Abstract: A system for clamping two tubular members together in an end-to-end relationship uses a split ring with a V-shaped outer rim that can engage a clamping surface on each member. The split ring has a relaxed closed state where the ends of the ring are adjacent and the outside diameter of the split ring is less than the minimum inside diameter of the members at their ends. The members are clamped when the split ring is spread into an elastically stretched position where the ring rim is pressed tightly against the interior surfaces of the members. Mechanisms are provided for removing the spreader so the split ring will return to the relaxed state, releasing the clamped members.

Abstract: The mathematical foundations of conventional numerical simulation of physical systems provide no consistent description of the behavior of such systems when subjected to discontinuous physical influences. As a result, the numerical simulation of such problems requires ad hoc encoding of specific experimental results in order to address the behavior of such discontinuous physical systems. In the present invention, these foundations are replaced by a new combination of generalized function theory and nonstandard analysis. The result is a class of new approaches to the numerical simulation of physical systems which allows the accurate and well-behaved simulation of discontinuous and other difficult physical systems, as well as simpler physical systems. Applications of this new class of numerical simulation techniques to process control, robotics, and apparatus design are outlined.

Abstract: A method of forming a shock-free supersonic elliptic nozzle, in which the nozzle to be designed is divided into three sections, a circular-to-elliptic section which begins at a circular nozzle inlet, an elliptic subsonic section downstream from the circular-to-elliptic section and a supersonic section downstream from the elliptic subsonic section. The maximum and minimum radii for each axial point in the circular-to-elliptic section and the elliptic subsonic section are then separately determined, the maximum and minimum radii being the radii for the widest part of an elliptic cross-section and the narrowest part of the elliptic cross-section, respectively. The maximum and minimum radii for each axial point in the supersonic section are determined based on the Method of Characteristics, Then, each of the three sections are based on the maximum and minimum radii for each axial point in the section. The resulting nozzle is acoustically superior.