Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “applied math”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Statistics of base polytopes in F-theory

We propose a new statistical ensemble of toric bases for elliptic Calabi-Yaus used in F-theory models, by focusing on only the convex hull of the base, i.e., the base polytope. This physically motivated coarse-graining greatly simplifies the combinatorial complexity of the part of the 4d F-theory landscape with toric bases. We develop a Monte Carlo approach that randomly samples the base polytopes within fixed boxes, with proper statistical weights. We first apply the algorithm to the set of 2d base polytopes, generating an enlarged set of toric 2d bases that include certain types of codimension-two (4,6) points, and we validate our approach against exact numbers. We then explore the set of 3d base polytopes which fit in a set of “maximal” 3d boxes, and estimate the total number of inequivalent 3d base polytopes to be 10 85 –10 90 . We provide statistical data such as the distribution of non-Higgsable gauge groups on these bases. Amusingly, a similar method can also be applied to generate reflexive polytopes in various dimensions. In both the reflexive and base polytope cases, the number of relevant polytopes obeys a Gaussian distribution as a function of the number of vertices, which can be understood in terms of other results on random polytopes in the math literature.

Differential and algebraic geometry↗
NASA NTRS1988

Design of a rotary stepped auger for a lunar environment

A lunar outpost will have need for deep drilling operations for both explorative and practical purposes. As in any drilling operation, the cuttings must be cleared from the hole. The hard vacuum of the lunar environment renders conventional flushing methods of cutting removal unfeasible, and requires a new system of removal. A rotary stepped auger (RSA) is a simple mechanical method of removing dry cuttings from a deep hole, and is ideally suited to the lunar environment. The RSA consists of a helical auger with stepped ramps which allow cuttings to slide up the helix, but will prevent them from sliding back down. The auger is driven in a pulsed manner by applying a periodic function of acceleration to the auger shaft. These pulses will compel the cuttings to slide up the auger's helix while the stepped ramps prevent the cuttings from backsliding while the auger accelerates. A mathematical model of the RSA was developed and experimentally evaluated. The math model produced a good baseline design, but the experimental model required some tuning to account for the approximations made in the math model. This design is suited for lunar drilling because it is mechanically simple, integral to the drill string, requires no fluids, is suited to the dry soil, and has relatively low weight and power requirements.

Dardet, Eduardo↗
DOE OSTI2021

Computational Math Problems for a Clean Energy Future

Cutting edge computational mathematics are ubiquitous in renewable energy research. Problems in resilient and reliable electric grid operations, infrastructure planning, wind farm yaw control, and more demand sophisticated and scalable computational tools that enable the transition of renewable energy technologies from proof of concept to deployment into our energy system. The mission of the Computational Science Center at NREL is to lead the lab's efforts to solve energy challenges using high-performance computing (HPC), computational science, applied mathematics, scientific data management, visualization, and informatics. In this poster, we provide a short overview of three areas of computational mathematics research at NREL: wind power scenario generation for stochastic grid operations and infrastructure planning, improved rational function approximations for electromagnetic transients codes, and wind farm yaw control using a combination of the Alternating Direction Method of Multipliers (ADMM) and reinforcement learning (RL). Increasing penetrations of renewable energy into power grids motivate the investigation of new approaches to characterizing uncertainty for five-minute economic dispatch problems. Similarly, as the penetration of distributed energy resources on power grids increases, it becomes important to revisit our methods of modelling transient phenomena, i.e. electromagnetic transients programs. Finally, the combination of ADMM and RL for wind farm yaw control presented here can potentially increase the efficiency of the deployed distributed controllers by orders of magnitude.

ADMM↗
NASA NTRS1976

Study leading to the refinement of the SRB structural analysis program

The constructed SRB math model was used for the analysis of the 85/32/5(VV/VH/theta) cavity collapse load condition for the aft end of the SRB structure. Linear, nonlinear collapse and bifurcation buckling analyses were performed. The linear and bifurcation buckling analyses showed that structural integrity and positive margins of safety are maintained for the applied maximum load case using a design factor of 1.25. The nonlinear collapse analysis predicts stresses in the skirt above the yield for a load factor of 1.0. Applying the 1.25 design factor gives a negative margin of safety against the material ultimate. The predicted collapse occurs at a load factor higher than 1.25.

