chapter  2
NUMERICAL ANALYSIS OF LOCAL FIELDS IN A SYSTEM OF CLOSELY PLACED BODIES
Pages 20

In this chapter, we present results of numerical analysis of electric ﬁelds in and around closely placed bodies. Although numerical analysis provides us with the information about a special system of bodies / particles, the results of numerical analysis may be used as heuristic arguments for developing a general approach to the problem. In other words, numerical analysis can play a role of natural (physical) experiment. Considering closely placed bodies or highly-ﬁlled composite materials, we have diﬃculties with experimental observations of ﬁelds because it is necessary to observe and measure ﬁelds in small gaps between closely placed bodies / particles. This is a problem of technical nature. But there is another problem of principal value. With modern experimental technique we can observe many types of ﬁelds but not all of them. For example, there exist methods for measuring temperature or strains in experimental specimen (although these are not trivial experiments [74]). But, to the best knowledge of the authors, there are no eﬀective methods for observation of distribution of local energy. The numerical analysis allows us to observe numerous physical characteristics which can not be observed in a physical experiment. In the problems related to closely placed bodies or highly-ﬁlled composite materials, the problem of the “energy channel” plays very important role. The idea of the energy channel emerged in a paper [166] and it was formulated in [41] as the fundamental property of a system of closely placed systems of disks. Nevertheless, the energy channels were not observed in experiment (the authors assume that the energy channels cannot be observed in experiment for the reasons mentioned above). The ﬁrst image of the energy channel between disks was obtained using numerical method in [174]. The images of numerical energy channel presented in [174] were in full agreement with the theoretical predictions.