Abstract: In accordance with a first aspect of the instant invention, there is provided a method of gas pool balancing which provides a method of simultaneously and systematically balancing an entire gas transmission network. In a first embodiment, the instant method operates by identifying pools with input amounts of gas available, numerically distributing that gas throughout a representation of the gas network, and, thereafter, physically distributing gas in that network according to the solution obtained. In another embodiment, the instant method operates by forming a system of equations that define the topology of the gas transmission network. Solution of the resulting system of equations yields a rapid and accurate system-wide solution to the gas balancing problem which heretofore was solved by repeated iterations of an algorithm which balanced one pool at a time.

Abstract: A method for modeling visual images and wave propagation describes a scene mathematically, calculates certain parameters and visibility areas from input data, and traces the passage of wavefronts through the scene. The scene represents a particular configuration of objects having distinct boundaries, such as interfacing strata. Wavefronts are considered to emanate from a particular source, for multiple sources. Each wavefront is subdivided into discrete front elements that impinge on boundary elements, as determined from computed visibility areas. Each front element that impinges on a boundary element is analyzed to determine reflected front elements and refracted front elements. Those front elements are traced to see if they impinge on another boundary element or a receiver. A front element is traced until its energy falls below a threshold or it leaves the scene. Ray paths from each source to each receiver are computed from which wave-related output parameters are computed and displayed.