Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytical mathematics”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Immersive Particle Advection: Through the Scales of Renewable Energy: Preprint

We describe the benefits of immersive flow analysis for three large-scale computational science studies in the field of renewable energy. The studies encompass a range of scales, spanning from the large atmospheric scale of a wind farm to the human scale of an electric vehicle cabin down to the microscopic scale of battery material science. In these studies, users explored the flow patterns and dynamics through immersive particle advection. The integration of high-performance computing with immersive analysis provided a deeper understanding of these systems, helping develop more effective solutions for a sustainable energy future.

computational fluid dynamics↗
DOE OSTI2022

Mining Air for Fuels and Fine Chemicals

The Intergovernmental Panel on Climate Change’s 2021 report underscores that Direct Air Capture (DAC) is an essential component to limiting global warming to 2 °C, yet separating CO 2 from air and its subsequent concentration for conversion into carbon neutral fuels/chemicals or permanent storage remains energy intensive and costly. Further, most DAC technologies rely on repetitive capture and release cycles that reduces the amount of time the DAC materials are able to collect CO 2 and increases wear and tear. Moisture swing (MS) sorption within anion exchange materials utilizes differences in relative humidity to capture and concentrate CO 2 up to 500-fold with negligible energy inputs and low-cost sorbents. Molecular modeling predicts that membranes with a dry and wet side would actively transport CO 2 from its dry side to its wet side against a counter flow of H 2 O evaporating on the dry side, however, existing MS materials are too brittle to be processed into membranes to test this hypothesis. This project brought together experts in DAC materials and design, techno-economic analysis and project management at Arizona State University (ASU), polymer processing at University of Texas at Austin (UTA) and modeling gas transport and exchange at Norther Arizona University (NAU) to develop hollow fiber membranes that use energy from water evaporation to continuously pump CO 2 from air against a concentration gradient to the membranes interior and requiring significantly less energy than current DAC technologies. While this project did not meet its ultimate objectives of demonstrating an active CO 2 pumping membrane, a number of key accomplishments were made in developing low-cost, flexible anion exchange membranes (AEM) at 3.5 m 2 scale, characterizing the ionic and molecular transport within MS materials, and developing several analytical and mathematical models of the MS and pumping process leading to new fundamental knowledge about key rate limiting steps of CO 2 flux in anion exchange membranes at low water activity. Technoeconomic models show that if CO 2 fluxes ≥ 25 µmol CO 2 m -2 s -1 (membrane surface area) are achieved that cost ≤ $\$$100/tonne CO 2 captured, purified and compressed to pipeline quality is possible. The knowledge gained in this research will guide future research in developing new materials toward overcoming these rate limiting steps that in turn could enable transformative and disruptive DAC technologies needed for capturing gigatons of CO 2 per year needed to limiting global warming to 2 °C.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Limits on Mode Coherence in Pulsating DA White Dwarfs Due to a Nonstatic Convection Zone

The standard theory of pulsations deals with the frequencies and growth rates of infinitesimal perturbations in a stellar model. Modes which are calculated to be linearly driven should increase their amplitudes exponentially with time; the fact that nearly constant amplitudes are usually observed is evidence that nonlinear mechanisms inhibit the growth of finite amplitude pulsations. Models predict that the mass of convection zones in pulsating hydrogen-atmosphere (DAV) white dwarfs is very sensitive to temperature (i.e., M CZ α T –90 eff ), leading to the possibility that even low-amplitude pulsators may experience significant nonlinear effects. In particular, the outer turning point of finite-amplitude g-mode pulsations can vary with the local surface temperature, producing a reflected wave that is out of phase with what is required for a standing wave. This can lead to a lack of coherence of the mode and a reduction in its global amplitude. In this paper we show that: (1) whether a mode is calculated to propagate to the base of the convection zone is an accurate predictor of its width in the Fourier spectrum, (2) the phase shifts produced by reflection from the outer turning point are large enough to produce significant damping, and (3) amplitudes and periods are predicted to increase from the blue edge to the middle of the instability strip, and subsequently decrease as the red edge is approached. Furthermore, this amplitude decrease is in agreement with the observational data while the period decrease has not yet been systematically studied.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Transverse Vector Decomposition Method for Analytical Inversion of Exoplanet Transit Spectra

