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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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In this article we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail. In particular we demonstrate explicitly how the same formulas for six-particle NMHV helicity amplitudes are obtained from summing Feynman diagrams and from computing the canonical form of the n=6, k=1, m=4 amplituhedron.
An optimization problem is formulated motivated by the desire to remove temperature peaks, i.e., 'hot spots', along the bounding surfaces of containers of fluid flows. The heat equation of the solid container is coupled to the energy equations for the fluid. Heat sources can be located in the solid body, the fluid, or both. Control is effected by adjustments to the temperature of the fluid at the inflow boundary. Both mathematical analyses and computational experiments are given.
As computational models scale to larger computers, the rate at which they produce data has far outstripped the same computers ability to write that data and further the file systems ability to store that data. Almost all of the SciDAC applications, but especially those related to fusion solve very large scale PDEs whose scientific output his impacted by this problem. To gain access to dynamics in an exascale simulation that are not identifiable a priori and to make that dynamical data available to machine learning requires fundamental research in the area of in situ data data analytics. Here data analytics includes compression, visualization, uncertainty quantification, and machine learning. This in situ data analytics will enable on-the-fly spatial and temporal compression of solution dynamics, expose that space-time compressed field to machine learning algorithms that have been specialized to work with dynamically evolving data (existing machine learning algorithms treat data sets as static), greatly improving the opportunity for machine learning to provide feedback to the compression, all within an ongoing simulation, without the need to write data to files. The same concepts are also being applied to uncertainty quantification and multi-fidelity modeling which have similar needs for spatial and temporal compression of the ongoing exascale simulation to perform either without the typical, unacceptable writing of data to files.
Human cognitive responses, behavioral responses, and disease dynamics co-evolve over the course of any disease outbreak, and can result in complex feedbacks. We present a dynamic agent-based model that explicitly couples the spread of disease with the spread of fear surrounding the disease, implemented within the EpiCast simulation framework. EpiCast models transmission within a realistic synthetic population, capturing individual-level interactions. In our model, fear propagates through both in-person contact and broadcast media, prompting individuals to adopt protective behaviors that reduce disease spread. In order to better understand these coupled dynamics, we create and compare a range of compartmental models to ensure that introducing additional disease states does not prevent the emergence of multiple waves in these simpler models. Additionally, we compare a range of behavioral scenarios within EpiCast, varying the level and intensity of fear and behavior change. Our results show that the addition of asymptomatic, exposed, and pre-symptomatic disease states can impact both the rate at which an outbreak progresses and its overall trajectory in compartmental models. In EpiCast, the combination of non-local fear spread via broadcasters and strong behavioral responses by fearful individuals generally leads to multiple epidemic waves, an outcome that occurs only within a narrow parameter range when fear spreads purely through local contact. Accounting for the coupled spread of fear and disease is critical for understanding disease dynamics and designing timely, targeted responses to emerging infectious threats.
This 'Project Mathematics' series video from CalTech presents the tunnel of Samos, a famous underground aquaduct tunnel located near the capital of Pithagorion (named after the famed Greek mathematician, Pythagoras, who lived there), on one of the Greek islands. This tunnel was constructed around 600 BC by King Samos and was built under a nearby mountain. Through film footage and computer animation, the mathematical principles and concepts of why and how this aquaduct tunnel was built are explained.
Improved mathematical models based on fundamental principles of conservation of mass, energy, and momentum developed for use in computer simulation of atomization of jets of liquid fuel in rocket engines. Models also used to study atomization in terrestrial applications; prove especially useful in designing improved industrial sprays - humidifier water sprays, chemical process sprays, and sprays of molten metal. Because present improved mathematical models based on first principles, they are minimally dependent on empirical correlations and better able to represent hot-flow conditions that prevail in rocket engines and are too severe to be accessible for detailed experimentation.
This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. Furthermore, we also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.
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Low Earth orbit (LEO) satellite systems have become a crucial enabler of broadband access for maritime industries, where traditional networks are unavailable. However, the high mobility of LEO constellations and constantly changing weather conditions result in unpredictable link fluctuations, limiting the ability of maritime platforms to plan bandwidth usage proactively. To the best of our knowledge, no prior work has developed a short-term predictive model for maritime LEO connectivity using real experimental field measurements. This paper proposes a data-driven forecasting model that predicts future downlink throughput using multi-horizon RandomForest regression. The model is trained using real experimental coastal measurement data incorporating recent throughput history, network-layer indicators, and environmental variables. The proposed approach reduces mean absolute error by approximately 31% compared to a persistence baseline for 15-minute horizons. It maintains a measurable improvement at 30 minutes, despite increased stochasticity. These findings confirm that proactive bandwidth awareness is feasible on maritime platforms and can effectively support operational decisions such as adaptive streaming, routing, and resource scheduling. The performance gap between forecasting horizons also highlights the need for expanded offshore datasets to improve prediction robustness under harsher maritime environments.
Herein this paper focuses on developing a reduction-based algebraic multigrid (AMG) method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure advection to pure diffusion. Initial motivation comes from a new reduction-based AMG approach, $\ell \text{AIR}$ (local approximate ideal restriction), that was developed for solving advection-dominated problems. Though this new solver is very effective in the advection-dominated regime, its performance degrades in cases where diffusion becomes dominant. This is consistent with the fact that in general, reduction-based AMG methods tend to suffer from growth in complexity and/or convergence rates as the problem size is increased, especially for diffusion-dominated problems in two or three dimensions. Motivated by the success of $\ell \text{AIR}$ in the advective regime, our aim in this paper is to generalize the AIR framework with the goal of improving the performance of the solver in diffusion-dominated regimes. To do so, we propose a novel way to combine mode constraints as used commonly in energy-minimization AMG methods with the local approximation of ideal operators used in $\ell \text{AIR}$. The resulting constrained $\ell \text{AIR}$ algorithm is able to achieve fast scalable convergence on advective and diffusive problems. In addition, it is able to achieve standard low complexity hierarchies in the diffusive regime through aggressive coarsening, something that was previously difficult for reduction-based methods.
