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Third-order nonlinear processes in isotropic media have been successfully used for tripling the efficiency of high-power laser radiation for the production of tunable and fixed-frequency coherent vacuum UV radiation and for up-conversion of IR radiation. The effects of focusing on two processes of this type are studied theoretically and experimentally.
Rayleigh-Ritz and modified Rayleigh-Ritz procedures are used to construct approximate solutions for the response of a thick-walled sphere to uniform pressure loads and an arbitrary radial temperature distribution. The thermoelastic properties of the sphere are assumed to be transversely isotropic and nonhomogeneous; variations in the elastic stiffness and thermal expansion coefficients are taken to be an arbitrary function of the radial coordinate and temperature. Numerical examples are presented which illustrate the effect of the temperature-dependence upon the thermal stress field. A comparison of the approximate solutions with a finite element analysis indicates that Ritz methods offer a simple, efficient, and relatively accurate approach to the problem.
A research program is described which was devised to determine experimentally the elastic properties in tension and bending of quasi-isotropic laminates made from high-modulus graphite fiber and epoxy. Four laminate configurations were investigated, and determinations were made of the tensile modulus, Poisson's ratio, bending stiffness, fracture strength, and fracture strain. The measured properties are compared with those predicted by laminate theory, reasons for scatter in the experimental data are discussed, and the effect of fiber misalignment on predicted elastic tensile properties is examined. The results strongly suggest that fiber misalignment in combination with variation in fiber volume content is responsible for the scatter in both elastic constants and fracture strength.
Rate distortion functions for two-dimensional homogeneous isotropic images are compared with the performance of 5 source encoders designed for such images. Both unweighted and frequency weighted mean square error distortion measures are considered. The coders considered are differential PCM (DPCM) using six previous samples in the prediction, herein called 6 pel (picutre element) DPCM; simple DPCM using single sample prediction; 6 pel DPCM followed by entropy coding; 8 x 8 discrete cosine transform coder, and 4 x 4 Hadamard transform coder. Other transform coders were studied and found to have about the same performance as the two transform coders above. With the mean square error distortion measure DPCM with entropy coding performed best. The relative performance of the coders changes slightly when the distortion measure is frequency weighted mean square error. The performance of all the coders was separated by only about 4 dB.
This paper presents results from a comprehensive investigation of large-eddy simulations of homogeneous isotropic turbulence. Calculations have been made using grid meshes, a number of flowfield filters, and two simple subgrid scale turbulence models. Particular attention has been paid to the degree of isotropy and the ability of the approach to predict higher-order statistical quantities (skewness and flatness). Directions for needed improvement in the simulation approach are indicated, and a plea is made to experimenters to process their data in a way which will facilitate comparison with large eddy simulations.
The energetic isotropic turbulence generated by a waterfall of low head was found to be developed in part through the unstable two-phase flow of entrained air bubbles. The resulting turbulent field had a turbulent Reynolds number in excess of 20,000 and maintained a self-similar structure throughout the decay period studied. The present study may provide some insight into the structure of turbulence produced by breaking waves over the ocean.
The problem of decaying isotropic turbulence has been studied using a Wiener-Hermite expansion with a renormalized time-dependent base. The theory is largely deductive and uses no modeling approximations. It has been found that many properties of large-Reynolds-number turbulence can be calculated (at least for moderate time) using the moving-base expansion alone. Such properties found are the spectrum shape in the dissipation range, the Kolmogorov constant, and the energy cascade in the inertial subrange. Furthermore, by using a renormalization scheme, it is possible to extend the calculation to larger times and to initial conditions significantly different from the equilibrium form. If the initial spectrum is the Kolmogorov spectrum perturbed with a spike or dip in the inertial subrange, the process proceeds to eliminate the perturbation and relax to the preferred spectrum shape. The turbulence decays with the proper dissipation rate, and several other properties are found to agree with measured data. The theory is also used to calculate the energy transfer and the flatness factor of turbulence.
Spatial fluctuations in the surface brightness of the extragalactic hard X-ray sky that are characteristic of distant unresolved discrete sources as well as the possible clumpiness of a hot universal plasma are being studied with the HEAO-1 A-2 experiment. The energy spectrum for this fluctuating component is directly compared to that of the isotropic background. The spectra of identified extragalactic objects recently obtained with experiments aboard both OSO-8 and HEAO-1 are used for examining the contribution of such sources to this fluctuating component of the background.
The results of a series of tests of graphite-polyimide honeycomb sandwich panels are presented. The panels were 1.22 m long, 0.508 m wide, and approximately 13.3 m thick. The face sheets were a T-300/PMR-15 fabric in a quasi-isotropic layup and were 0.279 mm thick. The core was Hexcel HRH 327-3/16 - 4.0 glass reinforced polyimide honeycomb, 12.7 mm thick. Three panels were used in the test: one was cut into smaller pieces for testing as beam, compression, and shear specimens; a second panel was used for plate bending tests; the third panel was used for in-plane stability tests. Presented are the experimental results of four point bending tests, short block compression tests, core transverse shear modulus, three point bending tests, vibration tests, plate bending tests, and panel stability tests. The results of the first three tests are used to predict the results of some of the other tests. The predictions and experimental results are compared, and the agreement is quite good.