Abstract We develop a new method for analytical inversion of binned exoplanet transit spectra and for retrieval of planet parameters. The method has a geometrical interpretation and treats each observed spectrum as a single vector r → in the multidimensional spectral space of observed bin values. We decompose the observed r → into two orthogonal components: a wavelength-independent component r → ∥ corresponding to the spectral mean across all observed bins, and a transverse component r → ⊥ that is wavelength dependent and contains the relevant information about the atmospheric chemistry. The method allows us to extract, without any prior assumptions or additional information, the relative mass (or volume) mixing ratios of the absorbers in the atmosphere, the scale height to stellar radius ratio, H / R S , and the atmospheric temperature. The method is illustrated and validated with several examples of increasing complexity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

A Wind-driven Origin for the Firework Morphology of the Supernova Remnant Pa 30

Pa 30—the likely remnant of the Galactic Type Iax supernova of 1181 AD—displays an unusual, firework-like morphology, consisting of radial filaments extending from a common center, where a white dwarf (WD) currently drives a very fast wind (speed ≳10 4 km s −1 ). We propose the filaments arose from the Rayleigh–Taylor-unstable nature of the interface between the circumstellar medium (CSM) and the shocked wind launched by the natal WD; the filaments then elongated intact due to the Kelvin–Helmholtz-stable nature of the large initial density contrast between the wind and CSM, supplemented by the slowly declining wind density profile (relative to homologously expanding ejecta). To support this interpretation, we present two-dimensional hydrodynamical simulations and derive the filament properties, including their speed, density, and temperature, all of which are consistent with observations. We suggest the filaments elongate until the wind and CSM densities become comparable at the contact discontinuity, which occurs within 1–10 yr, and then truncate because the Rayleigh–Taylor instability (RTI) halts. The subsequent Kelvin–Helmholtz instability growth timescale across the current width of the filaments is longer than the age of Pa 30, so they remain intact. The filament-less central region in Pa 30 is therefore more likely a consequence of the finite timescale over which the RTI operates, rather than a wind termination shock. In general, firework-like filaments may form in other systems, provided there is a sufficiently large density contrast between the ejecta and its surroundings.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Immersive Digital Twins and Decision Making

This work focuses on developing and implementing immersive digital twins to support decision-making processes in construction automation and energy simulation analysis. The use of digital twins enables users to explore and interact with virtual replicas of physical systems, providing a unique and valuable perspective for problem-solving. In the context of construction automation, we present two case studies that integrate immersive visualization and worker-machine interaction. In the context of energy simulation analysis using digital twins, we describe our digital twin framework that combines interactive visualization with machine learning techniques to approximate computationally expensive simulations, allowing for faster and more efficient analysis of complex energy systems. Through these research endeavors, we demonstrate the potential of immersive digital twins in decision-making across various domains.

digital twins↗
DOE OSTI2023

A comparison of machine learning methods to classify radioactive elements using prompt-gamma-ray neutron activation data

The detection of illicit radiological materials is critical to establishing a robust second line of defence in nuclear security. Neutron-capture prompt-gamma activation analysis (PGAA) can be used to detect multiple radioactive materials across the entire Periodic Table. However, long detection times and a high rate of false positives pose a significant hindrance in the deployment of PGAA-based systems to identify the presence of illicit substances in nuclear forensics. In the present work, six different machine-learning algorithms were developed to classify radioactive elements based on the PGAA energy spectra. The model performance was evaluated using standard classification metrics and trend curves with an emphasis on comparing the effectiveness of algorithms that are best suited for classifying imbalanced datasets. We analyse the classification performance based on Precision, Recall, F1-score, Specificity, Confusion matrix, ROC-AUC curves, and Geometric Mean Score (GMS) measures. The tree-based algorithms (Decision Trees, Random Forest and AdaBoost) have consistently outperformed Support Vector Machine and K-Nearest Neighbours. Based on the results presented, AdaBoost is the preferred classifier to analyse data containing PGAA spectral information due to the high recall and minimal false negatives reported in the minority class.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Symbolic construction of the chemical Jacobian of quasi-steady state (QSS) chemistries for Exascale computing platforms

