Search NASA⌕ Search

SEARCH · Search NASA

Results for “MATHEMATICS - BOUNDARY VALUES”

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 631 records · Page 35

Launch window definition for sky target experiments.

This paper is a brief report on the computer program developed for the Extraterrestrial Physics Barium Ion Cloud (BIC) Project. The mathematical analysis developed for the program along with its programing characteristics are pointed out to show that this program is adaptable to similar sky target projects. Definite viewing constraints are specified so that the chosen ground tracking stations can photograph the behavior of the sky target after its release. Viewing factors include the illumination of the target by the sun, the relative elevation look angle to the target from each tracking station, the solar and lunar depression angles at each tracking station, and the total sky background brightness of the target relative to each tracking station. Numeric values are assigned to each factor through program input. The program output is flexible so that the results of the window calculations can be studied to the depth required.

Michaud, N. H.↗

New Secondary Batteries Utilizing Electronically Conductive Polypyrrole Cathode

To gain a better understanding of the dynamic behavior in electronically conducting polypyrroles and to provide guidance toward designs of new secondary batteries based on these polymers, two mathematical models are developed; one for the potentiostatically controlled switching behavior of polypyrrole film, and one for the galvanostatically controlled charge/discharge behavior of lithium/polypyrrole secondary battery cell. The first model is used to predict the profiles of electrolyte concentrations, charge states, and electrochemical potentials within the thin polypyrrole film during switching process as functions of applied potential and position. Thus, the detailed mechanisms of charge transport and electrochemical reaction can be understood. Sensitivity analysis is performed for independent parameters, describing the physical and electrochemical characteristic of polypyrrole film, to verify their influences on the model performance. The values of independent parameters are estimated by comparing model predictions with experimental data obtained from identical conditions. The second model is used to predict the profiles of electrolyte concentrations, charge state, and electrochemical potentials within the battery system during charge and discharge processes as functions of time and position. Energy and power densities are estimated from model predictions and compared with existing battery systems. The independent design criteria on the charge and discharge performance of the cell are provided by studying the effects of design parameters.

Yeu, Taewhan↗

Gravitational influences on the behavior of confined diffusion flames

Closed form, mathematical representations for the shapes of laminar diffusion flames stabilized on two-dimensional slot burners are derived for arbitrary gravitational levels. The solution technique employs the Schvab-Zeldovich conserved species variable. Effects of gravity on the velocity field are incorporated through the momentum equation; these effects, in turn, influence the species field. The results reduce smoothly to the classical Burke-Schumann solution as gravity approaches zero. It is shown that both flame height and width increase with decreasing gravity levels. Several interesting cases are considered explicitly; these include effects of negative and extremely high values of gravity. In the latter case, it is shown that the flame collapses onto the burner surface. The analysis finds application in the modeling of steady and unsteady gas and solid propellant diffusion flames.

Hegde, U.↗

Impact of Increased Monte Carlo Parameters on Sensitivity Calculations with SCALE [Slides]

For both models and tests, NPG and NSK parameters have only small effects on calculated sensitivity coefficients. Outside of NPG=100, only differences in CFP affected sensitivity coefficient values. Fission reactions ( 235 U) require more NPG values than scattering ( 238 U) reactions – more particles are needed to locate fission sources in the model more accurately. This work confirms the previous results with the IFP method where the CFP parameter has the greatest impact on calculated sensitivity coefficients. While immediate work focuses on fast systems, other model specifications may require a different set of MC parameters.

