Factorization of spectra by discrete Fourier transforms
Discrete Fourier transform method for factoring spectral density functions, calculating absolute error
Rino, C. L.↗
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Code CUGEL: A code to unfold Ge(Li) spectrometer polyenergetic gamma photon experimental distributions
A FORTRAN code was developed for the Univac 1108 digital computer to unfold lithium-drifted germanium semiconductor spectrometers, polyenergetic gamma photon experimental distributions. It was designed to analyze the combination continuous and monoenergetic gamma radiation field of radioisotope volumetric sources. The code generates the detector system response matrix function and applies it to monoenergetic spectral components discretely and to the continuum iteratively. It corrects for system drift, source decay, background, and detection efficiency. Results are presented in digital form for differential and integrated photon number and energy distributions, and for exposure dose.
Steyn, J. J.↗
Discrete optimal control approach to a four-dimensional guidance problem near terminal areas
Description of a computer-oriented technique to generate the necessary control inputs to guide an aircraft in a given time from a given initial state to a prescribed final state subject to the constraints on airspeed, acceleration, and pitch and bank angles of the aircraft. A discrete-time mathematical model requiring five state variables and three control variables is obtained, assuming steady wind and zero sideslip. The guidance problem is posed as a discrete nonlinear optimal control problem with a cost functional of Bolza form. A solution technique for the control problem is investigated, and numerical examples are presented. It is believed that this approach should prove to be useful in automated air traffic control schemes near large terminal areas.
Nagarajan, N.↗
Nonlinear initial-boundary value solutions by the finite element method
The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.
Baker, A. J.↗
Nonparametric probability density estimation by optimization theoretic techniques
Two nonparametric probability density estimators are considered. The first is the kernel estimator. The problem of choosing the kernel scaling factor based solely on a random sample is addressed. An interactive mode is discussed and an algorithm proposed to choose the scaling factor automatically. The second nonparametric probability estimate uses penalty function techniques with the maximum likelihood criterion. A discrete maximum penalized likelihood estimator is proposed and is shown to be consistent in the mean square error. A numerical implementation technique for the discrete solution is discussed and examples displayed. An extensive simulation study compares the integrated mean square error of the discrete and kernel estimators. The robustness of the discrete estimator is demonstrated graphically.
Scott, D. W.↗
Design and simulation of stratified probability digital receiver with application to the multipath communication
One approach to the problem of simplifying complex nonlinear filtering algorithms is through using stratified probability approximations where the continuous probability density functions of certain random variables are represented by discrete mass approximations. This technique is developed in this paper and used to simplify the filtering algorithms developed for the optimum receiver for signals corrupted by both additive and multiplicative noise.
Deal, J. H.↗
Computation of three-dimensional inviscid flow over hypersonic missile configurations using the GIM code
A three-dimensional computational technique was used to obtain flowfield solutions to the Euler equations over selected hypersonic missile configurations. The General Interpolants Method (GIM) computer code was used with interpolation functions in an algebraic approach to generate a discrete computational grid for each configuration. The spatial marching version of the GIM code, which treats the parabolized Navier-Stokes (PNS) equations or the Euler equations with a shock capturing, 'MacCormack-like' scheme, was used to advance the solution hyperbolically over each configuration. The inviscid flowfield solutions over the two three-dimensional missile configurations, calculated using the GIM hyperbolic scheme, are presented here. The flow field over a wing/body configuration at zero degree angle of attack is presented. Flow over the fuselage of a tactical missile, termed the TAME 10, at both zero degree and 7.5 degree angles of attack is presented. In addition, an inviscid, two-dimensional analysis of an inlet configuration designed to mount on the TAME 10 is included. Contour maps of velocity and pressure are included for each configuration. Comparison of calculation and data show good agreement.
Xiques, K. E.↗
Computer simulation of surface and film processes
All the investigations which were performed employed in one way or another a computer simulation technique based on atomistic level considerations. In general, three types of simulation methods were used for modeling systems with discrete particles that interact via well defined potential functions: molecular dynamics (a general method for solving the classical equations of motion of a model system); Monte Carlo (the use of Markov chain ensemble averaging technique to model equilibrium properties of a system); and molecular statics (provides properties of a system at T = 0 K). The effects of three-body forces on the vibrational frequencies of triatomic cluster were investigated. The multilayer relaxation phenomena for low index planes of an fcc crystal was analyzed also as a function of the three-body interactions. Various surface properties for Si and SiC system were calculated. Results obtained from static simulation calculations for slip formation were presented. The more elaborate molecular dynamics calculations on the propagation of cracks in two-dimensional systems were outlined.
