Computer modeling, aggregate shape

An alternative approach is to use a coarse-grained structural model for the surfactant and the other components so that the self-assembly of the surfactants can be monitored in the simulations [11,12]. The early studies of Karaborni, Smit, and coworkers [13-15] are such an example. These studies are mostly qualitative and primarily demonstrate that the basic features of surfactant self-assembly can be modeled by simple MD simulations. However, the more recent work of Esselink et al. [16] takes advantage of parallel processing techniques and faster computers to provide some insights into the forces of importance for surfactant aggregation and the effects of surfactant structure on the size and shape of the micelle. Moreover, Esselink et al. [16] also present a preliminary study of the mechanism of oil solubilization inside micelles. We restrict ourselves here to some of the details of the simulation and the results presented in their paper. 

Fig. 6. Domain shape obtained by computer simulation with the diffusion limited aggregation model (a), in comparison with experimental observation following a pressure jump (b).

An inference system commonly used to develop fuzzy models is the Mamdani fuzzy inference system. The Mamdani approach was developed in the 1970s and was the first inference method applied to control systems [15]. The Mamdani inference procedure describes the output variables as fuzzy sets. The approach uses max-min composition in which the minimum of the two antecedents is taken for a particular rule and the maximum combination of the rules is determined for aggregating the effects of aU the rules. The effect of the max combiner on the output membership functions is to generate an "envelope" of the fired output membership functions. In order to defuzzify this output set, the centroid (weighted average) of the envelope is found by integrating over the 2-dimensional shape. The defuzzification process of the Mamdani approach is computationally intensive. 

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