97 MATHEMATICS AND COMPUTING↗

Business Case Analysis for Artificial Intelligence-Large Language Model Technology Integration

AI-assisted processes are expected to enhance operational efficiency and improve decision-making, supporting the long-term economic viability of nuclear power plants. However, detailed business analyses of AI-generated cost savings are rarely performed. Given the recent industry interest in Large Language Model (LLM), the U.S. Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) Program has conducted a comprehensive business case analysis of LLM Artificial Intelligence (AI) implementation in nuclear plant engineering workflows. The research employed three complementary business case approaches to evaluate impact of an LLM, using three representative engineering processes as use-cases: Boric Acid Corrosion (BAC) Evaluations, Maintenance Rule Evaluations, and 10 CFR 50.59 Screenings. Through detailed workload analyses and structured interviews, the study quantified significant efficiency improvements ranging from 11% to 59% across these processes. The research further considers how these efficiency gains could translate into tangible reliability improvements through enhanced engineering capacity. Analysis of historical plant trip data indicates that enabling engineers to focus on proactive reliability activities could provide substantial financial benefits through avoided outages, potentially generating greater value than the direct efficiency improvements alone. By documenting successful applications, implementation challenges, and strategic opportunities, this research provides nuclear utilities with a practical framework for evaluating the value of AI technology to support long-term operations through advanced digital technologies.

97 MATHEMATICS AND COMPUTING↗

Modeling of Bulk Evaporation and Condensation

This report describes the modeling and mathematical formulation of the bulk evaporation and condensation involved in liquid-vapor phase change processes. An internal energy formulation, for these phase change processes that occur under the constraint of constant volume, was studied. Compared to the enthalpy formulation, the internal energy formulation has a more concise and compact form. The velocity and time scales of the interface movement were obtained through scaling analysis and verified by performing detailed numerical experiments. The convection effect induced by the density change was analyzed and found to be negligible compared to the conduction effect. Two iterative methods for updating the value of the vapor phase fraction, the energy based (E-based) and temperature based (T-based) methods, were investigated. Numerical experiments revealed that for the evaporation and condensation problems the E-based method is superior to the T-based method in terms of computational efficiency. The internal energy formulation and the E-based method were used to compute the bulk evaporation and condensation processes under different conditions. The evolution of the phase change processes was investigated. This work provided a basis for the modeling of thermal performance of multi-phase nuclear fuel elements under variable gravity conditions, in which the buoyancy convection due to gravity effects and internal heating are involved.

Anghaie, S.↗

Parameter identification of material constants in a composite shell structure

One of the basic requirements in engineering analysis is the development of a mathematical model describing the system. Frequently comparisons with test data are used as a measurement of the adequacy of the model. An attempt is typically made to update or improve the model to provide a test verified analysis tool. System identification provides a systematic procedure for accomplishing this task. The terms system identification, parameter estimation, and model correlation all refer to techniques that use test information to update or verify mathematical models. The goal of system identification is to improve the correlation of model predictions with measured test data, and produce accurate, predictive models. For nonmetallic structures the modeling task is often difficult due to uncertainties in the elastic constants. A finite element model of the shell was created, which included uncertain orthotropic elastic constants. A modal survey test was then performed on the shell. The resulting modal data, along with the finite element model of the shell, were used in a Bayes estimation algorithm. This permitted the use of covariance matrices to weight the confidence in the initial parameter values as well as confidence in the measured test data. The estimation procedure also employed the concept of successive linearization to obtain an approximate solution to the original nonlinear estimation problem.

Martinez, David R.↗

The Impact of Deviation from Michaelis-Menten Saturation on Mathematical Model Stability Properties

Based on purely abstract ecological theory, it has been argued that a system composed of two or more consumers competing for the same resource cannot persist. By analysis on a Monod format mathematical model, Hubble and others demonstrated that this assertion is true for all but very special cases of such competing organisms which are determined by an index formed by a grouping of. the parameters which characterize the biological processes of the competing organisms. In the laboratory, using a bioreactor, Hansen and Hubble obtained confirmatory results for several cases of two competing species, and they characterized it as "qualitative confirmation" of the assertion. This result is amazing, since the analysis required the exact equality of the hey index, and it seems certain that no pair of organism species could have exactly equal values. It is quite plausible, however, that pairs of organism species could have approximately equal indices, and the question of how different they could be and still have coexistence of the two (or more) presents itself. In this paper, the pursuit of this question and a compatible resolution is presented.

