Kinetic parameter distribution system model

It should be emphasized that for Markovian copolymers a knowledge of the values of structural parameters of such a kind will suffice to find the probability of any sequence Uk, i.e. for an exhaustive description of the microstructure of the chains of these copolymers with a given average composition. As for the composition distribution of Markovian copolymers, this obeys for any fraction of Z-mers the Gaussian formula whose covariance matrix elements are Dap/l where Dap depend solely on the values of structural parameters [2]. The calculation of their dependence on time, and the stoichiometric and kinetic parameters of the reaction system permits a complete statistical description of the chemical structure of Markovian copolymers to be accomplished. The above reasoning reveals to which extent the mathematical modeling of the processes of the copolymer synthesis is easier to perform provided the alternation of units in macromolecules is known to obey Markovian statistics. 

It should be emphasized that for the Markovian copolymers, the knowledge of these structure parameters will suffice for finding the probabilities of any sequences LZ, i.e., for a comprehensive description of the structure of the chains of such copolymers at their given average composition. As for the CD of the Markovian copolymers, for any fraction of Z-mers it is described at Z 1 by the normal Gaussian distribution with covariance matrix, which is controlled along with Z only by the values of structure parameters (Lowry, 1970). The calculation of their dependence on time and on the kinetic parameters of a reaction system enables a complete statistical description of the chemical structure of a Markovian copolymer. It is obvious therewith to which extent a mathematical modeling of the processes of the synthesis of linear copolymers becomes simpler when the sequence of units in their macromolecules is known to obey Markov statistics. 

The concentration of free metal species in soil solution is controlled by several factors, the most significant of which are thermody-namic/kinetic parameters. Mathematical approaches to modeling soil solution -solid-phase equilibria - are broadly described in numerous publications (Lindsay 1979, Sposito etal. 1984, Waite 1991, Wolt 1994, Sparks 1995, Suarez 1999), and several models for calculating activity coefficients for trace metals are overviewed and discussed. Waite (1991) concluded that mathematical modeling clearly has a place in extending the information that can be obtained on trace element species distributed by other methods and will be of practical use in systems for which determination of concentrations of all species of interest is impossible because of sensitivity constrains or other analytical difficulties . 

Overall the analysis here should convey the message that generalizations concerning selectivity or yield performance in nonideal reactors with reference to an ideal model are slippery conversion, however, is perhaps somewhat more predictable. We may normally expect modest taxes on conversion as the result of nonideal exit-age distributions if the reaction system involves selectivity/yield functions these will also be influenced by the exit-age distribution, but the direction is not certain. Normally nonideality is reflected in a decrease in yield and selectivity, but there are possible interactions between the reactor exit-age distribution and the reaction kinetic parameters that can force the deviation in the opposite direction. Keep in mind that the comparisons being offered here are not analogous to those for PFR-CSTR Type III selectivities given in Chapter 4, which were based on the premise of equal conversion in the two reactor types. 

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