Schwartz-Christoffel transformations

Besides the work with Carr and Schmidt, I had a very pleasant interaction with Ed Cussler over some problems in mass transfer through membranes with barriers [238], through anisotropic membranes [232], and by facilitated diffusion [247]. A severely mathematical problem of diffusion through a slot could be solved by a Schwartz-Christoffel transformation,41 and provided an asymptotic formula that proved useful in the barrier problem [223]. Cussler was delightful to work with because he refused to accept any mathematical solution that could not be unpacked and shown to be physically sensible (cf. [244]). Next to Bosanquet, he is the most intuitive problem solver with whom I have worked. Chapter 19 [232] is reprinted here. 

The obtained geometry can be transformed into a halfplane (fig. 3) by means of a Schwartz-Christoffel transformation. 

Using a Schwartz-Christoffel transformation, the primary current distribution along the cathode presented in fig. 1 is calculated. 

Fig. 22.6 Structure of a conductance transducer based on an interdigitated electrode is coated by a thick sensing layer. The relationship between the resistivity of the sensing layer and the actual resistance measured at the terminal contacts can be calculated by a Schwartz-Christoffel transform...

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