Surface model construction continued

As an alternative to film models, McNamara and Amidon [6] included convection, or mass transfer via fluid flow, into the general solid dissolution and reaction modeling scheme. The idea was to recognize that diffusion was not the only process by which mass could be transferred from the solid surface through the boundary layer [7], McNamara and Amidon constructed a set of steady-state convective diffusion continuity equations such as... 

Perhaps the most widely used scheme for SCRF implementations of the Poisson equation is the surface area boundary element approach. This was first formalized by Miertus, Scrocco, and Tomasi (1981), and these authors referred to their construction as the polarized continuum model (PCM). While that name continues to find ample use in the literature, MST (the initials... 

An interesting open problem is to construct and analyze a model which, following [Cu2], treats growth and consumption as in Chapter 9 (i.e., as proportional to surface area) and which treats cell division as in [MD]. Questions of existence, uniqueness, and continuous dependence of solutions on initial data were not considered for the model discussed in Chapter 9. This problem seems to be an open one. The analysis should follow along the lines of arguments given in [MD, p. 238]. 

Imagine a network model of the diamond structure (Fig. 1.17(e)), blue lattice), constructed from rubber tubes. Now inflate the network, swelling the hollow tubes. The resulting structure is a curved continuous network, enclosing the tunnels in the diamond network. If the inflation procedure is continued, the surface closes up around a complementary diamond network. The D-surface is the "half-way point" during the procedure. 

The spatial continuity relationship (correlation) for each indicator, I(x zi ), was characterized by an empirical variogram model of the apparent continuity within the near-surface soil in each of two dimensions. The construction of such a model is based on the assumption that the value of the indicator at location x, i.e., l(x zk), may be greatly influenced by values of that indicator at nearby locations and less influenced by more distant values. 

Thus, we construct a model featuring a sequence of volume elements extending away from the interface as shown in Figure B.1.1. The electrode surface is usually envisioned as being in the center of the first box, and each box j is taken to characterize the solution at a distance X = (j - l)Ax from the interface. If species A, B,... are present, their concentrations C aCj), Cb(7),. .. What we have created, then, is a discrete model of the solution, comprising arrays of concentrations whose properties approximate those of the continuous system. Since we can choose the size of Ax, it is said to be a model variable. The smaller we set Ax, the more elements will be needed in the arrays and the more refined our model will be. 

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