Instead of radical reactions, models based on molecular reactions have been proposed for the cracking of simple alkanes and Hquid feeds like naphtha and gas oil (40—42). However, the vaUdity of these models is limited, and caimot be extrapolated outside the range with confidence. With sophisticated algorithms and high speed computers available, this molecular reaction approach is not recommended. [Pg.437]

With modern high-speed computers, an easier method is to numerically integrate equation (6.15), written in the form... [Pg.256]

With the advent of modern high-speed computers, this is not difficult to do for diatomic molecules, and it is the procedure followed when energy level information is available to perform the summation. Similar procedures have been followed for some nonlinear molecules, although as we have noted earlier, Table 10.4 gives reliable values for these molecules under most circumstances. References can be found in the literature to formulas and tables for calculating corrections for selected nonlinear molecules.12... [Pg.564]

With modern high-speed computers, the corrections can easily be calculated from either set of equations. [Pg.647]

These steps may be completed separately or together, statistical methods can be employed and the computational labour reduced through the use of high speed computers. [Pg.82]

Chemistry, like other sciences, progresses through the use of models. Models are the means by which we attempt to understand nature. In this book, we are primarily concerned with models of complex systems, those systems whose behaviors result from the many interactions of a large number of ingredients. In this context, two powerful approaches have been developed in recent years for chemical investigations molecular dynamics and Monte Carlo calculations [4-7]. Both techniques have been made possible by the development of extremely powerful, modern, high-speed computers. [Pg.6]

All this requires a high speed computer with large memory storage capacity and RAM (something not possible until recently). Image aneifysis software... [Pg.236]

Although the condensation of phenol with formaldehyde has been known for more than 100 years, it is only recently that the reaction could be studied in detail. Recent developments in analytical instrumentation like GC, GPC, HPLC, IR spectroscopy and NMR spectroscopy have made it possible for the intermediates involved in such reactions to be characterized and determined (1.-6). In addition, high speed computers can now be used to simulate the complicated multi-component, multi-path kinetic schemes involved in phenol-formaldehyde reactions (6-27) and optimization routines can be used in conjunction with computer-based models for phenol-formaldehyde reactions to estimate, from experimental data, reaction rates for the various processes involved. The combined use of precise analytical data and of computer-based techniques to analyze such data has been very fruitful. [Pg.288]

The fabrication of logic elements using such devices allows in principle the construction of a large capacity, compact, high-speed computer [50], Major problems with the technology are that large fan-out ratios are difficult to achieve and that superconducting circuits have a very low inherent impedance and so are difficult to couple with conventional elements at room temperature. [Pg.320]

Prior to the advent of high-speed computers, methods of optimization were limited primarily to analytical methods, that is, methods of calculating a potential extremum were based on using the necessary conditions and analytical derivatives as well as values of the objective function. Modem computers have made possible iterative, or numerical, methods that search for an extremum by using function and sometimes derivative values of fix) at a sequence of trial points x1, x2,. [Pg.153]

In the 1-butene isomerization example which we discuss in Section III,B we solved Eq. (65) for (x/u) by Newton s method on a high-speed computer to facilitate this otherwise laborious approximation method. The solutions to Eqs. (66) and (67) are then straightforward. From the definitions of u, x, y,... [Pg.116]

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