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Fortran ii computer program for evaluation of donnell type differential equation for orthotropic circular-conical shell
Automatic differentiation is a popular technique for computing derivatives of computer programs. While automatic differentiation has been successfully used in countless engineering, science, and machine learning applications, it can sometimes nevertheless produce surprising results. In this paper, we categorize problematic usages of automatic differentiation, and illustrate each category with examples such as chaos, time-averages, discretizations, fixed-point loops, lookup tables, linear solvers, and probabilistic programs, in the hope that readers may more easily avoid or detect such pitfalls. We also review debugging techniques and their effectiveness in these situations.
Writing programs in interactive FORMAC language to implement Picard iteration in solving systems of ordinary differential equations
NASA-Langley has conducted a flight test program evaluating a differential GPS/inertial navigation system's (DGPS/INS) utility as an approach/landing aid. The DGPS/INS airborne and ground components are based on off-the-shelf transport aircraft avionics, namely a global positioning/inertial reference unit (GPIRU) and two GPS sensor units (GPSSUs). Systematic GPS errors are measured by the ground GPSSU and transmitted to the aircraft GPIRU, allowing the errors to be eliminated or greatly reduced in the airborne equipment. Over 120 landings were flown; 36 of these were fully automatic DGPS/INS landings.
Fortran ii computer program for use with univac 80 solid-state computer for solving differential equations of simply-supported cylindrical shells
The equations of motion are developed for a perfectly flexible, inelastic tether with a satellite at its extremity. The tether is attached to a space vehicle in orbit. The tether is allowed to possess electrical conductivity. A numerical solution algorithm to provide the motion of the tether and satellite system is presented. The resulting differential equations can be solved by various existing standard numerical integration computer programs. The resulting differential equations allow the introduction of approximations that can lead to analytical, approximate general solutions. The differential equations allow more dynamical insight of the motion.
Development of characteristic tissue patterns requires that individual cells be switched locally between different phenotypes or "fates;" while one cell may proliferate, its neighbors may differentiate or die. Recent studies have revealed that local switching between these different gene programs is controlled through interplay between soluble growth factors, insoluble extracellular matrix molecules, and mechanical forces which produce cell shape distortion. Although the precise molecular basis remains unknown, shape-dependent control of cell growth and function appears to be mediated by tension-dependent changes in the actin cytoskeleton. However, the question remains: how can a generalized physical stimulus, such as cell distortion, activate the same set of genes and signaling proteins that are triggered by molecules which bind to specific cell surface receptors. In this article, we use computer simulations based on dynamic Boolean networks to show that the different cell fates that a particular cell can exhibit may represent a preprogrammed set of common end programs or "attractors" which self-organize within the cell's regulatory networks. In this type of dynamic network model of information processing, generalized stimuli (e.g., mechanical forces) and specific molecular cues elicit signals which follow different trajectories, but eventually converge onto one of a small set of common end programs (growth, quiescence, differentiation, apoptosis, etc.). In other words, if cells use this type of information processing system, then control of cell function would involve selection of preexisting (latent) behavioral modes of the cell, rather than instruction by specific binding molecules. Importantly, the results of the computer simulation closely mimic experimental data obtained with living endothelial cells. The major implication of this finding is that current methods used for analysis of cell function that rely on characterization of linear signaling pathways or clusters of genes with common activity profiles may overlook the most critical features of cellular information processing which normally determine how signal specificity is established and maintained in living cells. Copyright 2000 Academic Press.
Computer program implements a stability criterion that can be applied directly to the numerical solutions of systems of differential equations. The program accepts as input the time function of the system, a time to view the transient, and an acceptable amplitude boundary for any steady-state oscillation.
A wall-stabilized, constricted-arc heater was investigated by extensive measurements of pressure, voltage, and wall heat flux at different axial locations along the constrictor. Radial temperature profiles were measured at one axial location by the radiance of a single line method and also by the continuum radiance at a wavelength of 4955 A. The arc heater with an inside diameter of 2.37 cm and a constrictor length of 42 cm was operated with nitrogen flow rate from about 2 to 10 g/sec, and are currents from 400 to 1200 amperes. Based on a literature search, two different digital computer programs were selected which were used to predict the pertinent parameters by numerical solutions to the governing differential equations. The program selections were based on completeness and availability. In general the predictions were adequate when laminar flow was assumed, and the greatest difficulty was encountered in the predictions of wall heat flux. The results of the measurements are shown in graphical form, along with the theoretical predictions from both computer programs.
The governing differential equations of motion for a high speed cylindrical roller bearing are programmed for numerical solution and plotted output. This computer program has the capability of performing a two dimensional or three dimensional simulation. Two numerical solutions of the governing differential equations were obtained to simulate the motion of a roller bearing, one for the two dimensional equations of motion and one for the three dimensional equations of motion. Computer generated plots were obtained and present such data as roller/cage interaction forces, roller/race traction forces, roller/race relative slip velocities and cage angular speed over a nondimensional time equivalent to 1.2 revolutions of the inner race. Roller axial displacement, roller skew angle, and skew moment are also plotted for the three dimensional solution. The trajectory of the cage center is plotted for both the two dimensional and three dimensional solutions.
