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At least 163 records · Page 9

Numerical solution of differential equations by artificial neural networks

Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks (ANN's) are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed by the author to mate the adaptability of the ANN with the speed and precision of the digital computer. This method has been successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

Meade, Andrew J., Jr.

COMOC: Three dimensional boundary region variant, programmer's manual

The three-dimensional boundary region variant of the COMOC computer program system solves the partial differential equation system governing certain three-dimensional flows of a viscous, heat conducting, multiple-species, compressible fluid including combustion. The solution is established in physical variables, using a finite element algorithm for the boundary value portion of the problem description in combination with an explicit marching technique for the initial value character. The computational lattice may be arbitrarily nonregular, and boundary condition constraints are readily applied. The theoretical foundation of the algorithm, a detailed description on the construction and operation of the program, and instructions on utilization of the many features of the code are presented.

Orzechowski, J. A.

A program to evaluate a control system based on feedback of aerodynamic pressure differentials. Part 2: Data report for phase 1 wind tunnel test

Wind tunnel test data are presented. The purpose of the test was to determine the sensor location for sensitivity to flap deflection and to determine the range required of the sensor. The calculations followed to correct the raw pressure measurements, the corrected measurements, which represent the static pressures along the airfoil surface, and the static pressures tabulated and in coefficient form are described. However, the chordwise locations of the upper and lower surface taps do not coincide. An interpolation routine is performed to find the lower surface pressure coefficients at the upper surface tap locations. The difference, C sub P(lower) - C sub P(upper), is calculated and listed and the data are reorganized with respect to each tap location. A numerical regression performed to quantify the slopes of the graphs allows more accurate comparison of sensitivity and linearity.

Hrabak, R. R.

A program to evaluate a control system based on feedback of aerodynamic pressure differentials

The use of aerodynamic pressure differentials to position a control surface is evaluated. The system is a differential pressure command loop, analogous to a position command loop, where the surface is commanded to move until a desired differential pressure across the surface is achieved. This type of control is more direct and accurate because it is the differential pressure which causes the control forces and moments. A frequency response test was performed in a low speed wind tunnel to measure the performance of the system. Both pressure and position feedback were tested. The pressure feedback performed as well as position feedback implying that the actuator, with a break frequency on the order of 10 Rad/sec, was the limiting component. Theoretical considerations indicate that aerodynamic lags will not appear below frequencies of 50 Rad/sec, or higher.

Levy, D. W.

The 3DGRAPE book: Theory, users' manual, examples

A users' manual for a new three-dimensional grid generator called 3DGRAPE is presented. The program, written in FORTRAN, is capable of making zonal (blocked) computational grids in or about almost any shape. Grids are generated by the solution of Poisson's differential equations in three dimensions. The program automatically finds its own values for inhomogeneous terms which give near-orthogonality and controlled grid cell height at boundaries. Grids generated by 3DGRAPE have been applied to both viscous and inviscid aerodynamic problems, and to problems in other fluid-dynamic areas. The smoothness for which elliptic methods are known is seen here, including smoothness across zonal boundaries. An introduction giving the history, motivation, capabilities, and philosophy of 3DGRAPE is presented first. Then follows a chapter on the program itself. The input is then described in detail. A chapter on reading the output and debugging follows. Three examples are then described, including sample input data and plots of output. Last is a chapter on the theoretical development of the method.

Sorenson, Reese L.

Optimized solution of Kepler's equation

A detailed description is presented of KEPLER, an IBM 360 computer program used for the solution of Kepler's equation for eccentric anomaly. The program KEPLER employs a second-order Newton-Raphson differential correction process, and it is faster than previously developed programs by an order of magnitude.

Kohout, J. M.

Recent advances in methods for numerical solution of O.D.E. initial value problems

In the mathematical modeling of physical systems, it is often necessary to solve an initial value problem (IVP), consisting of a system of ordinary differential equations (ODE). A typical program produces approximate solutions at certain mesh points. Almost all existing codes try to control the local truncation error, while the user is really interested in controlling the true or global error. The present investigation provides a review of recent advances regarding the solution of the IVP, giving particular attention to stiff systems. Stiff phenomena are customarily defined in terms of the eigenvalues of the Jacobian. There are, however, some difficulties connected with this approach. It is pointed out that an estimate of the Lipschitz constant proves to be a very practical way to determine the stiffness of a problem.

Bui, T. D.

