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Combat games are formulated as zero-sum differential games with unilateral event constraints. An interior penalty function approach is employed to approximate optimal strategies for the players. The method is very attractive computationally and possesses suitable approximation and convergence properties.
Properly combining optical design with 3-by-3 element mask reduces number of required computations by factor of as much as 100. Spatial and spatial-frequency responses obtained in system of combination of optical design and signal-processing algorithm. Closely approximate difference-of-Gaussian-function response.
The problem of calculating the stability of steady state solutions of differential equations is addressed. Leading eigenvalues of large matrices that arise from discretization are calculated, and an efficient multigrid method for solving these problems is presented. The resulting grid functions are used as initial approximations for appropriate eigenvalue problems. The method employs local relaxation on all levels together with a global change on the coarsest level only, which is designed to separate the different eigenfunctions as well as to update their corresponding eigenvalues. Coarsening is done using the FAS formulation in a nonstandard way in which the right-hand side of the coarse grid equations involves unknown parameters to be solved on the coarse grid. This leads to a new multigrid method for calculating the eigenvalues of symmetric problems. Numerical experiments with a model problem are presented which demonstrate the effectiveness of the method.
A new, near-optimal feedback control technique is introduced that is shown to provide excellent vibration attenuation for those distributed parameter systems that are often encountered in the areas of aeroservoelasticity and large space systems. The technique relies on a novel solution methodology for the classical optimal control problem. Specifically, the quadratic regulator control problem for a flexible vibrating structure is first cast in a weak functional form that admits an approximate solution. The necessary conditions (first-order) are then solved via a time finite-element method. The procedure produces a low dimensional, algebraic parameterization of the optimal control problem that provides a rigorous basis for a discrete controller with a first-order like hold output. Simulation has shown that the algorithm can successfully control a wide variety of plant forms including multi-input/multi-output systems and systems exhibiting significant nonlinearities. In order to firmly establish the efficacy of the algorithm, a laboratory control experiment was implemented to provide planar (bending) vibration attenuation of a highly flexible beam (with a first clamped-free mode of approximately 0.5 Hz).
The extent to which the properties of the waves observed at comet Halley during the Giotto encounter can be understood within the context of linearized Vlasov theory is investigated. In the region that is magnetically connected to the comet, fluctuations in the plasma frame of reference are detected near 4 and 10 mHz, close to the water cyclotron frequency, as well as at 20-60 mHz, which is well above the water cyclotron frequency. Using a variety of approximations for the ion distribution function, it is shown that waves having properties similar to those observed can then be generated with appropriate choices of plasma parameters. In the region that is magnetically disconnected from the comet, distinct peaks are observed in the magnetic power spectrum at 7, 21, 29, and 35 mHz, with a hint of a peak at 14 mHz.
Traditional experimental modal testing methods are used to determine the damping properties of a Euler-Bernoulli beam with offset inertial tip mass. Both viscous and strain rate damping models are considered in bending and in torsion. A partial differential equation model of the coupled system is used. Eigenfunctions are derived for the coupled system by using a Green's function approach to derive the approximate uncoupled eigenfunctions. These eigenfunctions are used in a decoupled fashion with experimental modal data to estimate the damping parameters of the coupled system. The experimental modal data were obtained from both free and impulse responses using a combined translational and rotational accelerometer.
The authors present the design of an optimal control system for the Space Station Freedom's Solar Dynamic Fine Pointing and Tracking (SDFPT) module. A very large state model of six rigid body modes and 272 flexible modes is used in conjunction with classical LQG optimal control to produce a full-order controller which satisfies the requirements. The results obtained are compared with those of a classically designed PID (proportional plus integral plus derivative) controller that was implemented for a six-rigid-body-mode forty-flexible-mode model. A major difficulty with designing LQG controllers for large models is solving the Riccati equation that arises from the optimal formulation. A Riccati solver based on a Pade approximation to the matrix sign function is used. A symmetric version of this algorithm is derived for the special class of Hamiltonion matrices, thereby yielding, for large problems, a nearly twofold speed increase over a previous algorithm.
Quantifying the vegetative surface's reflectance anisotropy was an important part of the First ISLSCP Field Experiment, as its major objectives focused on retrieval of surface parameters from satellite-derived reflectances. The explicit remote measurements for approximating the bidirectional reflectance distribution function (BRDF) of photosynthetically active radiation had not been previously undertaken. In this paper the proper expression of reflectance for BRDFs for retrieval of canopy parameters is assessed.
We show how observations of the density perturbation (scalar) spectrum and the gravitational wave (tensor) spectrum allow a reconstruction of the potential responsible for cosmological inflation. A complete functional reconstruction or a perturbative approximation about a single scale are possible; the suitability of each approach depends on the data available. Consistency equations between the scalar and tensor spectra are derived, which provide a powerful signal of inflation.
A new method for the solution of non-linear mathematical programming problems in the field of structural optimization is presented. It is an iterative scheme which for each iteration refines the approximation of objective and constraint functions by accumulating the function values of previously visited design points. The method has proven to be competitive for a number of well-known examples of which one is presented here. Furthermore because of the accumulation strategy, the method produces convergence even when the sensitivity analysis is inaccurate.
In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.
The ascent of the human into high altitudes required a 2-D life support system that supplied: oxygen, and heat. At lower altitudes, increased oxygen concentration in the inhaled gases was useful, but at higher altitudes for longer durations, this 'clever' life support approach was no longer adequate--physiologic requirements had to provide a natural pressure-based environment. In space, the life support system requires a third dimension, gravity. Although substituting for gravity has been successful on a limited number of physiologic functions for short-duration stays in space, long durations will require the effects of the real thing for critical physiologic functions. It has been known for over a hundred years that the forces of acceleration (G) and gravity are equivalent. Therefore, gravitational stimulation in space can be achieved with centrifugation. However, for this stimulation to be effective, the dosage of G required to maintain normal physiologic function must be determined. An approximation of this dosage of G for the human can be determined with 3-day bed-rest studies including periodic centrifuge exposure. Recent research on this topic is reviewed.
