A numerical solution of the Kirchhoff equation for the propagation constant of longitudinal sound waves in infinitely long cylindrical tubes has been obtained. The solution, which avoids the wide-tube approximations, shows that the percentage errors in the von Helmholtz-Kirchhoff tube velocity correction and tube absorption are both roughly equal to the percentage the velocity correction is of the free-space velocity. The error in the von Helmholtz-Kirchhoff equations can be plotted as a function of fD/a, pD/ηa, and γ. (f is the sound frequency, D the tube diameter, a the free-space velocity, p the gas pressure, η the viscosity, and γ the ratio of specific heats.) Recent absorption measurements in Ar are in agreement with values calculated numerically, but measured velocities indicate the need for considering molecular slip at the tube wall. Thermal relaxation is introduced into Kirchhoff's basic equation by using the Eucken relation k/coη − (9γ −5)/4 and considering γ to be the ratio of complex relaxing specific heats. Viscothermal and relaxation effects are found to be additive only if the frequency is near the cutoff frequency for the first unsymmetric mode and the f/p values do not extend to the megacycle/second atmospheres range.

Most of the compute intensive SDI problem solving processors rely on a common set of algorithms found in numerical matrix algebra. Typically, all these problems are broken up into a set of linear equations where it is the processors task to solve this set. Algorithmic solutions range from the extensive use of the fast Fourier transform to the robust singular value decomposition method. Over the past several years considerable research has been focused on the use of arrays of computational processing elements, which, when configured correctly, will process these algorithms at extremely high speeds and with great algorithmic efficiency. To obtain these high speeds hardware development has progressed primarily in two areas: (1) semiconductor VLSI arrays utilizing 2-D planar semiconductor technology and (2) acoustooptic analog and digital arrays utilizing 3-D optical interconnect technology. This paper will focus on the formulation of 3-D optical interconnect methodology for numerical and general purpose binary combinatorial logic based optical computers.

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