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At least 1,603 records · Page 89

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NASA NTRS1994

Numerical Analysis of an Impinging Jet Reactor for the CVD and Gas-Phase Nucleation of Titania

We model a cold-wall atmospheric pressure impinging jet reactor to study the CVD and gas-phase nucleation of TiO2 from a titanium tetra-iso-propoxide (TTIP)/oxygen dilute source gas mixture in nitrogen. The mathematical model uses the computational code FIDAP and complements our recent asymptotic theory for high activation energy gas-phase reactions in thin chemically reacting sublayers. The numerical predictions highlight deviations from ideality in various regions inside the experimental reactor. Model predictions of deposition rates and the onset of gas-phase nucleation compare favorably with experiments. Although variable property effects on deposition rates are not significant (approximately 11 percent at 1000 K), the reduction rates due to Soret transport is substantial (approximately 75 percent at 1000 K).

Gokoglu, Suleyman A.↗

NASA NTRS2015

Software Validation via Model Animation

This paper explores a new approach to validating software implementations that have been produced from formally-verified algorithms. Although visual inspection gives some confidence that the implementations faithfully reflect the formal models, it does not provide complete assurance that the software is correct. The proposed approach, which is based on animation of formal specifications, compares the outputs computed by the software implementations on a given suite of input values to the outputs computed by the formal models on the same inputs, and determines if they are equal up to a given tolerance. The approach is illustrated on a prototype air traffic management system that computes simple kinematic trajectories for aircraft. Proofs for the mathematical models of the system's algorithms are carried out in the Prototype Verification System (PVS). The animation tool PVSio is used to evaluate the formal models on a set of randomly generated test cases. Output values computed by PVSio are compared against output values computed by the actual software. This comparison improves the assurance that the translation from formal models to code is faithful and that, for example, floating point errors do not greatly affect correctness and safety properties.

Dutle, Aaron M.↗

DOE OSTI2022

A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice

The evolution of breast tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. This study takes advantage of newly collected rich spatio-temporal mouse data to develop a data-driven mathematical model of breast tumors that considers cells’ location and key interactions in the tumor. The results show that cancer cells have a minor presence in the area with the most overall immune cells, and the number of activated immune cells in the tumor is depleted over time when there is no influx of immune cells. Interestingly, in the case of the influx of immune cells, the highest concentrations of both T cells and cancer cells are in the boundary of the tumor, as we use the Robin boundary condition to model the influx of immune cells. In other words, the influx of immune cells causes a dominant outward advection for cancer cells. We also investigate the effect of cells’ diffusion and immune cells’ influx rates in the dynamics of cells in the tumor micro-environment. Sensitivity analyses indicate that cancer cells and adipocytes’ diffusion rates are the most sensitive parameters, followed by influx and diffusion rates of cytotoxic T cells, implying that targeting them is a possible treatment strategy for breast cancer.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2002

Stochastic Models of Human Errors

Humans play an important role in the overall reliability of engineering systems. More often accidents and systems failure are traced to human errors. Therefore, in order to have meaningful system risk analysis, the reliability of the human element must be taken into consideration. Describing the human error process by mathematical models is a key to analyzing contributing factors. Therefore, the objective of this research effort is to establish stochastic models substantiated by sound theoretic foundation to address the occurrence of human errors in the processing of the space shuttle.

Elshamy, Maged↗

NASA NTRS2023

Advances in Aero-Propulsive Modeling for Fixed-Wing and eVTOL Aircraft Using Experimental Data

Small unmanned aircraft and electric vertical takeoff and landing (eVTOL) aircraft have recently emerged as vehicles able to perform new missions and stimulate future air transportation methods. This dissertation presents several system identification research advancements for these modern aircraft configurations enabling accurate mathematical model development for flight dynamics simulations based on wind-tunnel and flight-test data. The first part of the dissertation focuses on advances in flight-test system identification methods using small, fixed-wing, remotely-piloted, electric, propeller-driven aircraft. A generalized approach for flight dynamics model development for small fixed-wing aircraft from flight data is described and is followed by presentation of novel flight-test system identification applications, including: aero-propulsive model development for propeller aircraft and nonlinear dynamic model identification without mass properties. The second part of the dissertation builds on established fixed-wing and rotary-wing aircraft system identification methods to develop modeling strategies for transitioning, distributed propulsion, eVTOL aircraft. Novel wind-tunnel experiment designs and aero-propulsive modeling approaches are developed using a subscale, tandem tilt-wing, eVTOL aircraft, leveraging design of experiments and response surface methodology techniques. Additionally, a method applying orthogonal phase-optimized multisine input excitations to aircraft control effectors in wind-tunnel testing is developed to improve test efficiency and identified model utility. Finally, the culmination of this dissertation is synthesis of the techniques described throughout the document to form a flight-test system identification approach for eVTOL aircraft that is demonstrated using a high-fidelity flight dynamics simulation. The research findings highlighted throughout the dissertation constitute substantial progress in efficient empirical aircraft modeling strategies that are applicable to many current and future aeronautical vehicles enabling accurate flight simulation development, which can subsequently be used to foster advancement in many other pertinent technology areas.

