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A generalized notion of a nonlocal tensor order parameter is introducedwithin the framework of the phenomenological approach. This parameter has theform of a traceless tensor correlation function or a tensor integral operator.Based on this form, the governing relations are written, which determine thesteady states and phase transitions of the deformed liquid crystal. Linearrelations for eigenfunctions of the introduced operator are derived. Aprincipal drawback of currently available models of liquid crystals based onthe local presentation of the tensor order parameter (equality of two Frankconstants in the case of a quadratic form of the strain part of the freeenergy) is eliminated. Particular examples are considered, which demonstratethe model workability and the absence of contradictions in the model as well asits adequacy when describing small-scale structures.

Nonlocal tensor order parameter of the deformed state of liquid crystals