Tiller, W. A.↗
Streamline-upwind/Petrov-Galerkin procedures for the vorticity-stream function form of the Navier-Stokes equations
The paper presents procedures for the solution of the Navier-Stokes equations in the vorticity-stream function form. The difficulties involved are related to the convection term in the vorticity transport equation and to the lack of boundary conditions for voritcity at no-slip surfaces. The use of a streamline-upwind/Petrov-Galerkin finite element formulation for the solution of the vorticity transport equation. In the present scheme, the weighting functions are dependent on both spatial and temporal discretizations. A proper numerical treatment of the boundary conditions leading to an implicit treatment of the vorticity at no-slip surfaces is presented. These procedures have successfully been employed to simulate various flows of engineering interest.
Tezduyar, T. E.↗
Do clusters of galaxies affect the spectrum of the microwave background?
The distortion, averaged over the sky, due to the Compton scattering of background photons with electrons in the hot gas in clusters of galaxies is calculated. Using an existing sample of X-ray clusters, various values of the density parameter Omega, and plausible models for cluster evolution, Monte Carlo realizations of the microwave sky are generated. The spatial structure of these simulations shows a network of discrete sources whose properties can be a strong function of both evolution and Omega. The amount of spectral distortion in the models is greatest for models characterized by self-similar cluster evolution in an open universe and is within an order of magnitude of the current upper limits. Thus, improved observational sensitivity must inevitably detect some deviation from a blackbody spectrum.
Markevitch, M.↗
A PC program to optimize system configuration for desired reliability at minimum cost
High reliability is desired in all engineered systems. One way to improve system reliability is to use redundant components. When redundant components are used, the problem becomes one of allocating them to achieve the best reliability without exceeding other design constraints such as cost, weight, or volume. Systems with few components can be optimized by simply examining every possible combination but the number of combinations for most systems is prohibitive. A computerized iteration of the process is possible but anything short of a super computer requires too much time to be practical. Many researchers have derived mathematical formulations for calculating the optimum configuration directly. However, most of the derivations are based on continuous functions whereas the real system is composed of discrete entities. Therefore, these techniques are approximations of the true optimum solution. This paper describes a computer program that will determine the optimum configuration of a system of multiple redundancy of both standard and optional components. The algorithm is a pair-wise comparative progression technique which can derive the true optimum by calculating only a small fraction of the total number of combinations. A designer can quickly analyze a system with this program on a personal computer.
Hills, Steven W.↗
Viscous aerodynamic design using the adjoint variable approach
The use of classical optimal control methods, in particular variational methods, to solve the airfoil optimization problem, by deriving a set of adjoint (costate) equations and boundary conditions has already been done for inviscid (potential and Euler flows) and two dimensional, steady state, incompressible flow governed by the Navier-Stokes equations. The interior and boundary terms of the volume integral have been derived (in this work) for the steady Navier-Stokes equations in three dimensions for a viscous, compressible heat conducting fluid. This can be used to derive the adjoint equations and numerical boundary conditions for general classes of problems and hence paves the way for a solution to the aerodynamic optimization problem for compressible viscous flows. The next steps to the realization of that goal are projected as below. The usual square integral pressure functional as an objective function is being replaced by a more realistic drag functional subject to a lift constraint. The feasibility of attempting the more difficult time dependent problem is being investigated. It remains to get the full system of adjoint equations and boundary conditions with the new functional. The state and adjoint equations must be discretized and coded. An appropriate optimization program must be used (steepest descents seems inadequate) and various known airfoil shapes should be recovered in test cases of the computer program.
DeRise, George↗
A-Posteriori Error Estimation for Hyperbolic Conservation Laws with Constraint
This lecture considers a-posteriori error estimates for the numerical solution of conservation laws with time invariant constraints such as those arising in magnetohydrodynamics (MHD) and gravitational physics. Using standard duality arguments, a-posteriori error estimates for the discontinuous Galerkin finite element method are then presented for MHD with solenoidal constraint. From these estimates, a procedure for adaptive discretization is outlined. A taxonomy of Green's functions for the linearized MHD operator is given which characterizes the domain of dependence for pointwise errors. The extension to other constrained systems such as the Einstein equations of gravitational physics are then considered. Finally, future directions and open problems are discussed.
