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NASA NTRS1985

The dispersive evolution of charged-particle bunches in random magnetic fields

Shortly after a strongly anisotropic beam of charged particles is injected along a guiding magnetic field on which is superimposed a small random conponent, the particle density can be represented by a Gaussian profile whose center moves with the coherent velocity and whose width increases with time at a rate controlled by the coefficient of dispersion. Both parameters depend upon the mean free path, which characterizes scattering by the random fields, and the focusing length, which characterizes spatial variations of the guiding field. These dependencies are known explicitly for the coherent velocity. Formulae for coefficient of dispersion are available only in the limits of very weak and very strong focusing. A new expression for coefficient of dispersion, which spans this gap, is presented.

Earl, J. A.↗

NASA NTRS1984

Non-enzymatic template-directed synthesis on RNA random copolymers - Poly(C, U) templates

Random copolymer templates containing cytosine and uracil in ratios of 3:1 and 1:1 are used to explore the optimum conditions for efficient synthesis of guanine and adenine-containing oligonucleotides. The experimental procedure is described, including the preparation of mononucleoside 5'-phospho-2-methylimidazolides and random copolymers, the template-directed oligomerization, the removal and reintroduction of mononucleotides in interrupted reactions, the determination of oligomerization efficiency, the alkaline and enzymatic hydrolysis of reaction products, and the column chromatography. Results are presented and discussed for the dependence of adenine incorporation on the formation of short oligo(G)s, optimization of incorporation efficiencies by adjusting monomer concentrations, the characterization of oligomeric product distribution, and the regiospecificity of adenine incorporation. The prebiotic significance of the results is assessed.

Joyce, G. F.↗

NASA NTRS1985

Systematic and random variations in Thematic Mapper digital radiance data

Studies are reported of the systematic and random variations in digital radiance data obtained by the Landsat-4 and Landsat-5 Thematic Mappers over an agricultural crop area which was apparently uniform and cloud-free. Systematic variations appeared to be time-dependent and bandpass-dependent. The predominant effect seemed to be random variations, which appeared to be in keeping with those expected from prior investigations. It is suggested that uncorrected variations will provide a limitation on the nonphotointerpretative analysis of images.

Duggin, M. J.↗

NASA NTRS1986

At least some errors are randomly generated (Freud was wrong)

An experiment was carried out to expose something about human error generating mechanisms. In the context of the experiment, an error was made when a subject pressed the wrong key on a computer keyboard or pressed no key at all in the time allotted. These might be considered, respectively, errors of substitution and errors of omission. Each of seven subjects saw a sequence of three digital numbers, made an easily learned binary judgement about each, and was to press the appropriate one of two keys. Each session consisted of 1,000 presentations of randomly permuted, fixed numbers broken into 10 blocks of 100. One of two keys should have been pressed within one second of the onset of each stimulus. These data were subjected to statistical analyses in order to probe the nature of the error generating mechanisms. Goodness of fit tests for a Poisson distribution for the number of errors per 50 trial interval and for an exponential distribution of the length of the intervals between errors were carried out. There is evidence for an endogenous mechanism that may best be described as a random error generator. Furthermore, an item analysis of the number of errors produced per stimulus suggests the existence of a second mechanism operating on task driven factors producing exogenous errors. Some errors, at least, are the result of constant probability generating mechanisms with error rate idiosyncratically determined for each subject.

Sellen, A. J.↗

NASA NTRS1985

The effect of material heterogeneity and random loading on the mechanics of fatigue crack growth

This paper reviews experimental work on the influence of variable amplitude or random loads on the mechanics and micromechanisms of fatigue crack growth. Implications are discussed in terms of the crack driving force, local plasticity, crack closure, crack blunting, and microstructure. Due to heterogeneity in the material's microstructure, the crack growth rate varies with crack tip position. Using the weakest link theory, an expression for crack growth rate is obtained as the expectation of a random variable. This expression is used to predict the crack growth rates for aluminum alloys, a titanium alloy, and a nickel steel in the mid-range region. It is observed, using the present theory, that the crack growth rate obeys the power law for small stress intensity factor range, and that the power is a function of a material constant.

