Dimensional Source Research Articles

Stokes flow for a stokeslet between two parallel flat plates

Velocity and pressure fields for Stokes flow due to a force singularity of arbitrary orientation and arbitrary distance between two parallel plates are found, using the image technique and a Fourier transform. Two alternative expressions for the solution, one in terms of infinite integrals and the other in terms of infinite series, are given. The infinite series solution is especially suitable for computation purposes being an exponentially decreasing series. From the series the “far field” behaviour is extracted. It is found that a force singularity parallel to the two planes has a far field behaviour of source and image for the parallel components (a two dimensional source doublet of height-dependent strength) whereas the normal component, and all fields due to a force singularity normal to the planes, die out exponentially. Velocity fields are compared with those of the one plane case. An estimate of the influence of the second wall and when its effect can be disregarded is obtained.

Gas Content and X-Ray Sources in Globular Clusters

dimensional sources at a projected distance !J., disregarding or cutting off the radiation from sources beyond the astigmatic point, then only the zone n/2-a<e<nl2+a, where a=cos1 (2-2rr 2/w2!J.2) 1i 2, of the celestial sphere will be illuminated; n!w<!J. 'rrv2/w. A formula for apparent luminosity3' • 7 ' as a function of (!J., e, ¢) will be published elsewhere. Grateful thanks are due to the International Centre for Theoretical Physics,

Detection of gamma-rays by means of organic scintillators

We present a Monte Carlo calculation to determine efficiencies and response functions of organic scintillators when used as gamma-rays detectors. The calculation is also valid for high energy gamma-rays and for finite dimensional sources because the primary gamma-rays, the secondary electrons and their bremsstrahlung radiation are followed both in the source and in the detector. To well reproduce the response functions, particularly in the case of large dimensional scintillators, the calculation takes also into account the phenomena related to the absorption and reflexion of the scintillation light in its way to the photocathode, together with the finite resolution of the photomultiplier. Results obtained for NE 213 organic scintillator detectors are shown.

On transient development of surface waves due to two dimensional sources

An initial value investigation into the two dimensional linearized problem of surface wave propagation in a fluid of limited and unlimited depth due to harmonically oscillating sources has been made. An asymptotic analysis of the problem has been carried out in a considerable detail for a clear understanding of both the steady state and the transient solutions. The limiting behaviour of the asymptotic solution as timeT tends to infinity has also been given due attention. Lastly, the corresponding steady state solution is obtained as a limiting case, and a discussion about the wave motions is made in some detail.

The behavior of analog communication systems

We consider the problem of transmission of analog data over a noisy channel. It is assumed that the channel input is of the form \surd S f(t, X) , where X is an n -dimensional source vector, and S is the allowable transmitted power. The performance of any given modulation scheme f(t, \cdot ) as a function of the transmitted power S is studied. Lower bounds on the average distortion produced by noise for a class of distortion functions are derived. These bounds relate the smoothness of modulation techniques to the minimum error that can be achieved with them. It is shown that when the analog source emits a sequence of mutually independent real random variables at a rate of R per second, the mean-square error that is associated with any practical modulation scheme f(t, \cdot) decays no faster than S^{-2} as the signal power S \rightarrow \infty . It follows that in the case of a band-limited additive white Gaussian channel no single modulation scheme f(t, \cdot ) can achieve the ideal rate-distortion bound on the mean-square error for all values of S , if the channel bandwidth is larger than the source rate R .

On the singing phenomenon in the offshore seismic experiments

Offshore areas are sometimes found in which seismic record assumes the appearance of a sine wave or a simple combination of sine waves. It is more interesting to note that the dominant frequency on the singing records is the third harmonic of a fundamental whose wave length is four times the water depth. In this paper it has been proved that this peculiar phenomenon happens due to the slope of the sedimentary layer near the observational points. Using the method introduced byCovert (1958) of finding the Green's function for built in bodies, pressure field has been obtained in the water layer for a two dimensional point source in the same medium and it has been proved that due to the slope of the sedimentary layer singing is caused by waves of wave-length equal to four times the water depth.

Two dimensional source flow of a viscous fluid

The steady two-dimensional source-type flow of a viscous heat-conducting perfect gas is investigated. The solutions of physical significance all contain shocks, and bounds are given for the shock-thickness in terms of the shock-strength and the Reynolds number of the flow. It is found that the entropy rises to a maximum within the shock, and this maximum does not disappear even when the viscosity tends to zero.