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At least 145 records · Page 8

Solution of the symmetric eigenproblem AX=lambda BX by delayed division

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity.

Thurston, G. A.↗

A Strassen-Newton algorithm for high-speed parallelizable matrix inversion

Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.

Bailey, David H.↗

Event-driven charge-coupled device design and applications therefor

An event-driven X-ray CCD imager device uses a floating-gate amplifier or other non-destructive readout device to non-destructively sense a charge level in a charge packet associated with a pixel. The output of the floating-gate amplifier is used to identify each pixel that has a charge level above a predetermined threshold. If the charge level is above a predetermined threshold the charge in the triggering charge packet and in the charge packets from neighboring pixels need to be measured accurately. A charge delay register is included in the event-driven X-ray CCD imager device to enable recovery of the charge packets from neighboring pixels for accurate measurement. When a charge packet reaches the end of the charge delay register, control logic either dumps the charge packet, or steers the charge packet to a charge FIFO to preserve it if the charge packet is determined to be a packet that needs accurate measurement. A floating-diffusion amplifier or other low-noise output stage device, which converts charge level to a voltage level with high precision, provides final measurement of the charge packets. The voltage level is eventually digitized by a high linearity ADC.

Doty, John P.↗

Shock Capturing via Limiting for High-Order Methods including Discontinuous Galerkin

High-order methods, such as discontinuous Galerkin (DG), spectral, and flux reconstruction (FR), are prone to generating unwanted oscillations near shocks and discontinuities. Conventional limiting techniques, while effective in suppressing oscillations near shocks, often compromise accuracy near extrema, where the solution is only first-order accurate. This paper introduces a novel limiting technique for these high-order schemes, aimed at effectively managing shocks while preserving accuracy. The key idea is to expand the standard monotonicity limits to provide “room” near smooth extrema, ensuring that limiting has no effect and thus preserving accuracy. Near a discontinuity, these expanded limits effectively reduce to the original monotonicity limits, suppressing oscillations. Additional motivation is drawn from a formula for the derivative of Radau polynomials, which depicts the behavior of oscillations resulting from discontinuities. This behavior leads to a simplification by applying the limits to the sum of magnitudes of all modes, linear and higher degree. Unlike typical approaches, which rely on successful detection to activate limiting, our limiter depends continuously on the data, there by avoiding potential issues if detection fails. To reduce computing time, efficient criteria for detecting smooth regions where limiting is unnecessary are presented. Combined with detection, the continuous dependence on the data is lost, but the method is more economical. A notable characteristic of the entire process is its simplicity in both concept and implementation. Numerical tests for advection and Euler equations are conducted to demonstrate the effectiveness of the proposed method.

numerical methods↗

Shock Capturing via Limiting for High-Order Methods including Discontinuous Galerkin

High-order methods, such as discontinuous Galerkin (DG), spectral, and flux reconstruction (FR), are prone to generating unwanted oscillations near shocks and discontinuities. Conventional limiting techniques, while effective in suppressing oscillations near shocks, often compromise accuracy near extrema, where the solution is only first-order accurate. This paper introduces a novel limiting technique for these high-order schemes, aimed at effectively managing shocks while preserving accuracy. The key idea is to expand the standard monotonicity limits to provide “room” near smooth extrema, ensuring that limiting has no effect and thus preserving accuracy. Near a discontinuity, these expanded limits effectively reduce to the original monotonicity limits, suppressing oscillations. Additional motivation is drawn from a formula for the derivative of Radau polynomials, which depicts the behavior of oscillations resulting from discontinuities. This behavior leads to a simplification by applying the limits to the sum of magnitudes of all modes, linear and higher degree. Unlike typical approaches, which rely on successful detection to activate limiting, our limiter depends continuously on the data, there by avoiding potential issues if detection fails. To reduce computing time, efficient criteria for detecting smooth regions where limiting is unnecessary are presented. Combined with detection, the continuous dependence on the data is lost, but the method is more economical. A notable characteristic of the entire process is its simplicity in both concept and implementation. Numerical tests for advection and Euler equations are conducted to demonstrate the effectiveness of the proposed method.

numerical methods↗

Modeling of aircraft unsteady aerodynamic characteristics. Part 1: Postulated models

A short theoretical study of aircraft aerodynamic model equations with unsteady effects is presented. The aerodynamic forces and moments are expressed in terms of indicial functions or internal state variables. The first representation leads to aircraft integro-differential equations of motion; the second preserves the state-space form of the model equations. The formulations of unsteady aerodynamics is applied in two examples. The first example deals with a one-degree-of-freedom harmonic motion about one of the aircraft body axes. In the second example, the equations for longitudinal short-period motion are developed. In these examples, only linear aerodynamic terms are considered. The indicial functions are postulated as simple exponentials and the internal state variables are governed by linear, time-invariant, first-order differential equations. It is shown that both approaches to the modeling of unsteady aerodynamics lead to identical models.

