Layered structures in twodimensional nonequilibrium systems

2014 The role of the defects in twodimensional layered structures is analysed. It is shown that the melting of these structures at large amplitudes can be understood within a soliton picture. J. Physique LETTRES 42 (1981) L-361 L-364 Classification Physics Abstracts 05.70L 64.60 47.20 1 er AOUT 1981, Many instabilities lead to twodimensional layered dissipative structures [1] such as for instance the Rayleigh-Benard instability [2] and the convective instabilities in nematic liquid crystals [3]. It has been suggested that when one decreases the bifurcation parameter a Kosterlitz-Thouless type melting may occur. However, these structures also vanish when one increases the constraint (contrary to the equilibrium situation where perfect rigidity is reached for T = 0). We here want to study these two possible transitions leading to the destruction of the layered pattern. It is well known that these structures can be described in terms of a Landau type generalized potential for the order parameter r(r) [4, 5, 6] : In the convecting region, we may ignore the amplitude fluctuations and take R = Ro ~ C(~, 112. Here À is the bifurcation parameter, Àc, the meanfield critical point and 2 7r/~ the critical wavelength. The potential for the phase fluctuations which dominate at long wavelengths may then be written where