This article describes PyOED, a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-constrained OED. The package targets scientists and researchers interested in understanding the details of OED formulations and approaches. It is also meant to enable researchers to experiment with standard and innovative OED technologies with a wide range of test problems (e.g., simulation models). OED, inverse problems (e.g., Bayesian inversion), and data assimilation (DA) are closely related research fields, and their formulations overlap significantly. Thus, PyOED is continuously being expanded with a plethora of Bayesian inversion, DA, and OED methods as well as new scientific simulation models, observation error models, and observation operators. These pieces are added such that they can be permuted to enable testing OED methods in various settings of varying complexities. The PyOED core is completely written in Python and utilizes the inherent object-oriented capabilities; however, the current version of PyOED is meant to be extensible rather than scalable. Specifically, PyOED is developed to “enable rapid development and benchmarking of OED methods with minimal coding effort and to maximize code reutilization.” This article provides a brief description of the PyOED layout and philosophy and provides a set of exemplary test cases and tutorials to demonstrate the potential of the package.
NovoNutrients’ fermentation technology uses energy from hydrogen to transform industrial CO2 emissions into premium animal feed ingredients and other valuable products. A single NovoNutrients’ commercial manufacturing plant will capture and convert over 200,000 tons/yr of CO2 into over 100,000 tons/yr of high-protein feed. Key to the rapid and widespread deployment of the technology is maximization of its productivity and energy efficiency. Robust, physically based computational models of the technology will significantly increase productivity and efficiency, accelerating NovoNutrients’ technology to manufacturing scale. NREL has unique capabilities for creating and running such computational models. NREL's existing aerobic bioreaction computational fluid dynamics (CFD) models will be adapted to NovoNutrients’ gas fermentation (CO2, H2, O2) technology. The multiphysics CFD simulations require thousands of high-performance computing (HPC) node hours to simulate the complex geometries and contents of NovoNutrients’ industrial bioreactors. The experimentally validated CFD models were used to identify optimally efficient and productive bioreactor designs and operating conditions.
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In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have been performed using a hydraulic/gas flow analog. Results of comparisons of DREA computations with experimental data, which include entrainment, thrust, and local profile information, are overall good. Computational time studies indicate that DREA provides considerably more information at a lower computational cost than contemporary ejector nozzle design models. Finally. physical limitations of the method, deviations from experimental data, potential improvements and alternative formulations are described. This report represents closure to the NASA Graduate Researchers Program. Versions of the DREA code and a user's guide may be obtained from the NASA Lewis Research Center.
Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN’s ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN’s solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN’s local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN’s hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.
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.
The widespread application of genetically modified microorganisms (GMMs) across diverse sectors underscores the pressing need for robust strategies to mitigate the risks associated with their potential uncontrolled escape. This study merges computational modeling with CRISPR interference (CRISPRi) to refine GMM metabolic robustness. Utilizing ensemble modeling, we achieved high-throughput in silico screening for enzymatic targets susceptible to expression alterations. Translating these insights, we developed functional CRISPRi, boosting fitness control via multiplexed gene knockdown. Our method, enhanced by an insulator-improved gRNA structure and an off-switch circuit controlling a compact Cas12m, resulted in rationally engineered strains with escape frequencies below National Institutes of Health standards. The effectiveness of this approach was confirmed under various conditions, showcasing its ability for secure GMM management. This research underscores the resilience of microbial metabolism, strategically modifying key nodes to halt growth without provoking significant resistance, thereby enabling more reliable and precise GMM control. A record of this paper's transparent peer review process is included in the supplemental information.
My work with mathematical modeling and computer simulations began in earnest in 1987 when I signed on with the National Aeronautics and Space Administration, better known as NASA. At the time I was developing computer simulations to support the design of carbon dioxide (CO2) removal systems for the International Space Station (ISS) life support system. CO2 is a human metabolic waste, produced at a rate of a kilogram per day per crewmember. CO2 must be removed from the crew cabin, as it will quickly become detrimental to crew health. The systems used to remove CO2 are typically based on sorption processes, which include complex interactions of heat transfer, mass transfer, and gas flow through porous media. At this time, there were no commercial options for solving a set of coupled mathematical models such as partial differential equations (PDEs); you either force-fit the physics into a thermal analysis package or wrote your own code, complete with discretization, meshing, and solution algorithms. Unfortunately, coding CO2 removal processes from scratch did not allow an appropriate focus on the challenging yet crucial task of understanding and capturing the underlying physics via appropriate mathematical models. Configuration control was often simply ignored due to tight schedules, resulting in a code that would be quicker for a second party to rewrite than modify. In the early 2000s, I decided to move CO2 removal simulations to a platform with built-in meshing, solvers, and postprocessing capabilities, and that could solve user-defined multiphysics PDEs. The program chosen to meet these needs was COMSOL Multiphysics®. Along with freeing the engineer to focus on the underlying physics, a degree of configuration control was automatically achieved via a consistent user interface, thus allowing COMSOL users to share computer models. My team has developed simulations that are already providing a valuable debugging capability for the ISS CO2 removal system, and will provide guidance in upgrades to that system.