Klein, Vladislav↗

Evaluation of a Treadmill with Vibration Isolation and Stabilization (TVIS) for Use on the International Space Station

A treadmill with vibration isolation and stabilization designed for the International Space Station (ISS) was evaluated during Shuttle mission STS-81. Three crew members ran and walked on the device, which floats freely in zero gravity. For the majority of the more than 2 hours of locomotion studied, the treadmill showed peak to peak linear and angular displacements of less than 2.5 cm and 2.5 deg, respectively. Vibration transmitted to the vehicle was within the microgravity allocation limits that are defined for the ISS. Refinements to the treadmill and harness system are discussed. This approach to treadmill design offers the possibility of generating 1G-like loads on the lower extremities while preserving the microgravity environment of the ISS for structural safety and vibration free experimental conditions.

McCrory, Jean L.↗

Image processing applied to gravity and topography data covering the continental United States

The applicability of fairly standard image processing techniques to processing and analyzing large geologic data sets in addressed. Image filtering techniques were used to interpolate between gravity station locations to produce a regularly spaced data array that preserves detail in areas with good coverage, and that produces a continuous tone image rather than a contour map. Standard image processing techniques were used to digitally register and overlay topographic and gravity data, and the data were displayed in ways that emphasize subtle but pervasive structural features. The potential of the methods is illustrated through a discussion of linear structures that appear in the processed data between the midcontinent gravity high and the Appalachians.

Arvidson, R. E.↗

High resolution TVD schemes using flux limiters

Roe (1981, 1985) has utilized flux limiters to obtain second order monotonicity preserving schemes. In the present paper, the foundation for flux limiters in the formulation of first order three-point schemes are discussed, and a systematic outline is provided of the method of using flux limiters to obtain second order accurate TVD schemes. Attention is given to Phi limiters, the Van Leer limiter, the Chakravarthy-Osher limiter, the linear advection equation and square wave data, the inviscid Burger's equation, and the extension of flux limiters to irregular grids, systems of equations, and implicit calculations.

Sweby, P. K.↗

Neutral line chaos and phase space structure

Phase space structure and chaos near a neutral line are studied with numerical surface-of-section (SOS) techniques and analytic methods. Results are presented for a linear neutral line model with zero crosstail electric field. It was found that particle motion can be divided into three regimes dependening on the value of the conserved canonical momentum, Py, and the conserved Hamiltonian, h. The phase space structure, using Poincare SOS plots, is highly sensitive to bn = Bn/B0 variations, but not to h variations. It is verified that the slow motion preserves the action, Jz, as evaluated by Sonnerup (1971), when the period of the fast motion is smaller than the time scale of the slow motion. Results show that the phase space structure and particle chaos depend sensitively upon Py and bn, but are independent of h.

Burkhart, Grant R.↗

Multistep matrix integrators for real-time simulation

An explicit linear multistep matrix-integration technique is presented for vector systems of ODEs which employs the stability region placement approach to permit the time-step to be chosen independently of system eigenvalues. Closed-form solutions for the general p-step method and the case where the system matrix has zero eigenvalues are given. It is shown that system mode shapes are preserved over the integration process, and that the technique remains applicable to systems with eigenvalues at their origin without need for computing a matrix inversion.

De Abreu-Garcia, J. A.↗

Application of precomputed control laws in a reconfigurable aircraft flight control system

A self-repairing flight control system concept in which the control law is reconfigured after actuator and/or control surface damage to preserve stability and pilot command tracking is described. A key feature of the controller is reconfigurable multivariable feedback. The feedback gains are designed off-line and scheduled as a function of the aircraft control impairment status so that reconfiguration is performed simply by updating the gain schedule after detection of an impairment. A novel aspect of the gain schedule design procedure is that the schedule is calculated using a linear quadratic optimization-based simultaneous stabilization algorithm in which the scheduled gain is constrained to stabilize a collection of plant models representing the aircraft in various control failure modes. A description and numerical evaluation of a controller design for a model of a statically unstable high-performance aircraft are given.

