RAND algorithm

Notice that the number NA of atoms is usually small compared to the number NS of species, and hence the RAND algorithm is very effective in terms of computational effort. The rank of the atom matrix, however, must be equal to the number NA of atoms. At this point it is interesting to remark that instead of the atom matrix we can use a virtual atom matrix, i.e., the matrix of reaction invariant coefficients if the atom matrix is not available or we are interested in a restricted equilibrium. For details see Section 1.8.1. 

The following main program is an implementation of the RAND algorithm. Its use is illustrated on the example of hydrazin combustion at T = 3500 and P = 5.17X106 pa (ref. 27). The elemental abundances of hydrogen, nitrogen and... 

R. E. Gomory. An algorithm for the mixed integer problem. Technical Report RM-2597, The Rand Corporation, 1960. 

RAND [1971] published an algorithm which enables comparison of cluster solutions by their similarity. So, the results of even conceptually different clustering procedures may be contrasted. 

Gordon and McBride (27), working at the NASA Lewis Research Center, developed an algorithm similar to the RAND Method. They minimized ... 

In many systems, slow reactions occur to an appreciable extent in the presence of fast, reversible reactions. Given extents of reaction measured experimentally, or computed by integration of a kinetic model, it is desired to compute compositions of a system. This has been accomplished using EQUILK (19) given specifications for extents or temperature approaches for less than R reactions, or the moles of some species in the product. The RAND Method has been extended to permit these specifications, as well (38). In principle, these specifications are easily added to the mass balances for any nonlinear programming algorithm. 

Rand, W. (1971). Objective Criteria for the Evaluation of Clustering Algorithms, Journal of the American Statistical Association 66, 846-850. 

For a general discussion, see Chemical Reaction Equilibrium Analysis Theory and Algorithms by W. R. Smith and R. W. Missen, John Wiley Sons, New York, 1982. Also see Fortran TV Computer Program for Calculation of Thermodynamic and Transport Properties of Complex Chemical Systems by R.A. Svehla and B. J. McBride, National Aeronautics and Space Administration Technical Note D-7055, January 1973 Rand s Chemical Composition Program, Rand Corporation, Santa Monica, Calif. and others. 

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