herein, we report on the results of Grand Challenge 4 (GC4). GC4 focused on proteins beta secretase 1 and Cathepsin S, and was run in an analogous manner to prior challenges. In Stage 1, participant ability to predict the pose and affinity of BACE1 ligands were assessed. Following the completion of Stage 1, all BACE1 co-crystal structures were released, and Stage 2 tested affinity rankings with co-crystal structures. Finally, we provide an analysis of the results and discuss insights into determined best practice methods.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Inverse methods for design of soft materials

Functional soft materials, comprising colloidal and molecular building blocks that self-organize into complex structures as a result of their tunable interactions, enable a wide array of technological applications. Inverse methods provide a systematic means for navigating their inherently high-dimensional design spaces to create materials with targeted properties. Furthermore, while multiple physically motivated inverse strategies have been successfully implemented in silico, their translation to guiding experimental materials discovery has thus far been limited to a handful of proof-of-concept studies. In this perspective, we discuss recent advances in inverse methods for design of soft materials that address two challenges: (1) methodological limitations that prevent such approaches from satisfying design constraints and (2) computational challenges that limit the size and complexity of systems that can be addressed. Strategies that leverage machine learning have proven particularly effective, including methods to discover order parameters that characterize complex structural motifs and schemes to efficiently compute macroscopic properties from the underlying structure. We also highlight promising opportunities to improve the experimental realizability of materials designed computationally, including discovery of materials with functionality at multiple thermodynamic states, design of externally directed assembly protocols that are simple to implement in experiments, and strategies to improve the accuracy and computational efficiency of experimentally relevant models.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Exploring solvation structure and transport behavior for rational design of advanced electrolytes for next generation of lithium batteries

The efficacy of electrolytes significantly affects battery performance, leading to the development of several strategies to enhance them. Despite this, the understanding of solvation structure remains inadequate. It is imperative to understand the structure–property–performance relationship of electrolytes using diverse techniques. Here, this review explores the recent advancements in electrolyte design strategies for high capacity, high-voltage, wide-temperature, fast-charging, and safe applications. To begin, the current state-of-the-art electrolyte design directions are comprehensively reviewed. Subsequently, advanced techniques and computational methods used to understand the solvation structure are discussed. Additionally, the importance of high-throughput screening and advanced computation of electrolytes with the help of machine learning is emphasized. Finally, future horizons for studying electrolytes are proposed, aimed at improving battery performance and promoting their application in various fields by enhancing the microscopic understanding of electrolytes.

25 ENERGY STORAGE↗
DOE OSTI2021

Barriers to carriers: faults and recombination in non-stoichiometric perovskite scintillators

Abstract Tuning the efficiency and speed of charge carrier recombination in inorganic scintillators can potentially improve their performance in diverse applications. Recent work suggests that this maybe be achieved via a two-phase scintillator AB that naturally phase separates into A -rich and B -rich domains. In addition, a favorable electronic structure and band-edge alignment such that the charge carriers are confined or are thermodynamically driven to preferentially accumulate in one of the two domains, might lead to an improved radiative recombination rate. Here, we use density functional theory computations and ab initio molecular dynamics (AIMD), including non-adiabatic molecular dynamics (NAMD) simulations, to examine an alternative phase structure and its potential impact on recombination. Using a model perovskite SrTiO $$_3$$ 3 system with one-, two- and three-dimensional Ruddlesden–Popper (RP) phases, we demonstrate that RP faults induce band structure changes in the material that can act as barriers to carrier transport. Our AIMD/NAMD simulations indicate competing effects of a lower mean free path (potentially enhancing the desired radiative recombination and overall scintillating efficiency) and faster non-radiative recombination (undesired) due to enhanced electron–phonon coupling in the faulted system. Full exploitation of such a rational design approach would require tuning of the effective scintillation efficiency by varying the perovskite chemistry using appropriate arrangements of RP faults in the bulk material. Finally, other effects, such as the tendency of point defects to segregate at the interface, that might affect the overall performance, are briefly discussed. We expect the basic results found here to apply to other nanostructured scintillators. Graphical Abstract

36 MATERIALS SCIENCE↗
DOE OSTI2025

SchrödingerNet: A Universal Neural Network Solver for the Schrödinger Equation

Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schrödinger equation (SE) by integrating various neural network (NN)-based wave function ansatzes with variational Monte Carlo methods. Nevertheless, such NN-based methods are all based on the Born–Oppenheimer approximation (BOA) and require computationally expensive training for each nuclear configuration. In this work, we propose a novel NN architecture, SchrödingerNet, to solve the full electronic-nuclear SE by defining a loss function designed to equalize local energies across the system. This approach is based on a translationally, rotationally and permutationally symmetry-adapted total wave function ansatz that includes both nuclear and electronic coordinates. Furthermore, this strategy not only allows for an efficient and accurate generation of a continuous potential energy surface at any geometry within the well-sampled nuclear configuration space, but also incorporates non-BOA corrections, through a single training process. Comparison with benchmarks of atomic and small molecular systems demonstrates its accuracy and efficiency.