system identification↗

DOE OSTI2021

Maximum bound principle preserving integrating factor Runge–Kutta methods for semilinear parabolic equations

A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP) in the sense that the time-dependent solution preserves for any time a uniform pointwise bound imposed by its initial and boundary conditions. Here, the MBP plays a crucial role in understanding the physical meaning and the well-posedness of the mathematical model. Investigation on numerical algorithms with preservation of the MBP has attracted increasingly attentions in recent years, especially for the temporal discretizations, since the violation of MBP may lead to nonphysical solutions or even blow-ups of the algorithms. In this paper, we study high-order MBP-preserving time integration schemes by means of the integrating factor Runge-Kutta (IFRK) method. Beginning with the space-discrete system of semilinear parabolic equations, we present the IFRK method in general form and derive the sufficient conditions for the method to preserve the MBP. In particular, we show that the classic four-stage, fourth-order IFRK scheme is MBP preserving for some typical semilinear systems although not strong stability preserving, which can be instantly applied to the Allen-Cahn type of equations. To our best knowledge, this is the first time to present a fourth-order linear numerical method preserving the MBP. In addition, convergence of these numerical schemes is proved theoretically and verified numerically, as well as their efficiency by simulations of 2D and 3D long-time evolutional behaviors. Numerical experiments are also carried out for a model which is not a typical gradient flow as the Allen-Cahn type of equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A comprehensive modeling method for proton exchange membrane electrolyzer development

Hydrogen attracts significant interests as an effective energy carrier that can be derived from renewable sources. Hydrogen production using a proton-exchange membrane (PEM) electrolyzer can efficiently convert renewable power via water splitting in wide scales—from large, centralized generation to on-site production. Mathematical models with multiple scales and fidelities facilitate the continuing improvements of PEM electrolyzer development to improve performance, cost, and reliability. The model scopes and methods are presented in this paper, which also introduces a comprehensive PEM electrolysis modeling tool based on computational fluid dynamics (CFD) software, ANSYS/Fluent. The modeling tool incorporates electrochemical model of a PEM electrolysis cell to simulate the performance of coupled thermal-fluid, species transport, and electrochemical processes in a product-scale cell or stack by leveraging the powerful meshing generation and CFD solver of ANSYS/Fluent. The thermal-fluid modeling includes liquid water/gas two-phase flow and simulates a PEM electrolysis cell by using Fluent user-defined functions as add-on modules accounting for PEM-specific species transport and electrochemical processes. The modeling outcomes expediate PEM electrolyzer scaling up from basic material development and laboratory testing.

08 HYDROGEN↗

DOE OSTI2022

Design and application of a kinetic model of lipid metabolism in Saccharomyces cerevisiae

Lipid biosynthesis plays a vital role in living cells and has been increasingly engineered to overproduce various lipid-based chemicals. However, owing to the tightly constrained and interconnected nature of lipid biosynthesis, both understanding and engineering of lipid metabolism remain challenging, even with the help of mathematical models. Here we report the development of a kinetic metabolic model of lipid metabolism in Saccharomyces cerevisiae that integrates fatty acid biosynthesis, glycerophospholipid metabolism, sphingolipid metabolism, storage lipids, lumped sterol synthesis, and the synthesis and transport of relevant target-chemicals, such as fatty acids and fatty alcohols. The model was trained on lipidomic data of a reference S. cerevisiae strain, single knockout mutants, and lipid overproduction strains reported in literature. The model was used to design mutants for fatty alcohol overproduction and the lipidomic analysis of the resultant mutant strains coupled with model-guided hypothesis led to discovery of a futile cycle in the triacylglycerol biosynthesis pathway. In addition, the model was used to explain successful and unsuccessful mutant designs in metabolic engineering literature. Thus, this kinetic model of lipid metabolism can not only enable the discovery of new phenomenon in lipid metabolism but also the engineering of mutant strains for overproduction of lipids.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1978

The dynamics and control of large flexible space structures. Part A: Discrete model and modal control

Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems were investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit was analyzed. First order effects of gravity gradient were included. A mathematical model which describes the system rotations and deflections within the orbital plane was developed by treating the beam as a number of discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of the system are simulated and, in addition, the effects of the control devices were considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, was examined. The effect of varying the number of modes in the model as well as the number and location of the control devices were also considered.

Bainum, P. M.↗

NASA NTRS1978

A model for dynamic allocation of human attention among multiple tasks

The problem of multi-task attention allocation with special reference to aircraft piloting is discussed with the experimental paradigm used to characterize this situation and the experimental results obtained in the first phase of the research. A qualitative description of an approach to mathematical modeling, and some results obtained with it are also presented to indicate what aspects of the model are most promising. Two appendices are given which (1) discuss the model in relation to graph theory and optimization and (2) specify the optimization algorithm of the model.

