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Results for “Mathematical Computing”

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

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Computer-aided light sheet flow visualization

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) data sets, was chosen to interactively display the reconstructed light sheet images, along with the numerical surface geometry for the model or aircraft under study. A description is provided of the photogrammetric reconstruction technique, and the image processing and computer graphics techniques and equipment. Results of the computer aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images and CFD solutions in the same graphics environment is also demonstrated.

Stacy, Kathryn↗
NASA NTRS1994

Computer-aided light sheet flow visualization using photogrammetry

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and a visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) results, was chosen to interactively display the reconstructed light sheet images with the numerical surface geometry for the model or aircraft under study. The photogrammetric reconstruction technique and the image processing and computer graphics techniques and equipment are described. Results of the computer-aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images with CFD solutions in the same graphics environment is also demonstrated.

Stacy, Kathryn↗
NASA NTRS1993

Computer-Aided Light Sheet Flow Visualization

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) data sets, was chosen to interactively display the reconstructed light sheet images, along with the numerical surface geometry for the model or aircraft under study. A description is provided of the photogrammetric reconstruction technique, and the image processing and computer graphics techniques and equipment. Results of the computer aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images and CFD solutions in the same graphics environment is also demonstrated.

Stacy, Kathryn↗
NASA NTRS2000

NASA Tech Briefs, February 2000

Topics covered include: Test and Measurement; Computer-Aided Design and Engineering; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Bio-Medical; Mathematics and Information Sciences; Computers and Peripherals.

Source record↗
NASA NTRSDate not supplied

A Brief Review of Equivalent Available Pressure Measurement and Purpose

This presentation is intended as a lead to a workshop on the subject of Equivalent Available Pressure (EAP). EAP is a concept that has been introduced to the Pressure Gain Combustion (PGC) community in recent years. It is a technique for determining an equivalent steady state figure of merit from the fundamentally unsteady PGC process. The workshop is centered on reviewing the efforts by various organizations to implement the EAP technique specifically on rotating detonation engines (RDE's). RDE's are a type of PGC device. This presentation is a very brief (15 minute) review of the EAP technique for both computational simulations and laboratory experiments. The mathematical equations required to compute EAP are shown and an example RDE simulation is presented showing results.

combustion↗
DOE OSTI2024

Decision Points and Practical Considerations for AI Projects

In this presentation, I will present business-relevant decisions, risks, and considerations for practical implementations of AI projects. I will use energy efficiency and renewable energy AI projects at NREL as examples and case-studies highlighting the journey from concept to implementation. First, I present challenges, questions, and trade-offs related to system inputs: the data. Next, I will examine issues with system behavior and trust, presenting examples, risks, and mitigation strategies. Finally, I will discuss challenges to effective widespread deployment of AI systems including energy, compute, and time requirements.

AI↗
NASA NTRS1984

A micro-computer based system to compute magnetic variation

A mathematical model of magnetic variation in the continental United States (COT48) was implemented in the Ohio University LORAN C receiver. The model is based on a least squares fit of a polynomial function. The implementation on the microprocessor based LORAN C receiver is possible with the help of a math chip, Am9511 which performs 32 bit floating point mathematical operations. A Peripheral Interface Adapter (M6520) is used to communicate between the 6502 based micro-computer and the 9511 math chip. The implementation provides magnetic variation data to the pilot as a function of latitude and longitude. The model and the real time implementation in the receiver are described.

Kaul, R.↗
NASA NTRS1972

A theory of supercritical wing sections, with computer programs and examples.

Mathematical methods for the design of supercritical wings, which depend on the numerical solution of the partial differential equations of two-dimensional gas dynamics, are developed. The main contribution is a computer program for the design of shockless transonic airfoils using the hodograph transformation and analytic continuation into the complex domain. The mathematical theory is described, and a manual for users of the programs is provided. Numerical examples are given and computational results are discussed, and the computer programs themselves are listed. The analysis routine can be used to ascertain whether the profiles behave well at off-design conditions, or to smooth coordinates and obtain a desirable shape more quickly when perfectly shockless flow is not essential.

