Abstract
Competition between repulsive long-range and attractive short-range interactions leads to modulated phases and structure formation on mesoscopic length scales in a variety of different systems. The patterns may be trapped in different metastable configurations, and the experimentally observed pattern generally depends on the history of preparation. In the present paper, we simulate the relaxation of non-equilibrium patterns towards equilibrium. We derive general equations for the driving force of the motion at the phase boundaries and for the corresponding flow field. As an example, we apply these equations to a dipolar long-range potential, as in Langmuir monolayers or ferrofluid films. We simulate the two-fold shape instability of an isolated domain and the formation of labyrinth patterns—unconfined and confined in a circular trap. Our simulations are in qualitative agreement with the experiments.An erratum page was added to the end of the published paper on 12 July 2005.
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