1993
DOI: 10.1103/physrevlett.70.662
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Elastic string in a random potential

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Cited by 73 publications
(71 citation statements)
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“…It is now well known that at very low driving, the response is highly nonlinear, leading to the so-called creep regime. Phenomenological arguments based on the Arrhenius activation of segments of the interface (thermal nuclei) showed that, instead of a linear response, one should expect a stretched exponential response [13][14][15][16][17], where the average velocity of the wall is exponentially small in a power law of the external force. This behavior was later confirmed by more microscopic derivations based on a functional renormalization group procedure (FRG) in d ¼ 4 − ϵ dimensions [18,19].…”
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confidence: 99%
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“…It is now well known that at very low driving, the response is highly nonlinear, leading to the so-called creep regime. Phenomenological arguments based on the Arrhenius activation of segments of the interface (thermal nuclei) showed that, instead of a linear response, one should expect a stretched exponential response [13][14][15][16][17], where the average velocity of the wall is exponentially small in a power law of the external force. This behavior was later confirmed by more microscopic derivations based on a functional renormalization group procedure (FRG) in d ¼ 4 − ϵ dimensions [18,19].…”
mentioning
confidence: 99%
“…The only available theoretical tools to address the dynamics of low dimensional interfaces, so far, are numerical simulations. In this respect, traditional molecular dynamics techniques have difficulties reaching the very long times which are necessary to deal with the ultraslow motion characterizing creep [17,20]. Thus, a well-controlled numerical technique that would not suffer from slowing down when the force is reduced would be highly suitable.…”
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“…The direct numerical simulation of the dynamics, especially of long-range systems, in the depinning region is extremely tedious because the velocity of the manifold vanishes at the threshold, which is thus difficult to approach [18,19]. Many authors therefore preferred to treat the problem within the framework of cellular automaton models.…”
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confidence: 99%
“…dx dh ηη = 1, describes the movement of an elastic band over a rough surface [16] pulled by a transverse force acting at one end point only. Below it is shown that the λ-term disappears in the continuum, establishing the first rigorous identification of the Oslo model and the qEW equation.…”
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confidence: 99%