Blackwell, Charles↗

Artificial Intelligence-Aided Wind Plant Optimization for Nationwide Evaluation of Land Use and Economic Benefits of Wake Steering

If clean energy pathways are to harness massive increases in wind power, innovations with broad geographic viability will be needed to support buildout in diverse locations. However, geodiversity in impact potential is seldom captured in technology assessment. Here we propose a scalable approach to plant-level optimization using artificial intelligence to evaluate land sparing and economic benefits of wake steering at more than 6,800 plausible onshore wind locations in the USA. This emerging controls strategy optimizes plant energy production by directing turbine wakes. On the basis of estimates from our artificial intelligence model trained on engineering wind flow simulations, co-optimizing plant layouts with wake steering can reduce land requirements by an average of 18% per plant (site-specific benefits range from 2% to 34%), subject to errors and uncertainties in the flow model, wind resource estimates, buildout scenario and geographic factors. According to model estimates, wake steering is predicted to increase power production during high-value (relatively low wind) periods, boosting the annual revenue of individual plants by up to US$3.7 million (equivalent to US$13,000 MW-1 yr-1) but producing negligible gains in some settings. Consideration of wake steering’s geographic potential reveals divergent nationwide prospects for improved economics and siting flexibility.

deployment↗

Computational Modeling for Non-equilibrium Shock Tube Flows

Time accurate simulation of non-equilibrium flows inside shock tube facilities presents several challenges from both physical and mathematical aspects. Furthermore, the drastic computational cost makes it non-practical to support real-time experimental test campaign. In this work, we explore other methods for modeling the shock tube prob- lem with the main focus on the post-shock region and the absolute radiation emanating from it. The proposed alternative approach is several orders of magnitude less computa- tionally expansive while still accurate enough with regards to the quantities of interest. Excellent agreement is found with the well-established stagnation-line approach. Comparison with the time-accurate simulation shows good agreement close to the peak values and disagreement of the temperatures relaxation and radiance profiles toward equilibrium, due to shock speed unsteadiness.

Bensassi, Khalil↗

Primary instabilities and bicriticality in flow between counter-rotating cylinders

The primary instabilities and bicritical curves for flow between counter-rotating cylinders have been computed numerically from the Navier-Stokes equations assuming axial periodicity. The computations provide values of the Reynolds numbers, wavenumbers, and wave speeds at the primary transition from Couette flow for radius ratios from 0.40-0.98. Particular attention has been focused on the bicritical curves that separate (as the magnitude of counter-rotation is increased) the transitions from Couette flow to flows with different azimuthal wavenumbers m and m + 1. This lays the foundation for further analysis of nonlinear mode interactions and pattern formation occurring along the bicritical curves and serves as a benchmark for experimental studies. Preliminary experimental measurements of transition Reynolds numbers and wave speeds presented here agree well with the computations from the mathematical model.

