The Courant-Snyder invariants become Lyapunov functions when the [beta]-functions admit non-zero lower, and finite upper bounds. The long-term stability of motion then follows. This alternative criterion for the long-term stability of motion can be generalized to the nonlinear case. A single particle subjected to an arbitrary static magnetic field is considered in some detail, as an example.

The Courant-Snyder invariants become Lyapunov functions when the {beta}-functions admit non-zero lower, and finite upper bounds. The long-term stability of motion then follows. This alternative criterion for the long-term stability of motion can be generalized to the nonlinear case. A single particle subjected to an arbitrary static magnetic field is considered in some detail, as an example.

The main purpose of this project is engineering development of advanced column flotation and selective agglomeration technologies for cleaning coal. Development of these technologies is an important step in the Department of Energy program to show that ultra-clean fuel can be produced from selected United States coals and that this fuel will be a cost-effective replacement for a portion of the premium fuels (oil and natural gas) burned by electric utility and industrial boilers in this country. Capturing a relatively small fraction of the total utility and industrial oil-fired boiler fuel market would have a significant impact on domestic coal production and reduce national dependence on petroleum fuels. Significant potential export markets also exist in Europe and the Pacific Rim for cost-effective premium fuels prepared from ultra-clean coal. The replacement of premium fossil fuels with coal can only be realized if retrofit costs, and boiler derating are kept to a minimum. Also, retrofit boiler emissions must be compatible with national goals for clean air. These concerns establish the specifications for the ash and sulfur levels and combustion properties of ultra-clean coal discussed below. The cost-shared contract effort is for 48 months beginning September 30, 1992, and ending September 30, 1996. …

The Indiana University Task C group is participating in the experiments GEM at the SSC and MACRO at the Gran Sasso. After an introduction to GEM in {paragraph}II, a detailed report is presented on the work done during the current contract period on the design of the outer region of the GEM Central Tracker. The Central Tracker Monte Carlo, which was the other significant GEM activity by the group, is included. In {paragraph}III is introduced MACRO and a brief status report is given. Muon Astronomy analysis done using MACRO data is also presented.

During this quarter we (1) received the last of the field tapes and survey information for the seismic field data acquisition which was finished at the very end of the previous quarter, (2) began the large task of processing the seismic data, (3) collected well logs and other informination to aid in the interpretation, and (4) initiated some seismic modeling studies. As already reported, the field data acquisition was at Amoco`s Powder River Basin site in southeast Wyoming. This is a low permeability fractured site, with both gas and oil present. The reservoir is highly compartmentalized, due to the low permeability, with the fractures providing the only practical drainage paths for production. The two formations of interest are: The Niobrara: a fractured shale and limey shale to chalk, which is a reservoir rock, but also its own source rock. The Frontier: a tight sandstone lying directly below the Niobrara, brought into contact with it by an unconformity. The fractures are thought to lie in a roughly northwest-southeast trend, along the strike of a flexure, which forms one of the boundaries of the basin.