The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed, which aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, we investigate the use of Bernstein-Szego weights.
From a compilation of experimental data on the mutagenic effects of heavy ions in bacteria, main conclusions have been drawn as follows: (1) The mutagenic efficacy of heavy ions in bacteria depends on physical and biological variables. Physical variables are the radiation dose, energy and charge of the ion; the biological variables are the bacterial strain, the repair genotype of bacteria, and the endpoint investigated (type of mutation, induction of enzymes related to mutagenesis); (2) The responses on dose or fluence are mainly linear or linear quadratic. The quadratic component, if found for low LET radiation, is gradually reduced with increasing LET; (3) At low values of Z and LET the cross section of mutation induction sigma m (as well as SOS response, sigma sos. and lambda phage induction, sigma lambda versus LET curves can be quite consistently described by a common function which increases up to approximately 100 keV/mu m. For higher LET values, the sigma(m) versus LET curves show the so-called 'hooks' observed also for other endpoints; (4) For light ions (Z is less than or equal to 4), the cross sections mostly decrease with increasing ion energy, which is probably related to the decrease of the specific energy departed by the ion inside the sensitive volume (cell). For ions in the range of Z = 10, sigma(m) is nearly independent on the ion energy. For heavier ions (Z is greater than or equal to 16), sigma(m) increases with the energy up to a maximum or saturation around 10 MeV/u. The increment becomes steeper with increasing atomic number of the ion. It correlates with the increasing track radius of the heavy ion; (5) The mutagenic efficiency per lethal event changes slightly with ion energy, if Z is small indicating a rough correlation between cellular lethality and mutation induction, only. For ions of higher Z this relation increases with energy, indicating a change in the 'mode' of radiation action from 'killing-prone' to 'mutation-prone'; and (6) Repair genotype substantially influences the radiation induced mutagenesis. Different mechanisms of mutation induction and/or different types of biologically significant lesions in wild type cells compared to repair deficient strains are a likely explanation.
We present results from simultaneous L- and S-Band slant-path fade measurements through trees. One circularly-polarized antenna was used at each end of the dual-frequency link to provide information on the correlation of tree shadowing at 1620 and 2500 MHz. Fades were measured laterally in the shadow region with 5 cm spacing. Fade differences between L- and S-Band had a normal distribution with low means and standard deviations from 5.2 to 7.5 dB. Spatial variations occurred with periods larger than 1-2 wavelengths. Swept measurements over 160 MHz spans showed that the stdv. of power as function of frequency increased from approximately 1-6 dB at locations with mean fades of 4 and 20 dB, respectively. At a 5 dB fade, the central 90% of fade slopes were within a range of 0.7 (1.9) dB/MHz at L-(S-) Band.
Average power effects relative to the operation of parametric oscillators and amplifiers have been calculated. Temperature gradients have been calculated for both radial and longitudinal heat extraction. In many instances, the thermal load on a parametric oscillator is higher than the thermal load on a parametric amplifier with the same pump power. Having one or both these wavelengths resonant increases the chances that a generated photon will be absorbed by the nonlinear crystal. Temperature profiles and thermal diffusion time constants have been calculated for Gaussian beams, given the heat-deposition rate. With radical heat extraction the temperature profile can be expressed in a power series or approximated by a Gaussian distribution function.
Momentum accommodation was determined experimentally for gas-surface interactions simulating in a practical way those of near-earth satellites. Throughout the ranges of gas energies and incidence angles of interest for earth-conditions, two components of force were measured by means of a vacuum microbalance to determine the normal and tangential momentum-accommodation coefficients for nitrogen ions on technical-quality aluminum surfaces. For these experimental conditions, the electrodynamics of ion neutralization near the surface indicate that results for nitrogen ions should differ relatively little from those for nitrogen molecules, which comprise the largest component of momentum flux for near-earth satellites. The experimental results indicated that both normal and tangential momentum-accommodation coefficients varied widely with energy, tending to be relatively well accommodated at the higher energies, but becoming progressively less accommodated as the energy was reduced to and below that for earth-satellite speeds. Both coefficients also varied greatly with incidence angle, the normal momentum becoming less accommodated as the incidence angle became more glancing, whereas the tangential momentum generally became more fully accommodated. For each momentum coefficient, an empirical correlation function was obtained which closely approximated the experimental results over the ranges of energy and incidence angle. Most of the observed variations of momentum accommodation with energy and incidence angle were qualitatively indicated by a calculation using a three-dimensional model that simulated the target surface by a one-dimensional attractive potential and hard sphere reflectors.
Semispan-wing models were tested at angles of attack from 0 to 180 deg at low subsonic speeds. Eight plan forms were considered, both swept and unswept with aspect ratios ranging from 2 to 6. Except for a delta-wing model of aspect ratio 2. all models had a taper ratio of 0.5 and an NACA 64AO10 airfoil section. The delta-wing model had an NACA 0005 (modified) airfoil section. With two exceptions, the models were tested both with and without a full-span trailing-edge flap deflected 25 deg. The Reynolds numbers based on the mean aerodynamic chord were between 1.5 and 2.2 million. Lift, drag, and pitching-moment coefficients are presented as functions of angle of attack. Approximate corrections for the effects of blockage were applied to the data.