Langford, W. F.↗

Mind the Gap: Exploring the Underground of the NASA Space Cancer Risk Model

The REID quantifies the lifetime risk of death from radiation-induced cancer in an exposed astronaut. The NASA Space Cancer Risk (NSCR) 2012 mode incorporates elements from physics, biology, epidemiology, and statistics to generate the REID distribution. The current model quantifies the space radiation environment, radiation quality, and dose-rate effects to estimate a NASA-weighted dose. This weighted dose is mapped to the excess risk of radiation-induced cancer mortality from acute exposures to gamma rays and then transferred to an astronaut population. Finally, the REID is determined by integrating this risk over the individual's lifetime. The calculated upper 95% confidence limit of the REID is used to restrict an astronaut's permissible mission duration (PMD) for a proposed mission. As a statistical quantity characterized by broad, subjective uncertainties, REID estimates for space missions result in wide distributions. Currently, the upper 95% confidence level is over 350% larger than the mean REID value, which can severely limit an astronaut's PMD. The model incorporates inputs from multiple scientific disciplines in the risk estimation process. Physics and particle transport models calculate how radiation moves through space, penetrates spacecraft, and makes its way to the human beings onboard. Epidemiological studies of exposures from atomic bombings, medical treatments, and power plants are used to quantify health risks from acute and chronic low linear energy transfer (LET) ionizing radiation. Biological studies in cellular and animal models using radiation at various LETs and energies inform quality metrics for ions present in space radiation. Statistical methodologies unite these elements, controlling for mathematical and scientific uncertainty and variability. Despite current progress, these research platforms contain knowledge gaps contributing to the large uncertainties still present in the model. The NASA Space Radiation Program Element (SRPE) defines the knowledge gaps that impact our understanding of the cancer risks. These gaps are outlined in NASA's Human Research Roadmap [4], which identifies the research questions and actions recommended for reducing the uncertainty in the current NSCR model and for formulation of future models. The greatest contributors to uncertainty in the current model include radiation quality, dose rate effects, and the transfer of exposure-based risk from other populations to an astronaut population. Future formulations of the risk model may benefit from including other potential sources of uncertainty such as space dosimetry, errors in human epidemiology data, and the impact of microgravity and other spaceflight stressors. Here, we discuss the current capabilities of the NSCR-2012 model and several immediate research needs, highlighting areas expected to have an operational impact on the current model schema. The following subway-style route map outlines the NSCR-2012 model (Green Line), emphasizing the research gaps in the Human Research Roadmap for risk of radiation-induced carcinogenesis (Stops on Dashed Lines). The map diagrams how these research gaps feed specific portions of the model.

Chappell, L. J.↗

A Python Script to Read MCNP6.3 Surface-Source Files

This report provides a Python script to read an MCNP ® surface source file created with the SSW card with SYM = 0 (i.e., the default symmetry treatment). For background: the general format of an MCNP surface-source file is described in; however, that document did not provide coding and/or a tool to interrogate such files. The current format will not be given in this document other than through the record-read statements necessary for the script to function. The reader capability in this report is augmented with the ability to directly write a couple demonstrative outputs: 1. A comma-separated value (CSV) file containing particle phase-space state information and 2. A Matplotlib histogram of the energy distribution of the particles. This report also describes accompanying verification work that shows the script performing as required with MCNP6.2, MCNP6.3, and (expected) MCNP6.4 surface-source files. However, users of the enclosed script must still verify that the script is behaving correctly for their own work.

97 MATHEMATICS AND COMPUTING↗

Full-envelope aerodynamic modeling of the Harrier aircraft

A project to identify a full-envelope model of the YAV-8B Harrier using flight-test and parameter identification techniques is described. As part of the research in advanced control and display concepts for V/STOL aircraft, a full-envelope aerodynamic model of the Harrier is identified, using mathematical model structures and parameter identification methods. A global-polynomial model structure is also used as a basis for the identification of the YAV-8B aerodynamic model. State estimation methods are used to ensure flight data consistency prior to parameter identification.Equation-error methods are used to identify model parameters. A fixed-base simulator is used extensively to develop flight test procedures and to validate parameter identification software. Using simple flight maneuvers, a simulated data set was created covering the YAV-8B flight envelope from about 0.3 to 0.7 Mach and about -5 to 15 deg angle of attack. A singular value decomposition implementation of the equation-error approach produced good parameter estimates based on this simulated data set.

Mcnally, B. David↗

Equilibrium fluid interface behavior under low- and zero-gravity conditions

We describe here some of our recent mathematical work, which forms a basis for the Interface Configuration Experiment scheduled for USML-2. The work relates to the design of apparatus that exploits microgravity conditions for accurate determination of contact angle. The underlying motivation for the procedures rests on a discontinuous dependence of the capillary free surface interface S on the contact angle gamma, in a cylindrical capillary tube whose section (base) omega contains a protruding corner with opening angle 2 alpha. Specifically, in a gravity-free environment, omega can be chosen so that, for all sufficiently large fluid volume, the height of S is uniquely determined as a (single-valued) function mu(x,y) entirely covering the base; the height mu is bounded over omega uniformly in gamma throughout the range absolute value of (gamma -(pion/2)) less than or equal to alpha, while for absolute value of (gamma - (pion/2)) greater than alpha fluid will necessarily move to the corner and uncover the base, rising to infinity (or falling to negative infinity) at the vertex, regardless of volume. We mention here only that procedures based on the phenomenon promise excellent accuracy when gamma is close pion/2 but may be subject to experimental error when gamma is close to zero (orpion), as the 'singular' part of the domain over which the fluid accumulates (or disappears) when a critical angle gamma theta is crossed then becomes very small and may be difficult to observe. We ignore the trivial case gamma is equal to pion/2 (planar free surface), to simplify the discussion.

