Abstract.
We have used linear stability analysis to study the depinning of an elastic chain with long range interactions submitted to a random pinning potential. In this paper, we provide, for the first time, evidence of a pronounced change from a strong pinning regime to a weak pinning regime. This change depends on the strength of disorder, and takes place only in finite size systems. For a given disorder, we show a characteristic length separating the weak pinning regime from the strong pinning regime. This length depends on the long range of the algebraic decay of the elastic couplings. The weak pinning regime is very well described by perturbation theory. As an example, we discuss more specifically the case of wetting of heterogeneous surfaces, where the change from a strong to a weak pinning regime could be induced in the wetting front by varying the surface tension of the liquid-air interface.
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Let us recall that, in the context of this paper, temperature is zero. Thus an equilibrium position is simply one of the configurations of the contact line, where the sum of forces acting on the line, is equal to zero
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We have checked that this kind of distribution corresponds precisely to the distribution of pinning forces along the chain when it reaches its first equilibrium position: using conjugated gradient method, we have quenched very quickly a chain initially flat on a random surface. When the disorder on the surface, here the amplitude of the pinning centers, is decorrelated, the disorder along the chain at equilibrium is also decorrelated. The morphology of the line is not the same in the s trong or in the weak pinning regime. The roughness exponent of the chain at equilibrium in the weak pinning regime is \(\zeta =(2\alpha -3)/2\) as found already by Larkin et al. [22, 25]. A. Tanguy and T. Vettorel, in preparation (2003)
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Received: 12 September 2003, Published online: 20 April 2004
PACS:
05.10.-a Computational methods in statistical physics and nonlinear dynamics - 68.08.Bc Wetting - 02.50.Fz Stochastic analysis
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Tanguy, A., Vettorel, T. From weak to strong pinning I: A finite size study. Eur. Phys. J. B 38, 71–82 (2004). https://doi.org/10.1140/epjb/e2004-00101-6
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DOI: https://doi.org/10.1140/epjb/e2004-00101-6