Bauer, F.↗
DOE OSTI2026

Higher-order LaSDI: Reduced order modeling with multiple time derivatives

Solving complex partial differential equations (PDEs) is essential across scientific disciplines but often requires numerical models that can be prohibitively expensive in time-sensitive applications. Reduced-order models (ROMs) address this challenge by exploiting low-dimensional structure to create fast approximations. The Latent Space Dynamics Identification (LaSDI) framework has demonstrated success in learning ROMs for parameterized PDE families, but remains limited to first-order systems. Here, in this paper, we propose Higher-Order LaSDI (HLaSDI), which extends the LaSDI framework to PDEs with arbitrary order of time derivatives. This generalization significantly expands the applicability of LaSDI-based methods to systems previously outside their scope, including hyperbolic PDEs. We demonstrate HLaSDI’s accuracy and efficiency on several linear and nonlinear benchmark problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

Design concepts of the Shuttle mission simulator

The Shuttle mission simulator is designed to simulate all phases of the Space Shuttle mission from the last 30 minutes of countdown to launch, ascent, operations in orbit, deorbit, reentry, and landing with full participation by astronaut trainees and the mission control center. This paper reviews the design concepts of the simulator with attention given to the simulation hardware, crew stations, instructor/operator stations, digital computers, flight computer simulation interface device, mission control center interface, visual systems, aural cue system, mathematical modeling, digital computer complex, motion system, and the payload accommodation system.

Bird, J. D.↗
NASA NTRS1985

Computer simulation studies in fluid and calcium regulation and orthostatic intolerance

The systems analysis approach to physiological research uses mathematical models and computer simulation. Major areas of concern during prolonged space flight discussed include fluid and blood volume regulation; cardiovascular response during shuttle reentry; countermeasures for orthostatic intolerance; and calcium regulation and bone atrophy. Potential contributions of physiologic math models to future flight experiments are examined.

Source record↗
DOE OSTI2024

Practical and Optimal Sequential Bayesian Experimental Design for Complex Systems Incorporating Human Experimenter Preferences (Final Scientific/Technical Report)

Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Data-Conforming Data-Driven Control: Avoiding Premature Generalizations Beyond Data

Data-driven and adaptive control approaches face the problem of introducing sudden distributional shifts beyond the distribution of data encountered during learning. Therefore, they are prone to invalidating the very assumptions used in their own construction. This is due to the linearity of the underlying system, inherently assumed and formulated in most data-driven control approaches, which may falsely generalize the behavior of the system beyond the behavior experienced in the data. This article seeks to mitigate these problems by enforcing consistency of the newly designed closed-loop systems with data and slowing down any distributional shifts in the joint state-input space. This is achieved through incorporating affine regularization terms and linear matrix inequality constraints to data-driven approaches, resulting in convex semi-definite programs that can be efficiently solved by standard software packages. We discuss the optimality conditions of these programs and then conclude this article with a numerical example that further highlights the problem of premature generalization beyond data and shows the effectiveness of our proposed approaches in enhancing the safety of data-driven control methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2005

Simulation of Dynamics of a Flexible Miniature Airplane

A short report discusses selected aspects of the development of the University of Florida micro-aerial vehicle (UFMAV) basically, a miniature airplane that has a flexible wing and is representative of a new class of airplanes that would operate autonomously or under remote control and be used for surveillance and/or scientific observation. The flexibility of the wing is to be optimized such that passive deformation of the wing in the presence of aerodynamic disturbances would reduce the overall response of the airplane to disturbances, thereby rendering the airplane more stable as an observation platform. The aspect of the development emphasized in the report is that of computational simulation of dynamics of the UFMAV in flight, for the purpose of generating mathematical models for use in designing control systems for the airplane. The simulations are performed by use of data from a wind-tunnel test of the airplane in combination with commercial software, in which are codified a standard set of equations of motion of an airplane, and a set of mathematical routines to compute trim conditions and extract linear state space models.

Waszak, Martin R.↗
NASA NTRS1999

A Symmetry Breaking Experiment Aboard Mir and the Stability of Rotating Liquid Films

We discuss results from two parts of our study on the behavior of liquids under low-gravity conditions. The first concerns the Interface Configuration Experiment (ICE) aboard the Space Station Mir on the Mir-21/NASA-2 mission; for a certain 'exotic' container, distinct asymmetric liquid configurations are found as locally stable ones, even though the container itself is rotationally symmetric, in confirmation of mathematical results and numerical computations. The second investigation concerns the behavior of slowly rotating liquids; it is found that a rotating film instability observed previously in a physical experiment in 1-g, scaled to render gravity effects small, does not correspond to mathematical and computational results obtained for low gravity. These latter results are based on the classical equilibrium theory enhanced with a van der Waals potential of adhesion.

Concus, P.↗