Estimation of stick-fixed neutral points of airplanes
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PROPELLERS - WINDMILLING↗
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FFT Computation with Systolic Arrays, A New Architecture
The use of the Cooley-Tukey algorithm for computing the l-d FFT lends itself to a particular matrix factorization which suggests direct implementation by linearly-connected systolic arrays. Here we present a new systolic architecture that embodies this algorithm. This implementation requires a smaller number of processors and a smaller number of memory cells than other recent implementations, as well as having all the advantages of systolic arrays. For the implementation of the decimation-in-frequency case, word-serial data input allows continuous real-time operation without the need of a serial-to-parallel conversion device. No control or data stream switching is necessary. Computer simulation of this architecture was done in the context of a 1024 point DFT with a fixed point processor, and CMOS processor implementation has started.
Boriakoff, Valentin↗
Minimum time aircraft trajectories between two points in range altitude space
Calculus of variations used to determine minimum time aircraft trajectories between two fixed points in range-altitude space
TRAJECTORY ANALYSIS↗
On a class of approximate iterative processes
Investigation into approximating a solution of fixed point equations
FIXED POINT↗
Research in stability of periodic motions Quarterly progress report, 5 May - 4 Aug. 1966
Instability of periodic orbits in restricted and reduced three-body problems using mapping by fixed point method
MAPPING↗
Compressed basis GMRES on high-performance graphics processing units
Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the communication bandwidth in current computer architectures, motivating the investigation of sophisticated techniques to avoid, reduce, and/or hide the message-passing costs (in distributed platforms) and the memory accesses (in all architectures). This article leverages Ginkgo’s memory accessor in order to integrate a communication-reduction strategy into the (Krylov) GMRES solver that decouples the storage format (i.e., the data representation in memory) of the orthogonal basis from the arithmetic precision that is employed during the operations with that basis. Given that the execution time of the GMRES solver is largely determined by the memory accesses, the cost of the datatype transforms can be mostly hidden, resulting in the acceleration of the iterative step via a decrease in the volume of bits being retrieved from memory. Together with the special properties of the orthonormal basis (whose elements are all bounded by 1), this paves the road toward the aggressive customization of the storage format, which includes some floating-point as well as fixed-point formats with mild impact on the convergence of the iterative process. We develop a high-performance implementation of the “compressed basis GMRES” solver in the Ginkgo sparse linear algebra library using a large set of test problems from the SuiteSparse Matrix Collection. We demonstrate robustness and performance advantages on a modern NVIDIA V100 graphics processing unit (GPU) of up to 50% over the standard GMRES solver that stores all data in IEEE double-precision.
97 MATHEMATICS AND COMPUTING↗
Effects of walking velocity on vertical head and body movements during locomotion
Trunk and head movements were characterized over a wide range of walking speeds to determine the relationship between stride length, stepping frequency, vertical head translation, pitch rotation of the head, and pitch trunk rotation as a function of gait velocity. Subjects (26-44 years old) walked on a linear treadmill at velocities of 0.6-2.2 m/s. The head and trunk were modeled as rigid bodies, and rotation and translation were determined using a video-based motion analysis system. At walking speeds up to 1.2 m/s there was little head pitch movement in space, and the head pitch relative to the trunk was compensatory for trunk pitch. As walking velocity increased, trunk pitch remained approximately invariant, but a significant head translation developed. This head translation induced compensatory head pitch in space, which tended to point the head at a fixed point in front of the subject that remained approximately invariant with regard to walking speed. The predominant frequency of head translation and rotation was restricted to a narrow range from 1.4 Hz at 0.6 m/s to 2.5 Hz at 2.2 m/s. Within the range of 0.8-1.8 m/s, subjects tended to increase their stride length rather than step frequency to walk faster, maintaining the predominant frequency of head movement at close to 2.0 Hz. At walking speeds above 1.2 m/s, head pitch in space was highly coherent with, and compensatory for, vertical head translation. In the range 1.2-1.8 m/s, the power spectrum of vertical head translation was the most highly tuned, and the relationship between walking speed and head and trunk movements was the most linear. We define this as an optimal range of walking velocity with regard to head-trunk coordination. The coordination of head and trunk movement was less coherent at walking velocities below 1.2 m/s and above 1.8 m/s. These results suggest that two mechanisms are utilized to maintain a stable head fixation distance over the optimal range of walking velocities. The relative contribution of each mechanism to head orientation depends on the frequency of head movement and consequently on walking velocity. From consideration of the frequency characteristics of the compensatory head pitch, we infer that compensatory head pitch movements may be produced predominantly by the angular vestibulocollic reflex (aVCR) at low walking speeds and by the linear vestibulocollic reflex (1VCR) at the higher speeds.
