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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:We consider for the first time the electric field due to a fractal distribution of the field sources, a problem of interest for a number of aggregation phenomena. Two model examples are studied, both of which show non-trivial dependences for the field. The first one refers to a two-dimensional (2D) cluster of normally oriented dipoles where results, averaged over the rotations around the center of aggregation, are obtained. The second example is an exact solution for a 1D charged Cantor bar; various asymptotic regimes of this solution are analyzed in detail. In both cases, the decrease of the field with the distance from the fractal object within the self-similarity range is described by the corresponding fractional power laws, the exponents being determined by the Hausdorff dimension, D, of the system. When D tends to the topological dimension we investigate how the field transforms to the corresponding Euclidean mode.