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Statistical distribution of first occurrence and recurrence of crossing of given level in continuous random process determined, using approximate forms and exponential distribution
Mutual coupling between rectangular apertures in a finite antenna array, in an infinite ground plane, is analyzed using the vector potential approach. The method of moments is used to solve the equations that result from setting the tangential magnetic fields across each aperture equal. The approximation uses a set of vector potential model functions to solve for equivalent magnetic currents. A computer program was written to carry out this analysis and the resulting currents were used to determine the co- and cross-polarized far zone radiation patterns. Numerical results for various arrays using several modes in the approximation are presented. Results for one and two aperture arrays are compared against published data to check on the agreement of this model with previous work. Computer derived results are also compared against experimental results to test the accuracy of the model. These tests of the accuracy of the program showed that it yields valid data.
Following spaceflight, changes in renal function of humans have been suggested. To assess the effects of readaptation on renal function, urine was collected from male rats ( approximately 245 g) over a 2-wk period following a 14-day spaceflight. Rats were assigned to three groups: flight animals (n = 6), flight controls (n = 6) housed in the flight cages on the ground, and vivarium controls (n = 5) housed in standard shoe box cages. Animals were placed into individual metabolic cages for urine collection. Urine output was significantly increased for 3 days following flight. Excretion rates of Na+ and K+ were increased, resulting in an increased osmotic excretion rate. Creatinine excretion rate increased over the first two postflight days. Glomerular filtration rate increased immediately following spaceflight without changes in plasma creatinine, Na+, K+, or osmolality. Increased excretion of solute was thus the result of increased delivery and a decreased percent reabsorption of the filtered load. Osmolal clearance was increased immediately postflight while free water clearance was decreased. In growing rats, the diuresis after short-duration spaceflight is the result of an increase in solute excretion with an accompanying reduction in free water clearance.
New improved curve fits for the thermodynamic properties of equilibrium air were developed. The curve fits are for p = p(e,rho), a = a(e,rho), T = T(e,rho), s = s(e,rho), T = T(p,rho), h = h(p,rho), rho = rho(p,s), e = e(p,s) and a = a(p,s). These curve fits can be readily incorporated into new or existing Computational Fluid Dynamics (CFD) codes if real-gas effects are desired. The curve fits were constructed using Grabau-type transition functions to model the thermodynamic surfaces in a piecewise manner. The accuracies and continuity of these curve fits are substantially improved over those of previous curve fits appearing in NASA CR-2470. These improvements were due to the incorporation of a small number of additional terms in the approximating polynomials and careful choices of the transition functions. The ranges of validity of the new curve fits are temperatures up to 25,000 K and densities from 10 to the minus 7th to 100 amagats (rho/rho sub 0).
The scattering of a plane wave obliquely incident on a half space of densely distributed spherical dielectric scatterers is studied. The quasi-crystalline approximation is applied to truncate the hierarchy of multiple scattering equations, and the Percus-Yevick and the Verlet-Weis results are used to represent the pair distribution function. The coherent reflected wave is studied with these approximations. The incoherent scattered wave is calculated with the distorted Born approximation. In the low-frequency limit, closed-form expressions are obtained for the effective propagation constants, the coherent reflected wave, and the bistatic scattering coeficients. Results at higher frequencies are calculated numerically. The advantage of the present approach is that, in the low-frequency limit, it reproduces the effects of specular reflection, Fresnel reflection coefficient, Brewster angle, and Clausius-Mosotti relation. In addition to the classical results, the bistatic scattering coefficients are also calculated. The theory is also applied to match backscattering data from dry snow at microwave frequencies.
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
A method for computing the far-field adjoint Green's function of the generalized acoustic analogy equations under a locally parallel mean flow approximation is presented. The method is based on expanding the mean-flow-dependent coefficients in the governing equation and the scalar Green's function in truncated Fourier series in the azimuthal direction and a finite difference approximation in the radial direction in circular cylindrical coordinates. The combined spectral/finite difference method yields a highly banded system of algebraic equations that can be efficiently solved using a standard sparse system solver. The method is applied to test cases, with mean flow specified by analytical functions, corresponding to two noise reduction concepts of current interest: the offset jet and the fluid shield. Sample results for the Green's function are given for these two test cases and recommendations made as to the use of the method as part of a RANS-based jet noise prediction code.
Elliptic orbits are substituted for circular orbits in the first approximation, in an analysis of the common retrograde motion of Jupiter's satellites. A modification of the de Sitter theory, made possible by extended observations of the satellites, is presented with attention to that aspect of the theory which eliminates small divisors at all stages of the solution. The convergence problem is circumvented by use of Poincare's canonical relative coordinates. In addition, modified Delaunay variables and their associated Poincare variables are applied to the disturbing function, which is expanded by means of generalized Newcomb operators.
Electronic charge density for ground state of helium as function of nuclear charge
Runge-Kutta fourth order formula used to obtain approximate solution to differential equations
Approximative solution for tunnel diode switching delay function
Approximate optimal atmospheric entry trajectories maximizing terminal function of velocity, heading angle, flight path angle, and altitude
Microphase separation in homopolymer-block copolymer mixtures as function of composition, molecular weight and interaction parameters
Reentry glider approximate optimal atmospheric entry trajectories for maximizing function of terminal velocity, altitude, flight path and heading angle under terminal nonlinear constraints
Heisenberg ferromagnet magnetic and thermodynamic properties in random phase approximation, determining magnetization and susceptibility with Green function theory
In the investigation, the filtering problem is considered in the continuous time domain. The postulated simple suboptimal nonlinear filter structure closely parallels the structure of the Kalman-Bucy optimal linear filter algorithm. Two filter performance evaluation methods are developed based on the Kolmogorov equations for the transition density of Markov processes. The expansions in the approximations for the nonlinear system and observation functions are in effect carried out up to second-order terms in both methods. The description of the filter's performance is sought in terms of second-order statistics in both methods.
Simultaneous observations of low energy electrons in the plasma sheet and in the auroral zone were analyzed. Data from the MIT plasma experiment on the OGO-3 satellite and from the Lockheed experiment on the OV1-18 satellite were processed and compared. The OV1-18 carried thirteen magnetic electron spectrometers designed to measure the intensity, angular, and energy distributions of the auroral electrons and protons in the energy range below 50 keV. Two computer programs were developed for reduction of the OV1-18 data. One program computed the various plasma properties at one second intervals as a function of Universal Time and pitch angle; the other program produced survey plots showing the outputs of the various detectors on the satellite as a function of time on a scale of approximately 100 seconds per cm. The OV1-18 data exhibit the high degree of variability associated with substorm controlled phenomena.
An approach is developed to the application of the perturbation method for the solution of problems with essential external nonlinearities, based on identification in the boundary condition of a small nonlinear complex which is considered a perturbing function. The solutions obtained in the first approximation with error of 1 to 2% in calculating the unsteady temperature fields are then used to determine the temperature stresses and deformations in solid bodies of classical form.