The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of chemical mechanisms for implementation in computational reacting flow solvers. However, for many applications, the resulting model still requires implicit methods for efficient time integration. Here, in this paper, we outline an approach to formulating the QSSA reduction that is coupled with a strategy to generate C++ source code to evaluate the net species production rates, and the chemical Jacobian. The code-generation component employs a symbolic approach enabling a simple and effective strategy to analytically compute the chemical Jacobian. For computational tractability, the symbolic approach needs to be paired with common subexpression elimination which can negatively affect memory usage. Several solutions are outlined and successfully tested on a 3D multipulse ignition problem, thus allowing portable application across chemical model sizes and GPU capabilities. The implementation of the proposed method is available at https://github.com/AMReX-Combustion/PelePhysics under an open-source license.

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

Verification of Bison fission product species conservation under TRISO reactor conditions

When assessing the reliability and predictive capabilities of a simulation tool, code verification is used to ensure that the implemented numerical algorithm is a faithful representation of its underlying mathematical model, including partial differential or integral equations, initial and boundary conditions, and auxiliary relationships. During this process, numerical results in a discrete solution are compared to the analytical solution of the mathematical model. Here, in this paper, the code verification process is applied to one-dimensional spatiotemporal problems that exercise partial differential equation governing the conservation of fission product species (or mass diffusion). Numerical experiments were performed in the Bison fuel performance code to evaluate its predictive capability under various TRISO reactor conditions such as base irradiation and safety heating test conditions for either short- or long-lived fission product species, as well as a case concerning evaporation from the outer surface of a particle. The code predictions were compared with the expected exact results obtained from the analytical expressions, and the fact that they demonstrate the correct analytical behavior provides strong evidence of proper numerical algorithm implementation.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2025

Basin-Size Mapping: Prediction of Metastable Polymorph Synthesizability Across TaC–TaN Alloys

The sizes of the basins of attraction on the potential energy surface are helpful indicators in determining the experimental synthesizability of metastable phases. In principle, these basins can be controlled with changes in thermodynamic conditions such as composition, pressure, and surface energy. Herein, we use random structure sampling to computationally study how alloying smoothly perturbs basin of attraction sizes. The TaC 1-x N x pseudobinary is an ideal test system given the structural and polymorphic contrast of its parent compounds and their technological relevance as epitaxial substrates for Al 1-x Ga x N. While we find limited thermodynamic stability across all computationally observed phases, random structure sampling shows a significant composition region where the rocksalt basin dominates. As such, we predict the potential for the nonequilibrium synthesis of metastable rocksalt TaC 1-x N x alloys as substrates for Al 1-x Ga x N. At higher nitrogen concentrations, other low-energy metastable polymorphs emerge that continue to retain the hexagonal close packing suitable for III-N growth. Confidence in these trends was established through uncertainty quantification of the basin sizes and energy distributions; such analysis utilized the Beta and Dirichlet distributions. In conclusion, we also find (a) polymorph basin sizes can be rationalized in terms of energetic preferences for different coordination environments; and (b) basin sizes universally shrink with increasing nitrogen content, making the system more prone to amorphous growth.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Impact of Sr-Containing Secondary Phases on Oxide Conductivity in Solid-Oxide Electrolyzer Cells

