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First order RKR turning points were computed for (C-12)O16, (C-12)O17, (C-13)O16, (C-12)O18, and (C-13)O18 for vibrational levels up to v = 40. These turning points should be useful in the numerical computation of matrix elements of powers of the internuclear separation.
Observations of X-ray bursts from binary pulsars and globular clusters are reviewed. The previously proposed hypothesis is considered that such X-ray bursts result from thermonuclear flashes on accreting neutron stars. A general scenario for this mechanism is outlined, and numerical computations of the evolution of the surface layers of an accreting neutron star are discussed. The relation of these calculations to X-ray bursts and other phenomena is examined. Possible improvements in the numerical calculations are suggested.
Performing a variety of numerical computations efficiently and, at the same time, in a portable fashion requires both an overarching design followed by a number of implementation strategies. All of these are exemplified below as we present transitioning the PLASMA numerical library from relying on dependence-driven large tasks to achieving utilization of fine grain tasking and offload to hardware accelerators while keeping its core dependence sets: OpenMP source code pragmas and runtime for most system-level functionality and basic low-level numerical kernels provided directly by hardware vendors or open source projects with vendor contributions. We also present new algorithmic methods and their efficient parallel implementations including fine grained tasking for eigen-spectrum slicing and offload for mixed-precision eigenvalue refinement. We provide performance, scaling, and numerical results showing sizable gains over the available solutions from either the open source and vendor-provided packages.
A series of time-dependent numerical computations have been performed for the flow of an unsteady boundary layer over an embedded cavity, which is aligned normal to the flow direction. The unsteady flow is the result of the imposition of a Stuart vortex, at the inflow boundary of the computational domain, onto an otherwise unperturbed two-dimensional laminar boundary layer flow. This produces a strongly vortical, but spatially monochromatic, motion at inflow which is allowed to evolve downstream through the time-dependent numerical solution of appropriate conservation equations. As the imposed vortex evolves over the solid boundary, a weaker induced vortical motion is produced and together these perturbing motions interact with the fluid motion in the embedded cavity. An analysis of the pertinent dynamic variables as well as the time-dependent drag characteristics for this type of non-planar geometry is performed; with particular emphasis on the relative contribution of both pressure drag and frictional drag at various times in the evolution process.
An objective analysis technique has been developed to extrapolate tidal amplitudes and phases over entire ocean basins using existing gauge data and the altimetric measurements which are now beginning to be provided by satellite oceanography. The technique was previously tested in the Lake Superior basin. The method has now been developed and applied in the Atlantic-Indian ocean basins using a 6 deg x 6 deg grid to test its essential features. The functions used in the interpolation are the eigenfunctions of the velocity potential (Proudman functions) which are computed numerically from a knowledge of the basin's bottom topography, the horizontal plan form and the necessary boundary conditions. These functions are characteristic of the particular basin. The gravitational normal modes of the basin are computed as part of the investigation, they are used to obtain the theoretical forced solutions for the tidal constituents, the latter provide the simulated data for the testing of the method and serve as a guide in choosing the most energetic modes for the objective analysis. The results of the objective analysis of the M2 and K1 tidal constituents indicate the possibility of recovering the tidal signal with a degree of accuracy well within the error bounds of present day satellite techniques.
An estimation technique was developed to extrapolate tidal amplitudes and phases over entire ocean basins using existing gauge data and the altimetric measurements provided by satellite oceanography. The technique was previously tested. Some results obtained by using a 3 deg by 3 deg grid are presented. The functions used in the interpolation are the eigenfunctions of the velocity (Proudman functions) which are computed numerically from a knowledge of the basin's bottom topography, the horizontal plan form and the necessary boundary conditions. These functions are characteristic of the particular basin. The gravitational normal modes of the basin are computed as part of the investigation; they are used to obtain the theoretical forced solutions for the tidal constituents. The latter can provide the simulated data for the testing of the method and serve as a guide in choosing the most energetic functions for the interpolation.
This paper develops a new model, using matrices, for the analysis of fault-tolerant multiprocessor systems. The relationship between processors computing useful data, the output data, and the check processors is defined in terms of matrix entries. Unlike the matrix-based models proposed previously for the analysis of digital systems, this model uses only numerical computations rather than logical operations for the analysis of a system. Algorithms to evaluate the fault detection and location capability of the system are proposed which are much less complex than the existing ones. The new model is used to analyze some fault-tolerant architectures proposed for signal-processing applications.
