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A theoretical model for studying pattern formation in electroconvection isproposed in the form of a modified Swift-Hohenberg equation. A localized stateis found in two dimension, in agreement with the experimentally observed``worm" state. The corresponding one dimensional model is also studied, and anovel stationary localized state due to nonadiabatic effect is found. Theexistence of the 1D localized state is shown to be responsible for theformation of the two dimensional ``worm" state in our model

Worm structure in the modified Swift-Hohenberg equation for electroconvection