The zinc finger transcription factor Gfi1, implicated in lymphomagenesis, is required for inner ear hair cell differentiation and survival

Gfi1 was first identified as causing interleukin 2-independent growth in T cells and lymphomagenesis in mice. Much work has shown that Gfi1 and Gfi1b, a second mouse homolog, play pivotal roles in blood cell lineage differentiation. However, neither Gfi1 nor Gfi1b has been implicated in nervous system development, even though their invertebrate homologues, senseless in Drosophila and pag-3 in C. elegans are expressed and required in the nervous system. We show that Gfi1 mRNA is expressed in many areas that give rise to neuronal cells during embryonic development in mouse, and that Gfi1 protein has a more restricted expression pattern. By E12.5 Gfi1 mRNA is expressed in both the CNS and PNS as well as in many sensory epithelia including the developing inner ear epithelia. At later developmental stages, Gfi1 expression in the ear is refined to the hair cells and neurons throughout the inner ear. Gfi1 protein is expressed in a more restricted pattern in specialized sensory cells of the PNS, including the eye, presumptive Merkel cells, the lung and hair cells of the inner ear. Gfi1 mutant mice display behavioral defects that are consistent with inner ear anomalies, as they are ataxic, circle, display head tilting behavior and do not respond to noise. They have a unique inner ear phenotype in that the vestibular and cochlear hair cells are differentially affected. Although Gfi1-deficient mice initially specify inner ear hair cells, these hair cells are disorganized in both the vestibule and cochlea. The outer hair cells of the cochlea are improperly innervated and express neuronal markers that are not normally expressed in these cells. Furthermore, Gfi1 mutant mice lose all cochlear hair cells just prior to and soon after birth through apoptosis. Finally, by five months of age there is also a dramatic reduction in the number of cochlear neurons. Hence, Gfi1 is expressed in the developing nervous system, is required for inner ear hair cell differentiation, and its loss causes programmed cell death.

NASA Discipline Developmental Biology

Further Improvement in 3DGRAPE

3DGRAPE/AL:V2 denotes version 2 of the Three-Dimensional Grids About Anything by Poisson's Equation with Upgrades from Ames and Langley computer program. The preceding version, 3DGRAPE/AL, was described in Improved 3DGRAPE (ARC-14069) NASA Tech Briefs, Vol. 21, No. 5 (May 1997), page 66. These programs are so named because they generate volume grids by iteratively solving Poisson's Equation in three dimensions. The grids generated by the various versions of 3DGRAPE have been used in computational fluid dynamics (CFD). The main novel feature of 3DGRAPE/AL:V2 is the incorporation of an optional scheme in which anisotropic Lagrange-based trans-finite interpolation (ALBTFI) is coupled with exponential decay functions to compute and blend interior source terms. In the input to 3DGRAPE/AL:V2 the user can specify whether or not to invoke ALBTFI in combination with exponential-decay controls, angles, and cell size for controlling the character of grid lines. Of the known programs that solve elliptic partial differential equations for generating grids, 3DGRAPE/AL:V2 is the only code that offers a combination of speed and versatility with most options for controlling the densities and other characteristics of grids for CFD.

Alter, Stephen

Unified differentiable digital twin for the IOTA/FAST facility

As the design complexity of modern accelerators grows, there is more interest in using advanced simulations that have fast execution time or produce insights about accelerator state. One notable example of additional information are gradients of physical observables with respect to design parameters produced by differentiable simulations. The IOTA/FAST facility has recently begun a program to implement and experimentally validate a unified start-to-end differentiable digital twin to serve as a virtual accelerator test stand, allowing for rapid prototyping of new software and experiments with minimal beam time costs. In this contribution we will discuss our plans and progress. Specifically, we will cover the selection and benchmarking of both physics and ML codes, the development of generic interfaces between device models and surrogate or physics-based sections, and the export of the parameters through either a deterministic event loop or a fully asynchronous EPICS soft input/output controller. We will also discuss challenges in model calibration and uncertainty quantification, as well as future plans to support larger proton accelerators like PIPII and Booster.

Kuklev, Nikita [Fermilab]

FORTRAN 4 computer program for calculating critical speeds of rotating shafts

A FORTRAN 4 computer program, written for the IBM DCS 7094/7044 computer, that calculates the critical speeds of rotating shafts is described. The shaft may include bearings, couplings, extra masses (nonshaft mass), and disks for the gyroscopic effect. Shear deflection is also taken into account, and provision is made in the program for sections of the shaft that are tapered. The boundary conditions at the ends of the shaft can be fixed (deflection and slope equal to zero) or free (shear and moment equal to zero). The fixed end condition enables the program to calculate the natural frequencies of cantilever beams. Instead of using the lumped-parameter method, the program uses continuous integration of the differential equations of beam flexure across different shaft sections. The advantages of this method over the usual lumped-parameter method are less data preparation and better approximation of the distribution of the mass of the shaft. A main feature of the program is the nature of the output. The Calcomp plotter is used to produce a drawing of the shaft with superimposed deflection curves at the critical speeds, together with all pertinent information related to the shaft.

