Average earliness

A consideration of the transition probabilities allows us to prove that microscopic reversibility holds, and that canonical ensemble averages are generated. This approach has greatly extended the range of simulations that can be perfonned. An early example was the preferential sampling of molecules near solutes [77], but more recently, as we shall see, polymer simulations have been greatly accelerated by tiiis method. 

Data for the production and sales of maleic anhydride and fumaric acid ia the United States between 1979 and 1992 are shown ia Table 5. Production of maleic anhydride during this time grew - 2% on average per year. Production of fumaric acid has declined during the same period as customers have switched to the less cosdy maleic anhydride when possible. All production of maleic anhydride in the United States in 1992 was from butane-based plants which used fixed-bed reactor technology as shown in Table 6. The number of fumaric acid producers has been reduced considerably since the early 1980s with only two producers left in the United States in 1992 as shown in Table 6. Pfizer shut down its fumaric acid plant at the end of 1993. However, Bartek of Canada will start up an expanded fumaric acid faciUty to supply the North American market for both their own and Huntsman s requirements. 

In the early years of reactor development, electricity from nuclear sources was expected to be much cheaper than that from other sources. Whereas nuclear fuel cost is low, the operating and maintenance costs of a nuclear faciHty are high. Thus on average, electric power from coal and nuclear costs about the same. 

Owing to environmental regulations, the consumption of lead-based pigments, lead chromate [7738-97-6], in particular, has been decreasing steadily at an average aimual rate of about 5% since the early 1980s. In 1993 production was estimated to be around 20,000 t (see Lead compounds). 

Ammonia and urea prices from 1968 to 1986 are shown in Figure 22 (82). The average FOB price of ammonia on the U.S. Gulf Coast in early 1991 was 105/t. 

Nonintrusive Instrumentation. Essential to quantitatively enlarging fundamental descriptions of flow patterns and flow regimes are localized nonintmsive measurements. Early investigators used time-averaged pressure traverses for holdups, and pilot tubes for velocity measurements. In the 1990s investigators use laser-Doppler and hot film anemometers, conductivity probes, and optical fibers to capture time-averaged turbulent fluctuations (39). 

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