A fully-implicit finite-volume algorithm for two-dimensional axisymmetric flows has been coupled to a detailed hydrogen-air reaction mechanism (13 species and 33 reactions) so that supersonic combustion phenomena may be investigated. Numerical computations are compared with ballistic-range shadowgraphs of Lehr (1972) that exhibit two discontinuities caused by a blunt body as it passes through a premixed stoichiometric hydrogen-air mixture. The suitability of the numerical procedure for simulating these double-front flows is shown. The requirements for the physical formulation and the numerical modeling of these flowfields are discussed. Finally, the sensitivity of these external flowfields to changes in certain key reaction rate constants is examined.
Time-dependent evolutions of the profile of the free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been studied. Numerical computations have been carried out with the following situations: (1) linear functions of spin-up and spin-down in low- and microgravity environments, (2) linear functions of increasing and decreasing gravity environments at high- and low-rotating cylinder speeds, and (3) step functions of spin-up and spin-down in a low-gravity environment.
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science during the period October 1, 1983 through March 31, 1984 is summarized.
The proposed use of a Cargo Transport Vehicle (CTV) to carry hardware to the Space Station Freedom (SSF) during the construction phase of the SSF project requires remote maneuvering of the CTV. The CTV is not a manned vehicle. Obtaining the relative positions of the CTV and SSF for remote auto-rendezvous and capture (AR&C) scenarios will rely heavily on the Global Positioning System (GPS). The GPS system is expected to guide the CTV up to a distance of 100 to 300 meters from the SSF. At some point within this range, an optical docking system will take over the remote guidance for capture. During any remote guidance by GPS it is possible that significant multipath signals may be caused by large objects in the vicinity of the module being remotely guided. This could alter the position obtained by the GPS system from the actual position. Due to the nature of the GPS signals, it has been estimated that if the difference in distance between the Line of Sight (LOS) path and the multipath is greater than 300 meters, the GPS system is capable of discriminating between the direct signal and the reflected (or multipath) signal. However, if the path difference is less than 300 meters, one must be concerned. This report details the work accomplished by the Electromagnetic Simulations Laboratory at Marquette University over the period December 1993 to May 1995. This work is an investigation of the strength and phase of a multipath signal arriving at the CTV relative to the direct or line of sight (LOS) signal. The signal originates at a GPS satellite in half geo-stationary orbit and takes two paths to the CTV: (1) the direct or LOS path from the GPS satellite to the CTV; and (2) a scattered path from the GPS satellite to the SSF module and then to the CTV. The scattering from a cylinder has been computed using the physical optics approximation for the current. No other approximations or assumptions have been made including no assumptions regarding the far field or Fresnel field approximations. The integrations required to obtain the scattered field have been computed numerically using an N dimensional Romberg integration. The total scattered electric field is then projected onto the RCP component in the direction of propagation only. The direct or line of sight signal is then used to compute the relative strength and phase of the scattered field. The trajectory of the CTV has been parameterized into 4,214 points that are calculated for each of the geometries investigated. The motion of the CTV between points is small enough for the magnitude data (dB down from direct signal) to appear very smooth; however, because of the distances and wavelengths involved, the phase of the scattered field relative to the direct signal varies very rapidly.
Since its inception, numerically controlled (NC) machining methods have been used throughout the aerospace industry to mill, drill, and turn complex shapes by sequentially stepping through motion programs. However, the recent demand for more precision, faster feeds, exotic sensors, and branching execution have existing computer numerical control (CNC) and distributed numerical control (DNC) systems running at maximum controller capacity. Typical disadvantages of current CNC's include fixed memory capacities, limited communication ports, and the use of multiple control languages. The need to tailor CNC's to meet specific applications, whether it be expanded memory, additional communications, or integrated vision, often requires replacing the original controller supplied with the commercial machine tool with a more powerful and capable system. This paper briefly describes the process and equipment requirements for new controllers and their evolutionary implementation in an aerospace environment. The process of controller retrofit with currently available machines is examined, along with several case studies and their computational and architectural implications.
