Computer Simulation of Chute Flows of Granular Materials

The purpose of the present paper is to present results from computer simulations of the flow of granular materials down inclined chutes or channels and to compare the results of these calculations with existing experimental measurements of velocity, solid fraction and mass flow rate profiles

Geometric interpretations of the Discrete Fourier Transform (DFT)

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward

Data processing improvements for the Skylab S-191 EREP spectrometer

The characteristics of the S-191 spectrometer (filter wheel infrared spectrometer) are discussed. Inherent deficiencies in previous spectrometers are described and the techniques for correcting the deficiencies are explained. The radiance errors caused by error in wavelength are identified and the effects on the accuracy of the spectrometer are described. It is stated that the most important source of error in the S-191 spectrometer is off-band radiation in which the detected radiation is far from the wavelength which is expected to be detected by the sensor at that particular time. A numerical analysis of the effects of off-band radiation is developed

An efficient algorithm for generating random number pairs drawn from a bivariate normal distribution

An efficient algorithm for generating random number pairs from a bivariate normal distribution was developed. Any desired value of the two means, two standard deviations, and correlation coefficient can be selected. Theoretically the technique is exact and in practice its accuracy is limited only by the quality of the uniform distribution random number generator, inaccuracies in computer function evaluation, and arithmetic. A FORTRAN routine was written to check the algorithm and good accuracy was obtained. Some small errors in the correlation coefficient were observed to vary in a surprisingly regular manner. A simple model was developed which explained the qualities aspects of the errors

Spool for releasing and retracting flat conductor cable

Spool design and operation permit installation of up to 8 cables on single unit. Heat treating the cables while wound in a coil obtains effective recoil action

Convergence of Newton's method for a single real equation

Newton's method for finding the zeroes of a single real function is investigated in some detail. Convergence is generally checked using the Contraction Mapping Theorem which yields sufficient but not necessary conditions for convergence of the general single point iteration method. The resulting convergence intervals are frequently considerably smaller than actual convergence zones. For a specific single point iteration method, such as Newton's method, better estimates of regions of convergence should be possible. A technique is described which, under certain conditions (frequently satisfied by well behaved functions) gives much larger zones where convergence is guaranteed

Collimated beam manifold with the number of output beams variable at a given output angle

An optical manifold is described which transforms a collimated beam, such as a laser beam, into a plurality of parallel beams having uniform intensity or having a desired intensity ratio. The manifold comprises an optical substrate coated on its rear surface with a fully reflective layer and on its front surface with a partially reflecting layer having a reflectivity gradient. An input collimated beam entering the rear surface and impinging on the front surface is reflected, multiply between the front and rear surfaces producing a plurality of parallel beams that emerge from the front surface. The intensities of the emerging beams have a relationship that depends on the reflectivity of the front surface at the points where the beams emerge. By properly selecting the reflectivity gradient, the emerging beams have uniform intensity or a desired intensity ratio