Jones, W. E.↗
NASA NTRS1998

Recent Dynamic Measurements and Considerations for Aerodynamic Modeling of Fighter Airplane Configurations

As airplane designs have trended toward the expansion of flight envelopes into the high angle of attack and high angular rate regimes, concerns regarding modeling the complex unsteady aerodynamics for simulation have arisen. Most current modeling methods still rely on traditional body axis damping coefficients that are measured using techniques which were intended for relatively benign flight conditions. This paper presents recent wind tunnel results obtained during large-amplitude pitch, roll and yaw testing of several fighter airplane configurations. A review of the similitude requirements for applying sub-scale test results to full-scale conditions is presented. Data is then shown to be a strong function of Strouhal number - both the traditional damping terms, but also the associated static stability terms. Additionally, large effects of sideslip are seen in the damping parameter that should be included in simulation math models. Finally, an example of the inclusion of frequency effects on the data in a simulation is shown.

Brandon, Jay M.↗
NASA NTRS2012

Engaging Girls in STEM: How to Plan or Revamp Your EPO Resources or Activities to be More Effective for Girls

This two-hour workshop, which was held as a follow-on to the plenary session "Engaging Girls in STEM: A Discussion of Foundational and Current Research on What Works," offered research-based insights, resources, and tips to help participants plan or revamp programs and resources aimed at encouraging girls in science. Led by Karen Peterson, PI for the National Girls Collaborative Project,1 the workshop included: a brief discussion about effective strategies recommended for encouraging girls in STEM; hands-on experience, where participants-availing of the expert's guidance-applied the recommended strategies to alter or tailor an existing or planned program/resource to be more girl-friendly; and a sharing out, where the participants reflected on the results of the hands-on exercise and developed action items to continue carrying out the girl-friendly best practices in science, technology, engineering, and math education and public outreach.

Bleacher, Lora V.↗
NASA NTRS1987

Piloted simulator study of allowable time delay in pitch flight control system of a transport airplane with negative static stability

A piloted simulation study was conducted to determine the permissible time delay in the flight control system of a 10-percent statically unstable transport airplane during cruise flight conditions. The math model used for the simulation was a derivative Lockheed L-1011 wide-body jet transport. Data were collected and analyzed from a total of 137 cruising flights in both calm- and turbulent-air conditions. Results of this piloted simulation study verify previous findings that show present military specifications for allowable control-system time delay may be too stringent when applied to transport-size airplanes. Also, the degree of handling-qualities degradation due to time delay is shown to be strongly dependent on the source of the time delay in an advanced flight control system. Maximum allowable time delay for each source of time delay in the control system, in addition to a less stringent overall maximum level of time delay, should be considered for large aircraft. Preliminary results also suggest that adverse effects of control-system time delay may be at least partially offset by variations in control gearing. It is recommended that the data base include different airplane baselines, control systems, and piloting tasks with many pilots participating, so that a reasonable set of limits for control-system time delay can be established to replace the military specification limits currently being used.

Grantham, William D.↗
DOE OSTI2025

ChatHPC: Building the Foundations for a Productive and Trustworthy AI-Assisted HPC Ecosystem

ChatHPC democratizes large language models for the high-performance computing (HPC) community by providing the infrastructure, ecosystem, and knowledge needed to apply modern generative AI technologies to rapidly create specific capabilities for critical HPC components while using relatively modest computational resources. Our divide-and-conquer approach focuses on creating a collection of reliable, highly specialized, and optimized AI assistants for HPC based on the cost-effective and fast Code Llama fine-tuning processes and expert supervision. We target major components of the HPC software stack, including programming models, runtimes, I/O, tooling, and math libraries. Thanks to AI, ChatHPC provides a more productive HPC ecosystem by boosting important tasks related to portability, parallelization, optimization, scalability, and instrumentation, among others. With relatively small datasets (on the order of KB), the AI assistants, which are created in a few minutes by using one node with two NVIDIA H100 GPUs and the ChatHPC library, can create new capabilities with Meta’s 7-billion parameter Code Llama base model to produce high-quality software with a level of trustworthiness of up to 90% higher than the 1.8-trillion parameter OpenAI ChatGPT-4o model for critical programming tasks in the HPC software stack.