NASA Discipline Neuroscience↗
Interactive Visualization of High-Dimensional Petascale Ocean Data
We describe an application for interactive visualization of 5 petabytes of time-varying multivariate data from a high-resolution global ocean circulation model. The input data are 10311 hourly (ocean time) time steps of various 2D and 3D fields from a 22-billion point 1/48- degree “lat-lon cap” configuration of the MIT General Circulation Model (MITgcm). We map the global horizontal model domain onto our 128-screen (8x16) tiled display wall to produce a canonical tiling with approximately one MITgcm grid point per display pixel, and using this tiling we encode the entire time series for multiple native and computed scalar quantities at a collection of ocean depths. We reduce disk bandwidth requirements by converting the model’s floating point data to 16-bit fixed point values, and compressing those values with a lossless video encoder, which together allow synchronized playback at 24 time steps per second across all 128 displays. The application allows dynamic assignment of any two encoded tiles to any display, and has multiple interfaces for quickly specifying various orderly arrangements of tiles. All subsequent rendering is done on the fly, with run time control of colormaps, transfer functions, histogram equalization, and labeling. The two data streams on each screen can be rendered independently and combined in various ways, including blending, differencing, horizontal/ vertical wipes, and checkerboarding. The two data streams on any screen can optionally be displayed as a scatterplot in their joint attribute space. All scatterplots and map-view plots from the same x/y location and depth are linked so they all show the current brushable selection. Ocean scientists have used the system, and have found previously unidentified features in the data.
Interactive↗
On Lipschitz structures.
Uniform structure for Lipschitz condition on functions between sets, extensions to nonmetric spaces and fixed point theorem for uniform spaces
LIPSCHITZ CONDITION↗
On a class of approximate iterative processes.
Combination into unified setting of various results for approximate solution of fixed point equation, using iterative process
APPROXIMATION METHOD↗
Bounded state space
This investigation is divided functionally into three different areas: (1) study of bounded state space, (2) nonlinear smoothing theory, and (3) system identification. (1) Study of bounded state space: necessary and sufficient conditions for an optimal control are obtained for a bounded state space optimal control problem. The difficulty of determining the so-called jump conditions is eliminated; however, the problem of determining the points where the response either enters or leaves the boundary still remains unsolved. (2) Nonlinear smoothing theory: nonlinear fixed-interval, fixed-point and fixed-lag smoothing of a random signal generated by a stochastic differential equation are investigated. Results on the asymptotic stability of a linear constant-parameter fixed-interval smoothing filter are obtained. (3) System identification: a particular stochastic modelling problem is solved. An Ito stochastic integral equation is used to mathematically model a black box having multiple inputs and multiple outputs. A new method for identifying system parameters is presented.
Eyman, E. D.↗
Analysis of Vector Particle-In-Cell (VPIC) memory usage optimizations on cutting-edge computer architectures
Vector Particle-In-Cell (VPIC) is one of the fastest plasma simulation codes in the world, with particle numbers ranging from one trillion on the first petascale system, Roadrunner, to ten trillion particles on the more recent Blue Waters supercomputer. As supercomputers continue to grow rapidly in size, so too does the gap between computing capability and memory capability. Current memory systems limit VPIC simulations greatly as the maximum number of particles that can be simulated directly depends on the available memory. In this study, we present a suite of VPIC memory optimizations (i.e., particle weight, half-precision, and fixed-point optimizations) that enable a significant increase in the number of particles in VPIC simulations. Here, we assess the optimizations’ impact on memory and runtime performance for a suite of cutting-edge computer architectures such has the NVIDIA V100 GPU, the IBM Power9, and the Fujitsu A64FX architectures. Our optimizations enable a 31.25% reduction in memory usage and up to 40% increase in the number of particles. This paper extends our work on developing particle storage format optimizations Tan et al.
97 MATHEMATICS AND COMPUTING↗
Experimental determination of the particle motions associated with the low order acoustic modes in enclosures
A procedure for experimentally determining, in terms of the particle motions, the shapes of the low order acoustic modes in enclosures is described. The procedure is based on finding differentiable functions which approximate the shape functions of the low order acoustic modes when these modes are defined in terms of the acoustic pressure. The differentiable approximating functions are formed from polynomials which are fitted by a least squares procedure to experimentally determined values which define the shapes of the low order acoustic modes in terms of the acoustic pressure. These experimentally determined values are found by a conventional technique in which the transfer functions, which relate the acoustic pressures at an array of points in the enclosure to the volume velocity of a fixed point source, are measured. The gradient of the function which approximates the shape of a particular mode in terms of the acoustic pressure is evaluated to give the mode shape in terms of the particle motion. The procedure was tested by using it to experimentally determine the shapes of the low order acoustic modes in a small rectangular enclosure.