Trivisonno, R. J.

A study of the Sabatier-methanation reaction kinetics

The kinetics of the Sabatier methanation reaction, the reduction of carbon dioxide with hydrogen to methane and water, was investigated for 58 percent nickel on kieselguhr catalyst and 20 percent ruthenium on alumina catalyst. Differential rate data from an experimental program were correlated with a power function rate equation both for forward and reverse reactions. The kinetic parameters of activation energy, frequency rate constant and reaction order were determined for the rate equation. The values of these parameters were obtained from an Arrhenius plot of the experimental differential rate data. Also the carbon monoxide side reaction effect was measured and included in the correlation of parameters. The reaction was found to fit the rate equation experimentally within the temperature range 421 K, where the reaction effectively begins, the 800 K where the reaction rate drops and departs from the rate equation form.

Verostko, C. E.

Phototransistors Development and their Applications to Lidar

Custom-designed two-micron phototransistors have been developed using Liquid Phase Epitaxy (LPE), Molecular Beam Epitaxy (MBE) and Metal-Organic Chemical Vapor Deposition (MOCVD) techniques under Laser Risk Reduction Program (LRRP). The devices were characterized in the Detector Characterization Laboratory at NASA Langley Research Center. It appears that the performance of LPE- and MBE-grown phototransistors such as responsivity, noise-equivalent-power, and gain, are better than MOCVD-grown devices. Lidar tests have been conducted using LPE and MBE devices under the 2-micrometer CO2 Differential Absorption Lidar (DIAL) Instrument Incubator Program (IIP) at the National Center for Atmospheric Research (NCAR), Boulder, Colorado. The main focus of these tests was to examine the phototransistors performances as compared to commercial InGaAs avalanche photodiode by integrating them into the Raman-shifted Eye-safe Aerosol Lidar (REAL) operating at 1.543 micrometers. A simultaneous measurement of the atmospheric backscatter signals using the LPE phototransistors and the commercial APD demonstrated good agreement between these two devices. On the other hand, simultaneous detection of lidar backscatter signals using MBE-grown phototransistor and InGaAs APD, showed a general agreement between these two devices with a lower performance than LPE devices. These custom-built phototransistors were optimized for detection around 2-micrometer wavelength while the lidar tests were performed at 1.543 micrometers. Phototransistor operation at 2-micron will improve the performance of a lidar system operating at that wavelength. Measurements include detecting hard targets (Rocky Mountains), atmospheric structure consisting of cirrus clouds and boundary layer. These phototransistors may have potential for high sensitivity differential absorption lidar measurements of carbon dioxide and water vapor at 2.05-micrometers and 1.9-micrometers, respectively.

Abedin, M. N.

Surface characterization and testing II; Proceedings of the Meeting, San Diego, CA, Aug. 10, 11, 1989

Various papers on surface characterization and testing are presented. Individual topics addressed include: simple Hartmann test data interpretation, optimum configuration of the Offner null corrector, system for phase-shifting interferometry in the presence of vibration, fringe variation and visibility in speckle-shearing interferometry, functional integral representation of rough surfaces, calibration of surface heights in an interferometric optical profiler, image formation in common path differential profilometers, SEM of optical surfaces, measuring surface profiles with scanning tunneling microscopes, surface profile measurements of curved parts, high-resolution optical profiler, scanning heterodyne interferometer with immunity from microphonics, real-time crystal axis measurements of semiconductor materials, radial metrology with a panoramic annular lens, surface analysis for the characterization of defects in thin-film processes, Spacelab Optical Viewport glass assembly optical test program for the Starlab mission, scanning differential intensity and phase system for optical metrology.

Greivenkamp, John E.

Scrutinizing Variables for Checkpoint Using Automatic Differentiation

Checkpoint/Restart (C/R) saves the running state of the programs periodically, which consumes considerable time and system resources. We observe that not every piece of data is involved in the computation in typical HPC applications; such unused data should be excluded from checkpointing for better storage and compute efficiency. We propose a systematic approach that leverages automatic differentiation (AD) to scrutinize every element within variables (e.g., arrays) necessary for checkpointing. This allows us to identify critical and uncritical elements and eliminate uncritical elements from checkpointing. Specifically, we inspect every single element within a variable necessary for checkpointing with an AD tool to determine whether the element has an impact on the application output or not. We validate our approach with all benchmarks from the NPB suite. We visualize the distribution of critical and uncritical elements within a variable with respect to its binary impact (yes or no) on the application output.

Huang, Xin [Kobe University]