Young, Aaron [ORNL] (ORCID:0000000254484667)↗
DOE OSTI2025

The persistent shadow of the supermassive black hole of M87. II. Model comparisons and theoretical interpretations

The Event Horizon Telescope (EHT) observation of M87∗ in 2018 has revealed a ring with a diameter that is consistent with the 2017 observation. The brightest part of the ring is shifted to the southwest from the southeast. In this paper, we provide theoretical interpretations for the multi-epoch EHT observations for M87∗ by comparing a new general relativistic magnetohydrodynamics model image library with the EHT observations for M87∗ in both 2017 and 2018. The model images include aligned and tilted accretion with parameterized thermal and nonthermal synchrotron emission properties. The 2018 observation again shows that the spin vector of the M87∗ supermassive black hole is pointed away from Earth. A shift of the brightest part of the ring during the multi-epoch observations can naturally be explained by the turbulent nature of black hole accretion, which is supported by the fact that the more turbulent retrograde models can explain the multi-epoch observations better than the prograde models. The EHT data are inconsistent with the tilted models in our model image library. Assuming that the black hole spin axis and its large-scale jet direction are roughly aligned, we expect the brightest part of the ring to be most commonly observed 90 deg clockwise from the forward jet. This prediction can be statistically tested through future observations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

A Compositional Relevance Model for Adaptive Information Retrieval

There is a growing need for rapid and effective access to information in large electronic documentation systems. Access can be facilitated if information relevant in the current problem solving context can be automatically supplied to the user. This includes information relevant to particular user profiles, tasks being performed, and problems being solved. However most of this knowledge on contextual relevance is not found within the contents of documents, and current hypermedia tools do not provide any easy mechanism to let users add this knowledge to their documents. We propose a compositional relevance network to automatically acquire the context in which previous information was found relevant. The model records information on the relevance of references based on user feedback for specific queries and contexts. It also generalizes such information to derive relevant references for similar queries and contexts. This model lets users filter information by context of relevance, build personalized views of documents over time, and share their views with other users. It also applies to any type of multimedia information. Compared to other approaches, it is less costly and doesn't require any a priori statistical computation, nor an extended training period. It is currently being implemented into the Computer Integrated Documentation system which enables integration of various technical documents in a hypertext framework.

Mathe, Nathalie↗
NASA NTRS2003

Progress in Developing a New Field-theoretical Crossover Equation-of-State

A new field-theoretical crossover equation-of-state model is being developed. This model of a liquid-gas critical point provides a bridge between the asymptotic equation-of-state behavior close to the transition, obtained by the Guida and Zinn-Justin parametric model [J. Phys. A: Math. Gen. 31, 8103 (1998)], and the expected mean field behavior farther away. The crossover is based on the beta function for the renormalized fourth-order coupling constant and incorporates the correct crossover exponents and critical amplitude ratios in both regimes. A crossover model is now being developed that is consistent with predictions along the critical isochore and along the coexistence curve of the minimal subtraction renormalization approach developed by Dohm and co-workers and recently applied to the O(1) universality class [Phys. Rev. E, 67, 021106 (2003)]. Experimental measurements of the heat capacity at constant volume, isothermal susceptibility, and coexistence curve near the He-3 critical point are being compared to the predictions of this model. The results of these comparisons will be presented.

Rudnick, Joseph↗
NASA NTRS1994

EEG and chaos: Description of underlying dynamics and its relation to dissociative states

The goal of this work is the identification of states especially as related to the process of error production and lapses of awareness as might be experienced during aviation. Given the need for further articulation of the characteristics of 'error prone state' or 'hazardous state of awareness,' this NASA grant focused on basic ground work for the study of the psychophysiology of these states. In specific, the purpose of this grant was to establish the necessary methodology for addressing three broad questions. The first is how the error prone state should be conceptualized, and whether it is similar to a dissociative state, a hypnotic state, or absent mindedness. Over 1200 subjects completed a variety of psychometric measures reflecting internal states and proneness to mental lapses and absent mindedness; the study suggests that there exists a consistency of patterns displayed by individuals who self-report dissociative experiences such that those individuals who score high on measures of dissociation also score high on measures of absent mindedness, errors, and absorption, but not on scales of hypnotizability. The second broad question is whether some individuals are more prone to enter these states than others. A study of 14 young adults who scored either high or low on the dissociation experiences scale performed a series of six tasks. This study suggests that high and low dissociative individuals arrive at the experiment in similar electrocortical states and perform cognitive tasks (e.g., mental math) in a similar manner; it is in the processing of internal emotional states that differences begin to emerge. The third question to be answered is whether recent research in nonlinear dynamics, i.e., chaos, offer an addition and/or alternative to traditional signal processing methods, i.e., fast Fourier transforms, and whether chaos procedures can be modified to offer additional information useful in identifying brain states. A preliminary review suggests that current nonlinear dynamical techniques such as dimensional analysis can be successfully applied to electrocortical activity. Using the data set developed in the study of the young adults, chaos analyses using the Farmer algorithm were performed; it is concluded that dimensionality measures reflect information not contained in traditional EEG Fourier analysis.

