Problems of the Synthesis of Connectionist Representations and Continuum Models of the Environment on the Example of Memristors

Methods of complementarity of the local parameters of the С-system and the integral characteristics of the environment in which it is immersed are discussed. The calculation of the conductivity of the memristor filament region, percolation phenomena, and chemically enhanced photoresists are examples of such a model situation. The simplest case of interaction between a С-system and a medium is associated with the jumping conductivity of polymers, and for the analysis of more complex cases, we identify four pairs of oppositions. For the first time, a hidden contradiction is discovered in the formal definition of the С-system. To avoid this contradiction in materials science models, it is necessary to use fast variables when describing transport signals. We formalize the concept of a medium as a tuple of continuous functions, for example, an electric field given in space. These functions are interpolated over a certain volume, from which small-radius balls located at the points of the elements of the С-system are punched out. The immediate semantics of such a ball is a nanocrystal inside an amorphous dielectric.