Srivatsan, T. S.↗

NASA NTRS1985

A multiple scattering theory for EM wave propagation in a dense random medium

For a dense medium of randomly distributed scatterers an integral formulation for the total coherent field has been developed. This formulation accounts for the multiple scattering of electromagnetic waves including both the twoand three-particle terms. It is shown that under the Markovian assumption the total coherent field and the effective field have the same effective wave number. As an illustration of this theory, the effective wave number and the extinction coefficient are derived in terms of the polarizability tensor and the pair distribution function for randomly distributed small spherical scatterers. It is found that the contribution of the three-particle term increases with the particle size, the volume fraction, the frequency and the permittivity of the particle. This increase is more significant with frequency and particle size than with other parameters.

Karam, M. A.↗

NASA NTRS1986

Random scattering approach to gravitational microlensing

Small random deflections of a narrow beam of radiation due to gravitational scattering by stars randomly distributed within the deflector plane are considered. Using a Fouriere transform method, the probability of scattering is obtained as a function of scattering angle for an arbitrary number of stars with an arbitrary distribution of masses. The probability density, expressed in proper units, depends on one parameter only: the effective number of stars. At small scattering angles the density is a Gaussian, and at large angles it falls off as the scattering angle to the minus fourth power. The probability distribution for scatterings is simply related to the angular distribution of the surface brightness of a macroimage, averaged over many microimages. The isophotes are ellipses, with the ratio of the major axis to the minor axis, determined by the dimensionless surface mass density and the shear of the lensing system. The number of stars that has to be included in the modeling of microlensing is proportional to the amplification due to the macrolens, and to the square of the dimensionless surface mass density.

Katz, N.↗

NASA NTRS1984

Post and a random-walk search mode

Multidisciplinary analysis often requires optimization of nonlinear systems that are subject to constraints. Trajectory optimization is one example of this situation. The Program to Optimize Simulated Trajectories (POST) was used successfully for a number of problems. The purpose is to describe POST and a new optimization approach that has been incorporated into it. Typical uses of POST will also be illustrated. The projected-gradient approach to optimization is the preferred option in POST and is discussed. A new approach to optimization, the random-walk approach, is described, and results with the random-walk approach are presented.

Martin, J. A.↗

NASA NTRS1986

Effective medium approximation for effective propagation constant calculation in a dense random medium

The effective medium approximation (EMA) formalism developed for scalar wave calculations in solid state physics is generalized to electromagnetic wave scattering in a dense random medium. Results are applied to compute the effective propagation constant in a dense medium involving discrete spherical scatterers. When compared with a common quasicrystalline approximation (QCA), it is found that EMA accounts for backward scattering and the effect of correlation among three scatterers which are not available in QCA. It is also found that there is not much difference in the calculated normalized phase velocity between the use of these two approximations. However, there is a significant difference in the computed effective loss tangent in a nonabsorptive random medium. The computed effective loss tangent using EMA and measurements from a snow medium are compared, showing good agreement.

Zhu, P. Y.↗

NASA NTRS1988

Thermal expansion behavior of randomly oriented short carbon fiber reinforced copper composites

Several experiments were carried out on Cu composites with random orientation of short C fibers. The composite with random orientation of short C fibers swelled due to the elastic deformation of the fiber skeleton above 573 K. In a 3-D isotropic composite, the Cu matrix softened above 573 K and was fractured by the repulsive force of C fibers which were elastically deformed and released during heating. Swelling of the composite occurred when the fiber content was greater than or = 20 volume percent or the fiber length exceeded 0.5 millimeters. The addition of carbide-forming elements such as Ti was effective in preventing the swelling.

Kuniya, Keiichi↗

NASA NTRS1988

Maximum dynamic responses using matched filter theory and random process theory

This paper describes and illustrates two ways of performing time-correlated gust-load calculations. The first is based on Matched Filter Theory; the second on Random Process Theory. The two yield theoretically identical results and both employ novel applications of the theories and unconventional interpretations of the intermediate and final results. Both approaches are computationally fast and are general enough to be applied to dynamic-response problems other than gust loads. A brief mathematical development and example calculations using both Matched Filter Theory and Random Process Theory are presented.

Pototzky, Anthony S.↗

NASA NTRS1988

Large deflection random response of cross-ply laminated plates with elastically restrained edges and initial imperfections

The large deflection random response of symmetrically laminated cross-ply rectangular thin plates subjected to random excitation is studied. The out-of-plane boundary conditions are such that all the edges are rigidly supported against translation, but elastically restrained against rotation. The plate is also assumed to have a small initial imperfection. The assumed membrane boundary conditions are such that all the edges are free from normal and tangential forces in the plane of the plate. Mean-square deflections and mean-square strains are determined for a three-layered cross-ply laminate.