Ray, William J.↗
NASA NTRS2019

Comparison of Electrical Output Format Options for the Analysis of Strain-Gage Balance Calibration Data

Fundamental characteristics of three gage output formats are discussed that may be used to both interpret and analyze wind tunnel strain-gage balance data. The first output format uses raw outputs, i.e., absolute voltage measurements, for the analysis. This choice requires an intercept term in the regression model of the outputs if the Iterative Method is chosen for the load prediction. Raw outputs can be used for the analysis of all known output characteristics as long as the Iterative Method is applied. However, raw outputs cannot be used to analyze data of a balance with bi-directional outputs if the Non-Iterative Method is chosen for the analysis. The second output format, i.e., difference type 1, uses the difference between raw outputs and the natural zeros of the balance gages for the analysis. In this case, the use of the intercept term becomes optional. Analysis results for difference type 1 will exactly match analysis results obtained by using raw outputs as long as identical math models are used for the regression analysis. In addition, difference type 1 may be used to analyze data of a balance with bi directional outputs if an analyst prefers to process data using the Non-Iterative Method. The third output format, i.e., difference type 2, uses the difference between raw outputs and the outputs of the zero load point of a load series for the data analysis. The application of this format is only recommended if the maximum magnitude of all tare loads of a given balance calibration data set is less than two percent of capacity. Data from the calibration of a force balance is used to illustrate the application of the three gage output formats.

Wind Tunnel Strain-Gage Balance↗
DOE OSTI2020

Dissertation Proposal: Innovations in Pulsed Power and Plasma Science Theory Simulation and Experiment

Pulsed power and plasma physics are topics of great study at both Sandia National Laboratories (SNL or Sandia) and the University of New Mexico (UNM). The goal of this research is to further knowledge and understanding of these fields using the resources of both SNL and UNM in three ways. The first way is through the comprehension, application, and testing of theory. Reading and analytically deriving theoretical solutions of problems both real-world and simplified will allow for a fresh perspective and the furthering of the theory. One such theory is Ottinger's generalized theory for voltage measurement in magnetically insulated transmission lines (MITLs). By working through the math, a deeper understanding of the theory is gained from which one may add more physically accurate and/or more detailed physics into the theory. Additionally, understanding the theory lays a good foundation from which one can analyze, test, and compare results to the theory in the following two ways that will advance the fields of pulsed power and plasma physics. The second way is through the modeling and simulation of real-world and simplified problems that utilize and test the afore mentioned theories. Theory can be applied to a simulation domain by using the unstructured time-domain electromagnetic (UTDEM) codes EMPHASIS and EMPIRE as well as the physical modeling software CUBIT, all of which were developed at SNL. Problems such as the modeling and design of the extended MITL on HERMES III, the understanding of space-charge-limited emission from vacuum cathodes, and the interaction between a relativistic electron beam and an ideal gas can all be modeled, simulated, and analyzed with this set of codes. Here the advantage is three-fold. Firstly, theory that describes our understanding of these problems can be put to the test and advanced through iterative simulation and analysis. Secondly, the understanding of these problems will have a positive impact on national security through the advancement of the technological capability of the United States of America. Thirdly, and not unrelated to the prior advantage, is the validation and verification of EMPIRE and EMPHASIS. This segues into the third way, which is through experiment and the comparison of experiment to simulated and theoretical results. Performing experimental comparisons completes the scientific method and grounds all of the work in reality. Being able to physically test theory and simulation is necessary for any real conclusions to be drawn. Another advantage for carrying out experimental work is to advance the physical testing capabilities of SNL. Several systems will be developed and tested through the course of this work that positively impact technological advancement of Sandia National Labs. Lastly, all of the above work will converge to yield a well-rounded perspective that ties the three categories of research together.