Bignami et al (1979) have recently studied the problem of the origin of the diffuse gamma-ray isotropic radiation. They have concluded that within standard cosmology with Lambda = 0 and p = 0, BL Lacertae objects and Seyfert galaxies can account for most of the diffuse radiation if they have not evolved in time. For QSOs, an evolutionary factor is allowed by the data. From the study of radio data, however, it is known that strong evolutionary effects are expected. The discrepancy cannot be explained by changing the geometry of the universe. Contrary to the case of standard cosmology, it is found that in order to fit the diffuse gamma-ray background, the evolutionary function required is almost identical to the one previously determined from the study of the log N-log S relation.
General theoretical relationships consistent with experiments are obtained for isotropic homogeneous incompressible-fluid turbulence governed by the Navier-Stokes flow equation. A key quantity that structures the turbulence is the 'broadness' B of the probability measure over velocity fields. Both the decay law and the longitudinal correlation function for small r appear as simple functions of this quasiconstant parameter B.
An asymptotic form is derived for the longitudinal correlation function for isotropic homogeneous turbulence in an incompressible fluid governed by the Navier-Stokes equation. The result is obtained from an analysis of the algebraic-differential structure of the two-point correlation tensor contained in the complex-valued Fourier transform of the probability measure over the turbulence ensemble, which reveals that the Hopf characteristic functional (the complex-valued Fourier transform of the probability measure) satisfies the Fourier interference inequality. Consequences of the expression obtained, in which the correlation function is a positive definite function of the inverse cube of the spatial coordinate as it approaches infinity, are shown to include the nonexistence of the Loitsianskii invariant, and the solution is shown to be consistent with empirical formulas.
In order to calculate the velocity and scalar fields, the three dimensional, time-dependent equations of motion and the diffusion equation were solved numerically. The following cases were treated: isotropic, homogeneous turbulence with decay of a passive scalar; and homogeneous turbulent shear flow with a passive scalar whose mean varies linearly in the spanwise direction. The solutions were obtained at relatively low Reynolds numbers so that all of the turbulent scales could be resolved without modeling. Turbulent statistics such as integral length scales, Taylor microscales, Kolmogorov length scale, one- and two-point correlations of velocity-velocity and velocity-scalar, turbulent Prandtl/Schmidt number, r.m.s. values of velocities, the scalar quantity and pressure, skewness, decay rates, and decay exponents were calculated. The results are compared with the available expermental results, and good agreement is obtained.
Sixteen ply, quasi-isotropic laminates of Celanese Celion 6000/PMR-15 and Celion 6000/LARC-160 with a fiber orientation of (0/45/90/-45) sub 2S were evaluated. Tensile and open hole specimens were tested at room temperature to establish laminate tensile strength and net tensile strength at an unloaded bolt hole. Double lap joint specimens with a single 4.83-mm (0.19 in.) diameter bolt torqued to 1.7 N-m (15 lbf-in.) were tested in tension at temperatures of 116 K (-250F), 297 K (75F), and 589 K (600F). The joint ratios of w/d (specimen width to hole diameter) and e/d (edge distance to hole diameter) were varied from 4 to 6 and from 2 to 4, respectively. The effect of joint geometry and temperature on failure mode and joint stresses are shown. Joint stresses calculated at maximum load for each joint geometry and test temperature are reported. Joint strength in net tension, bearing, and shear out at 116 K (-250F), 297 K (75F), and 589 K (600F) are given for the Celion 6000/PMR-15 and Celion 6000/LARC-160 laminates.
Consistent with the observed t to the -n decay laws for isotropic homogeneous turbulence and the form of the longitudinal correlation function f(r, t) for small r, the Hopf Phi equation is shown to be satisfied approximately by an asymptotic power series in t to the -n. This solution features a self-similar universal equilibrium functional which manifests Kolmogoroff-type scaling.
Observations of the August 15, 1980, Uranus occultation of KM 12, obtained from Cerro Tololo InterAmerican Observatory, European Southern Observatory, and Cerro Las Campanas Observatory, are used to compare the atmospheric structure at points separated by approximately 140 km along the planetary limb. The results reveal striking, but by no means perfect correlation of the light curves, ruling out isotropic turbulence as the cause of the light curve spikes. The atmosphere is strongly layered, and any acceptable turbulence model must accommodate the axial ratios of greater than about 60 which are observed. The mean temperature of the atmosphere is 150 plus or minus 15 K for the region near number density 10 to the 14th per cu cm. Derived temperature variations of vertical scale approximately 130 km and amplitude plus or minus 5 K are in agreement for all stations, and correlated spikes correspond to low-amplitude temperature variations with a vertical scale of several kilometers.
The reflection of electromagnetic waves at a plane boundary between isotropic and biaxial media has been investigated using the kDB approach. The general case has been considered in which the principal dielectric axes of the biaxial medium are oriented at an arbitrary angle to the normal of the plane boundary. In general, two characteristic waves propagate in the biaxial medium, leading to coupling of vertical and horizontal polarizations in the reflected waves. Some special cases are illustrated. The results have applications to problems in remote sensing and integrated optics.
A pulsar and the earth may be thought of as end masses of a free-mass gravitational wave antenna in which the relative motion of the masses is monitored by observing the Doppler shift of the pulse arrival times. Using timing residuals from PSR 1133 + 16, 1237 + 25, 1604-00, and 2045-16, an upper limit to the spectrum of the isotropic gravitational radiation background has been derived in the frequency band 4 x 10 to the -9th to 10 to the -7th Hz. This limit is found to be S(E) = 10 to the 21st f-cubed ergs/cu cm Hz, where S(E) is the energy density spectrum and f is the frequency in Hz. This would limit the energy density at frequencies below 10 to the -8th Hz to be 0.00014 times the critical density.