Byrne, K. P.↗
Completing the forward kinematic calibration of open loop manipulators when single point position sensors are used
Single-point sensors can measure the position of one point fixed to a manipulator's end effector. When single-point sensors have been used for calibration, it has not been possible to calibrate the orientation of the tool. Furthermore, it can be difficult to calibrate the sensor system. Results in the literature seldom provide a complete kinematic calibration of the manipulator. Presented here is a technique that enables single-point sensors to gather sufficient information to complete kinematic calibration. In addition, the method can reduce the burden of calibrating the sensor system.
Everett, Louis J.↗
Magnetospherically reflected whistlers as a source of plasmaspheric hiss
Ray-tracing simulations and estimates of whistler wave damping show that magnetospherically reflected whistlers can persist for about 100 s in a LF band (about 1 kHz). The combined contribution from whistler rays produced by a single lightning flash but entering the magnetosphere at different points form a continuous hisslike signal, as observed at a fixed point. Estimates indicate that the total whistler wave energy input into the magnetosphere from lightning discharges may maintain experimentally observed levels of magnetospheric hiss.
Draganov, A. B.↗
Orbital Operations for Phobos and Deimos Exploration
One of the deep-space human exploration activities proposed for the post-Shuttle era is a mission to one of the moons of Mars, Phobos or Deimos. There are several options available to the mission architect for operations around these bodies. These options include distant retrograde orbits (DROs), Lagrange-point orbits such as halos and Lyapunov orbits, and fixed-point stationkeeping or "hovering." These three orbit options are discussed in the context of the idealized circular restricted three body problem, full-dynamics propagations, and a concept of operations. The discussion is focused on Phobos, but all results hold for Deimos
distant retrograde orbits (DROs)↗
Nuclear Materials Process Modeling at the Y-12 National Security Complex
The Y-12 National Security Complex (Y-12) has implemented process modeling for various accountable nuclear materials operations that are performed throughout the plant. Using a discrete, event-based dynamic simulation program, key nuclear material streams are modeled, allowing Y-12 to effectively manage numerous points of interest within the plant’s production operations. Integration of the various material processes into a single, interdependent supply and demand model is one of the ongoing focuses within Y-12’s process modeling effort. The primary purpose of using dynamic simulation modeling is to allow for analysis of the nuclear materials inventories and forecasted supplies based on future demands. Analysis of these inventories includes capacity evaluation, bottleneck mitigation, and assessments of individual pieces of equipment to inform future facility investment decisions and associated project schedules. Modeling of the nuclear materials processes throughout the complex also allows for incorporation of changes relevant to production capabilities such as the upcoming transition of specific operations to the new Uranium Processing Facility. Prior to implementation of process modeling, Y-12 forecasted supply and demand of accountable nuclear materials streams using Microsoft Excel. With deterministic models such as Microsoft Excel, the annual forecasts, generated within data input condition parameters, can only provide a fixed point of data. Fixed data cannot simulate integrated material streams and account for the possibility of occurrences and other changes that dynamic simulations take into consideration. Y-12’s dynamic process modeling allows integrated simulations of multiple accountable nuclear materials processes, including supply and demand forecasting and analysis, and is a coordinated effort involving many steps of verification and validation (V&V), site briefings, testing, reporting, data mining, planning, and documentation that spans various programs throughout the Y-12 complex.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Solar wind disturbances caused by solar flares - Equatorial plane
The propagation of solar wind disturbances caused by single, double and six successive flares in the dipolar and quadrupolar patterns of the interplanetary magnetic field (IMF) and the associated solar wind flow is studied. This study is based on a kinematic and empirical method developed by Hakamada and Akasofu (1982). Each flare is characterized by six parameters (such as the highest speed flow, its extent and duration). The successive IMF patterns in the equatorial plane of the heliosphere during a time span of 0.5-60 days after flares are presented for a variety of flares. The solar wind speed and IMF magnitude are given as a function of distance along a radial line fixed in space and also as a function of time at several points fixed in space (simulating approximately space probe observations). Some of the results are qualitatively compared with recent space probe observations, demonstrating fair similarity with the observed time profiles of solar wind speed variations over a wide range of both distances (0-10 AU) and time spans (60 days). The method provides a first-order construction, temporal and spatial, of flare-induced shocks and their multiple interactions with each other, as well as with the corotating interaction regions.
Akasofu, S.-I.↗