Machine computation

Szymanski S, Gryff-Keller A M and Binsch G A 1986 Liouville space formulation of Wangsness-Bloch-Redfield theory of nuclear spin irelaxation suitable for machine computation. I. Fundamental aspects J. Magn. Reson. 68 399-432... 

The alloys can be processed into parts requiring hydrolytic and autoclave stabiHty, such as desalinization filter frames and medical devices. Foamed products are used in cabinets for business machines, computers, and copiers. Automotive seat backs are made by blow mol ding and replacements for metal parts by injection mol ding. 

Hendrickson JB. Molecular geometry. I. Machine computation of the common rings. J Am Chem Soc 1961 83 4537-47. 

Carpenter, G. A., and Grossberg, S., A massively parallel architecture for a self-organizing neural pattern recognition machine, Comput. Vis. Graphics Image Process 37,54 (1987b). 

Rosen, E. M. (1962) Chem. Eng. Prog. 58 (Oct.) 69. A machine computation method for performing material balances. 

The remainder of this text attempts to establish a rational framework within which many of these questions can be attacked. We will see that there is often considerable freedom of choice available in terms of the type of reactor and reaction conditions that will accomplish a given task. The development of an optimum processing scheme or even of an optimum reactor configuration and mode of operation requires a number of complex calculations that often involve iterative numerical calculations. Consequently machine computation is used extensively in industrial situations to simplify the optimization task. Nonetheless, we have deliberately chosen to present the concepts used in reactor design calculations in a framework that insofar as possible permits analytical solutions in order to divorce the basic concepts from the mass of detail associated with machine computation. 

This procedure obviously requires machine computation capability if it is to employed in reactor design calculations. Fortunately, there are many reactions for which the global rate reduces to the intrinsic rate, which avoids the necessity for calculations of this type. On the other hand, several high tonnage processes (e.g., S02 oxidation) are influenced by heat and mass transfer effects and one must be fully cognizant of their implications for design purposes. 

A few words concerning the results of our analyses in Illustrations 12.8 and 12.9 are in order. Obviously, better estimates of the catalyst requirements could be obtained by using smaller conversion increments. We have not attempted to fully optimize the reactor stages in terms of catalyst minimization. Furthermore, we have again neglected pressure drop in each stage. Further calculations would remedy each of the aforementioned shortcomings of the analysis. They are readily accomplished with the aid of machine computation. 

Generalized flow sheet for simulation of pyrolysis reactor by machine computation. 

Lebowitz, J. L. Percus, J. K. Verlet, L., Ensemble dependence of fluctuations with application to machine computations, Phys. Rev. 1967,153, 250... 

Benzene ETS, solvents, paints, stains, fax machines, computer terminals, printers, water-based adhesives, carpets, plastics, synthetic fibres. 12 1... 

Trichloroethylene Solvents, dry-cleaned fabrics, printing inks, paints, varnishes, adhesives, fax machines, computer terminals and printers, correction pen fluids, paint removers, spot removers. 28 2A... 

Tetrachloroethylene Dry-cleaned fabrics, spoftextile cleaners, fax machines, computer terminals and printers 27 2A... 

Armed with the band masses and relative positions of the band centres one may easily sketch the likely valence electron energies in actinide metals and compounds. This is useful because it is easy to understand, involves no computation and gives a rough idea of what to expect from large machine computations of electronic structure. 

Using the methods of Taylor s analysis as the basis of machine computation, Lutzky has computed "Spherical Taylor Wave for several high explosives (TNT, Pentolite, 65/35 60/40-Cyclotols, TNEtB, RDX, Tetryl and NGu) with the equation of state ... 

Zirkind reviews investigations of radiation emission of rocket exhausts since 1940 (Ref 11). Emission characteristics of the exhaust plume are strongly dependent on rocket engine parameters the propellant system. If these motor operating conditions are stipulated, machine computations can give exhaust composition sometimes temperatures... 

At the current state of the art, such estimates warrant at least the same, and in some cases possibly greater, reliance than the results of complex machine computations (see Appendix C and subsequent papers). 

Molded parts (e.g., TV sets/business machines, computer housings, household appliances [hairdryer, curler], automotive parts, electronics,... 

In the general case, in which both back reaction and ribosome interference are accounted for, the influence of larger values of L on steady state solutions, analogous to those shown in Figures 2-7, has recently been determined14 via machine computations of Eq. (19) with n/r) =tij and qft) = q, as indicated by Eq. (15) with dnj t)jdt — 0. 

Equation (12.53) gives the desired evaluation of the general thermodynamic derivative V in a system of/degrees of freedom, expressed in terms of known geometrical quantities. As in the two-dimensional case, other expressions for V would be possible in other special choices of basis. Equation (12.53) is suitable for machine computation in multicomponent thermodynamic systems of arbitrary complexity. 

Machine computation was used to obtain kcx and as functions of 7 and 3. The thermographic test procedure was then employed to obtain k and e, from observed A Tmax vs T0 plots, for mixts of Tetryl and Picric Acid (claimed to be a first-order decompn reaction), and for a Tetryl/chalk mixt (claimed to be an autocatalytic decompn). Agreement between calcd and observed k s and e s was excellent All these studies are somewhat pedantic, in that they provide rigorous proof for a well-established fact, namely that quenching the thermal expln of expl materials is well-nigh impossible if 0 is sufficiently large. Merzhanov and co-workers also show that many exothermic... 

The h-S diagram becomes most convenient in following rocket motor processes and this is the reason for its introduction. The conveniences obtained are generally hidden by machine computation programs which essentially deal with the enthalpy-entropy process for the expansion process, h is the sensible enthalpy only. Theoretical performance calculations are performed in terms of the total enthalpy which is here defined as the sum of the sensible and chemical enthalpies only. 

As the mixture ratio approaches stoichiometric proportions, the dissociation products become more important and the distinction between maj or and minor products becomes indistinguishable. In this range of mixture ratio, one needs more refined analytical techniques than that just described. A method due to Huff < / af (22) will be described and is particularly appropriate for digital machine computation. 

For reactor design calculations it is necessary to know the total devolatilization rate as well as the species production rates. Therefore, one needs to include in the reactor model all the reaction rates that are available for the devolatilization of the particular coal. Kayihan and Reklaitis (8) show that the kinetic data provided by Howard, et al. (5,6) can be easily incorporated in the design calculations for fluidized beds where the coal residence times are long. However, if the residence time of pulverized coal in the reactor is short as it is in entrained bed reactors, then the handling of ordinary differential equations arising from the reaction kinetics require excessive machine computation time. This is due to the stiffness of the differential equations. It is found that the model equations cannot be solved... 

Comparison of the Computation Results. As indicated above, Gear s method was used to solve the model equations only for a fraction of the total residence time in the reactor which took 8.59 minutes of machine computation time. The same set of equations was solved by the approximate iterative technique for the same time interval in 5.8 seconds of computer time. As a comparison of the accuracy overall devolatilization Vj = Z Z v j as predicted by the two techniques are plotted on a dimensionless scale in Figure 1. The definitions for the dimensionless quantities used are ... 

Computational Techniques. For evaluation of kf by eqs. (7) and (8), the vibrational energy level sum at a given total energy must be found. It has been shown, both through experiment and computation,9 19 20 that for polyatomic molecules, even with energies above 100 kcal. mole-1, it is necessary to use a quantum statistical treatment to find this sum. Classical approximations are totally inadequate and drastically in error. High speed machine computational techniques and simplified approximation formulas have been developed, which allow this quantum-statistical summation to be done with relative ease these methods are described and summarized in Appendix I. 

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