Sheridan, T. B.↗

NASA NTRS1981

A title-gap flow model for use in aerodynamic loads assessment of space shuttle thermal protection system: Parallel gap faces

The problem of predicting aerodynamic loads on the insulating tiles of the space shuttle thermal protection system (TPS) is discussed and seen to require a method for predicting pressure and mass flux in the gaps between tiles. A mathematical model of the tile-gap flow is developed, based upon a slow viscous (Stokes) flow analysis, and is verified against experimental data. The tile-gap pressure field is derived from a solution of the two-dimensional Laplace equation; the mass-flux vector is then calculated from the pressure gradient. The means for incorporating this model into a lumped-parameter network analogy for porous-media flow is given. The means for incorporating this model into a lumped-parameter network analogy for porous-media flow is given. The flow model shows tile-gap mass flux to be very sensitive to the gap width indicating a need for coupling the TPS flow and tile displacement calculation. Analytical and experimental work to improve TPS flow predictions and a possible shuttle TPS hardware modification are recommended.

Dwoyer, D. L.↗

NASA NTRS1984

Predictions of Cockpit Simulator Experimental Outcome Using System Models

This study involved predicting the outcome of a cockpit simulator experiment where pilots used cockpit displays of traffic information (CDTI) to establish and maintain in-trail spacing behind a lead aircraft during approach. The experiments were run on the NASA Ames Research Center multicab cockpit simulator facility. Prior to the experiments, a mathematical model of the pilot/aircraft/CDTI flight system was developed which included relative in-trail and vertical dynamics between aircraft in the approach string. This model was used to construct a digital simulation of the string dynamics including response to initial position errors. The model was then used to predict the outcome of the in-trail following cockpit simulator experiments. Outcome included performance and sensitivity to different separation criteria. The experimental results were then used to evaluate the model and its prediction accuracy. Lessons learned in this modeling and prediction study are noted.

Sorensen, J. A.↗

NASA NTRS1993

Mathmatical modeling for diffractive optics

We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design.

Dobson, David↗

NASA NTRS2014

Multivariate Dynamical Modeling to Investigate Human Adaptation to Space Flight: Initial Concepts

The array of physiological changes that occur when humans venture into space for long periods presents a challenge to future exploration. The changes are conventionally investigated independently, but a complete understanding of adaptation requires a conceptual basis founded in intergrative physiology, aided by appropriate mathematical modeling. NASA is in the early stages of developing such an approach.

Shelhamer, Mark↗

NASA NTRS2014

Multivariate Dynamic Modeling to Investigate Human Adaptation to Space Flight: Initial Concepts

The array of physiological changes that occur when humans venture into space for long periods presents a challenge to future exploration. The changes are conventionally investigated independently, but a complete understanding of adaptation requires a conceptual basis founded in integrative physiology, aided by appropriate mathematical modeling. NASA is in the early stages of developing such an approach.

Shelhamer, Mark↗

DOE OSTI2024

Vibration Studies for the CLARA Interferometer

The purpose of the CLARA experiment is to study the nature of undulator radiation emitted by single electrons circulating in the IOTA storage ring. The classical and quantum properties of the radiation are investigated by measuring its coherence length, intensity fluctuations and time correlations. The experiment took data in IOTA Run 4 (2022-2023). The key component of the apparatus is a Mach-Zehnder interferometer (MZI), in which the optical length of one of the arms can be precisely controlled. For some measurements, the fine regulation of the arm length must be smaller than the radiation wavelength. For this reason, the apparatus is particularly sensitive to mechanical vibrations. In this note, we model and measure the effect of vibrations on the performance of the MZI under various conditions. Several improvements of the setup were implemented to minimize systematic distortions of the observed interference patterns. In this report, we present a mathematical model of the effect of mechanical vibrations on observed detector and coincidence rates. We also describe the measurements that were made to estimate the magnitude and spectra of rate fluctuations and their sources in the CLARA MZI under various conditions. Finally, we estimate the magnitude of arm length fluctuations and we deduce the sensitivity to coincidence-rate variations in our apparatus.

43 PARTICLE ACCELERATORS↗

NASA NTRS1987

An adaptive Cartesian control scheme for manipulators

A adaptive control scheme for direct control of manipulator end-effectors to achieve trajectory tracking in Cartesian space is developed. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for online implementation with high sampling rates.

Seraji, H.↗

NASA NTRS2010

Calibration Modeling Methodology to Optimize Performance for Low Range Applications

Calibration is a vital process in characterizing the performance of an instrument in an application environment and seeks to obtain acceptable accuracy over the entire design range. Often, project requirements specify a maximum total measurement uncertainty, expressed as a percent of full-scale. However in some applications, we seek to obtain enhanced performance at the low range, therefore expressing the accuracy as a percent of reading should be considered as a modeling strategy. For example, it is common to desire to use a force balance in multiple facilities or regimes, often well below its designed full-scale capacity. This paper presents a general statistical methodology for optimizing calibration mathematical models based on a percent of reading accuracy requirement, which has broad application in all types of transducer applications where low range performance is required. A case study illustrates the proposed methodology for the Mars Entry Atmospheric Data System that employs seven strain-gage based pressure transducers mounted on the heatshield of the Mars Science Laboratory mission.

McCollum, Raymond A.↗