Solid-oxide electrolyzer cells (SOECs) based on a yttria-stabilized zirconia (YSZ) oxide electrolyte produce hydrogen from water with the assistance of excess thermal energy; however, Sr diffusion within the Gd-doped CeO 2 (GDC) barrier layer during processing or operation can lead to the formation of unwanted secondary phases such as SrO and SrZrO 3 . Here, to establish and compare the degree of impact of these phases on SOEC performance, we conduct first-principles calculations to study their bulk oxide conductivities and compare them to that of the YSZ electrolyte. We find that SrO has a low conductivity arising from the poor mobility and low concentration of mobile oxygen vacancies, and its presence in SOECs should therefore be avoided. SrZrO 3 also has a lower oxide conductivity than YSZ; however, this discrepancy is primarily due to lower vacancy concentrations rather than low mobility. We find that sufficient levels of Y-doping on the Zr site can increase oxygen vacancy concentrations in SrZrO 3 to achieve an oxide ionic conductivity on par with that of YSZ, thereby mitigating any potential deleterious effect on transport performance. Energy-dispersive X-ray spectroscopy confirms that Y is the most common minority element present in SrZrO 3 forming near the GDC–YSZ interface, alleviating concerns regarding the impact of SrZrO 3 on device performance. These results from our combined computational–experimental analysis can inform future engineering strategies designed to limit the detrimental effects of Sr-induced secondary phase formation on SOEC performance.

08 HYDROGEN↗
DOE OSTI2021

Mapping the Path Forward to Next Generation Algal Technologies: Workshop on Understanding the Rules of Life and Complexity in Algal Systems

Algal technology offers enormous potential as a source of renewable biomass and bioproducts for fuels, biochemicals, nutrients, and numerous other applications. While tremendous opportunities exist, significant challenges are also present in harnessing and utilizing this valuable and potentially sustainable bioproduction platform. Funded by a joint partnership between the Bioenergy Technologies Office (BETO) at the Department of Energy (DOE) and the National Science Foundation (NSF), the recent virtual workshop, "Understanding the Rules of Life: Complexity in Algal Systems Workshop," was organized to bring together thought leaders from academia, national laboratories and other government agencies, and industry to identify key challenges and propose research strategies to overcome these barriers. Two parallel sessions were undertaken: 1) algae strain and toolkit development and 2) algal ecosystem and microbiome dynamics, in order to advance algae engineering and cultivation efforts. In each session, attendees discussed the most pressing challenges from the perspective of model systems and omics analysis. Themes such as genetic engineering toolboxes, translation from the laboratory to outdoor cultivation, functional genomics, metabolomics, algal ecology, consortial design, microbiome dynamics, mathematical models, and data analytics emerged from the discussion. Overall, this workshop has served to elucidate the key hurdles and many opportunities present as we continue to advance algal science and technology from the laboratory and into the commercial realm.

09 BIOMASS FUELS↗
DOE OSTI2021

Turbulence theories and statistical closure approaches

When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range [A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941)]. The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) [R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959)] and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Finally, turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Solvated Nuclear–Electronic Orbital Structure and Dynamics

Nonadiabatic dynamical processes such as proton-coupled electron transfer and excited state intramolecular proton transfer have been the subject of much research. One of the promising theoretical methods to describe these processes is the nuclear–electronic orbital (NEO) approach. This approach inherently accounts for nuclear quantum effects within quantum chemistry calculations, and it has recently been extended to directly simulate nonadiabatic processes with the development of real-time NEO methods. These processes can also be significantly dependent on the surrounding chemical environment, however, and capturing the effects of the environment is often necessary for analyzing experimentally relevant systems. This work couples the NEO density functional theory and real-time time-dependent density functional theory approaches with solvation through the polarizable continuum model. Here, the effects of this coupling are investigated for ground state properties, solvent-dependent vibrational frequencies, and direct excited state intramolecular proton transfer dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Implementation and Performance

Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and substrates. Methods based on many-body perturbation theory, such as the random phase approximation (RPA), have previously been limited due to their computational complexity. However, this is now a surmountable barrier due to the advances in computational power available, in particular through modern GPU-based supercomputers. In this work, we describe the implementation of RPA calculations within BerkeleyGW and show its favorable computational performance on large complex systems relevant for catalysis and electrochemistry applications. Our implementation builds off of the static subspace approximation which, by employing a compressed representation of the frequency dependent polarizability, enables the evaluation of the RPA correlation energy with significant acceleration and systematically controllable accuracy. We find that the computational cost of calculating the RPA correlation energy scales only linearly with system size for systems containing up to 50 thousand bands, and is expected to scale quadratically thereafter. We also show excellent strong scaling results across several supercomputers, demonstrating the performance and portability of this implementation.

algorithmic development↗
DOE OSTI2021

3D-Scaffold: A Deep Learning Framework to Generate 3D Coordinates of Drug-like Molecules with Desired Scaffolds

The prerequisite of therapeutic drug design is to identify novel molecules with desired biophysical and biochemical properties. Deep generative models have demonstrated their ability to find such molecules by exploring a huge chemical space efficiently. An effective way to obtain molecules with desired target properties is the preservation of critical scaffolds in the generation process. To this end, we propose a domain aware generative framework called 3D-Scaffold that takes 3D coordinates of a desired scaffold as an input and generates 3D coordinates of novel therapeutic candidates as an output while always preserving the desired scaffolds in generated structures. We show that our framework generates predominantly valid, unique, novel, and experimentally synthesizable molecules that have drug-like properties similar to the molecules in the training set. Using domain specific datasets, we generate covalent and non-covalent antiviral inhibitors. Therefore, to measure the success of our framework in generating therapeutic candidates, generated structures were subjected to high throughput virtual screening via docking simulations, which shows favorable interaction against SARS-CoV-2 main protease and non-structural protein endoribonuclease (NSP15) targets. Most importantly, our model performs well with relatively small volumes of training data and generalizes to new scaffolds, making it applicable to other domain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Spectral Signatures of Ultrafast Excited-State Intramolecular Proton Transfer from Computational Multi-edge Transient X-ray Absorption Spectroscopy

Excited state intramolecular proton transfer (ESIPT) is a fundamental chemical process with several applications. Ultrafast ESIPT involves coupled electronic and atomic motions and has been primarily studied using femtosecond optical spectroscopy. X-ray spectroscopy is particularly useful because it is element-specic and enables direct, individual probes of the proton donating and accepting atoms. Here, we report a computational study to resolve the ESIPT in 10-Hydroxybenzo[h]quinoline (HBQ), an intramolecularly hydrogen bonded compound, using time-dependent density functional theory combined with ab initio molecular dynamics (AIMD) and time-resolved X-ray absorption spectroscopy (XAS) computations to track the ultrafast excited-state dynamics. Overall, our results reveal clear X-ray spectral signatures of coupled electronic and atomic motions during and following ESIPT at the oxygen and nitrogen K-edge paving the way for future experiments at X-ray free electron lasers.

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

Anomalies and Local Structure of Liquid Water from Boiling to the Supercooled Regime as Predicted by the Many-Body MB-pol Model

For the past 50 years, researchers have sought molecular models that can accurately reproduce water’s microscopic structure and thermophysical properties across broad ranges of its complex phase diagram. Herein, molecular dynamics simulations with the many-body MB-pol model are performed to monitor the thermodynamic response functions and local structure of liquid water from the boiling point down to deeply supercooled temperatures at ambient pressure. The isothermal compressibility and isobaric heat capacity show maxima near 223 K, in excellent agreement with recent experiments, and the liquid density exhibits a minimum at ~208 K. A local tetrahedral arrangement, where each water molecule accepts and donates two hydrogen bonds, is found to be the most probable hydrogen-bonding topology at all temperatures. Further, this work suggests that MB-pol may provide predictive capability for studies of liquid water’s physical properties across broad ranges of thermodynamic states, including the so-called water’s “no man’s land” which is difficult to probe experimentally.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