Prasad, C. B.↗

NASA NTRS1987

Three-dimensional test requirement for random vibration testing

An approach to defining and evaluating three-dimensional vibration test requirements is discussed. The approach is used to develop the three-dimensional space random-vibration test requirements for missile components subjected to truck transportation environments. One-dimensional testing parameters such as power spectral density and overall g rms values for three mutually perpendicular directions represent the test requirements. The coherence characteristics between each input axis were established and adjusted empirically in an attempt to simulate the cross-correlation in three-dimensional random vibration excitation.

Chang, Kurng↗

NASA NTRS1988

Scattering of electromagnetic waves from a periodic surface with random roughness

Equations for the scattering of electromagnetic waves from a randomly perturbed periodic surface have been formulated using the extended boundary condition method and solved using the small perturbation method. Surface currents and scattered fields are solved for up to the second order. The results indicate that as the correlation length of the random roughness increases, the bistatic scattering patterns of the scattered fields show several beams associated with each Bragg diffraction direction of the periodic surface. The beam shape becomes broader with smaller correlation length. Results obtained using the Kirchhoff approximation are found to agree well with the present results for the hh and vv polarized backscattering coefficients for small angles of incidence.

Yueh, H. A.↗

NASA NTRS1988

Multiple input/output random vibration control system

A multi-input/output random vibration control algorithm was developed based on system identification concepts derived from random vibration spectral analysis theory. The unique features of the algorithm are: (1) the number of input excitors and the number of output control responses need not be identical; (2) the system inverse response matrix is obtained directly from the input/output spectral matrix; and (3) the system inverse response matrix is updated every control loop cycle to accommodate system amplitude nonlinearities. A laboratory demonstration case of two imputs with three outputs is presented to demonstrate the system capabilities.

Unruh, James F.↗

NASA NTRS1988

Polarimetric microwave scattering from known randomly rough surfaces

Scattering from rough surfaces is reviewed, and artificial randomly rough surfaces are described. Measurements were made from 4 to 18 GHz for the 4 linear polarization states. The target consists of a metalized randomly rough surface constructed from known surface statistical information. The surface was generated using surface generation routines on the computer, and then the data was converted for the machining of the surface on a computer controlled mill. Bistatic and monostatic measurements were acquired at incident angles from 25 to 60 deg. At the 13.5 to 18 GHz frequencies, the effects of backscatter enhancement and depolarization effects can be studied in a regime which does not satisfy Kirchoff or small perturbation assumptions. This allows scattering mechanisms to be introduced into models, which may show missing elements in the more standard formulations. At lower frequency bands such as 4 to 8.5 GHz the scattering behavior was also examined to see the behavior as assumptions of other formulations are satisfied.

Nance, C. E.↗

NASA NTRS1989

Time-correlated gust loads using Matched-Filter Theory and Random-Process Theory: A new way of looking at things

Two ways of performing time-correlated gust-load calculations are described and illustrated. The first is based on Matched Filter Theory; the second on Random Process Theory. Both approaches yield theoretically identical results and represent novel applications of the theories, are computationally fast, and may be applied to other dynamic-response problems. A theoretical development and example calculations using both Matched Filter Theory and Random Process Theory approaches are presented.

Pototzky, Anthony S.↗

NASA NTRS1987

Spatially random models, estimation theory, and robot arm dynamics

Spatially random models provide an alternative to the more traditional deterministic models used to describe robot arm dynamics. These alternative models can be used to establish a relationship between the methodologies of estimation theory and robot dynamics. A new class of algorithms for many of the fundamental robotics problems of inverse and forward dynamics, inverse kinematics, etc. can be developed that use computations typical in estimation theory. The algorithms make extensive use of the difference equations of Kalman filtering and Bryson-Frazier smoothing to conduct spatial recursions. The spatially random models are very easy to describe and are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. The models can also be used to generate numerically the composite multibody system inertia matrix. This is done without resorting to the more common methods of deterministic modeling involving Lagrangian dynamics, Newton-Euler equations, etc. These methods make substantial use of human knowledge in derivation and minipulation of equations of motion for complex mechanical systems.

Rodriguez, G.↗