42 ENGINEERING↗
NASA NTRS2013

Analysis of Multivariate Experimental Data Using A Simplified Regression Model Search Algorithm

A new regression model search algorithm was developed that may be applied to both general multivariate experimental data sets and wind tunnel strain-gage balance calibration data. The algorithm is a simplified version of a more complex algorithm that was originally developed for the NASA Ames Balance Calibration Laboratory. The new algorithm performs regression model term reduction to prevent overfitting of data. It has the advantage that it needs only about one tenth of the original algorithm's CPU time for the completion of a regression model search. In addition, extensive testing showed that the prediction accuracy of math models obtained from the simplified algorithm is similar to the prediction accuracy of math models obtained from the original algorithm. The simplified algorithm, however, cannot guarantee that search constraints related to a set of statistical quality requirements are always satisfied in the optimized regression model. Therefore, the simplified algorithm is not intended to replace the original algorithm. Instead, it may be used to generate an alternate optimized regression model of experimental data whenever the application of the original search algorithm fails or requires too much CPU time. Data from a machine calibration of NASA's MK40 force balance is used to illustrate the application of the new search algorithm.

Ulbrich, Norbert M.↗
DOE OSTI2023

RadSim: Math, Utility & RTK

This package includes three parts, (1) gov.llnl.math, (2)gov.llnl.utility and (3)gov.llnl.rtk, which are utilized in the development of Radiation Detector Simulator (RadSim) project. RadSim is being developed to provide the capability to: (1) simulate radiation source emissions, (2) interpolate results from radiation transport tools into a common format to prepare incident flux, and (3) model radiation detector response to rapidly produce synthetic radiation measurement templates. RadSim is targeted for open-source release, which will enable researchers and industry partners to model gamma-ray detectors response to simulated flux from the transport tool of their choice. The techniques and implementation will be entirely transparent, which will allow for improvements and boutique modifications by future researchers beyond the lifespan of this specific project. The first tool of the package, gov.llnl.math, includes classes and functions to define and perform basic math operations. Some of the example features available in the package include defining statistical distributions and performing algebra and matrix operations, all of which are already accessible on publicly available software packages such as MATLAB and ROOT. The second package gov.llnl.utility includes tools commonly used to enable optimization and readability of various data structures such as Java lists and external xml files. Lastly, the gov.llnl.rtk package includes classes and functions to implement methods commonly used in radiation physics, such as data structures to represent and characterize photon spectra and tools to apply well-defined and published methods to calibrate a given spectra.

Cheung, Hoi Sing↗
NASA NTRS1981

LANDSAT-D MSS/TM tuned orbital jitter analysis model LDS900

The final LANDSAT-D orbital dynamic math model (LSD900), comprised of all test validated substructures, was used to evaluate the jitter response of the MSS/TM experiments. A dynamic forced response analysis was performed at both the MSS and TM locations on all structural modes considered (thru 200 Hz). The analysis determined the roll angular response of the MSS/TM experiments to improve excitation generated by component operation. Cross axis and cross experiment responses were also calculated. The excitations were analytically represented by seven and nine term Fourier series approximations, for the MSS and TM experiment respectively, which enabled linear harmonic solution techniques to be applied to response calculations. Single worst case jitter was estimated by variations of the eigenvalue spectrum of model LSD 900. The probability of any worst case mode occurrence was investigated.

Pollak, T. E.↗
NASA NTRS2005

Turbulence Hazard Metric Based on Peak Accelerations for Jetliner Passengers

Calculations are made of the approximate hazard due to peak normal accelerations of an airplane flying through a simulated vertical wind field associated with a convective frontal system. The calculations are based on a hazard metric developed from a systematic application of a generic math model to 1-cosine discrete gusts of various amplitudes and gust lengths. The math model simulates the three degree-of- freedom longitudinal rigid body motion to vertical gusts and includes (1) fuselage flexibility, (2) the lag in the downwash from the wing to the tail, (3) gradual lift effects, (4) a simplified autopilot, and (5) motion of an unrestrained passenger in the rear cabin. Airplane and passenger response contours are calculated for a matrix of gust amplitudes and gust lengths. The airplane response contours are used to develop an approximate hazard metric of peak normal accelerations as a function of gust amplitude and gust length. The hazard metric is then applied to a two-dimensional simulated vertical wind field of a convective frontal system. The variations of the hazard metric with gust length and airplane heading are demonstrated.

Stewart, Eric C.↗