The research project has been a computational study of computational aeroacoustics algorithms and numerical simulations of the flow and noise of supersonic jets. During this study a new method for the implementation of solid wall boundary conditions for complex geometries in three dimensions has been developed. In addition, a detailed study of the simulation of the flow in and noise from supersonic circular and rectangular jets has been conducted. Extensive comparisons have been made with experimental measurements. A summary of the results of the research program are attached as the main body of this report in the form of two publications. Also, the report lists the names of the students who were supported by this grant, their degrees, and the titles of their dissertations. In addition, a list of presentations and publications made by the Principal Investigators and the research students is also included.
The reduction of the O(cu epsilon) integro differential equations to ordinary differential equations using a set of orthogonal functions is described. Attention was focused on the hover flight condition. The set of Galerkin integrals that appear in the reduced equations was evaluated by making use of nonrotating beam modes. Although a large amount of computer time was needed to accomplish this task, the Galerkin integrals so evaluated were stored on tape on a permanent basis. Several of the coefficients were also obtained in closed form in order to check the accuracy of the numerical computations. The equilibrium solution to the set of 3n equations obtained was determined as the solution to a minimization problem.
The report presents the results of direct numerical simulations of chemically reacting turbulent mixing layers. The work consists of two parts: (1) the development and testing of a spectral numerical computer code that treats the diffusion reaction equations; and (2) the simulation of a series of cases of chemical reactions occurring on mixing layers. The reaction considered is a binary, irreversible reaction with no heat release. The reacting species are nonpremixed. The results of the numerical tests indicate that the high accuracy of the spectral methods observed for rigid body rotation are also obtained when diffusion, reaction, and more complex flows are considered. In the simulations, the effects of vortex rollup and smaller scale turbulence on the overall reaction rates are investigated. The simulation results are found to be in approximate agreement with similarity theory. Comparisons of simulation results with certain modeling hypotheses indicate limitations in these hypotheses. The nondimensional product thickness computed from the simulations is compared with laboratory values and is found to be in reasonable agreement, especially since there are no adjustable constants in the method.
A diamond turning process has made possible a significant advance in the art of whispering-gallery-mode (WGM) optical resonators. By use of this process, it is possible to fashion crystalline materials into WGM resonators that have ultrahigh resonance quality factors (high Q values), are compact (ranging in size from millimeters down to tens of microns), and support single electromagnetic modes. This development combines and extends the developments reported in "Few- Mode Whispering-Gallery-Mode Resonators" (NPO-41256), NASA Tech Briefs, Vol. 30, No. 1 (January 2006), page 16a and "Fabrication of Submillimeter Axisymmetric Optical Components" (NPO-42056), NASA Tech Briefs, Vol. 31, No. 5 (May 2007), page 10a. To recapitulate from the first cited prior article: A WGM resonator of this special type consists of a rod, made of a suitable transparent material, from which protrudes a thin circumferential belt of the same material. The belt is integral with the rest of the rod and acts as a circumferential waveguide. If the depth and width of the belt are made appropriately small, then the belt acts as though it were the core of a single-mode optical fiber: the belt and the rod material adjacent to it support a single, circumferentially propagating mode or family of modes. To recapitulate from the second cited prior article: A major step in the fabrication of a WGM resonator of this special type is diamond turning or computer numerically controlled machining of a rod of a suitable transparent crystalline material on an ultrahigh-precision lathe. During the rotation of a spindle in which the rod is mounted, a diamond tool is used to cut the rod. A computer program is used to control stepping motors that move the diamond tool, thereby controlling the shape cut by the tool. Because the shape can be controlled via software, it is possible to choose a shape designed to optimize a resonator spectrum, including, if desired, to limit the resonator to supporting a single mode. After diamond turning, a resonator can be polished to increase its Q. By virtue of its largely automated, computer-controlled nature, the process is suitable for mass production of nominally identical single-mode WGM resonators. In a demonstration of the capabilities afforded by this development, a number of WGM resonators of various designs were fabricated side by side on the surface of a single CaF2 rod (see figure).
In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.
The study presents one method of mathematically modeling the effects of gravity-induced free convection upon the melting phenomena of a finite paraffin slab. The theoretical model is based on the numerical computer solution of the solid phase and liquid phase energy equations, coupled with an imposed ideal-viscous flow approximation. An implicit alternating-direction technique is used as the finite-difference approximation for the basic energy equations in the numerical solution. The theoretical predictions are compared to experimental data from an annular test cell, in which n-octadecane, C18H38, was used as the test material. The results show that the model is a good first approximation to the solution of solid-liquid phase change involving gravity-induced free convection.