Cellular automata model

In this section, we will examine four examples that illustrate the steps, procedures, choices, and outputs involved in conducting some elementary cellular automata model simulations. The reader is advised to consult Chapter 10 to find the appropriate ways for entering parameters and making appropriate selections for each study. Following each prearranged example, some brief fiirther studies are indicated that will expand on, and fiirther illustrate, the concepts involved in the example. 

L. B. Kier, C.-K. Cheng, and R Seybold, Cellular automata models of chemical systems. SAR QSAR Environ. Res. 2000, 11, 79-98. 

In a cellular automata model of a solution, there are three different types of cells with their states encoded. The first is the empty space or voids among the molecules. These are designated to have a state of zero hence, they perform no further action. The second type of cell is the water molecule. We have described the rules governing its action in the previous chapter. The third type of cell in the solution is the cell modeling a solute molecule. It must be identified with a state value separate from that of water. 

Figure 4.1. (a) A cellular automata model of hydrophilic solutes in water, (b) A cellular automata model of hydrophobic solutes in water... 

Figure 4.2. A cellular automata model of a crystal in water...

L. B. Kier and C.-K. Cheng, A cellular automata model of solution phenomena. J. Math. Chem. 1997, 21, 71-77. 

L. B. Kier and T. M. Witten, in Cellular Automata Models of Complex Systems, in Complexity in Chemistry, Biology and Ecology, D. Bonchev and D. H. Rouvray, eds. Springer, New York (in press). 

We have introduced the use of cellular automata modeling of water and possibly some other solvent, and have observed the influence of solutes on the emergence of properties in these complex systems. In this chapter we consider a few, more complex chemical systems that may lend themselves to cellular automata modeling. We will discuss several of these and then suggest some studies for the reader. 

Figure 5.3. A cellular automata model of the interface between two immiscible bquids, after the demixing process has reached an equilibrium. A solute (encircled cells) has partitioned into the two phases according to its partition coefficient...

Studies described in earlier chapters used cellular automata dynamics to model the hydrophobic effect and other solution phenomena such as dissolution, diffusion, micelle formation, and immiscible solvent demixing. In this section we describe several cellular automata models of the influence of the hydropathic state of a surface on water and on solute concentration in an aqueous solution. We first examine the effect of the surface hydropathic state on the accumulation of water near the surface. A second example models the effect of surface hydropathic state on the rate and accumulation of water flowing through a tube. A final example shows the effect of the surface on the concentration of solute molecules within an aqueous solution. 

A series of rules describing the breaking, / B,and joining, J, probabilities must be selected to operate the cellular automata model. The study of Kier was driven by the rules shown in Table 6.6, where Si and S2 are the two solutes, B, the stationary cells, and W, the solvent (water). The boundary cells, E, of the grid are parameterized to be noninteractive with the water and solutes, i.e., / b(WE) = F b(SE) = 1.0 and J(WE) = J(SE) = 0. The information about the gravity parameters is found in Chapter 2. The characteristics of Si, S2, and B relative to each other and to water, W, can be interpreted from the entries in Table 6.6. 

In these studies, choose different sets of affinities (SiB) and (S2B), and run these with the same parameters for the other ingredient encounters, as in Example 6.5. The cellular automata modeling of chromatographic separation produces a very realistic picture of the events taking place. It provides a visual and a tabular representation of the influence of variables on the process. The student is challenged to pursue these models and to compare them with some of the mathematical descriptions possible from chromatography. 

In this section we describe a cellular automata model of a semipermeable membrane separating two compartments [5]. A solute in one compartment has varied parameters to reflect its relative polarity or lipophilicity. The passage of this solute into and through the membrane is observed, as this property is varied. 

Many, if not most, of the key reactions of chemistry are second-order reactions, and understanding this type of reaction is central to understanding chemical kinetics. Cellular automata models of second-order reactions are therefore very important they can illustrate the salient features of these reactions and greatly aid in this understanding. 

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