Chemical calculations↗
DOE OSTI2022

Controlling Structural, Electronic, and Energy Flow Dynamics of Catalytic Processes through Tailored Nanostructures

MoS 2 (molybdenum disulfide) is a highly-versatile catalyst material for support of numerous reactions from hydrodesulfurization and denitrogenation to the focus of this renewal proposal: hydrogenation of CO/CO 2 towards (higher) alcohols. At the same time, MoS 2 is a non-toxic, environmentally-benign and rather inert material- which under ambient conditions for some time has served as a lubricant and, more recently, as next-generation electronic material. The apparent contrast between inertness and stability in ambient, and catalytic activity under reactive conditions is puzzling and calls for a synergistic theoretical and experimental investigation with the long-term objective of enabling the rational design of MoS 2 -based catalysts for alcohol-formation reactions by providing a microscopic understanding of the environmental factors that determines site activity and selectivity. Our research project seeks answers to the questions (a) what conformation does MoS 2 adopt under reaction conditions (as opposed to that under ultrahigh vacuum and low temperatures)?; (b) what reaction pathways exist on such a material?; (c) how can the local environment of the active sites be manipulated so as to make MoS 2 an efficient catalyst for production of higher alcohol from syngas? In particular, research strategies will explore how the basal plane composed of sulfur atoms can be activated so as to exhibit a reactivity of its own, by addressing three research targets and building on extensive preliminary and enabling work: (1) vacancies and vacancy aggregates on the basal plane; (2) non-local catalyst transformation through alkali doping, hydrogenation and phase transition; (3) fabrication of a metal-nanoparticle-activated MoS 2 system, in which particle anchoring, reactive sites and pathways as well as selectivity are controlled by design, as an example of predictive development of a catalyst material,. All strategies are directed to improve the efficacy of the key reactive sites and selectivity of chemical pathways by design, to replace the inefficient methodology of trial and error in catalyst development. This research project represents a synergistic combination of computational guidance, foundational surface-science-based experiments and validation under reactive conditions that aims at transformative new insights into the working of MoS 2 -based hydrogenation-catalysts, a topic squarely at the center of the interest of DOE BES. Guided and led by Talat Rahman, a computational physicist, this project will apply density functional theory to understand structure, reaction pathways and chemical potentials associated with MoS 2 -based CO/CO 2 hydrogenation, augmented by kinetic Monte Carlo methods for reaction rates and prefactors as well as ab-initio molecular dynamics for evaluation of thermal stability. Complementary experimental input and validation will originate from co-PI Ludwig Bartels, a physical chemist and materials scientist, whose group focuses on local imaging and preparation of MoS 2 materials, from co-PI Peter Dowben, an experimental physicist, whose group is expert in the spectroscopy of occupied and unoccupied electronic states, and from senior collaborator Michael White of Brookhaven National Laboratory, whose group generates high-resolution electronic and activity information on size-selected well-defined metal chalcogenide clusters. This collaborative effort will enable a comprehensive understanding of the correlation of structural integrity and catalytic activity of MoS 2 in forms ranging from extended films to individual particles with known geometries and binding sites. Alcohol formation from syngas is a rapidly emerging application that has great potential through facile, economic, and decentralized biomass gasification. CO 2 activation is one of the most pressing concerns of our time: increasing CO 2 levels in the atmosphere change the climate and expose the globe to environmental transformations with the potential for enormous economic and societal impact. We will investigate CO/CO 2 hydrogenation via an interdisciplinary research collaboration with established synergy – one that, in accordance with the mission of the DOE, involves accredited Hispanic-Serving Institutions and that, through student exchange with international collaborators and National Labs, will directly benefit a broad spectrum of communities and generate human resources in sciences essential to their future.

2D materials↗
NASA NTRSDate not supplied

Enabling Open and Interoperable Science: Multi-Omics Data Processing Platform with NASA GeneLab Standardized Bioinformatics Workflows for Space and Earth Research

Multi-omics biological data continues to be generated at an astounding pace. Genomics, transcriptomics, metabolomics, and proteomics, or collectively known as multi-omics data, are used to assess biological functions, and provide invaluable insights into human, animal, plant, and environmental health both on Earth and in Space. Despite the abundance of these valuable data, the need for bioinformatics expertise, particularly as it relates to the niche filed of space biology, and a lack of accessible resources for processing these data limit their usefulness in deriving biological insights. The NASA Open Science Data Repository (OSDR) provides access to omics data from various spaceflight and analog studies. To enhance the accessibility and reusability of these data, GeneLab (part of OSDR) designs and implements standardized, community-driven, open-source bioinformatics workflows to transform raw omics data into standardized processed data. Currently, GeneLab-processed data from hundreds of space studies have been reused for meta-analyses. This has led to new insights and scientific publications that extend beyond the initial research, thereby enriching our understanding of molecular-scale biological responses to the space environment. To make these bioinformatics workflows open and accessible, GeneLab teamed up with DOE-funded initiatives, including the National Microbiome Data Collaborative (NMDC), to create the NASA EDGE [Empowering the Development of Genomics Expertise] Bioinformatics web-based platform. NASA EDGE utilizes shared compute resources to run the GeneLab standardized bioinformatics workflows, which eliminates the need for researchers to have their own high performance computing cluster. The web-based platform makes complicated biological analyses incredibly easy to perform, thus expanding the reach of these analyses to bioinformatics novices, students, and even citizen scientists enabling them to contribute to scientific discoveries and progress. The authors will demonstrate how the NASA EDGE platform can be used to process microbial omics data hosted on OSDR as well as user-generated omics datasets using GeneLab’s standard workflows.

Amanda M. Saravia-Butler↗