The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge's q ¼ À1 phenomenon. The phenomenon is shown to appear in various situations, involving q-binomial coefficients, Po´lya-Redfield theory, polygon dissections, noncrossing partitions, finite reflection groups, and some finite field q-analogues. r 2004 Elsevier Inc. All rights reserved.
Vapor-dominated ("dry-steam") geothermal systems are uncommon and poorly understood compared with hot-water systems. Critical physical data on both types were obtained from U.S. Geological Survey research in Yellowstone Park. Vapor-dominated systems require relatively potent heat supplies and low initial permeability. After an early hot-water stage, a system becomes vapor dominated when net discharge starts to exceed recharge. Steam then boils from a declining water table; some steam escapes to the atmosphere, but most condenses below the surface, where its heat of vaporization can be conducted upward. The main vapor-dominated reservoir actually is a two-phase heat-transfer system. Vapor boiled from the deep (brine?) water table flows upward; most liquid condensate flows down to the water table, but some may be swept out with steam in channels of principal upflow. Liquid water favors small pores and channels because of its high surface tension relative to that of steam. Steam is largely excluded from smaller spaces'but greatly dominates the larger channels and discharge from wells. With time, permeability of water-recharge channels, initially low, becomes still lower because of deposition of carbonates and CaSO 4, which decrease in solubility with temperature. The "lid" on the system consists in part of argillized rocks and CO2-saturated condensate. Our model of vapor-dominated systems and the thermodynamic properties of steam provide the keys for understanding why the major reservoirs of The Geysers, California, and Larderello, Italy, have rather uniform reservoir temperatures near 240 ø C and pressures near 34 kg/cm • (absolute; gases other than H•.O increase the pressures).Local supply of pore liquid and great stored heat of solid phases account for the physical characteristics and the high productivity of steam wells.We suggest that vapor-dominated systems provide a good mechanism for separating volatile mercury from all other metals of lower volatility. Mercury is likely to be enriched in the vapor of these systems; the zone of condensation that surrounds the uniform reservoir is attractive for precipitating HgS.A more speculative suggestion is that porphyry copper deposits form below the deep water tables hypothesized for the vapor-dominated systems. Some enigmatic characteristics of these copper deposits are consistent with such a relationship, and warrant consideration and testing. • Publication authorized by the Director, U.S. Geologlcal Survey. 75 than a hundred meters or so •' and near centers of surface activity were found to yield slightly superheated steam (Burgassi, 1964). Some wells on the borders of the active systems * produced hot water •-The metric system is used throughout this paper. Some readers may find useful the following conversion factors: Length: 1 m = 3281 ft; 1 km= 3,281 ft ----0.6214 mi. Temperature: (øC X 9/5) + 32 = øF. Pressure: 1 kg/cm • = 0.9678 atto --0.9807 bars --14.22 psi. All pressures absolute, with 0.78 kg/cm • added to gage pressure for Yellow.stone Park, an(} 1.03 kg/...
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