Concus, Paul↗

Interpretation of high-speed flows in the plasma sheet

Pursuing an idea suggested by Pontius and Wolf (1990), we propose that the `bursty bulk flows' observed by Baumjohann et al. (1990) and Angelopoulos et al. (1992) are `bubbles' in the Earth's plasma sheet. Specifically, they are flux tubes that have lower values of pV(exp 5/3) than their neighbors, where p is the thermal pressure of the particles and V is the volume of a tube containing one unit of magnetic flux. Whether they are created by reconnection or some other mechanism, the bubbles are propelled earthward by a magnetic buoyancy force, which is related to the interchange instability. Most of the major observed characteristics of the bursty bulk flows can be interpreted naturally in terms of the bubble picture. We propose a new `stratified fluid' picture of the plasma sheet, based on the idea that bubbles constitute the crucial transport mechanism. Results from simple mathematical models of plasma sheet transport support the idea that bubbles can resolve the pressure balance inconsistency, particularly in cases where plasma sheet ions are lost by gradient/curvature drift out the sides of the tail or bubbles are generated by reconnection in the middle of plasma sheet.

Chen, C. X.↗

Deep-Learning Interatomic Potential Connects Molecular Structural Ordering to the Macroscale Properties of Polyacrylonitrile

Polyacrylonitrile (PAN) is an important commercial polymer, bearing atactic stereochemistry resulting from nonselective radical polymerization. As such, an accurate, fundamental understanding of governing interactions among PAN molecular units is indispensable for advancing the design principles of final products at reduced processability costs. While ab initio molecular dynamics (AIMD) simulations can provide the necessary accuracy for treating key interactions in polar polymers, such as dipole–dipole interactions and hydrogen bonding, and analyzing their influence on the molecular orientation, their implementation is limited to small molecules only. Herein, we show that the neural network interatomic potentials (NNIPs) that are trained on the small-scale AIMD data (acquired for oligomers) can be efficiently employed to examine the structures and properties at large scales (polymers). NNIP provides critical insight into intra- and interchain hydrogen-bonding and dipolar correlations and accurately predicts the amorphous bulk PAN structure validated by modeling the experimental X-ray structure factor. Furthermore, the NNIP-predicted PAN properties, such as density and elastic modulus, are in good agreement with their experimental values. Overall, the trend in the elastic modulus is found to correlate strongly with the PAN structural orientations encoded in the Hermans orientation factor. In conclusion, this study enables the ability to predict the structure–property relations for PAN and analogues with sustainable ab initio accuracy across scales.

36 MATERIALS SCIENCE↗

Database and deep-learning scalability of anharmonic phonon properties by automated brute-force first-principles calculations

Understanding the anharmonic phonon properties of crystal compounds—such as phonon lifetimes and thermal conductivities—is essential for investigating and optimizing their thermal transport behaviors. These properties also impact optical, electronic, and magnetic characteristics through interactions between phonons and other quasiparticles and fields. In this study, we develop an automated first-principles workflow to calculate anharmonic phonon properties and build a comprehensive database encompassing more than 6500 inorganic compounds. Utilizing this dataset, we train a graph neural network model to predict thermal conductivity values and spectra from structural parameters, demonstrating a scaling law in which prediction accuracy improves with increasing training data size. High-throughput screening with the model enables the identification of materials exhibiting extreme thermal conductivities—both high and low. The resulting database offers valuable insights into the anharmonic behavior of phonons, thereby accelerating the design and development of advanced functional materials.

Ohnishi, Masato [University of Tokyo (Japan); Inst↗