Recently the determination of the best technique for numerically solving systems of ordinary differential equations on a digital computer has received much attention. The use of these formulas in conjunction with a stepsize control developed is explained, and one of the formulas is chosen for comparison with other integration techniques. This comparison of one of the best of Fehlberg's formulas with the different numerical techniques described in previous studies on a variety of test problems clearly shows the superiority of Fehlberg's formula. That is, on each of the test problems, the chosen Fehlberg formula is able to achieve a given accuracy in less computer time than any of the other techniques tested. Also, the computer program for the chosen Fehlberg formula is less complex and easier to use than the computer programs for most of the other techniques. To illustrate the use of the chosen Fehlberg formula, a computer listing of its application to several example problems is included along with a sample of the computer output from these applications.
Major results from the frequency analysis of system program (FASP) are reported. The FASP procedure was designed to analyze or design linear dynamic systems, but can be used to solve any problem that can be described by a system of linear time invariant differential equations. The program also shows plots of performance changes as design parameters are adjusted. Experimental results on narrowband FM distortion are also reported.
An analytical and computer study of the dynamic energy equations that describe the physical phenomena that occurs in a Stirling cycle engine. The basic problem is set up in terms of a set o hyperbolic partial differential equations. The characteristic lines are determined. The equations are then transformed to ordinary differential equations that are valid along characteristic lines. Computer programs to solve the differential equations and to plot pertinent factors are described.
Three computer programs for evaluating and testing numerical integration formulas used with fixed stepsize programs to solve initial value systems of ordinary differential equations are described. A program written in PASCAL SERIES, takes as input the differential equations and produces a FORTRAN subroutine for the derivatives of the system and for computing the actual solution through recursive power series techniques. Both of these are used by STAN, a FORTRAN program that interactively displays a discrete analog of the Liapunov stability region of any two dimensional subspace of the system. The derivatives may be used by CLMP, a FORTRAN program, to test the fixed stepsize formula against a good numerical result and interactively display the solutions.
Among the Keck Interferometer's high priority science programs will be the differential astrometric detection of planetary companions to nearby stars.
Computer program developed for solving nonlinear differential equations of motion of high-speed, lightly loaded, cylindrical roller bearing. Program organized into three major parts: Main program, controls input and output; differential equation solver; and subroutines, used to evaluate vector function. Program has capability of performing either twodimensional or three-dimensional simulation.
Alternatives to the Tracking and Data Relay Satellite (TDRS) orbit estimation procedure were studied to develop a technique that both produces more reliable results and is more amenable to automation than the prior procedure. The Earth Observing System (EOS) Terra mission has TDRS ephemeris prediction 3(sigma) requirements of 75 meters in position and 5.5 millimeters per second in velocity over a 1.5-day prediction span. Meeting these requirements sometimes required reruns of the prior orbit determination (OD) process, with manual editing of tracking data to get an acceptable solution. After a study of the available alternatives, the Flight Dynamics Facility (FDF) began using the Real-Time Orbit Determination (RTOD(Registered TradeMark)) Kalman filter program for operational support of TDRSs in February 2007. This extended Kalman filter (EKF) is used for daily support, including within hours after most thrusting, to estimate the spacecraft position, velocity, and solar radiation coefficient of reflectivity (C(sub R)). The tracking data used are from the Bilateration Ranging Transponder System (BRTS), selected TDRS System (TDRSS) User satellite tracking data, and Telemetry, Tracking, and Command (TT&C) data. Degraded filter results right after maneuvers and some momentum unloads provided incentive for a hybrid OD technique. The results of combining EKF strengths with the Goddard Trajectory Determination System (GTDS) Differential Correction (DC) program batch-least-squares solutions, as recommended in a 2005 paper on the chain-bias technique, are also presented.
This paper describes a program for analysis of output curves from Differential Thermal Analyzer (DTA). The program first extracts probabilistic qualitative features from a DTA curve of a soil sample, and then uses Bayesian probabilistic reasoning to infer the mineral in the soil. The qualifier module employs a simple and efficient extension of scale-space filtering suitable for handling DTA data. We have observed that points can vanish from contours in the scale-space image when filtering operations are not highly accurate. To handle the problem of vanishing points, perceptual organizations heuristics are used to group the points into lines. Next, these lines are grouped into contours by using additional heuristics. Probabilities are associated with these contours using domain-specific correlations. A Bayes tree classifier processes probabilistic features to infer the presence of different minerals in the soil. Experiments show that the algorithm that uses domain-specific correlation to infer qualitative features outperforms a domain-independent algorithm that does not.