Moerder, Daniel D.↗

Model reduction in the physical coordinate system

In the dynamics modeling of a flexible structure, finite element analysis employs reduction techniques, such as Guyan's reduction, to remove some of the insignificant physical coordinates, thus producing a dynamics model that has smaller mass and stiffness matrices. But this reduction is limited in the sense that it removes certain degrees of freedom at a node points themselves in the model. From the standpoint of linear control design, the resultant model is still too large despite the reduction. Thus, some form of the model reduction is frequently used in control design by approximating a large dynamical system with a fewer number of state variables. However, a problem arises from the placement of sensors and actuators in the reduced model, because a model usually undergoes, before being reduced, some form of coordinate transformations that do not preserve the physical meanings of the states. To correct such a problem, a method is developed that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. Then the model is converted to the state space form, and reduced again by the internal balancing method. At this point, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed, however, this reduced model is expressed by a subset of the original states.

Yae, K. Harold↗

Quasi-Linear Parameter Varying Representation of General Aircraft Dynamics Over Non-Trim Region

For applying linear parameter varying (LPV) control synthesis and analysis to a nonlinear system, it is required that a nonlinear system be represented in the form of an LPV model. In this paper, a new representation method is developed to construct an LPV model from a nonlinear mathematical model without the restriction that an operating point must be in the neighborhood of equilibrium points. An LPV model constructed by the new method preserves local stabilities of the original nonlinear system at "frozen" scheduling parameters and also represents the original nonlinear dynamics of a system over a non-trim region. An LPV model of the motion of FASER (Free-flying Aircraft for Subscale Experimental Research) is constructed by the new method.

Shin, Jong-Yeob↗

Mineralogy of Aeolian Sand in Gale Crater, Mars

Final Document is attached. Introduction: The Mars Science Laboratory Curi-osity rover landed in Gale crater in August 2012 to search for habitable enironments preserved in the rocks and sediments on the lower slopes of Aeolis Mons (i.e., Mount Sharp). Along the traverse, Curiosity encountered an active aeolian sand sheet, informally known as the Bagnold dune field. Orbital CRISM vis/near-IR data suggest that there are varying abun-dances of olivine and pyroxene across the dune field, where the barchan dunes on the edge of the dune field have stronger olivine signatures than the linear dunes.

Rampe, E. B.↗

A biased filter for linear discrete dynamic systems.

A recursive estimator, the ridge filter, was developed for the linear discrete dynamic estimation problem. Theorems were established to show that the ridge filter can be, on the average, closer to the expected value of the system state than the Kalman filter. On the other hand, Kalman filter, on the average, is closer to the instantaneous system state than the ridge filter. The ridge filter has been formulated in such a way that the computational features of the Kalman filter are preserved.

Chang, J. W.↗

Wind response characteristics of horizontal axis wind turbines

It was the objective of the work reported here, and in the companion paper 1 . A broader examination of wind turbine dynamic response to turbulence, and attempts to ascertain the features of turbulence that wind turbines are most sensitive to were made. A statistical description of the wind input including all three wind components and allowing linear wind gradients across the rotor disk, was used together with quasi-static aerodynamic theory and an elementary structural model involving only a few degrees of freedom. The idea was to keep the turbine model simple and show the benefits of this type of statistical wind representation before attempting to use a more complex turbine model. As far as possible, the analysis was kept in the simplest form, while still preserving key physical responses.

Thresher, R. W.↗

Biasing and hierarchical statistics in large-scale structure

In this paper we consider the consequences for galaxy formation of an arbitrary, effectively local biasing transformation of a hierarchical underlying matter distribution. We show that a general form of such a transformation preserves the hierarchical properties and the shape of the dispersion in the limit of small fluctuations, i.e., on large scales, although the values of the hierarchical amplitudes may change arbitrarily. We present expressions for the induced hierarchical amplitudes S(g,j) of the galaxy distribution in terms of the matter amplitudes S(j) and biasing parameters for j = 3-7. For higher order correlations, j greater than 2, restricting to a linear bias is not a consistent approximation even at very large scales. To draw any conclusions from the galaxy distribution about matter correlations of order j, properties of biasing must be specified completely to order j - 1.

Fry, J. N.↗