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Uniqueness of the thermodynamic limit for driven disordered elastic interfaces | | A. B. Kolton
; S. Bustingorry
; E. E. Ferrero
; A. Rosso
; | | Date: |
20 Aug 2013 | | Abstract: | We study the finite size fluctuations at the depinning transition for a
one-dimensional elastic interface of size $L$ displacing in a disordered medium
of transverse size $M=k L^zeta$ with periodic boundary conditions, where
$zeta$ is the depinning roughness exponent and $k$ is a finite aspect ratio
parameter. We focus on the crossover from the infinitely narrow ($k o 0$) to
the infinitely wide ($k o infty$) medium. We find that at the thermodynamic
limit both the value of the critical force and the precise behavior of the
velocity-force characteristics are {it unique} and $k$-independent. We also
show that the finite size fluctuations of the critical force (bias and
variance) as well as the global width of the interface cross over from a
power-law to a logarithm as a function of $k$. Our results are relevant for
understanding anisotropic size-effects in force-driven and velocity-driven
interfaces. | | Source: | arXiv, 1308.4329 | | Services: | Forum | Review | PDF | Favorites | |
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