Barth, Timothy↗
The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation
A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.
Campbell, Joel↗
Turbulent Output-Based Anisotropic Adaptation
Controlling discretization error is a remaining challenge for computational fluid dynamics simulation. Grid adaptation is applied to reduce estimated discretization error in drag or pressure integral output functions. To enable application to high O(10(exp 7)) Reynolds number turbulent flows, a hybrid approach is utilized that freezes the near-wall boundary layer grids and adapts the grid away from the no slip boundaries. The hybrid approach is not applicable to problems with under resolved initial boundary layer grids, but is a powerful technique for problems with important off-body anisotropic features. Supersonic nozzle plume, turbulent flat plate, and shock-boundary layer interaction examples are presented with comparisons to experimental measurements of pressure and velocity. Adapted grids are produced that resolve off-body features in locations that are not known a priori.
Park, Michael A.↗
Statistical mechanics of violent relaxation
We propose a functional that is extremized through violent relaxation. It is based on the Ansatz that the wave-particle scattering during violent dynamical processes can be approximated as a sequence of discrete scattering events that occur near a particle's perigalacticon. This functional has an extremum whose structure closely resembles that of spheroidal stellar systems such as elliptical galaxies. The results described here, therefore, provide a simple framework for understanding the physical nature of violent relaxation and support the view that galaxies are structured in accord with fundamental statistical principles.
Spergel, David N.↗
Aircraft/Air Traffic Management Functional Analysis Model: Technical Description
The Aircraft/Air Traffic Management Functional Analysis Model, Version 2.0 (FAM 2.0), is a discrete event simulation model designed to support analysis of alternative concepts in air traffic management and control. FAM 2.0 was developed by the Logistics Management Institute (LMI) under a National Aeronautics and Space Administration (NASA) contract. This document provides a technical description of FAM 2.0 and its computer files to enable the modeler and programmer to make enhancements or modifications to the model. Those interested in a guide for using the model in analysis should consult the companion document, Aircraft/Air Traffic Management Functional Analysis Model, Version 2.0 Users Manual.
Etheridge, Melvin↗
Automated Fiber Placement Through Thickness Defect Stacking Optimization
In its 2022 commercial market outlook, Boeing forecasted an 80% increase in the global fleet through 2041 compared to 2019 pre-pandemic levels. This sharp rise in demand will drive pressure onto airframe manufacturers to ramp up production and find more efficient ways to design and manufacture airplanes. Complicating this challenge is the industry’s recent transformation from traditional metal-based airframes towards hybrid composite-metal aircraft. While composites have been used in aviation for decades, aircraft manufacturers are still struggling to design and manufacture quality parts at a high rate. Automated Fiber Placement (AFP) is one of the main manufacturing techniques used to produce large-scale composite parts. After a design has been created, a manufacturing strategy has to be developed based on the working material, part geometry, and machine capabilities. This process planning stage is essential to the AFP workflow and currently requires a high level of manual input from an experienced process planner. In an effort to automate and optimize this stage, the Computer Aided Process Planning (CAPP) module was developed. CAPP assists process planners in identifying optimal starting point location and layup strategy for each ply of a laminate. This Ply-Level Optimization (PLO) phase operates on the quantification of ply quality through predictable geometry-based defects such as gaps, overlaps, angle deviation, and steering. As you move from PLO to Laminate-Level Optimization (LLO) the design space grows exponentially, emphasizing the need for automated optimization. The work presented in this thesis expands CAPP’s functionality by comparing the planned fiber paths through the thickness of the laminate to mitigate stacked area defects and achieve an optimal laminate-level manufacturing strategy. Within CAPP, predicted gap and overlap defects are imported from Vericut Composites Programming (VCP) and then discretized to streamline the through-thickness comparison. Two objective functions are used to score different combinations of ply layup strategies based on defect stacking both globally and locally. Four combinatorial optimization algorithms were coupled with these objective functions to investigate the laminate-level manufacturing strategy design space and converge on the optimal plan. These algorithms were evaluated based on accuracy and efficiency through virtual testing on a complex tool surface. A separate LLO approach was developed to achieve near-optimal laminates in significantly less time. The end result is a software package which greatly reduces the required input from process planners, shortening the design-build cycle time and improving part quality.
AFP↗